Incorporating Stochastic Road Capacity into Day-to ... - SAGE Journals

Incorporating Stochastic Road Capacity into Day-to-Day Traffic Simulation and Traveler Learning Framework Model Development and Case Study Anxi Jia, Xuesong Zhou, Mingxin Li, Nagui M. Rouphail, and Billy M. Williams tant modeling methodology for transportation planners and traffic engineers to describe congestion buildup and dissipation and analyze the effectiveness of various capacity enhancement and information provision strategies (2, 3). During the past three decades most research interests in the DTA field were concentrated on how to improve the realism of traveler behavior representation and demand modeling. Examples of DTA modeling innovations include incorporating within-day and day-to-day varying demand patterns, modeling departure time and mode choice, as well as simulating different levels of information availability. Conventional static and dynamic traffic assignment methods typically assume deterministic (i.e., fixed) road capacity. However, an emerging body of research indicates that freeway capacity is better represented as a random variable (4–9). Brilon et al. further suggested that in addition to freeway capacity, saturation flow rates at signalized intersections are also stochastic (10). A recent study by Jia et al. confirmed that the capacity of freeway bottlenecks is stochastic as are the queue discharge rates (11). Furthermore, on the basis of freeway sensor data, Jia et al. found that the expected or mean value of prebreakdown flow and queue discharge rates appears to be approximately 400 passenger cars per hour per lane (pc/h/ln) lower than Highway Capacity Manual (HCM) freeway segment capacity values (12). The implication of these stochastic variability findings is that network modeling that relies on the HCM capacity levels might not fully represent the frequency, duration and, consequently, the traffic operational impact of network bottlenecks. To better describe adaptive traveler behavior and simulate the resulting travel flow pattern in an environment in which roadway capacity varies within a single day and over multiple days, a day-today learning framework is needed to allow a realistic consideration and evaluation of different capacity-enhancing and traffic management scenarios. A wide variety of day-to-day learning models have been proposed to understand and simulate the medium-term traffic evolution process under various advanced traveler information provision strategies. An early study by Hu and Mahmassani took into account route and departure time choices as the sources of day-today traffic dynamics (13). Srinivasan and Guo examined network evolution and user response characteristics under varying market penetration levels of traveler information (14). Jha et al. adapted a Bayesian framework to model the traveler perception updating process (15). Chen and Mahmassani further studied triggering mechanism and termination conditions for the travel time learning process (16). However, existing day-to-day learning frameworks assume a

A key foundation for developing strategies aimed at improving the efficiency and reliability of an urban transportation network is identifying the locations and impact of system bottlenecks. Although free-flow capacity and queue discharge rates at system bottlenecks have traditionally been modeled as fixed values, they are in fact random variables. Therefore, assessing the operational impact of network bottlenecks requires reliable and realistic tools that account for stochasticity in prebreakdown flow rates and queue discharge rates. Focusing on methodological and analytic enhancements to existing dynamic traffic assignment models, this paper presents a method to seamlessly incorporate stochastic capacity models at freeway bottlenecks and signalized intersections and develops adaptive day-to-day traveler learning and route choice behavioral models under the travel time variability introduced by random capacity variations. To account for different levels of information availability and cognitive limitations of individual travelers, a set of bounded rationality rules are adapted to describe route choice rules for a traffic system with inherent process noise and different information provision strategies. A case study based on a real-world Portland, Oregon, subarea network is presented to illustrate the capabilities of the enhanced simulator and highlight the advantage of modeling stochastic capacity in a dynamic mesoscopic traffic simulator as compared with conventional tools that assume deterministic road capacity.

Contemporary urban traffic congestion leads to a wide range of adverse consequences such as significant traffic delay and travel time unreliability. The primary source of recurring congestion, physical system bottlenecks, contributes 40% of the travel delay on roadway networks (1). Considerable research efforts have been devoted to understanding the effects of these physical bottlenecks and analyzing the effectiveness of different traffic mitigation strategies. Dynamic traffic assignment (DTA) models have become an imporA. Jia and N. M. Rouphail, Institute for Transportation Research and Education, North Carolina State University, Centennial Campus, Box 8601, Raleigh, NC 27695-8601. X. Zhou, 210 CME, and M. Li, 119 CME, Department of Civil and Environmental Engineering, University of Utah, 122 South Central Campus Drive, Salt Lake City, UT 84112-0561. B. M. Williams, Department of Civil, Construction, and Environmental Engineering, North Carolina State University, Campus Box 7908, Raleigh, NC 27695-7908. Corresponding author: