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Traffic Scheduling Simulation and Assignment for Area-Wide Evacuation Yi-Chang Chiu

Abstract—Large-scale evacuation is called for when a natural or man-made extreme event strikes a populated area so that the population is exposed to immediate or foreseeable life-threatening danger. Evacuating a large population is an extremely complicated and difficult task, which primarily relies on efficient utilization of transportation systems, and effective evacuation schemes. This paper presents research that is aimed at developing an emergency evacuation modeling capability, which entails a careful integration of an optimal evacuation time and route choice model, as well as a traffic simulation model. Experiment results demonstrate the proposed methodology’s operational planning capability for large-scale emergency evacuation management.

I. INTRODUCTION Large-scale evacuation is called for when a natural or man-made extreme event (e.g. hurricane, hazmat release, or dirty bomb) strikes a populated area so that the population is exposed to immediate or foreseeable life-threatening danger. Evacuating a large population is an extremely complicated and difficult task, which primarily relies on efficient utilization of roadway capacities and Intelligent Transportation Systems (ITS) technologies and modeling techniques, and effective and coordinated evacuation schemes. For events with a high probability of occurrence and sufficient lead time, such as a hurricane, most of the emergency management agencies determine alternate evacuation routes a priori. When a hurricane strikes, citizens are given advanced advisory or mandatory warnings to evacuate to safe neighboring cities by using those pre-determined evacuation routes. However, in an unexpected extreme event scenario, evacuating a large population could be more devastating due to the short response time. Without proper coordination in choosing evacuation times and routes, evacuees often get stuck in the roadway gridlocks for an excessive period of time. This could lead to significant life and property loss that may have been otherwise saved. In the past, emergency evacuation schemes have been Manuscript received 7/28/2004. Prof. Yi-Chang Chiu is with the Department of Civil Engineering, University of Texas at El Paso, El Paso, TX 79968 (phone: 915-747-6918; fax: 915-747-8037; e-mail: [email protected]).

studied for various disaster strikes such as earthquakes, tornadoes, fires, and hurricanes. These evacuation procedures were developed using different method such as the following: A study conducted by Pal, Graettinger et al. [1] investigated emergency evacuation modeling using a Geographic Information System (GIS), with a focus on the coast of Alabama. Murray and Mahmassani [2] displayed the effectiveness of a simulation assignment tool DYNASMART-P in conjunction with two linear integer programs. This study created an evacuation-modeling framework that incorporates the trip-chain effect in times of evacuation. The proposed method was tested only on a small hypothetical network. Cova and Johnson [3] presented a network flow model for identifying optimal lane-based evacuation routing plans in a complex road network. The purpose of this research was to reduce evacuation delay times on street intersections. The case study for the lane-based evacuation routing was tested on the Salt Lake City, Utah area network. Wilmont and Mei [4], developed alternative forms of trip generation of evacuation traffic and compared them with customary evacuation demand models. This research conducted tests on the southwest part of Louisiana following Hurricane Andrew. With the use of the data set of evacuation behavior collected from Hurricane Andrew, logistic regression and different forms of neural network models were tested, and both were concluded to be effective flow prediction models. Nakanishi, Kim et al. [5] developed performance indicators that measure the benefits of having a transit agency prepared for emergency situations. Each agency would then perform self-reviews, address alternatives to the agency’s vulnerabilities, and develop a cost benefit analysis to accommodate the selection of the optimal alternatives. These methods would then prepare transit agencies for emergency situations whether on or off the transit routes. Another hurricane evacuation related study proposed by Barrett, Ran et al. [6] studied the development of a dynamic hurricane evacuation-modeling framework for the use of long-term and short-term planning, in addition to real time operational purposes. It focused more on the programming and planning aspect of emergency management than in

evacuation operations. Computer simulation models for network evacuation have been utilized for almost two decades. A research study by Radwan, Hbeika et al. [7] ran a macroscopic computer simulation model for an evacuation from highway networks undergoing a crisis. The model was tested on a Virginia area network. This study proved that the use of traffic simulation is an effective and efficient method to determine evacuation routes under disastrous conditions. Farahmand [8] developed a simulation model to prognosticate the optimal evacuation routes from the coastal areas of the Rio Grand Valley. With the use of Witness 7.0, a graphical interface software package, the network model was developed for evacuation for the area. Simulation tests concluded that the use of unidirectional traffic management is the best method for studying large evacuation participation rate. In summary, most of the prior research in the literature focuses on varying evacuation scenarios. The common issues related to all above research are the capability to realistically describe the traffic evolution in time of emergency, and to develop a computationally effective algorithm to solve for the optimal evacuation schemes for a city or regional network. Few of the studies address the evacuation scheduling in conjunction with route choices and assignments. The primary goal of this research is therefore to improve the modeling capabilities in these areas. II. RESEARCH METHODOLOGY Improving the current state-of-the-practice of emergency evacuation requires a fundamental breakthrough in modeling techniques. The theoretical challenges are two fold: x First, it requires constructing an optimization model. This model minimizes casualties, exposure or other relevant measures by determining the optimal evacuation schedules of different zones of the area and determining the optimal routes in conjunction with the evacuation schedule. x Second, it requires accurate estimations of traffic conditions based on traffic loadings resulting from varying evacuation time and route scenarios. The present research can be understood with Figure 1. In this framework, the integration of an optimal evacuationscheduling algorithm, a traffic simulation model (an enhanced version of DYNASMART-P with additional evacuation modeling features) and a Minimal Exposure Traffic Assignment (META) algorithms is necessary. The META algorithm includes the Minimal Exposure Shortest Path Algorithm and the traffic assignment procedure. At the convergence of the overall algorithm, the sought solutions include the optimal zonal evacuation departure

time schedule from evacuation zones to safe zones in conjunction with the corresponding optimal dynamic traffic assignment under the objectives of minimizing evacuation time and exposure. DYNASMART-P Model MoEs Evacuation Time, Exposure Level, Casualty, etc. META Node Transfer Optimal Evacuation Schedule Algorithm

Vehicle Generation

Vehicle Movement

Driver Behavior Modeling

Path Selection

Minimal Exposure Shortest Path Algorithm

Traffic Assignment

Figure 1. Minimal Exposure Traffic Assignment (META) Conceptual Structure

A. DYNASMART-P Dynamic Network Assignment Simulation Model for Advanced Road Telematics for Planning applications, also known as DYNASMART-P, is a state-of-the-art dynamic network analysis tool that was originally developed at the University of Texas at Austin (Jayakrishnan, Mahmassani et al. [9]; Chiu and Mahmassani et al. [10]; Mahmassani, et al. [11]) and has continued its development at the University of Maryland at College Park (Chiu and Mahmassani [12]; Mahmassani, Sbayti et al. [13]. DYNASMART-P is recognized as an effective tool in areas such as intelligent network designing, planning, evaluation, and traffic simulation. DYNASMART-P models individual travelers traveling adjustments as well as representing travelers pursuing to achieve a connection of activities at different points/locations in a network. Several known restrictions of static tools used in prevalent practices are overcome by DYNASMART-P. Details of DYNASMART-P can be found in (Chiu and Mahmassani [12]; Mahmassani, Sbayti et al. [13]. For the purposes of this study, features that are critical for the evacuation modeling have been developed and incorporated into DYNASMART-P. These features include: x Zonal aggregation for minimal-exposure flow modeling The traffic generation in DYNASMART-P is based on the specified zonal demand during each demand generation interval. Vehicles are generated on the links, specified as “generation links”, based on link capacity of user-specified weights. For evacuation modeling, safe zones and model inputs may be designated, but the traffic assignment to destinations in safe zones cannot be pre-specified, and have to be solved by the model. To address this issue, in the present research, all the designated safe zones are

aggregated into to a super safe zone. The super safe zone has a artificial centroid, which is modeled to be the “super sink node” for all the evacuation flows. The flows assigned to the safe zones are collapsed into one single zone. All flows are destined at the super sink node, by way of the physically exist destinations in the safe zones. The advantage of such a zonal aggregation is that more than one Traffic Analyze Zone (TAZ) can be designated as a safe zone. Once these safe zones are aggregated to a super zone, the model will automatically determine optimal traffic assignment to all the destinations nodes in theses safe zones. Figure 2 shows an example in which nodes 6,7, and 8 are the destinations. Their associated zones are specified as safe zones that are aggregated to super zone with centroid node 9. The connectors are artificial links with very high speed and infinite capacity. Traffic statistics on these connectors are not included in the final statistics. 1 4

2

8

3 5

7

9

6

Figure 2 Zonal Aggregation for minimal-exposure flow modeling

• Improved mesoscopic traffic flow model In the simulation core of DYNASMART-P, the vehicle movement during each time step is based on the speed in the link resulting from the density at the end of the previous time step. All moving vehicles in a link move at the same speed during each time step, depending on the density. The speed-density relationship currently used is a modified version of the Greenshield’s equation. A specified minimum speed at jam density ensures that the simulation does not ‘shut down’ due to zero speeds. The relationship used is: D v v0 v f v0 1 k k j where, v0 = a user-specified minimum (jam) speed,

v f = free-flow speed of the highway segment, k = link density, k j = density at the jam speed, and = a user-specified parameter. This speed-density based flow model has shown to obey flow conservation [9] and is advantageous for large network application because it does not require the partitioning of long links into short ones, thus making it more computational efficient. However, the drawback is that it assumes a fast forward-moving shockwave exists D

(leading vehicles are affected by trailing vehicles in each clock tick, even the trailing vehicles are miles behind). Second it does not explicitly handle flow discontinuities resulted from major capacity reduction or restorations. It often shows prolonged congestion and delay under certain traffic conditions. The present study overcomes this issue by combining a flow-density-based simulation procedure. Under normal traffic conditions, a density profile for each link is evaluated. For modeling flow discontinuities, a flow-density consistent with the designated speed-density function is used. Three flow states are explicitly considered for a link when major flow discontinuities take place. Vehicles movements are then updated based on the estimated shockwave speed and flow states propagation. Details of this procedure are documented in [14]. B. Evacuation departure time scheduling and traffic assignment An effective evacuation scheme should consider both evacuation departure time scheduling, determination of safe zone(s), and traffic assignment. Evacuation departure time scheduling concerns the sequence of evacuation zones to be evacuated. This decision will have to be coupled with traffic assignment decisions because one affects the other. In the present research, evacuation scheduling is formulated as a mathematical programming model: Given

ri , the objective is to minimize z making

riW, k

¦

decisions, subject to (1)

rW eiW,k by

i ,k ,W i ,k

riW

¦

rW ,

k i,k

i evacuation zones,

W feasible departure time

W

, i evacuation zones; and (4)

interval; (2) ri

¦W r

i

other traffic dynamic constraints. The zonal aggregation as mentioned previously allows the flows to be destined to one zone regardless the number of original TAZs that are designated as safe zones. The major challenge of this problem concerns the departure W time dimension. The decision variable ri ,k is found through a set of heuristic algorithms. Details of this problem formulation and solution procedure are documented in [15]. C. Experiment Test Bed Data The methodology was tested on the City of El Paso, TX network that consists of 2909 nodes, 8295 links and 681 TAZs. The demand data includes aggregated personal and truck trips combined all trip purposes for both internal and external trips. The network was originally received in TransCAD format from the El Paso MPO, and was later converted to DYNASMART-P format. An image of the network shown in DYNASMART-P is illustrated in Figure 3.

D. Plume Dispersion Scenario A hypothetical event was developed to test the proposed evacuation routing algorithm. A local refinery, Western Refining Company, was chosen as a location of a possible event due to its central location within the city of El Paso. The refinery is approximately three miles east of the downtown central business district and is embedded within a residential area and near several active shopping centers.

Figure 3. Western Refining Company Location

The scenario consists of an extreme event occurring within the refinery, creating a plume of a hazardous material. Because the objective of this research is to demonstrate and examine the proposed evacuation routing algorithms, reasonable assumptions have been made on the dispersion of the hazardous gas. The plume dispersion patterns can be further improved by applying a meteorological plume dispersion model. With toxic and life threatening airborne hazmat dispersing throughout central El Paso, and based on historical meteorological data, the temporal and spatial progression of the airborne hazardous material dispersion was estimated to travel 2 to 3 miles within 30 minutes, 4 to 5 miles within 45 minutes, and 6 to 7 miles within 60 minutes after the incident occurrence. Figure 4 indicates visual images of the different time frames with the hazmat plume being illustrated in red-color marks. Reading from left to right the images display dispersion rates from 30, 45, and 60 minutes after incident occurrence.

Figure 4. Plume Dispersion Scenario on El Paso network (from Left to Right, 30, 45, 60 Minutes After the Start of Simulation)

III. EXPERIMENT DESIGN The experiments conducted in this study are briefly described as follows: A. Base Case (BC) The (BC) scenario represents the traffic flow pattern of tripmakers under a normal traffic condition. Taking the input travel demand data, DYNASMART-P determines the time-dependent user-equilibrium (UE) paths and the corresponding traffic assignment onto the network. Under this scenario, the demand pattern is that of the morning peak-hour traffic, with heavier directional traffic heading toward the Central Business District (CBD). In total, about 280,000 vehicles are generated and simulated throughout all the scenarios in the 100-minute simulation period. B. Hazmat without information (HWOI) This scenario is to investigate the impact of the hazmat plume under the same UE assignment in terms of numbers of tripmakers who are under the exposure of the hazmat. The temporal dispersion of the plumes follows the scheme described in the preceding section. It is assumed that 60 minutes after the initial start of the hazmat release, the entire central El Paso area is exposed to the hazmat (Figure 4). For benchmarking purpose, it is also assumed that all the trip makers do not have knowledge about the hazmat release. As such, trip makers continue trips to the originally intended destinations. If the intended destinations are within the exposure zones, then the tripmakers are exposed to the hazmat. C. Hazmat with descriptive information (HWDI) This scenario examines the effectiveness of descriptive information for mitigating the hazmat release. In this scenario, it is assumed that the hazmat release information is broadcasted to the public through various media (TV, radio, website, etc.). Tripmakers are aware of the hazmat dispersion pattern at the time of departure to their destination, and try to find a minimal-risk route. In this scenario, tripmakers, however, do not evacuate to shelters and still intend to arrive to their original destinations. It is also assumed that once the tripmakers get in to the vehicles they do not have further information regarding to the spatial dispersion of the hazmat. The hazmat plume dispersion scenario is the same as that in the HWOI scenario. D. Hazmat with Minimal-Exposure Traffic Assignment (HMETA) This scenario examines the effectiveness of MinimalExposure Traffic Assignment (META) proposed by this research. The META is applied to provide the minimal exposure routing to individual tripmakers who may be potentially exposed to the hazmat. In this scenario, the

original origin-destination trip demand is not disturbed. Therefore, it is assumed that those who go in and out of the hazmat exposure zones will be subjected to the exposure; those who traverse through the exposure area will be rerouted to avoid the hazmat exposure. E. Hazmat with Evacuation and Minimal-Exposure Traffic Assignment (HEMETA) This scenario further applies the evacuation scheme in addition to the META. The evacuation scheme advises those tripmakers who are in the exposure zones to evacuate to the nearest evacuation zones in a timely manner. For those whose original destinations are in the contaminated zones, they are asked to postpone or cancel the trips. In this case, not only do the trip makers need to be evacuated before the hazmat plumes arrive, but also need to be assigned to the routes that allow for speedy exit of the exposure zones without being exposed to the hazmat. In this scenario, both the optimal evacuation shelter assignment and the META problems are solved jointly. In this scenario, the citizens are assumed to be in full compliance of the evacuation advisories, which is a quite optimistic assumption. Additional discussions of the impact of realistic evacuation advisory compliance behavior can be found in Chiu, Mirchandani, Korada [16]. IV. EXPERIMENT RESULTS As shown in Figure 5, the average travel times for all the tripmakers in the (BC) scenario is 11.2 minutes. If the hazmat release occurs and no mitigation action is taken (HWOI), the number of vehicles exposed to the hazardous materials is more than 107,600, approximately one third of the total generated vehicles in the simulation period. If the incident information is provided to the public (HWDI), the number of exposed vehicles are reduced to approximately 68,000 vehicles. 12 0 .0

received by the public so that trip makers are aware of the prevailing temporal and spatial dispersion progressions of the hazmat at the time of departure. However while enroute to the destination, tripmakers do not have further updates on the hazmat, thus may take a route that is contaminated. Furthermore, because no evacuation is put in effect, those whose final destinations are in the contaminated zones are eventually exposed to the hazmat. In the HWDI scenario, the average travel time increase 12.4 minutes from the 11.2 minutes in the BC scenario. It is primarily because the re-routing to longer routes due to the incident. If the Minimal-Exposure Traffic Assignment (META) is performed, the number of exposed vehicles is further reduced to about 18,400. META allows trip makers to collectively find the minimal-exposure routes to their destinations. There is a trade-off between the exposure reduction with the increased average travel time because more vehicles are routed through longer paths to arrive at the destinations. An example of such a diversion is illustrated in Figure 6. The minimal-exposure path from the east to the west side of El Paso is determined to be Loop 375 instead of the IH-10, since the downtown section has been entirely exposed to the hazmat. This type of assignment significantly reduced citizens’ risk of exposures by re-routing them away from the contaminated areas and using other portions of the highway networks that could have been otherwise underutilized.

IH-10 Loop 375

10 7 .6

10 0 .0 8 0 .0

6 8 .1

6 0 .0 4 0 .0

2 7 .7

2 3 .0

18 .4

2 0 .0

11.2

11.2

12 .4 1.8

0 .0

0 .0 BC

S c e na rios

HWO I

HWDI

HME TA

HE ME TA

Exposed Vehicles(1,000) Average Travel Time (min)

Figure 5. Evacuation Scenario Comparison

Although significantly less than that in the HWDI scenario, this number is still considered excessive. Nonetheless, the reduction of exposed vehicles from HWOI to HWDI scenario is attributed to the incident information

Figure 6. Minimal-Exposure Path from East El Paso to West El Paso

Furthermore, if the META in conjunction with the evacuation scheme is implemented, the number of the exposed vehicles is further reduced to less than 2,000. This result is mainly attributed to the timely evacuation of those citizens in the contaminated zones, which is accomplished through the forecast and simulation of the hazmat dispersion, and the minimal-exposure routing and evacuation in conjunction with the evacuation scheduling. In this scenario, about 15,000 vehicles are evacuated out of

the contaminated zones. Moreover, the travel time also improves comparing with the HMETA scenario. A likely reason for this occurrence is that about 23,000 vehicles cancel their trips into the contaminated zones, and result in a smaller number of vehicles in the network.

at El Paso University Research Institute. We thank Mr. Salvador Gonzales-Ayala at El Paso Metropolitan Planning Organization for providing network and demand data, Ms. Lourdes Cardenas at the City of El Paso for providing signal timing data, and Prof. Pitu Mirchandani from the University of Arizona for providing technical consultation in this research. Certainly the author is solely responsible for the viewpoints expressed in this paper. REFERENCES [1]

Figure 7. Network Traffic Flow Comparison between BC and HMETA scenarios

The temporal and spatial variation of plume dispersion and traffic dynamics can be visualized in DYNASMARTP. Figure 7 illustrates the traffic flow throughout the network between the BC and HMETA scenarios. In this diagram, network links are color-coded based on the link traffic density (number of vehicles per traffic lane per mile). Higher density indicates greater congestion. As shown in the diagram, scattered congestion in the east El Paso area is observed, which is consistent with morning traffic patterns in El Paso. Having the incident in place and HMETA implemented, the traffic flow pattern on the network has been significantly altered. Obvious congestion is observed on more urban streets in the northeast, north side (south of El Paso International Airport, and Fort Bliss), and Sunland Park areas on the west side of El Paso.

[2]

[3] [4]

[5]

[6]

[7] [8]

V. CONCLUDING REMARKS This paper presents research that is aimed at development of an emergency evacuation model through a careful integration of an optimal evacuation time and route choice model, as well as a traffic simulation model. The El Paso area network was established as a test bed for the case study in which a toxic airborne hazardous material release incident occurs in the morning during peak traffic conditions. The computational experiments show that the proposed methodology provides a critical operational planning capability for large-scale emergency evacuation management in response to an unexpected extreme event. Significant insights about evacuating citizens out of central El Paso were provided. VI. ACKNOWLEDGEMENT This research was partially supported by the National Science Foundation through Award Number 0332001 and the University of Arizona/Ohio State Research Foundation/US. Department of Transportation through Contract # DTRS56-00-T0004, and the University of Texas

[9] [10]

[11]

[12] [13] [14] [15] [16]

Pal, A., A., J. Graettinger, et al. (2003). "Emergency Evacuation Modeling Based On Geographical Information System Data." Transportation Research Board (CD-ROM), 82nd Annual Meeting, Washington, D.C. Murray, P. M. and H. S. Mahmassani (2003). "Model of Household Trip Chain Sequencing in an Emergency Evacuation." Transportation Research Board (CD-ROM), 82nd Annual Meeting, Washington, D.C. Cova, T. J. and J. P. Johnson (2003). "A Network Flow Model for Lane-based Evacuation Routing." Transportation Research Part A 37: 579-604. Wilmont, C. G. and B. Mei (2003). "Comparison of Alternative Trip Generation Models for Hurricane Evacuation." Transportation Research Board (CD-ROM), 82nd Annual Meeting, Washington, D.C. Nakanishi, Y., K. Kim, et al. (2003). "Assessing Emergency Preparedness of Transit Agencies: A Focus on Performance Indicators." Transportation Research Board (CD-ROM), 82nd Annual Meeting, Washington, D.C. Barrett, B., B. Ran, et al. (2000). "Developing A Dynamic Traffic Management Modeling Framework for Hurricane Evacuation." Transportation Research Board (CD-ROM), 79th Annual Meeting, Washington, D.C. Radwan, A. E., A. G. Hbeika, et al. (1985). "A Computer Simulation Model for Rural Network Evacuation Under Natural Disasters." Institute of Transportation Engineers Journal 55(9): 25-30. Farahmand, K. (1997). "Application of Simulation Modeling to Emergency Population Evacuation." Proceeding of 1997 Winter Simulation Conference: 1181-1188. Jayakrishnan, R., H. S. Mahmassani, et al. (1994). "An Evaluation Fool For Advanced Traffic Information and Management Systems in Urban Networks." Transportation Research Part C 2(3): 579-604. Chiu, Y.-C. e. al. (1998). Off-line Laboratory Test Results for the DYNASMART-X Real-Time Dynamic Traffic Assignment System. Technical Report ST067-85-TASK G, prepared for Federal Highway Administration, September, Austin, Texas, USA. Austin, Texas, USA, University of Texas at Austin. Mahmassani, H. S., A. A., et al. (2000). DYNASMART-P, Intelligent Transportation Network Planning Tool Volume I, II. Report ST067-85-PII, prepared for Federal Highway Administration, January, Austin, Texas, USA. Austin, University of Texas at Austin. Chiu, Y.-C. and H. S. Mahmassani (2003). "Routing Profile Updating Strategies for Online Dynamic Traffic Assignment Operations." Transportation Research Record 1781. Mahmassani, H. S., H. Sbayti, et al. (2003). TrEPS-P, Phase 1.5C, Final Report Volume 1 -- DYNASMART Calibration and Evaluation. College Park, MD, Maryland Transportation Initiative. Chiu, Y.-C. and L. Zhou (2004) An Improved Mesoscopic Traffic Simulation Procedure for Modeling Flow Discontinuity for Large Network Applications, INFORMS, Denver, USA. Chiu, Y.-C. (2004) Optimal Evacuation Scheduling and Traffic Assignment Problem Formulation and Solution Procedure. Working paper. Chiu, Y.-C., Mirchandani, P., Korada, P. (2004) Findings in Evacuation Route Choice Decision and Real-Time Control Schemes for Optimal Evacuation, INFORMS, Denver, CO, USA.

Dynamic Traffic Management for Evacuation Submission # 05-2369 Yi-Chang Chiu Civil Engineering Department University of Texas at El Paso Engineering Building E201P 500 W University Ave. El Paso, TX 79968 Email: [email protected] Phone: 915-747-6918 Fax: 915-747-8037 Pavan Korada The ATLAS Research Center Systems and Industrial Engineering Department The University of Arizona Tucson, Arizona, 85721 Email: [email protected] Phone: 520-548-2959 Fax: 520-621-6555 Pitu B. Mirchandani The ATLAS Research Center Systems and Industrial Engineering Department The University of Arizona Tucson, Arizona, 85721 Email: [email protected] Phone: 520-621-7284 Fax: 520-621-6555 Re-Submission Date: Word Count: 4952 (words) + 1 (Table) x 250 + 9 (figures) x 250 = 7452

Submitted for presentation and publication at the 84th Annual Meeting of Transportation Research Board, Washington, D.C. USA.

Chiu .Y.C., Rao .P. K. and Mirchandani .P.B.

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ABSTRACT Disaster response, to manmade and natural events, in areas of significant population density, is centered on evacuating the affected population quickly and efficiently to safer areas. Given the potential for large-scale loss of life and property, there is a need for ensuring the development of appropriate emergency plans and measures, to mitigate the adverse effects of these disasters. An effective evacuation strategy involves the proper co-ordination and interaction of the activities of a large number of entities, including emergency management authorities, security agencies and information broadcasters. Several notable area-wide traffic evacuation models have been proposed over the past two decades. They deal with situations ranging from nuclear disasters to hurricanes and earthquakes. But they are inherently restricted to being planning tools, given that they deal with providing evacuation plans measures for a single given scenario or one chosen from a set of probabilistic scenarios. In addition emergency response modeling in these tools significantly underplays the important role played by the evacuating drivers’ response to suggested evacuation strategies. This under emphasis on evacuee behavior is quite important to be overlooked. In this paper we discuss the development of a real-time traffic management system for evacuation, with applicability to flooding disasters. An emergency management scheme based on a structure that includes a feedback loop using surveillance systems is outlined. Of particular focus is the quantification of the system performance degradation which results from the route choice decisions made by evacuees and the real-time pre-trip control schemes, based on feedback from observed traffic to influence the system performance towards an optimum level.


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1. INTRODUCTION Floods are the most widely occurring form of all natural disasters. Floods are classified into several different types and the most common of these are usually the result of heavy rain and/or melting snow with rivers overflowing their banks [1]. These kinds of floods have significant levels of advance warning time. They can usually be predicted with considerable accuracy, and adequate emergency plans can be put into place thereby saving lives and reducing the loss of property. On the other end of the intensity scale lie, Flash Floods. They are the result of sudden changes in weather conditions such as an intense local storm development over the drainage basin of a river. Sudden loosening of ice and logjams can release large amounts of water. Dam collapses due to earthquakes and mudslides also result in flash floods, becoming torrents of water that are capable of causing tremendous amounts of damage. They can inundate urban areas on a large scale. Properties may become isolated. Major disruption occurs to traffic. The difference between floods and flash floods is the time of onset. Flash floods intensify on a much shorter time scale than floods and the advance warning time associated with these is also much shorter. In a flash flood situation over a significantly populated area, en mass evacuation offers the best or only means of ensuring the populations safety [2]. A complex process such as an area-wide evacuation involving many different entities is fraught with the risk of going awry. A well-developed emergency evacuation plan therefore plays an integral role in the effective disaster response process. 2. EXISTING EMERGENCY EVACUATION MODELS Evacuation is the best kind of protection for flooding disasters. The effectiveness of an evacuation process is measured by the estimate of the time required for evacuation. This is defined as the time required to evacuate a disaster affected population to a farther, safer area [3]. Evacuation from man-made or natural disasters is a disorderly process. It involves moving a large population of indeterminate size on a road network with severely reduced capacity towards safer regions, which cannot be easily determined. Conventional transportation models cannot cope with such levels of uncertainties. Thus, models that can specifically deal with the requirements of emergency evacuation are needed. These models can be used to develop contingency evacuation plans and help emergency agencies develop real-time strategies during an actual evacuation situation [4]. Over the years, a large number of computer simulation models have been used to model emergency evacuation planning for disasters ranging from nuclear plant failures to hurricanes. The evacuation model used by governmental emergency management authorities like the FEMA is DYNEV [5]. Other notable models include CLEAR, DYMOD, MASSVAC and NETSIM. Typically, these models consist of a set of computer programs that can be used to estimate evacuation time and to develop evacuation plans for different events or scenarios (e.g., good or bad weather conditions, day or nighttime evacuations) for a given affected zone. These models allow the user to experiment with alternative routes, destinations, traffic control and management, and evacuee response rates. They can help the planner identify the evacuation or clearance times, traffic operational characteristics (e.g., average speed), bottlenecks, and other information necessary to develop effective evacuation plans. These models simulate traffic conditions over the transportation network, as the evacuation progresses and determine the destinations selected by evacuees and the routes taken to reach the selected destinations. Through a detailed simulation of traffic operations on the evacuation network they allow one to identify performance characteristics of traffic, identify bottlenecks, and estimate evacuation times across various categories (links or roads, sectors, or regions). 2. 1. Traffic Simulation and Assignment approaches Evacuation models differ from each other significantly, in the level of detail which they incorporate into their traffic flow modeling approaches. Accordingly they can be classified as Microscopic, Mesoscopic or Macroscopic models. Microscopic models simulate individual vehicles, the interactions between them and


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other minute details. In contrast, macroscopic models consider traffic flow as a whole, by using equations relating aggregate traffic flow variables like speed, density and volume. Between these two levels of detail is the mesoscopic approach. Broadly these approaches model speeds and densities on a traffic section using macroscopic equations while moving vehicles individually or in a bunch [6]. Based on this distinction, the important evacuation models are classified as shown in Table 1. 2. 2. Dynamic Traffic Assignment Static traffic assignment models, like CLEAR and DYNEV have an inherent limitation in the fact that they cannot deal with time varying flows. They assume that the traffic conditions across the network remain at a fixed level through the simulation period. But in an emergency evacuation situation, such assumptions may not be valid, and it may take a vehicle longer to get out of the network than that predicted using static assignment techniques. Dynamic Traffic Assignment allows for the integration of time-varying traffic conditions as vehicles traverse a network. This inherent capability provides DTA based models an edge over conventional static assignment models, when it comes to estimating the traffic effects over time for given assumptions on travel behavior due to a planned or assumed realization of a scenario. 3. REAL-TIME EVACUATION MANAGEMENT SYSTEM ARCHITECTURE The objective of this work is to develop a real time feedback traffic management system capable of generating evacuation plans in times of flooding. Two crucial components of evacuation behavior: x x

Evacuee Response to Route Information System Performance Degradation,

are addressed explicitly, while also incorporating the benefits of a dynamic traffic assignment scheme. The real-time evacuation management system under discussion here is composed of different component modules, each performing different roles and contributing towards an overall robust evacuation strategy. The proposed system is as shown in Fig. 1. In the proposed framework, System Optimal traffic assignment schemes are used to initially generate safest evacuation routes. Information about these routes is passed on to evacuating drivers (by as yet undetermined means). The path strategy chosen and transmitted to the affected traffic is not going to completely replicate the routes chosen by evacuating traffic. Significant deviations are possible. To account for this, behavioral models replicating driver/evacuee behavior under information provision modes are used. This deviation of users from recommended routes is a significant factor in the degradation of the evacuation system performance (higher evacuation times). To correct for the user deviation from optimal prescribed routes, real-time control strategies based on limiting the original route choice set of the evacuees are applied to help push system performance towards the optimal values, thus closing the feedback loop. The actual details about each of these modules are provided in the sections that follow. 3.1. Behavioral Module Ideally, the behavior of evacuating drivers should be under complete control of the emergency management personnel. Typically though, user behavior will deviate from the ideal requirement for the system. Minimum total evacuation times based on a system optimum therefore may greatly underestimate the time it takes to actually move all the individuals to safe areas. Therefore, an important component in the development of a real-time traffic evacuation management system is a means of replicating (as opposed to predicting) deviations on the part of the drivers from system prescribed routes. In the sections that follow we describe the basic components of such a behavioral model, the Evacuation Route Choice Model. 3.1.1. LOGIT Models Multinomial Logit models are commonly used for allocating feasible paths to travelers. These models can typically be characterized by the following equation as:


P (i )

e

TLi

¦e jn

5

(1)

TLj

with, n = the choice set of feasible paths for an individual P(i) = probability of a traveler using path i Li, Lj = lengths of paths i and j respectively ș = utility coefficient. Traditional multinomial logit (MNL) models do not take into account the effect of overlap between the different paths in a choice set. For e.g. three paths of the same length, having some amount of overlap (assuming that path utility is based on the path length alone) will each receive a probability of 1/3. This probability is only valid when the overlap is infinitesimally small. Cascetta et al [7] proposed the CLogit model, which adjusts the path utilities based on the degree of overlap, by means of a Commonality Factor (CF) incorporated into the traditional form of the mutinomial logit model. One of the several forms of the proposed commonality factor is shown in Eq. 2.

CFi

E 0 ln

¦

a*i

la Na Li

(2)

with, ȕ0 = coefficient, to be calibrated la = length of link a Na = frequency of occurrence of link a in the n paths Ƚi = set of arcs in path i The Commonality Factor appears in the MNL formulation as: V CFi e i P (i ) V j CF j ¦e jn with,

(3)

Vi = the utility of path i to an individual CFi = Commonality factor applied to utility value of path i The logarithmic form of the Commonality Factor ensures its absence in the probability calculation, when dealing with a unique path. For overlapping paths, the argument is less than one and thereby reduces the utility of the paths under consideration. In addition, an individual’s awareness about the components of a choice set also result in higher utility values for those components. Cascetta et al [8] introduce a Implicit Availability/Perception Logit structure which accounts for this effect. Like the C-Logit model, it also incorporates a logarithmic correction factor, but here, this factor decreases the utility of a path to reflect the possibility that an individual is unaware of it. The IAP model takes the form: V ln P (i ) e i (4) P (i ) V j ln P ( j ) ¦e jn In the above formulation, µ(i) = 1 indicates that path i is available, while µ(i) = 0, indicates that path i is unavailable or the traveler is unaware of it.


6

3.1.2. Freeway Bias The day to day operation of a road network composed of arterials and freeways is typically assumed to take place under a user equilibrium mode. It is expected that drivers have tested different alternatives for their travel and have honed in on the route which minimizes their travel time. But, under certain situations motorists may actually prefer higher travel time paths, even with the existence of better alternatives. Freeway bias [9] has been shown to exist in case of arterial routes providing better travel times on the average, when compared to a parallel freeway route with significant congestion degraded performance. This bias can be explained by the complexity of arterial paths, greater variability in arterial travel time, commuter unfamiliarity with arterial paths, or safety concerns related to arterial environments. Freeway bias can especially be seen during accidents on the freeway, resulting in queue spillback. Drivers choose to remain on the queued freeway rather than switch to an arterial route with lower travel time. 3.1.3. Complete Evacuation Route Choice Model We propose to develop a model, mimicking the route choice process of evacuating drivers, when they are provided with safe evacuation routes (through suitable information dissemination means) prior to their departure. To achieve this goal, we combine salient features from previous research into route choice behavior, namely C-Logit and IAP along with our unique interpretation of Freeway Bias and Path Familiarity factors. The primary definition of the ERCM model is derived from the basic multinomial logit model and takes the form: V pk CF pk FB kp FF pk e (5) Ppk V jk CF jk FB kj FF jk ¦e j n with, n List of possible paths Ppk

Probability that user k chooses path p from all the n paths about which information is provided to him

V pk

Utility of route p for user k - D0Lp

D0

Coefficient of Utility function

Lp

Length of path p

CF pk , the Commonality Factor follows the definition of Cascetta et al and is used in this study in

the form: ª ·º l a §¨ - E 0 ln « G aj ¸» « a * L p ¨ j n ¸» ¹¼ ¬ p ©

CF pk

¦

¦

with,

E0

Coefficient of Commonality Factor function

la

Length of link a

*p

Set of links/arcs in path p

G aj 1, if path j uses link/arc a and 0 otherwise


7

Now, FB kp is the Freeway Bias factor, which accounts for the preference of motorists to freeways over arterials even in times of reduced capacity. Here, we quantify the magnitude of the bias as being directly proportional to the percentage of a path’s length that is composed of freeways and express this as: J 0 l (pf ) k FB p (6) Lp with, J 0 Coefficient of Freeway Bias function l (p f )

Total length of freeway links/arcs in path p

We also define a Familiarity Factor similar to that used in the IAP model proposed by Cascetta et al. Calculation of this factor includes historical analysis of traffic volume data, to obtain the frequency of travel over each link across all paths in a choice set. This frequency value is weighted by the length of the link; thereby giving preference to longer and more frequently traveled links. We have: (7) FF pk - K 0 Okp with, K 0 Coefficient of Familiarity Factor function _

¦ I (i, j, l ) l

l

lp

O kp

_

¦¦ I (i, j, l ) l p

l

lp

f (i, j , l )

I (i, j , l )

¦ f (i, j, l ) l

f(i,j,l)

Frequency that link l is used historically in all paths for (i, j )

¦ f(i,j,l)

total number of links in all paths for (i, j )

l

I (i, j , l ) _

ll

Relative frequency of usage of link l for (i, j )

Length of link l.

3.1.4. Validation of ERCM – Survey Design and Results Once the model for predicting the behavior of evacuees has been hypothesized, it is required that the choice of parameters in the model be validated and the coefficients Į0, ȕ0, Ȗ0 and Ș0 be determined. One method of doing so is by a survey. A properly designed survey with a questionnaire designed to accept or reject a hypothesis is very pertinent to our study. We start with the hypothesis that, an evacuating driver, when provided with a set of evacuation routes, by a reliable authority, prior to the start of his journey, picks a path from among the set of choices based on: x length of each path x past familiarity with each route x percentage of the route which is covered by freeways x the extent of the overlap between the various paths It should be noted that the last factor which deals with commonality among paths is an implicit variable. Then, a relevant survey questionnaire must ask the respondent to choose between a set of routes. Also, to account for the commonality between routes, it is necessary that the respondent have an idea of


8

how the various routes from his starting point are laid out. Such a questionnaire used for this study is shown in Fig. 2. The figure also shows the sample network from which respondents have to choose between different paths. 3.1.5. Survey Implementation Survey volunteers were picked from members of the Advanced Transportation Research Lab at UTEP. Respondents were asked to picture a scenario in which, after several days of heavy rain in their city, they had been asked to evacuate their homes. They were also told that prior to evacuating their homes, they had been provided with choices of evacuation routes and had information about the aforementioned four parameters associated with each route. They were also provided with an overall map of the hypothetical affected network with the routes highlighted using different colors. Then they were asked to rank the routes in their order of preference. 3.1.5. Survey Results Ten respondents were interviewed according to the procedure described in the previous section. Each respondent was asked to rank the paths in the 10 choice sets. 90 valid observations were used in a conditional logit scheme on LIMDEP, an econometric modeling tool, to obtain the following statistics for the coefficients of the parameters in the ERC mode, as shown in Fig. 3. The significance of the t-statistics implies that our choice of parameters was validated and that, as postulated, the commonality factor doesn’t play a major role. This method of validating a model for replicating evacuation route choice behavior is unique in the literature. 3.2. Control Strategy Module The likelihood of a flood engulfing a metropolitan area triggers into action a sequence of events, involving Emergency Management authorities, Local and State Governments, Law Enforcement agencies law and the flood affected population. An orderly evacuation therefore requires the smooth co-ordination of many entities, the most important of them being the affected citizens. In order that good contingency evacuation plans be developed, it is of the essence to identify the effect which the response of affected citizens, to evacuation orders plays on the efficacy of the overall evacuation plan. The open loop experiments in this study are designed to test and quantify this effect, so that appropriate control strategies can be devised and tested. This is carried out by simulating a flooding situation and an ensuing evacuation on a small scale network and testing the effectiveness of evacuation strategies for a variety of situations. Degradations in the performance of evacuation measures, highlighted in the open loop experiments are corrected using so-called control schemes in this experimental setup. Briefly, the effectiveness of evacuation strategies is studied after the application of pre-trip control strategies. A schematic which explains how the control strategy module achieves this result is shown in Figure 4. 3.3. Optimization Module and Ground Truth Simulator – DYNASMART-P DYNASMART-P [10], used in this study, is a state-of-the-art dynamic network analysis and evaluation tool originally conceived and developed at the University of Texas at Austin. It is an intelligent transportation network design, planning, evaluation, and traffic simulation tool. DYNASMART-P models the evolution of traffic flows in a traffic network that result from the travel decisions of individual travelers. The model is also capable of representing travel decisions of travelers seeking to fulfill a chain of activities at different locations in a network over a given planning horizon. It overcomes many of the known limitations of static assignment tools used in current practice. These limitations pertain to the types of alternative measures that may be represented and evaluated, and the policy questions that planning agencies are increasingly asked to address. DYNASMART-P allows consideration of an expanded set of such measures, compared to both conventional static assignment


9

models and traffic simulation tools. It can essentially perform two separate independent role, that of a traffic assignment module and a ground truth traffic simulator. Both of these functions are used in this study. 3.4. Experimental Test Network, Origin-Demand Matrices, Consider a traffic network represented as shown in Figure 5a, consisting of 18 nodes, 56 bi-directional links and 10 freeway links. It is originally divided into 5 traffic analysis zones. A day to day Origin Demand matrix for this network would then be of dimensions 5x5 to reflect travel between each of the zones. When an evacuation is ordered after a flooding situation, the objective is to remove people away from the affected network. The OD matrix should be changed to reflect this. Figure 5b shows how this is achieved. In the flooded network case, all users in Zones 1 and 2 which are the flooded zones are to be moved to safety towards the highlighted safe destinations. These are at the perimeter of the network away from the area of flooding, a logical choice. This is where an assumption is made that the destinations of the evacuees are known beforehand. Zones 3, 4 and 5 are collapsed into a new Zone 3, the destinations in which are connected by a supersink. Any vehicle reaching any of the destinations (highlighted in orange) is presumed to be safe. This new redesigned network will therefore have an O-D matrix of dimensions, 3x3 with all travel going to the new Zone 3. In the simulation studies that follow, pre-evacuation scenarios are studied using the original O-D matrix in Figure 6 and evacuation cases are analyzed using the redesigned O-D matrix in Figure 7. 4. OPEN LOOP ANALYSIS A real-life evacuation is fraught with the possibility of going awry because of the interactions of the numerous entities involved. It is important that this performance degradation be quantified. In the open loop analysis, we aim to test the effect of evacuee behavior on a baseline evacuation plan. We study the performance of a test network (Figure. 5a) under a variety of conditions and isolate the effect of user behavior on an evacuation plan’s degradation. 4.1 Experiments Six different scenarios were tested on the sample network, where a scenario differs from another in one or more of the following aspects: a. assumed travel behavior b. assumed objective c. available knowledge of disaster effects, and calculate the following measure’s of effectiveness (MOE) for each scenario: x Total and Average Travel Time x Total and Average Travel Distance The 6 scenarios are described below and depicted in terms of their features in Figure. 6. 4.1.1 User Equilibrium (UE) This is a base case scenario in which traffic is loaded onto the sample network using Origin-Demand matrices. For the sample network OD demand matrices which reflect travel between each of the five zones have been designed. MOE’s are collected over the entire simulation period. Flooding of the network is not modeled here. This scenario reflects the day to day traffic behavior in that, individual drivers use routes which work best for them.


10

4.1.2 User Equilibrium + Flooding + No Pre-trip Information (UE.FL.NP) In this scenario, flooding of the traffic network is modeled. It is assumed that drivers follow their original user equilibrium based paths and have no prior information about the impending flood. The objective of this run is to capture the unpreparedness of drivers in facing an emergency situation. 4.1.3. System Optimal Traffic Assignment (SO) We simulate traffic patterns across the given traffic network, from the perspective of minimizing total travel costs for all the users. This replicates a situation in which a super-user (TMC) assigns paths to individual drivers, which enable them to reach their destinations. 4.1.4. System Optimal Traffic Assignment + Flooding + Evacuation Ordered (SO.FL) This case is similar to that of SO, with the TMC assigning routes to users from a system optimal point of view, but for the fact that the traffic network is undergoing flooding. The route assignment differs from the previous case, in that traffic is redirected from the flooded areas as part of the TMC directed evacuation strategy. In a flooding situation, this scenario in which it is assumed that users follow the route assignments from the TMC, represents the best possible evacuation situation which can be achieved. 4.1.5. System Optimal Traffic Assignment + Flooding + Evacuees following ERC Model behavior (SO.FL.ERC) We use the Evacuation Route Choice (ERC) model to understand how drivers may show non-compliance to the TMC instructions and quantify the effect of this on the evacuation effectiveness. 4.1.6. System Optimal Traffic Assignment + Flooding + Evacuees choosing routes randomly (SO.FL.RM) Another method of studying the non-compliance of drivers with the evacuation route instructions is by assuming that drivers pick routes from the choice set in a random manner, without giving preference to any of the factors like Length, Freeway Bias and Familiarity. 4.2. Analysis of Results Each of the scenarios highlighted before, studies the effect of one parameter, condition or setting. All the cases can therefore not be compared against each other. The information that one can hope to extract from these 6 experiments depends on the scenarios which are compared against each other. So it is necessary to choose a base case scenario, against which comparisons can be made. We choose to focus on the system performance deterioration resulting from user deviations. 4.2.1 Effect of User Deviations from Prescribed Routes The degradation in the system performance which is postulated to occur, due to driver deviation from optimal paths can be clearly seen when the best possible evacuation case, namely System Optimal evacuation (SO.FL) is compared with the case where drivers are given route guidance, but, some choose to pick routes based on the parameters which matter to them the most, as suggested by the ERC Model (SO.FL.ERC) or pick routes in an arbitrary manner (SO.FL.RM). The results of exactly such a comparison are shown in Figures 7a and 7b. When we define, the Average Travel Times and Average Trip Distances to be with respect to vehicles already out of the network at the end of the simulation, we can draw the following conclusions from the above results: •

There is a significant increase in Average Travel Time and Average Trip Distance across all levels of vehicle loading (30-50% for higher loading levels).

Chiu .Y.C., Rao .P. K. and Mirchandani .P.B. • •

11

Large system performance degradation shows that there is significant room for improvement in evacuating drivers The MOE values for the SO.FL.RM are consistently lower than those predicted by the SO.FL.ERC case, showing that the use of random route choice while simulating traffic evacuation behavior, underestimates system performance degradation by a large amount

ERC model results in conjunction with appropriate traffic simulations can provide information about actual link flows and congestion points which can be “expected” during actual flooding evacuation. This information will then be used to develop suitable control strategies and close the real-time feedback loop 4.4. Quantification of User Deviation and its importance The open loop analysis also yields an important measure, namely the actual percentage of drivers who do not follow route guidance information. As per the authors’ understanding, no evacuation model to date has been able to actually measure this effect nor has addressed this issue. This effect is quantified by means of the following scheme. For a given Origin, Destination and Starting Time, with k paths, we have, Optimal Assignment %ge of path k - New Assignment %ge of path k 2 , Deviation

¦

where, the Optimal Assignment percentage corresponds to the fraction of users assigned to a given path k between O-D pair (i, j) as part of a system optimal routing scheme. The New Assignment percentage refers to the situation where drivers have been given system optimal guidance, but choose to pick paths based on the ERC model. Figure 7a shows that, 50% of drivers will not heed and follow system optimal evacuation routes. Such a high value of non-compliance magnifies the need for the incorporation of the behavioral deviation element into all kinds of emergency evacuation models which rely on information delivery to the evacuees. 5. CLOSED LOOP ANALYSIS Closed loop analysis and testing aims to reduce the large system performance degradation which results from user/driver induced deviations. There are different methods by which control strategies can be implemented. In this work we seek to implement these strategies (Pre-Trip) by using path travel time as the deciding factor in the usage of a given path against another path between the same origin-destination pair. DYNASMART-P is used to simulate a scenario in which drivers are ordered to evacuate and are given Pre-Trip information about safe evacuation routes, for a fixed Roll Horizon. Then information is collected about the average travel times for different paths between all origin-destination pairs. Based on this information, paths are ranked in the increasing order of travel times and the path with the highest travel time is eliminated. The reduced choice set is then presented to the evacuating drivers who have not yet started their journeys/trips. This is done for each successive roll horizon until the total simulation time is reached. The benefits of a control strategy are the most significant on scenarios which are theoretically observable, namely the SO.FL.ERC and SO.FL.RM scenarios from the open loop experiments. 5.1. Experimental Design & Results We study the effect of control strategies using a roll horizon duration of 10 minutes. In a physical sense this implies that every ten minutes, overall network conditions are analyzed, travel time information about each link is obtained, the worst paths for each (i,j) pair, out of the affected zone are eliminated and provided to evacuees who haven’t yet started their journeys. The results of the application of this strategy to the SO.FL.KL and SO.FL.RM cases are shown in Fig. 9. Tests have also been conducted to study the sensitivity of the results to the duration of the roll horizon. Their results are shown in Fig. 10. Analysis of the results leads to the following conclusions: • Application of control strategy does benefit the overall evacuation process as evinced by the reduction in average travel times.

Chiu .Y.C., Rao .P. K. and Mirchandani .P.B. • • •

12

Greatest reduction in average travel time (17% decrease) is found for the highest level of vehicle loading (35,000 vehicles) Travel time improvement after control strategy application, is significantly dependent on duration of roll horizon Improvement in travel time with decreasing roll horizon duration is the greatest for the highest level of vehicle loading

6. CONCLUSIONS & LIMITATIONS This paper is the first step towards showing that this approach of doing real-time traffic management for emergency situations based on feedback from observed traffic conditions, has sufficient merit to be used in larger scale evacuation studies. We propose a unique survey validated evacuee behavior model, able to accurately predict and quantify the number of evacuees who do not follow system optimal paths. We also discuss a pre-trip control strategy scheme used to push system performance closer to the optimal values, in the face of user deviations from recommended routes. Of course, an important issue may be the availability of information about all vehicles and conditions at different points in the traffic network. At present we assume that detector’s are available on all links of the traffic network. But, this is not practically feasible. One possibility of dealing with this limitation is the use of either airborne remote sensing detectors or in-vehicle two way communication devices. 6. ACKNOWLEDGEMENTS This research was partially supported by the National Science Foundation through Award Number 0332001 to the University of Texas at El Paso. The authors thank all the participants of this projects. Certainly the author is solely responsible for the viewpoints expressed in this paper.


13

REFERENCES 1.

http://www.crh.noaa.gov/riw/floods.htm

2.

Southworth, F. (1991), “Regional Evacuation Modelling: A State of the Art Review”, Centre for Transportation Analysis, Oak Ridge National Laboratory, A Report Prepared for the U.S. Department of the Army.

3.

CSEPP Accident Planning Base Review Group, Emergency Concept Plan for the Chemical Stockpile Emergency Preparedness Program (1997).

4.

B. Barrett, B. Ran, and R. Pillai. Developing a dynamic traffic management modeling framework for hurricane evacuation. Transportation Research Record, 1733:115–121, 2000.

5.

http://www.kldassociates.com/evac.htm, Development of IDYNEV and PCDYNEV, KLD Associates

6.

Peeta, S. (1994). System Optimal Dynamic Traffic Assignment in Congested Networks with Advanced Information Systems. Phd Thesis. University of Texas-Austin

7.

Ennio Cascetta, Agostino Nuzzolo, Francesco Russo and Antonino Vitetta (1996) “A Modified Logit Route Choice Model Overcoming Path Overlapping Problems: Specification and Some Calibration Results for Interurban Networks.” Transportation and Traffic Theory. Proceedings from the Thirteenth International Symposium on Transportation and Traffic Theory, Lyon, France. J.B. Lesort, ed. Pergamon.

8.

Ennio Cascetta and Andrea Papola (1998) “Implicit Availability/Perception Logit Models for Route Choice in Transportation Networks.” Presented at the 8th World Conference on Transport Research, Antwerp.

9.

V. P. Shah and K. Wunderlich. Detroit freeway corridor its evaluation. Technical report, MitreTek Systems, FHWA, Project No: 0998610D-01, July 2001.

10. H. S. Mahmassani, A. S. Hayssam, and Y. C. Chiu. Dynasmart-p, version 0.930.1. Users guide, University of Texas, Austin, 2002.

Chiu .Y.C., Rao .P. K. and Mirchandani .P.B. LIST OF TABLES 1.

Classification of evacuation models based on traffic simulation approach

LIST OF FIGURES 1.

Real-Time Evacuation Scheme Framework

2.

Survey Questionnaire

3.

Survey Results

4.

Application of Control Strategy

5.

Sample Network

6.

Open Loop Experimental Scenarios

7.

System Performance Degradation

8.

Quantification of Evacuee Deviations

9.

Effect of Pretrip Control Scheme

10. Roll Horizon Duration Sensitivity

14


15

Model

Micro

CLEAR

X

DYNEV

Meso

Macro

X

DYMOD

X

EVACD

X

MASSVAC

X

NETVAC

X

NETSIM

X

SNEM

X

Table 1: Classification of evacuation models based on traffic simulation approach


Developing Flooding Scenario

Optimization Module

16

Path Strategy

Behavioral Model

Expected Actual Congestion

Simulator / Real -Life

Control Strategies

Figure 2: Real-Time Evacuation Scheme Framework

Expected Evacuation Routes / Driver Path Strategies


Choice

Path 1 Path 2 Path 3

Path Length (miles) 2.43 2.96 2.51

17

Extent of Overlap among paths 2.29 1.00 1.55

Fraction of path which is freeway 0.00 0.00 0.31

Previous knowledge of path 0.377 0.000 0.245

Figure 2a: Survey Questionnaire - Sample Respondent Choice Set

Figure 2b: Survey Questionnaire - Sample Respondent Visual Aid

LEN CF FWAY FAM

Coeff. -1.015 -0.063 1.135 4.070

t-stats -10.504 -0.211 3.447 7.528

Figure 2c: Survey - Results

P[|Z| > z] 0.0000 0.8329 0.0006 0.0000

Node Sequence 18 7 2 18 12 11 6 18 7 6 1


18

replicate evacuee deviations from System Optimal Paths

Use Traffic Simulator to simulate traffic for predetermined time replicate evacuee response to restricted pre-trip path choice set

current simulation clock < roll horizon duration

No

Yes Record MOE’s, specifically Travel Time on the different paths between O-D pairs

Eliminate/Penalize Paths with higher travel times

Figure 3: Application of Control Strategy

Stop


19

Original Demand Matrix 5 Zones, 5 by 5 Matrix, Trips between All Nodes 11

6000

12 4038 3640

6000

Zone 5

4074

4589

4085

Zone 2

8

16

4301

17 9159

4115

4662

3020

5503

15

5491

10

4007

9

7

1

5844

4557

4315

18 3654

6

14

4001

13

Zone 1

4347

5538 Zone 4

5 Zone 3

4944

4038

3 5246

6705

2

4

Figure 4a: Sample Network

Evacuation Demand Matrix 3 Zones, 3 by 3 Matrix All Trips to Zone 3 11 Origin

Destination

6000

12 4038

12

6

3640 6000

7 4085

Zone 2

8

4301

17 9159

Super Sink

5

4944

4038

3 5246

16 4347

5538 Zone 3

2

4115

4662

3020

15

5491

10

4007

9

5503

1

5844

4557

4589

3654 4074

14

4001

4315

18

6

13

Zone 1

6705 4

Figure 4b: Sample Network with Flooding Scenario


UE UE.FL.NP SO SO.FL SO.FL.ERC SO.FL.RM

UE x x

SO

Flooding

20

Evacn.

Length

x x x

x

ERC Parameters FB FF

CF

Random

x x x x x

x x x

UE = User Equilibrium FL = Flooding NP = No Pretrip Info P = Pretrip Info SO = System Optimal

x

ERC = Evacuation Route Choice Model RM = Random FB = Freeway Bias FF = Familiarity Factor CF = Commonality Factor

Figure 5: Open Loop Experimental Scenarios

x

x x


21

57% 15,000 Vehicles 25,000 Vehicles

Percentage Deviation from Base Case

35,000 Vehicles

17% 12%

2.93

5.12

5.56

Avg. Travel Time

6%

2%

7%

1.64

1.74

1.61

Avg. Trip Distance

Figure 6a: System Performance Degradation. Drivers pick routes according to ERC model.

33% 15,000 Vehicles 25,000 Vehicles

Percentage Deviation from Base Case

35,000 Vehicles

13% 11%

10% 5%

2.93

5.12

5.56

Avg. Travel Time

1.64

7%

1.74

1.61

Avg. Trip Distance

Figure 6b: System Performance Degradation. Drivers make random route choices.


22

15000 Vehicles, SO + ERCM 60%

distribution (%)

50% 40% 30% 20% 10% 0% 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.7

0.8

0.7

0.8

sqrt(deviation)

25000 Vehicles, SO + ERCM 60% distribution (%)

50% 40% 30% 20% 10% 0% 0

0.1

0.2

0.3

0.4

0.5

0.6

sqrt(deviation)

35000 Vehicles, SO + ERCM 60% distribution (%)

50% 40% 30% 20% 10% 0% 0

0.1

0.2

0.3

0.4

0.5

0.6

sqrt(deviation)

Figure 7: Quantification of Evacuee Deviations for different vehicle loading levels


Avg. Travel Time percentage improvement over expected evacuation situation

23

Avg. Trip Distance

Avg. Travel Speed 20% 7%

-1% -1% -8% -8%

-4%

-10%

-17% 15,000 Vehicles

25,000 Vehicles

35,000 Vehicles

Figure 8a: Effect of Pretrip Control Scheme on SO.FL.ERC case (Fig. 7a)

Avg. Travel Time

Avg. Trip Distance

Avg. Travel Speed 6%

5%

percentage improvement over expected evacuation situation

2% 0%

-3% -8% 15,000 Vehicles

1%

-2%

-7% 25,000 Vehicles

35,000 Vehicles

Figure 8b: Effect of Pretrip Control Scheme on SO.FL.RM case (Fig. 7b)


24

Average Travel Time (minutes)

Drivers follow ERC Behavior 9.00 8.50 8.00 7.50 7.00 0

10

20

30

40

50

60

70

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Roll Horizon Duration (minutes)

Average Travel Time (minutes)

Drivers pick Random paths 9.00 8.50 8.00 7.50 7.00 0

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Figure 9: Roll Horizon Sensitivity of Results (35,000 Vehicles)

Gurian, Castro, and Chiu

A Bayesian Monte Carlo Approach to Model Calibration for Queuing Systems

Patrick L. Gurian Department of Civil, Architectural & Environmental Engineering Drexel University Philadelphia, PA 19104 Tel: (215) 895-2889, Fax: (215) 895-1363, Email: [email protected] Felipe Castro Department of Civil Engineering University of Texas at El Paso El Paso, TX 79968 Tel: (915) 621-6705, Fax: (915) 747-8037, Email: [email protected] Yi-Chang Chiu Assistant Professor Department of Civil Engineering University of Texas at El Paso, El Paso, Texas 79968 Tel: (915) 747-6918, Fax: (915) 747-8037, E-mail: [email protected]

Submitted for presentation at the 84th Annual Meeting of the Transportation Research Board, January 2005, Washington, DC Submitted: November 1, 2004 Number of words: 5,970 (4,470 words + 6 tables and figures)


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ABSTRACT Calibrating models of queuing processes typically requires the collection of data on the arrival and departure of individual vehicles. In this paper an alternative procedure is described which uses Bayesian Monte Carlo methods to update prior estimates of model parameters using observations of changes in queue length over time. Substantial reductions in parameter uncertainty can be achieved by this calibration procedure. The procedure is most effective at reducing uncertainty in arrival rates when service rates are already well characterized. A number of transportation systems, including toll plazas and inspections stations at ports-of-entry, have well-characterized service capacities, indicating that this method may be appropriate for use with these systems. In general, posterior uncertainties for arrival rates and service rates are higher than for conventional calibration procedures. This procedure is likely to be useful in cases, such as international ports-of-entry, where security and access concerns render the collection of data on individual vehicles infeasible, but abundant information is available on queue lengths. INTRODUCTION A variety of important transportation systems have elements that can be described as queuing systems (1), including toll plazas (2-3), international ports-of-entry (4-5) and freeway on-ramp traffic signals (6-9). Modeling the performance of these systems requires calibrating parameters for the arrival rates (trip demand), queue length, and service rates (departure rates). These quantities are related as queue length is the resultant of arrival rate and service rate (although feedback relationships may complicate this). Knowledge of any two of these variables allows determination of the third. For calibrating models of queuing systems, transportation researchers have relied on a variety of data collection techniques to record the arrival and departure of individual vehicles, including traffic detectors, video recording, manual observations, etc. This information can be used to inform estimates of arrival rates and service rates, and the calibrated model will then predict queue length. Unfortunately, collecting this information will generally require specialized monitoring equipment and a dedicated data collection effort. Using this approach to calibrate a performance model of a toll plaza would involve collecting information on all arrivals and departures at all lanes, a cumbersome and time-consuming task. Obtaining performance data for inspections stations at international ports-of-entry is even more problematic. The data requirements are roughly the same as for a toll plaza, but conducting the monitoring is more problematic. In the aftermath of the September 11 terrorist attacks, security concerns generally prevent the Department of Homeland Security from sharing archived data or allowing access to ports-of-entry for the collection of such data (L. Garcia, personal communication 2004). However, in many transportation systems, estimates of queue lengths may be obtained more easily, and may even be available as part of routine monitoring. For ports-of-entry, waiting time information is publicized in order to inform prospective border crossers of the current wait times. Wait times are commonly reported on local radio stations and on websites (such as 10). Photographs that allow the determination of queue length are also posted online (11). For other systems, routine video monitoring for security surveillance may provide a record of queue lengths over time. Even if archival data is not available, recording data on queue length is expected to require less effort than documenting the arrival and departure of individual vehicles, since a single photograph can capture queue length information for multiple lanes.


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It would, therefore, be desirable to calibrate a model based on observations of queue length over time. Unfortunately, queue length alone is not sufficient to calibrate a model, because a given queue length can be produced by an infinite number of combinations of arrival rates and services rates. Nevertheless, if some prior estimates of arrival rates and service rates are available, then queue length changes can be used to inform judgments as to the relative plausibility of different prior estimates. For example, if queue length is observed to grow during an observation period, estimates in which the arrival rate exceeds the service rate would appear more plausible and estimates with a lower arrival rate than service rate would appear less plausible. In many cases such prior estimates of arrival rates and service rates will be available from literature studies of similar transportation systems. In this paper, an approach is developed to calibrate parameters for transportation system queuing models that uses a combination of informed prior estimates of arrival and service rates and observations of changes in queue length of time. The performance of this calibration strategy is evaluated under a range of different scenarios using simulation methods and compared to more conventional approaches. BAYESIAN MONTE CARLO Bayesian Monte Carlo analysis is a model calibration technique developed in the field of risk assessment (12). The approach uses a Bayesian statistical framework to update prior estimates of model parameters by comparing predicted values with observed values. Bayesian statistics is generally associated with a subjectivist approach to probability. Model parameters are viewed as random variables with probability distributions describing the uncertainty in the true values of the parameters (by describing the probability that the true value is in a given range). Parameters are assigned prior probability distributions, which may be either diffuse (information-less) or informed. The prior distributions are then updated based on additional information from observed values (data). The updated distribution is referred to as a posterior distribution. The updated values reflect a combination of both the prior knowledge and the information gained from the observations. Bayes’ rule is the mathematical formula used to carry out this updating: Prob [θ | x] = Prob [x | θ] Prob [θ] / θ∫ Prob [x | θ] Prob [θ] dθ

(1)

where x indicates the observed data and θ the model parameters (bold is used to indicate that both are typically vectors). Prob [θ] is the prior probability of the model parameters. Prob [x| θ] is the probability of the data, given a value of the parameters and is known as the likelihood function. Prob [θ| x] is the updated probability of the model parameters, once the data, x, has been observed and (as described above) is known as the posterior probability of the parameters. The Bayesian Monte Carlo approach begins with a Monte Carlo simulation based on prior knowledge that is generally highly uncertain. The model outputs from the Monte Carlo simulation are then compared to actual observations of the model outputs and updated distributions of both the model inputs and outputs developed using Bayes’ rule. The strategy proposed here is to develop prior distributions for arrival and service rates based on literature information, and then use Bayesian Monte Carlo methods to update these estimates given observations of queue length. The mathematical details of this procedure are given in the following section.


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SIMULATION METHODOLOGY For this case a simple queuing model was used in which both arrivals and departures are Poisson distributed (an M/M/1 system). The model is specified by two parameters, the mean number of arrivals, λA, and the mean number of departures, λD for a time interval of a specified length. A lognormal distribution is used to represent prior uncertainty in the true values of the mean number of arrivals, as this constrains the arrival rate to be non-negative for all choices of parameter values: ln λA ~ N (µ A, σA2)

(2)

where µ A is the log-mean (or median) of the distribution for the number of arrivals and σA is the log-standard deviation of the number of arrivals. Uncertainty in the departures is modeled in an analogous fashion. Changes in queue length over the time interval, denoted by ∆Q, are determined by the difference in arrivals and departures: ∆Q = A – D

(3)

Once λA and λD have been specified, the mean (or expectation) and variance of ∆Q can be readily determined using the properties of the expectation and variance operators without the need for simulation methods: E[∆Q] = λA - λD

(4)

Var [∆Q] = Var [λA] + Var [λD]

(5)

given that λA and λD are independent. Monte Carlo simulation methods are used to sample the prior distributions of λA and λD and calculate the corresponding values of E[∆Q]. The model results presented here are based on 1000 realizations (1000 samples of λA and λD and corresponding computations of E[∆Q]). A second set of 1000 realizations was generated and found to give similar results indicating that sample variability had little influence on the results reported here. In accordance with the Bayesian Monte Carlo framework, the simulated values of λA, λD, and E[∆Q] are treated as a discrete prior distribution for these parameters with each set having prior probability of 1/N where N is the number of Monte Carlo samples taken. INCORPORATION OF DATA The goal of Bayesian Monte Carlo analysis is to update the results of a Monte Carlo simulation based on prior distributions, using actual observations of predicted variables. In this case, it was assumed that 1000 observations of changes in queue length over a fixed time interval are available. As the goal of this study was simply to test the effectiveness of the approach under a range of known conditions, synthetic observations were generated using Microsoft Excel’s random number generator. The true λA was fixed at 95 and the true λD at 70. Thus, the true E[∆Q] was 25. However, to simulate the situation in which the true parameters of the observations are unknown, an estimate of E[∆Q], denoted by ∆Qave, was obtained by averaging the 1000 queue length changes. The standard error of this estimate was in turn estimated by the


4

s/√n where s is the sample standard deviation and n is the number of queue length changes observed. Information from this sample was then used to calculate updated, or posterior, probabilities for each of the 1000 sets of parameters obtained from the Monte Carlo samples from the prior distributions. As shown in Equation 1, in order to calculate these posterior probabilities, one needs both the prior probability (simply 0.001 for all parameters sets here) and the likelihood, Prob [x | θ], which is the joint probability of observing the data, ∆Qave, given particular parameter values. The distribution describing the probability of obtaining a particular ∆Qave value, given sampled values of λA and λD, can be assumed to be roughly normal (given the sample size, the central limit theorem can be applied) with mean λA - λD and a standard deviation equal to s/√n, the standard error of the estimate (12). [While the error due to sampling variability could in this case be calculated analytically as {(λA+λD)/n}0.5, in general the error term should include all sources of measurement error, not just sampling variability. The authors feel it is best practice to estimate the error term from the data as this should include random variation introduced from the measurement process.] The only term remaining to be calculated in Equation 1 is the denominator. This is shown as an integral but in this case the distribution of θ, the model parameters, is a discrete distribution and the integral can be replaced by a sum: Σi Prob [x | θi] Prob [θi]

(6)

where i indexes the different discrete samples of model parameters. Equation 1 can now be simplified and made specific to this application by substituting the appropriate likelihood functions and canceling out Prob [θi] which has a constant value of 0.001: Prob [λA, λD, E[∆Q] | ∆Qave] = f(∆Qave|µ= λA- λD, σ=s/√n ) / Σi f(∆Qave|µ= λAi-λDi, σ=s/√n ) (7) where f(∆Qave) is the probability density function for a normal distribution. The result of this procedure is to develop a discrete posterior distribution for the model parameters. Moments and other quantities can be determined using standard procedures for discrete distributions. For example, the posterior mean and variance of λA can be found by: E [λA| ∆Qave] = Σi Prob [λAi ] λAj Var [λA| ∆Qave] = Σi Prob [λAi] (λAi - E [λA| ∆Qave ])2

(8) (9)

Where Prob [λAi ] is simply the posterior probability of each value of λAi as calculated by Equation 7. PERFORMANCE OF ESTIMATION METHOD This method allows for both forward updating (reducing the uncertainty of outputs of the Monte Carlo simulation, in this case E[∆Q]) and backward updating (reducing the uncertainty in inputs of the Monte Carlo simulation, in this case λA and λD). Thus the procedure updates estimates not only of changes in queue length, which are directly observed, but also of arrivals and departures, which are not directly observed. Table 1 summarizes the results of one simulation of the updating procedure. In all cases, the prior means are close to the true means. While the


5

posterior means differ somewhat from the true mean values due to sample variability, they are in all cases within one posterior standard deviation of the true value. The most notable differences are between the prior and posterior standard deviations. In all cases the posterior standard deviation is lower than the prior, reflecting the additional information gained by observing the data. The reduction in uncertainty of the parameters is substantial for λA and λD, as the posterior standard deviations are 60% and 45% lower, respectively. For E[∆Q] the difference between prior and posterior standard deviations is dramatic (21 compared to 0.42). As differences in queue length are directly observed, much more information is gained through the updating process for this parameter. These results show that this calibration method has the potential to substantially reduce uncertainty for all model parameters. However, direct observation of arrivals and departures would produce dramatically lower uncertainties. For example, observing 1000 time intervals with Poisson distributed arrivals with a mean and variance of 95 (that is, the true distribution of λA) would produce a standard error of 0.3, far lower than the posterior standard deviation of 6.7 that was obtained here for λA. The results in Table 1 are specific to a given set of input parameters. In order to generalize these results, a range of different scenarios were explored and the performance of the Bayesian Monte Carlo method characterized for each scenario. Based on trends observed in these scenarios, qualitative conclusions about the performance of the method under different circumstances are developed. The first step in the procedure is to consider the possible attributes of different scenarios under which one might apply the Bayesian Monte Carlo procedure. In very general terms, each of these scenarios has three attributes: The amount of information contained in the prior distributions. In cases where λA and λD are believed to be well known, their prior distributions will have small variances, and will be tightly concentrated around the best estimates. Conversely, in cases of great uncertainty, the prior distributions will be diffuse, with large variances. Prior distributions with smaller variances have more influence on the posterior estimates. Figures 1 shows the prior and posterior distributions for λA when the prior distribution is fairly diffuse (prior standard deviation of 37). Figure 2 shows the prior and posterior distributions using the same set of observations but a more informative prior distribution (standard deviation of 4.6). In both cases the posterior distribution has lower variance than the respective prior, but the posterior is much more tightly concentrated (indicating less uncertainty) in the case where the prior is more informative. The degree of bias in the prior distributions. Prior information may be accurate or inaccurate. In this paper “bias” is used to refer to a difference between the central tendency of the prior distribution and the true central tendency of the distribution that produces the observed data. The updating process should partially correct for biases that may be present in the prior. Figure 3 shows a case where the prior has a median of 110 and the true median is 95 (as in Figure 1, the prior standard deviation is 37). In this case the posterior distribution has a median of 96, indicating that the upward bias in the prior has been mostly, but not completely, eliminated. The amount of information in the data. The larger the sample size, the more information is contained in the data. Consequently, a larger sample size will result in the posterior distribution being influenced less by the prior and more by the data. In the limiting case, as the sample size becomes very large, the influence of the prior will become negligible.


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PERFORMANCE UNDER ALTERNATIVE SCENARIOS In order to gain insight into the conditions under which this calibration strategy would be most successful, 25 different scenarios were considered. These scenarios represent combinations of five different levels of prior uncertainty and five different levels of bias in the prior distributions. The third attribute described above, the amount of data, was not varied in these scenarios but was kept constant at 1000 observations of changes in queue length in order to reduce the number of scenarios to a manageable number. This is also in keeping with the assumption that this method will generally be used when observations of queue length changes are easily obtained so that a large sample size is available. The true values of λA and λD were also maintained at 95 and 70. Table 2 summarizes the five levels of uncertainty, and Table 3 summarizes the five levels of bias. Uncertainties are presented as log-standard deviations for mathematical clarity. To provide some intuitive insight into the level of uncertainty, one can note that the high uncertainty value corresponds roughly to an uncertainty factor of 2 (95% probability that a given value will be between ½ and 2 times the nominal value), the medium scenario corresponds to an uncertainty factor of 1.4, and the low uncertainty scenario corresponds to an uncertainty factor 1.1. The effectiveness of the calibration approach can be measured by the fractional reduction in uncertainty between the prior and posterior distribution of the model parameters. These values are shown in Tables 4, 5, and 6 for λA, λD, E[∆Q], respectively. A number of general trends can be noted that may help establish reasonable guidelines for the circumstances under which this method should be used, and the performance that should be expected from it. Reductions in uncertainty are greater for E[∆Q] than for the other parameters. As discussed above, this is to be expected as changes in queue length are observed directly, while arrivals and departures are not. Uncertainty reductions for the other parameters vary greatly depending on the exact scenario. In cases where uncertainty in arrival and departures is similar, the uncertainty reductions tend to fall into the range of 20-75%. This is broad range, but still one may conclude that this calibration method may noticeably reduce uncertainty under a range of different scenarios. Uncertainty reductions are greatest in cases where initial uncertainty is high. For example, if no bias is present and prior uncertainty is high, then the calibration procedure reduces uncertainty in λA by 56%. If prior uncertainty is low, then only a 45% reduction in uncertainty is achieved. An interesting effect is observed when uncertainty levels differ between the two parameters. Little improvement is seen in the estimate of the parameter which is relatively well characterized, while a large reduction in uncertainty is achieved for the parameter with high uncertainty. In Tables 4 and 5, the two right columns show the results for unequal levels of uncertainty. When λA has low uncertainty and λD has high uncertainty, the calibration process reduces uncertainty in λA by only 2-17% but by 82-89% for λD. Several results merit discussion as apparent anomalies. In two cases there is a negative reduction in uncertainty in λD. Updating does typically reduce uncertainty, but there is no inherent requirement that the variance of the posterior be smaller than the variance of the prior. In both cases prior uncertainty in λD is low and the prior is biased. The apparent increase in uncertainty in these cases is really an indication that the prior was not appropriately chosen. Thus something has in fact been learned through the updating process, and the posterior distribution can still be considered a more accurate representation of parameter uncertainty than the prior, despite the fact that the posterior actually has a higher variance. In the scenario of high uncertainty in λA, low uncertainty in λD, and high bias in both parameters, the posterior uncertainty of λD increases by 20%. The combination of


7

overconfidence coupled with the bias, means that the posterior distribution must be re-centered (moved away from the prior mean towards the mean of the data), and in the process it is rendered more diffuse. The prior is clearly inappropriate as the true value of λD is 70, more than 5 standard deviations from the prior value of 95. The initial variance of the prior was too small, given the amount of bias present. When the variance of the prior is underestimated, then one is overconfident in the prior information, a common problem in making subjective probability judgments (13). Another apparently anomalous result is the 100% reduction in uncertainty in the case of low uncertainty, arrival biased high, and departure biased low (indicated by the asterisk). In this particular case 999 of the 1000 prior samples had negligible likelihood. Thus the entire posterior distribution is reduced to a single discrete value which has zero variance (interpreted as zero uncertainty). This result is an artifact of the discrete nature of the Bayesian Monte Carlo process and the finite sample size employed. The result is shown here to illustrate the conditions under which such anomalies may occur. In this case, the anomaly is primarily the result of misspecification of the prior distributions. The bias of both prior distributions is such that very low probability is put on the true parameter values. The true value of each parameter is more than two standard deviations away from its respective prior mean. It is very unlikely that any of the parameters in the sample from the prior distribution will correspond to likely values once the data is observed. Under ordinary circumstances, 1000 samples will characterize both the prior and posterior distribution relatively well, but in this case a much larger sample size would be needed to yield enough samples with non-negligible likelihood. DISCUSSION The results presented here suggest that Bayesian Monte Carlo methods may allow information on queue length over time, coupled with informed prior estimates of arrival rates and service rates, to be used to calibrate models of queuing processes. Substantial reductions in prior uncertainty of the arrival and service rates may be achieved, but posterior uncertainties are generally much higher than for calibration by direct observation of arrivals and departures. Posterior uncertainties in queue length changes are small, because direct observations of this parameter are used in the calibration procedure. The use of this calibration procedure may be justified under a variety of conditions. In some cases, it may be fluctuations in queue length that are of primary interest, such as when the primary use of the model is to forecast delays caused by the queue. In other cases it may be impractical or prohibitively expensive to collect data on arrivals and departures, such as with some ports-of-entry where security and access issues prohibit direct observation of individual arrivals and departures. This method offers the greatest reduction in uncertainty of a given parameter when the other parameter is well characterized. Fortunately, this may be the case in many transportation systems. Both toll plazas and border inspections stations have inherent capacities that are fairly well characterized in the literature (14-15). Thus the prior distribution for λD would have a fairly low variance, which would permit a more accurate estimate of λA to be obtained. Similarly many systems have a relatively constant and well-characterized service capacity but are subject to large variations in demand over time. This calibration procedure may provide a convenient way to estimate the many arrival-rate parameters needed to calibrate time-varying demand functions for these systems. Further evaluation of the method is clearly needed. In particular this study did not consider the effects of sample size, which is clearly an important variable. It is expected that this


8

method will only yield good results when fairly large amounts of data on changes in queue length are available from routine monitoring records, but efforts to find the lower bound on the data requirements of this procedure would be of interest. Perhaps the highest priority for further research is to apply this method to a transportation dataset as a case study. Efforts are currently underway to pilot test this method for queuing processes at the international ports-of-entry in the El Paso area. ACKNOWLEDGMENTS This research was supported by the National Science Foundation through Award Number 0332001. Teresa Montoya assisted with editing the manuscript. REFERENCES 1. Fan, W. (1976). "Simulation of queuing network with time varying arrival rates." Mathematics and Computers in Simulation, 18(3): 165-170. 2. Wanisubut, S. (1991). A toll plaza simulation model and level-of-service criteria, Ph.D. thesis, Polytechnic University, 1989. 315 pp. Advisor: Walter Helly. 3. Zarrillo, M. L., A. E. Radwan, et al. (1997). "Modeling traffic operations at electronic toll collection and traffic management systems," Computers & Industrial Engineering, 33(34): 857-860. 4. Chaires, S. A. P. (2000). Simulation Modeling of Traffic Operations at International Port of Entry along the U.S. - Mexico Border: Case study from El Paso, Texas. M.S. thesis, Department of Civil Engineering, University of Texas at El Paso, El Paso, TX. 5. Pinal, G. (1997). A Queuing Analysis at an International Port of Entry. M.S. thesis, Department of Civil Engineering, University of Texas at El Paso, El Paso, TX. 6. Rakha, H. and B. Crowther (2003). "Comparison and calibration of FRESIM and INTEGRATION steady-state car-following behavior." Transportation Research Part A: Policy and Practice, 37(1): 1-27. 7. Ben-Akiva, M., D. Cuneo, et al. (2003). "Evaluation of freeway control using a microscopic simulation laboratory." Transportation Research Part C: Emerging Technologies, 11(1): 29-50. 8. Wu, J., M. Brackstone, et al. (2003). "The validation of a microscopic simulation model: a methodological case study." Transportation Research Part C: Emerging Technologies, 11(6): 463-479. 9. Evans, J. L., L. Elefteriadou, et al. (2001). "Probability of breakdown at freeway merges using Markov chains." Transportation Research Part B: Methodological, 35(3): 237-254.


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10. Border Wait Times. U.S. Customs and Border Protection, http://apps.cbp.gov/bwt/ accessed July 29, 2004. 11. Reporte de Puentes. ReportedePuentes.com, El Paso, TX, http://www.reportedepuentes.com/reportepuentes5.asp accessed July 29, 2004. 12. Brand, K.P. and M.J. Small. 1995. “Updating uncertainty in an integrated risk assessment: Conceptual framework and methods,” Risk Analysis, 15(6): 719-731. 13. Morgan, M. and M. Henrion (1992). Uncertainty: A Guide to Dealing with Uncertainty in Quantitative Risk and Policy Analysis. Cambridge University Press. 14. Lin, F. B., M. W. Lin. 2001. “Modeling Traffic Delays at Northern New York Border Crossings,” Journal of Transportation Engineering, 127(6):540-545. 15. Coleman, F., and Young-Jun Moon. 1999. “System Simulation of Commercial Vehicle Border Crossing Congestion: The Ambassador Bridge Case Study,” Proceedings of the Summer Computer Simulation Conference San Diego: Society for Computer Simulation.


LIST OF TABLES AND FIGURES TABLE 1. Inputs and results of the Bayesian Monte Carlo procedure TABLE 2. Levels of uncertainty considered in scenarios TABLE 3. Levels of bias considered in scenarios TABLE 4. Fractional reduction in prior uncertainty in λA TABLE 5. Fractional reduction in prior uncertainty in λD TABLE 6. Fractional reduction in prior uncertainty in E[∆Q] FIGURE 1. Prior and posterior distributions for λA, high uncertainty, unbiased FIGURE 2. Prior and posterior distributions for λA, low uncertainty, unbiased FIGURE 3. Prior and posterior distributions for λA, high uncertainty, biased high

10


11

TABLE 1. Inputs and results of a simulation showing the performance of the Bayesian Monte Carlo procedure. A simulated dataset of 1000 changes in queue length was used. True values refer to the values of the parameter used to generate the simulated data.

True value Prior mean Posterior mean Prior standard deviation Posterior standard deviation

λA 95 96 91 17 6.7

Parameters λD 70 71 66 12 6.7

E[∆Q] 25 25 25 21 0.42


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TABLE 2. Levels of uncertainty considered in scenarios. Prior Log-Standard Deviation of λA

Prior Log-Standard Deviation of λD

High uncertainty (factor of 2)

0.35

0.35

Medium uncertainty (factor of 1.4)

0.17

0.17

Low Uncertainty (factor of 1.1) High arrival uncertainty (factor of 2) Low departure uncertainty (factor of 1.1) Low arrival uncertainty (factor of 1.1) High departure uncertainty (factor of 2)

0.05

0.05

0.35

0.05

0.05

0.35

Description


13

TABLE 3. Levels of bias considered in scenarios. In all cases the data for updating was generated using a true mean of 95 for λA and a true mean of 70 for λD. Prior Mean of λA

Prior Mean of λD

No bias

95

70

Arrival and departure biased low

80

55

Arrival and departure biased high Arrival biased high Departure unbiased Arrival biased low Departure biased high

110

95

110

70

85

85

Scenario Name


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TABLE 4. Fractional reduction in prior uncertainty in λA. High uncertainty

Medium uncertainty

Low uncertainty

High arrival, low departure uncertainty 0.94

Low arrival, high departure uncertainty 0.13

0.56 0.54 0.45 No bias Arrival and 0.59 0.48 0.46 0.94 0.02 departure biased low Arrival and 0.47 0.29 0.25 0.87 0.12 departure biased high Arrival biased 0.75 0.52 0.42 0.94 0.17 high Departure unbiased Arrival biased low 0.48 0.41 1.0* 0.84 0.16 Departure biased high *Result is an anomaly created by the finite sample size of the Bayesian Monte Carlo procedure


15

TABLE 5. Fractional reduction in prior uncertainty in λD. High uncertainty

Medium uncertainty

Low uncertainty

High arrival, low departure uncertainty

Low arrival, high departure uncertainty

No bias 0.40 0.38 0.26 0.32 0.85 Arrival and departure biased low 0.41 0.24 0.22 0.23 0.82 Arrival and departure biased high 0.39 0.19 0.13 -0.20 0.87 Arrival biased high 0.12 0.22 0.84 Departure unbiased 0.60 0.25 Arrival biased low Departure biased high 0.48 0.41 1* -0.28 0.89 *Result is an anomaly created by the finite sample size of the Bayesian Monte Carlo procedure


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TABLE 6. Fractional reduction in prior uncertainty in E[∆Q] High uncertainty

No bias Arrival and departure biased low Arrival and departure biased high

Medium Low uncertainty uncertainty

High arrival, low departure uncertainty

Low arrival, high departure uncertainty

0.99

0.98

0.93

0.99

0.98

0.99

0.98

0.91

0.99

0.98

0.99

0.98

0.94

0.99

0.99

Arrival biased high Departure unbiased 0.99 0.98 0.93 0.99 0.98 Arrival biased low Departure biased 1* 0.99 0.98 high 0.99 0.98 *Result is an anomaly created by the finite sample size of the Bayesian Monte Carlo procedure


17

1 0.9

cumulative probability

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 50

70

90

110

130

150

170

190

arrivals Prior distribution

Posterior distribution

FIGURE 1. Prior and posterior distributions for λA. Prior uncertainty is high (prior standard deviation = 37), and prior is unbiased.


18

1 0.9


0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 50

70

90

110

130

150

170

190



FIGURE 2. Prior and posterior distributions for λA. Prior uncertainty is low (standard deviation = 4.6), and prior is unbiased.


19

1 0.9


0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 50

70

90

110

130

150

170

190



FIGURE 3. Prior and posterior distributions for λA. Prior uncertainty high (standard deviation = 37), and prior is biased high (prior median is 110, true median is 95).

Development of a Port of Entry Model Utilizing an AreaWide Simulation Approach to Assess Impact to Regional Infrastructure By Jorge A. Villalobos Graduate Research Assistant Department of Civil Engineering University of Texas at El Paso, El Paso, Texas 79968 Tel: (915)747-5084, Fax: (915) 747-8037 E-mail: [email protected] Yi-Chang Chiu Assistant Professor Department of Civil Engineering University of Texas at El Paso, El Paso, Texas 79968 Tel: (915) 747-6918, Fax: (915) 747-8037, E-mail: [email protected] Patrick Gurian Assistant Professor Department of Civil, Architectural & Environmental Engineering Drexel University, Philadelphia, PA 19104 Tel:(215) 895-2341, Fax:(215) 895-1363, E-mail: [email protected] Josiah McC. Heyman Chairman Department of Sociology and Anthropology The University of Texas at El Paso, El Paso, Texas 79968 Tel:(915) 747-7356, Fax:(915) 747-5505, E-mail: [email protected] Words: 5967 Number of tables and Figures: 6 Total: 7467 Submitted to: ABE40 Critical Transportation Infrastructure Protection on August 1, 2004 The 84th Annual Meeting of Transportation Research Board Washington D.C., USA, 2005

Villalobos, Chiu, Gurian, Heyman

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ABSTRACT Land border Ports of Entry (POE) are critical in both national and regional terms. By offering legal and safe crossing points, they help integrate people and economies between nations. As security continues to take a more prominent role, the impacts of periodically heightened security measures generate substantial short-term and long-term impacts on economy and social-demographics activities on border cities. This study discuses the development of a system dynamics model that incorporates the effects of a regional transportation infrastructure systems, in particular the POEs, on the economy and social behavior of a border region due to operational policy changes and/or extreme events. The development of a microscopic POE queuing model integrated with a mesoscopic regional transportation system model, utilizing the dynamic traffic assignment software DYNASMART-P, is discussed and as well as the POE modeling strategy. The results show that DYNASMART-P’s ability to model complex transportation system while incorporating driver behavior generates unique traffic behavior responses to extreme events or policy modifications at the ports which sets is apart from traditional static assignment models.


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INTRODUCTION Land border Ports of Entry (POE) are critical in both national and regional terms. By offering legal and safe crossing points, they help integrate people and economies between nations. Yet they also apply important controls and regulations by handling the entry of people and goods. Borders, especially ports, are thus partially permeable membranes crucial to the regulation of larger societies on each side [1] [2] [3]. The U.S.-Mexico border, the subject of this study, has become a significant region in population and economy [4] and cross border infrastructure linkages between El Paso, Texas and Ciudad Juarez, Chihuahua Mexico are critical to the economic health of the region and both nations. By volume, El Paso is the second largest port of entry for merchandise trade between Mexico and the United States. In 2001, nearly 7.2 million pedestrians crossed the three bridges from Ciudad Juarez to El Paso. Nearly 15.8 million automobiles entered the United States across these arteries during that period, as did more than 660 thousand cargo vehicles [5]. In addition to the economic role, the non-economics social science literature describes the presence of complex interpersonal relations across the border, including cross-border kinship and family-ritual visiting patterns [6] [7] [1]. Studies of urban form show that cities in both nations usually grow outward from ports of entry [8] [9] and there are important border crossing phenomena that combine economic and non-economic functions: use of health services in the two nations, attendance at universities, tourism, etc. The terrorist attack of September 11, 2001 emphasized the importance of strong vigilance along the U.S. POE systems consequently focusing a spotlight on its national security performance. As security continues to take a more prominent role, the impacts of periodically heightened security measures generate substantial short-term and longterm impacts on economy and social-demographics activities on border cities. The greater border controls and heightened security measures have raised the cost of international commerce between the United States and Mexico negating some of the natural advantages afforded by geographical proximity” [10]. Therefore, it is important to understand the effects of Port of Entry policy, results of extreme events and implementation of new technology as it relates to the economic, social and infrastructure requirements and their effects on the border. Key decisions made by port management, especially on the U.S. side, determine basic operating characteristics of the entire border crossing system, since the characteristic bottleneck is entry to the U.S. Fundamental qualitative research on U.S.-Mexico ports [11] shows that ports control movement by trading off depth of inspections (for specific objectives, narcotics, immigration violations, national security, etc.) against throughput of traffic. Recent research has sought to identify more sophisticated ways of achieving national security control while keeping traffic moving [12] [13], such as the so-called “smart border” based on advanced sensing and database technology. However, sophisticated management systems may break down in extreme events and how diverse extreme event scenarios affect the aims, intensity, and means of inspection, and their trade-offs with traffic throughput has not been thoroughly investigated, except some limited studied based on queuing theories [14] [15].


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BACKGROUND The University of Texas at El Paso (UTEP) was awarded a grant from the National Science Foundation (NSF) to study the dynamics of the U.S. – Mexico Port of Entry along the El Paso, TX region. The overall goal of this proposed research is to develop an integrated border infrastructure risk management framework, explicitly considering the interacting dynamics of the border infrastructure, social and economic systems. This integrated model will allow the further understanding of border system dynamics, predicting impacts of risk preventive policies, evaluating mitigation strategies, and modeling recovery processes after an extreme event. Of particular emphasis will be the assessment of the critical border crossing infrastructure systems, evaluating border security policy and operations, designing information dissemination and pubic- and business- preparedness schemes, and identifying transportation system operations strategies in time of extreme events. This model will contribute to the state-of-the-art of decision theory, particular in the modeling of sequential decision processes in response to extreme events. The integrated model will consist of the following sub-models, denoted as the CRitical InfrasTructure Inter-Connect Activity PLatform (CRITICAL), which is envisioned to be integrated utilizing Monte-Carlo simulation: 1: Development of Border Transportation Infrastructure Models 2: Development of Border Inspections Infrastructure Models 3: Development of Border Crossings Travel Behavior Models 4: Extreme Event Induced Economy Loss Models 5: Development of Infrastructure Risk Management Model 6: Simulation-Based Model Integration The research is currently in the first year of the project, therefore this paper will illustrate the results of the initial regional border transportation infrastructure and inspections infrastructure model. The crux of the current work is to develop an area-wide transportation model incorporating the El Paso TX, Juarez MX and the POE systems, essentially integrating the entire region into one dynamic traffic assignment (DTA) model. The end goals are to: 1. Capture key characteristics of POE operations in US/Mexico border 2. Provide a computational platform with desirable realm that can be used to evaluate possible security policy, and technology impacts on the operations of POE and resultant impacts on border cities. 3. Provide a framework and model for POE operation and policy decision-making. Previous POE Studies The analysis of port of entry performance is not unique. Typically, analysis like the ones performed by [16], [17], [14] [15] have focused on one particular port of entry attempting to understanding the development of queue. Microscopic modeling tools like CORSIM or queuing models like ARENA (Rockwell) are utilized to develop the detailed flow


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design and a great deal of energy is dedicated in the acquisition of data at that particular site to estimate a probability distribution of arrival, inspection times and departure rates. The end results of the study are recommendations to reduce bottlenecks within the system by either decreasing inspection times and/or increasing the number of inspection stations. Although useful in determining immediate effects on queue and vehicular crossing time, these models typically do not consider driver behavior and interactivity between similar systems within the same region. The arrival rate to the facility is taken as a constant irregardless of the queue length and travel time of that POE. In reality though, information concerning queue length and travel time is available to drivers via the radio, television and the internet resulting in modified driver route choice prior to and during the trip. The impact of these types of route choices is difficult to capture with careful integration of theoretically sound methods. One other important feature normally excluded from these analyses is feedback loops. Based on several interviews with Port of Entry officials in El Paso, Texas, queue length in primary, secondary, staffing levels, incidents such as a drug bust, etc. all have effects on the primary inspection time. Most studies lack this feature, creating a utopian crossing scenario that may not be as representative of the long-term behavior of the regional port of entry system. Modeling Tools One model that requires mentioning is Border Wizard, which is under development by the Federal Highway Administration (FHWA) in conjunction with Federal Inspection Agencies, The Border Station Partnership Council and FHWA’s Office of Freight Operations. According to information located on the FHWA website, the model was designed to microscopically model the operations of a port of entry, including customs, immigration, motor carrier, and security procedures to ensure a safe and secure operation. The system is intended to utilize operational data such as kinds of equipment used, federal and contractor personnel conducting inspections, process in use by all inspection agencies, including Customs, Immigration and Motor Carrier Safety. The intent of the FHWA is to utilize Border Wizard with other transportation modeling software in order to create an integrated regional model. This model promises to be an excellent tool for operational design of individual systems, but microscopic models have been prone to produce unstable and unreasonable results at times [18]. Calibration of this particular model may be an issue for general transportation researchers who are not affiliated with the national security organization. Since 9-11, Federal Agencies responsible for U.S. security are not as eager to disseminate critical information of POE operations as they may have been in the past. It will be difficult to obtain enough information to create a meaningful microscopic model of the magnitude proposed by Border Wizard unless the Department of Homeland Security (DHS) allows this information to be obtained. DYNASMART-P was chosen as the DTA platform of choice for the El Paso/Juarez Regional transportation model. Dynamic Network Assignment Simulation Model for Advanced Road Telematics for Planning applications, also known as DYNASMART-P, is a state-of-the-art dynamic network analysis tool that was originally developed at the University of Texas at Austin [19]; Chiu and Mahmassani et al. [20]; Mahmassani, et al. [21]) and has continued its development at the University of Maryland at College Park. DYNASMART-P is recognized as an effective tool in areas such as intelligent network designing, planning, evaluation, and traffic simulation.


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One critical feature currently unavailable in the base DYNASMART-P package is the ability to model the inspection stations, which are essential for the Port Of Entry representation. Therefore, it was decided to modify the DYNASMART-P base code to include logic to handle the port of entry. This is beneficial for various reasons. First it allows the port of entry system to be included in the regional transportation model, allowing for “real-time” integration of a microscopic simulation of the POE with the Mesoscopic simulation of the regional transportation system. Also, by adding this capability to the base DYNASMART-P package, it will be possible to perform toll plaza analysis for existing and proposed toll roads. One other unique feature of DYNASMART-P is that it models individual travelers traveling adjustments as well as representing travelers pursuing to achieve a connection of activities at different points/locations in a network. Several known restrictions of static tools used in prevalent practices are overcome by DYNASMART-P. Details of DYNASMART-P can be found in [22] [23].

PORT OF ENTRY General Description of El Paso/Juarez POE system The cross border infrastructure linkages between El Paso, Texas and Ciudad Juarez, Chihuahua are by volume, is the second largest port of entry for merchandise trade between Mexico and the United States. In 2001, nearly 7.2 million pedestrians crossed the three bridges from Ciudad Juarez to El Paso. Nearly 15.8 million automobiles entered the United States across these arteries during that period, as did more than 660 thousand cargo vehicles [5]. The major POEs that are located in the El Paso region are: x Santa Teresa – A relatively small POE which handles non-commercial and commercial traffic located west El Paso city (not included in current model) x Paso Del Norte (PDN) – A 9 inspection booth system of two individual bridges, located in the central business district of El Paso and Juarez. The crossing is dedicated to non-commercial traffic and pedestrians. The East Bridge, known as the Stanton Bridge, is dedicated for southbound traffic and has one Northbound lane dedicated for the “Fast Pass” users. The West Bridge, known as the Santa Fe Bridge, is dedicated for northbound traffic. (Included in current model) x Bridge of the Americas (BOTA) – The largest bridge and POE in El Paso. This 14 inspection booth POE system feeds directly into the IH-10 and IH54 systems. Further, a large number of commercial traffic flows through this particular POE. (included in current model) x Zaragoza – The second largest POE in the El Paso area, located in the far East Side of El Paso and located adjacent to the largest Maquiladora sites in Juarez. The POE handles a great deal of commercial traffic as well as non-commercial and pedestrian. (not included in current model) x Fabens – The farthest East POE in the El Paso area. Like the Santa Teresa POE, it is small and handles mainly non-commercial traffic. (not included in current model) Typical POE Operations Figure 1 illustrates the typical flow of operations for the non-commercial portion of the port of entry system. The flow chart can be expanded further to include commercial and pedestrian traffic but will not be done so in this particular paper. Prior to vehicles entering the primary queue of the POE, the media, in the form of television, radio or the internet, provides pre-trip information about the POEs. This pretrip information such as travel time and queue length will modify a driver’s route choice on which POE to utilize (if trip has not begun) or possibly modify the original choice as the driver reaches his original destination. Normally, drivers will tend to migrate to the POE which offers them the shortest travel time. Once at the POE, the vehicle enters the primary inspection queue and waits to be served by Primary inspections. Primary Inspection is the frontline of the DHS screening


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process to ensure people coming into the US are doing so legally. The inspector attempts to determine whether this person is allowed to enter the country, decipher if they are terrorists or trying to cross illegal commodities such as meats, fruits, animals and drugs. Normally, these inspections take approximately 30 seconds during elevated threat levels and can increase to over a minute when the threat level is increased. The inspector then makes a decision to either allow entrance to the US or send to secondary inspection for further analysis. Secondary inspection is of course a more though review of the crossers. The intent is still the same as the primary inspection process. The detention time at this stage can vary from 5 minutes to over 2 hours, depending on the complexity of the situation. If the matter is serious, such as a drugs bust, the detainee will be moved into a tertiary inspection point where prosecution of the individual will begin. Normally tertiary inspection is a lengthy process; therefore considering is an infinite sink within the model. At each step along the process, inspectors have to make decision on the movement of the vehicle. These inspections have several feed back loops and policy mandates which affect it operation (inspection time and routing decisions). In order to understand the interactive properties of the Port of Entry systems, a set of modeling “policies” were developed which guide the interactions within the model. Figure 1 also illustrates a partial listing of the modeling policies. The policies were broken up into three categories to define how they would be implemented into the program; Data Driven, Operational Driven and Event Driven. All these policies can be described with basically two variables – inspection time at each stage of the POE flow and probability of routing decision (El Paso, Return to Juarez or move to secondary, etc). Data Driven Policy Data Driven policy utilizes data from DYNASMART-P, such as queue length at inspection points and occurrence of an incident to trigger changes in the inspection procedure of the model during the simulation. For example, during the interview process with DHS staff, it was stated that the primary inspection time and/or routing decisions will fluctuate depending on the queue length of the secondary inspection. If the queue in secondary became congested, it may be possible that primary would either slow down primary inspections or possibly allow a driver with a minor issue continue through to El Paso. (Note: This is all dependent on other operational policies such as threat levels, etc. If the threat level is high, a different set of conditions may exist). In the modeling environment, the queue length of secondary is recalculated during each iteration. If the queue is larger than a defined length, then the primary inspection time may be adjusted and/or a probability guiding the routing decisions would change. One other feature of DYNASMART-P is that every vehicle is modeled individually. Therefore, an identification tag can be super imposed onto the vehicle information to indicate that this vehicle, for example, is a drug-runner. Logic can be programmed into the model to respond to such a tag and follow a pre-defined set of operational procedures. With this tool, one can illustrate how the system will respond when such a situation occurs.


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Operational Driven Policy Operational Driven Policy pertains to system decisions for the POEs. For example, the Threat Level, mandated by the DHS, affects the manner in which inspectors scrutinize vehicles, usually imposing increases in inspection time or higher probabilities of routing drivers to secondary inspections. This user-induced input would normally be static throughout the modeling process, but the ability to change this policy midway through a simulation is feasible. Event Driven Policy One of the objectives of the NSF project is to model extreme events on the POE to forecast the regional effects on border crossing behavior, economic impacts and effect on the transportation infrastructure. In order to associate an actual event to operational and data driven policies, a set of event driven policies will be created. Each event will trigger a set of operational and data driven policies which will affect the regional model’s performance. Events can range from a computer system failure to a terrorist attack on a particular POE. The user will be required to understand the operational effects of the POE of such an event in order to translate the event into the data and operational policies which will be utilized in the software program. The operational effects will consist of changes to inspection times and changes to routing decisions. The model will be able to incorporate many different modeling policies simultaneously, allowing the forecasting of complex scenarios. RESEARCH METHODOLOGY AND MODEL FORMULATION Mesoscopic (hybrid of macro and microscopic simulation) simulation allows modelers to reach a balance between model resolution and computational requirements for assessing area-wide traffic re-distributions resulted from POE operations status, benefit/impacts of security measures, technology options (inspection technology, information system improvement, etc.) and POE operation policies (southbound VISIT, flow re-distributions and impacts between POEs due to capacity/pricing changes). The POE module to DYNASMART-P will be the most “microscopic” simulation process within the modeling process. The design of the module is fully scalable; one can model a POE utilizing one node and a user-defined discharge rate (as will be demonstrated in the next section) or develop the detailed POE flow as will be performed at a later date. DYNASMART-P DYNASMART-P uses established macroscopic traffic flow models and relationships to model flow of vehicles through a network. Whereas macroscopic simulation models do not keep track of individual vehicles, DYNASMART-P moves vehicles individually or in packets, a technique referred to as mesoscopic modeling. The actual simulation consists of two major components, the Link Movement and Node Transfer [24]. The link transfer is the process in which moving vehicles traverse a link during each time step. The Node Transfer performs the link-to-link movement of vehicles, which includes the number of vehicles in a queue, traffic control measures for intersection and freeways, and now the


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inspection stations. The POE module consists of modifications made to the Node Transfer by adding two additional control functions: “Toll control” which controls the discharge of vehicles at a node and “Route Force” which forces a vehicle to follow a predetermined path. Figure 2 illustrates the structure of the assignment model and indicates the where modifications are located in the program structure. “Toll Control” discharges vehicles from a control node one at a time after a timer has expired. The value for the timer is a user defined, dynamic stochastic distribution; in the sense that it is modified at every time step based on the model policy (feedback loops, operational policy). This feature enables the POE inspection module to be as flexible as required. Toll Control was intended to be utilized as an inspection station or as the name indicates a toll booth/plaza. “Route Force” is an expandable feature that is currently under development. It will allow the user to specify vehicle transfer to pre-defined links within the system based on a probability of route choice. In the case of the POE model, this feature is required to accurately model the decision of inspection personnel in routing a vehicle into secondary inspection or send to on into the U.S. The functionality of the module can also be extended in dealing with lane closures within the POE. Currently, if a lane is closed during the simulation in DYNASMART-P (downstream node indicates a closed status), the queue waiting to be transferred by the closed inspection node is immobilized, creating false indication of queue. In reality, drivers would migrate to adjacent lanes in order to proceed through the POE. The Route Force module will assist in performing this task by reading an open/closed tag on the inspection node and translating that feedback to a route choice whereby forcing the driver in the closed lane to merge into adjacent lanes. (See Figure 3 for an illustrative example) This module will also consist of a load-balancing feature. As vehicles enter the POE, the driver will normally attempt to choose the queue with the shortest travel time (not necessarily the shortest queue). This functionality will evaluate downstream links and estimate a travel time based on queue length and average inspection time, consequently assigning vehicles to the path with the shortest travel time. The intent of the final project is to model the entire Port of Entry system in the El Paso/Juarez region. At this early stage though, a macroscopic, limited POE version of the POE is being utilized as a proof of concept. The PDN and BOTA Northbound POEs are currently the only interconnections between the El Paso and Juarez systems and each POE is modeled as a single node (in lieu of a detailed microscopic simulation). As will be apparent in some of the results, the Juarez model requires calibration and the insertion of a more detailed O-D matrix. The Juarez TransCAD data file does have an O-D matrix but is missing zone information, speed limit information, control types at each intersection, etc. The performance of the Juarez model will improve as more data is obtained from appropriate sources on the city’s system. Driver Behavior DYNASMART-P is equipped to simulate driver behavior during the simulation period, making it a unique model compared to others. In DYNASMART-P, vehicles are generated according to a time-dependent O-D matrix, and assigned to routes specified by


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assignment rules, depending on the particular rules adopted, the paths may be obtained either through direct application of individual path choice models, or through algorithmic steps intended to satisfy certain condition in the network [24]. The four assignment rules that are utilized are (1) Determine a user’s path through a network to minimize overall travel time. (2) Utilize user equilibrium (UE) in which no user can improve travel time by unilaterally switching routes. This emulates a long-term evolution of the system as drivers learn and adjust to the system. (3) Users receive descriptive information on prevailing trip times; a family of response rules, consisting of boundedly-rational path switching and selection rules, select the shortest path based on current conditions. (4) The vehicle is assigned to its current best path from the trip origin [24]. This capability creates the opportunity to model the regional transportation system in various ways. The initial model demand is based off the O-D matrix and is run through several iterations to find the user equilibrium of the system. This initial run creates paths for every vehicle in the simulation that can be utilized in subsequent scenarios. If the paths created from the initial run are utilized, it represents a scenario in which no information is disseminated prior to and during the trip. The vehicle follows the predetermined path through fruition, regardless of the effects on its travel time, which is similar to static assignment modeling techniques. A more realistic approach to model short-term effects of changing conditions within a system is to utilize the O-D matrix to define demand and allow DYNASMARTP to calculate the k shortest path for each vehicle (without the utilization of predetermined routes). As conditions change in the system, the new vehicles generated within the subsequent time steps consider the new information in the generation of it path; emulating pre-trip information. Further, the routes for every vehicle are evaluated at a user-defined interval to continually evaluate the performance of the initial path, changing if one is found to be more efficient. This simulates reality more closely. Finally, to simulate long-term behavior to an event or change in policy, one can run the model for several iterations to UE. The results of this simulation will resemble those of drivers who have learned about the system and adjusted their traveling behaviors.


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MODEL CALIBRATION AND PRELIMINARY EMPIRICAL RESULTS Several case studies were developed to test and demonstrate the capability of the developed model. The case studies are as follows: 1. Base Case Scenario – Same inspection times at each POE. Run to Equilibrium (inspection time = 30 seconds/vehicle/booth with a standard deviation of 1) 2. Increased Vigilance – One bridge (BOTA) increases its inspection times due to information about a possible drug runner, etc. The inspection process slow down to 45 seconds/vehicle/booth with a standard deviation of 1 during this period in order to properly inspect each vehicle. 3. Extreme Event –BOTA is shut down completely in both directions due to an extreme event (terrorist attack on POE or bridge failure due to natural causes); most of the access roads to the POE are also shut down. The inspection time at PDN is the same as in case 1. 4. New Inspection Technology – New inspection equipment is installed at both POEs, resulting in facilitated inspection process (inspection time on both POEs is reduced to 15 seconds/vehicle/booth with a standard deviation of 1). Note: Work is currently underway to determine the proper probability distributions for the inspection wait times. The average wait time is close to reality, but the distribution and standard deviation may eventually vary from what is stated above. Base Case This case utilized the O-D demand matrix that was supplied by the El Paso Metropolitan Planning Organization (MPO) for the El Paso area. The model was run to equilibrium and the following results were obtained. The results obtained from this scenario represent the normal traffic condition, and thus is illustrated as the baseline case for the following four cases. Increased Vigilance Several cases were run to study the results of increased vigilance at the BOTA POE. Figure 4 illustrates the results. The pictures represent the queue developed when running the short term (O-D) based scenario and the long term (UE) based scenarios. As can be seen, the long-term (UE) scenario does not show a significant queue formation at the POEs vs. the short-term analysis in which a significant queue is developed at the BOTA POE, which decreased its inspection discharge rate from an average of 270 vehicles/hour/port to 170 vehicle/hour/port. The volume measurements for the PDN POE illustrate how the proposed model captures the movement of vehicles move toward the PDN POE from BOTA, where the inspection time is shorter. This is good example of travel behavior affecting route choice. Overall though, the average system travel time only increased by 1% for this scenario.


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Extreme Event In the case of an extreme event at BOTA, it can be seen that the results of the incident can affect much more than just the port. The illustrations shown in Figure 5 show how traffic is backed up onto I-10 during the immediate time of the occurrence. The adjacent picture shows the queues developed in the long term if the POE was to remain decommissioned. Also seen from Figure 5, short after the extreme event, traffic at the PDN is not immediately increased, but over time, the usage of PDN is significantly increased as trip makers adapt to available remaining POE infrastructure capacity. Overall, the total average travel time of the system increased by 29% for this situation. New Technology This case was developed to illustrate the capability of the model to capture benefits of new technology. As can be seen in Figure 6, the queues at the POEs are at a reduced level and the volume passing through the sites have increased significantly. The Short term and Long Term results are similar, probably due to the fact that the inspection time is so low that the driver behavior was not modified much. Overall, the total average travel time of the system decreased by 8% indicating that the volume crossing the POEs contribute a great deal to the overall system travel time.

CALIBRATION OF THE MODELS As may be obvious, the models presented in this paper need further calibration. Data has been obtained from several sources and the calibration process in underway. The El Paso Metropolitan Planning Organization, Texas Department of Transportation, and other agencies have provided assistance for the calibration of the regional model. The calibration module will be written into the DYNASMART-P code in an attempt to have it calibrate itself based on certain performance factors supplied by the user. It is the intent of the research to develop a method in which vehicle count can be utilized to calibrate certain section of the model. An automated process will check the model-produced data against user supplied data and adjust input parameters by using several objective functions to calibrate itself. It is of up most importance that the model be calibrated to develop confidence from the planning organizations. It is a piece of business that will be explored with much vigor.

CONCLUDING REMARKS AND FUTURE RESEARCH This paper presents the benefits of utilizing an integrated, microscopic Port of Entry simulation with a regional mesoscopic dynamic traffic assignment model to represent the Port of Entry system in the El Paso area. The development of queuing-based POE model allows for the evaluation of various policy and technologies scenarios while the utilization of DYNASMART-P as the analysis tool allows for a representative analysis of the regional transportation system’s response to extreme events, changes in policy and testing of new technology by utilizing key features such as driver behavior. A successful integration of this model into the CRITICAL system will create a unique platform on which to analyze the interactions between transportation, economic and social systems. Future work will include the comprehensive development of the entire POE infrastructure by adding all the POEs in the El Paso area, develop the microscopic representation of each POE (including non-commercial, commercial and pedestrian) as well develop the calibration methodology and tools for the model. The resulting model will be incorporated into the CRITCAL system dynamics model which will enable researchers to illustrate the effects POEs have on the economy, border sociology and transportation infrastructure.

ACKNOWLEDGEMENTS This research was supported by the National Science Foundation through Award Number 0332001. We would like to thank the following organizations for their dedication in providing necessary research information and data for the creation of the models. National Science Foundation Award Number 0332001 The El Paso Metropolitan Planning Organization Instituto Municipal de Investigación y Planeación The Texas Department of Transportation – El Paso District Office Department of Homeland Security – Customs and Immigration and Naturalization Services Certainly, the authors are solely responsible for the viewpoints expressed in this paper.


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REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]

[18]

O. J. Martinez, Border People: Life and Society in the U.S.-Mexico Borderlands. Tucson: Univerity of Arizona Press, 1994. H. Donnan and T. M. Wilson, Borders: Frontiers of Indentity, Nation and State. Oxford: Berg Publishers, 1999. T. M. Wilson and D. Hastings, Border Identities. Cambridge and New York: Cambridge University Press, 1998. D. E. Lorey, The U.S.-Mecian Border in the Twentieth Centrury: A History of Economics and Social Transformation. Wilmington, DE: Scholarly Resources, 1999. T. M. Fullerton and R. Tinajero, "Borderplex Economic Outlook: 2002-2004," The Univeristy of Texas at El Paso Border Region Modeling Project, 2002, El Paso, TX Business Report SR02-2, 2002. J. M. Heyman, Life and Labor on the Border: Working People of Northeastern Sonora, Mexico, 1886-1986. Tucson: Univerity of Arizona Press, 1991. C. G. Vélez-Ibáñez, Border Visions: Mexican Cultures of the Southwest United States. Tucson, AZ: University of Arizona Press, 1996. D. D. Arreola and J. R. Curtis, THe Mexican Border Cities: Landscape Anatomy and Place Personality. Tucson, AZ: University of Arizona Press, 1993. L. A. Herzog, "Where North Meets South: Cities, Space, and Politics on the U.S.Mexico Border," Center for Mexican American Studies, Univerisity of Texas at Austin, Austin 1990. T. M. Fullerton and R. L. Sprinkle, "Technical Report TX03-1 Secuity Measrues, Public Policy, Immigration and Trade with Mexico," Border Region Modeling Project, The University of Texas at El Paso, El Paso, TX 2003. J. M. Heyman, "United States Ports of Entry on the Mexican Border," Journal of the Southwest, vol. 43, pp. 681-700, 2002. C. Perrow, Normal Accidents: Living with High-Risk Technologies. New York: Basic Books, 1984. E. D'Amico, "U.S.-Canada Take Names for 'Smart Border'," Chemical Week, vol. 164, pp. 12-16, 2002. F. B. Lin and M. W. Lin, "Modeling Traffic Delays at Northern New York Border Crossings," Journal of Transportation Engineering, vol. 127, pp. 540-545, 2001. F. Coleman and Y. J. Moon, "System Simulation of Commercial Vehicle Border Crossing Congestion: The Ambassador Brige Case Study," presented at Summer Computer Simulation Conference, San Diego, 1999. G. Pinal, "A Queuing Analysis at an Internation Port of Entry," in Department of Civil Engineering. El Paso: The University of Texas at El Paso, 1997, pp. 91. S. A. P. Chaires, "Simulation Modeling of Traffic Operations at International Port of Entry along the U.S. - Mexico Border: Case study From El Paso, Texas," in Department of Civil Engineering. El Paso: The University of Texas at El Paso, 2000, pp. 133. C. F. Daganzo, "The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory," Transportation Research Part B, vol. 28, pp. 269-287, 1994.


[19] [20]

[21]

[22] [23] [24]

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R. Jayakrishnan, H. S. Mahmassani, and e. al., "An Evaluation Tool for Advanced Traffic Information and Management Systems in Urban Networks," Transportation Research Part C, vol. 2, pp. 579-604, 1994. Y.-C. Chiu and H. S. Mahmassani, "Off-line Laboratory Test Results for the DYNASMART-X Real-Time Dynamic Traffic Assignement System; Technical Report ST067-85-TASK G, prepared for Federal Highway Administration," The University of Texas at Austin, Autin TX 1998. H. S. Mahmassani and e. al., "DYNASMART-P, Intellegent Transportation Network Planning Tool Volume I, II. Report ST067-85-PII, prepared for Federal Highway Administration," The University of Texas at Austin, Austin, TX 2000 2000. Y.-C. Chiu and H. S. Mahmassani, "Routing Profile Updating Strategies for Online Dynamic Traffic Assignment Operations," Transportation Research Board, vol. 1781, 2003. H. S. Mahmassani, H. Shayti, and e. al., "TrEPRS-P, Phase 1.5C, Final Report Volume I -- DYNASMART Calibration and Evaluation.," Maryland Transporation Initiative, College Park, MD 2003. H. S. Mahmassani, "Dynamic Network Traffic Assignment and Simulation Methodolgy for Advanced System Management Apllications," Networks and Spatial Economics, vol. 1, pp. 267-292, 2001.


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LIST OF FIGURES Figure 1: POE Flow Diagram and Corresponding Policies Affecting the Feedback System....................................................................................................................... 19 Figure 2: Structure of DYNASMART-P Simulation Assignment Model with POE modifications............................................................................................................. 20 Figure 3: Example of Logical Construction of POE utilizing DYNASMART-P. ........... 21 Figure 4: Modeling Results Due to Increased Vigilance at the BOTA POE.................... 22 Figure 5: Modeling Results Due to an Extreme Event at the BOTA POE. ...................... 23 Figure 6: Modeling Results Due to Implementation of New Inspection Technologies at the POE. .................................................................................................................... 24

Inspection Time Variations Vehicle Data Policy Vehicle Path may change based on feed back from system (Travel Time)

Vehicles

Probability of Route Choice TO El Paso

Parameter changes based on Policy

Non-Commercial Queue

NonCommercial Primary Inspection Node

Route Choice (El Paso, Secondary Inspection)

Inspection Time Variations Vehicle Data

Non-Commercial Queue Secondary Inspection

Probability of Route Choice

Non-Commercial Secondary Inspection Node

Route Choice (El Paso, Tertiary Inspection)

Car or Truck? Commercial Inspection may be similar to NonCommercial

Feedback Loop Feedback Loop

Feedback Loop Staffing Levels Severity of Inspections Events with Higher Priority

FeedBack Loop

Traffic Flow

Media Radio, Television, Web Sites

Policy Feedback

Variables: - Inspection Time - Routing Decision - Open/Close Lanes

Data Driven Policy

Event Driven Policy

Operation Driven Policy

Event at Commercial Inspection Queue Size of Vehicle (Car or Bus) Vehicle User Imposed Data Status of Secondary Inspection Queue/ Travel Time

National Threat Level

Computer System Failure Green Low Condition

Drug Bust

Blue Guarded Condition

Typical Delayed Inspection (doc problems, fruit, meats/ aminals)

Yellow Elevated Condition

Normal Inspection (All docs ok, no problems)

Orange High Condition

Inspected fits elevated risk profile

Red Severe Condition

Bomb Threat

Inspection Processing Type Individual Processing Batch Processing

Bridge Failure Natural Disaster (Earth Quake, Tornado) Man Made (Terrorist Attack, Hazmat Release) Structural Failure

Figure 1: POE Flow Diagram and Corresponding Policies Affecting the Feedback System.

Modeling Policy

En Route Driver Behavior

Path Processing

Densities, Travel Time on Links Expected Delay on Junctions

Link Movement

Path Selection

Node Transfer

Figure 2: Structure of DYNASMART-P Simulation Assignment Model with POE modifications

Inspection Control

Time-Dependent O-D

Simulation Component

Route Selection & Load Balancing

ROUTE FORCE

ROUTE FORCE

ROUTE FORCE

LANE CHANGING CAPABILITY

ROUTE FORCE

INSPECTION

OTHER PORT OF ENTRY

INEPCTION

SECONDARY AND TERTIARY INSPECTIONS

ROUTE FORCE

EL PASO NETWORK FIRST NODE

INSPECTION

PRIMARY ROUTES

SECONDARY ROUTES

OTHER PORT OF ENTRY

SIMILAR CONNECTIONS ARE MADE FOR EVERY ROUTE FORCE NODE (NOT SHOWN FOR CLARITY)

ROUTE FORCE

ROUTE FORCE

INSPECTION

INSPECTION

INSPECTION STATIONS

Figure 3: Example of Logical Construction of POE utilizing DYNASMART-P.

JUAREZ, MX TRANSPORTATION INFRASTRUCTURE

LOAD BALANCE

VEHICLE LOAD BALANCE


SINK

ROUTE FORCE

El Paso, TX Transportation Infrastructure

21

350

0

10

30

40

30

40

50 Model Time (Minutes)

60

PDN - Increase Vigilance - UE

20

PDN - Increase Vigilance - O-D

10

BOTA - Increase Vigilance - UE

0

PDN Base Run

60

BOTA - Increase Vigilance - O-D

50

70 60 50 40 30 20 10 0

Increased Vigilance Paso Del Norte

Resulting queue from the UE Case

PDN

BOTA

BOTA Base Run

Model Time (Minutes)

20

Increased Vigilance Bridge of the Americas

Resulting queue from the O-D Origination Case

PDN

Figure 4: Modeling Results Due to Increased Vigilance at the BOTA POE

0

50

100

150

200

250

300

Discharge Rate Discharge Rate (Vehicles/hour/lane) Vehicles/Hour/Port

BOTA


70

80

BOTA

0

30

40

50

60

PDN - Extreme Event - UE


20

PDN - Extreme Event - O-D PDN Base Run

10

Figure 5: Modeling Results Due to an Extreme Event at the BOTA POE.

70 60 50 40 30 20 10 0

BOTA

Queue developed during long term analysis of an extreme event

PDN

Throughput during an Extreme Event El Paso del Norte

Queue developed during short term analysis of an extreme event

PDN

Discharge Rate Discharge Rate Vehicles/Hour/Port (Vehicles/hour/lane)

90 80 70 60 50 40 30 20 10 0

10

30

40

50

PDN - New Technology - UE


20

PDN - New Technology - O-D PDN Base Run

0

Implementation of New Technology El Paso del Norte

60

0

10

.

30

40

50

BOTA - New Technology - UE


20

Implementation of New Technology Bridge of the Americas

BOTA - New Technology - O-D BOTA Base Run

800 700 600 500 400 300 200 100 0

Resulting Queue due to the implementation of New Technology

PDN

BOTA

Figure 6: Modeling Results Due to Implementation of New Inspection Technologies at the POE.



Discharge Rate Discharge Rate Vehicles/Hour/Port (Vehicles/hour/lane)

60

24

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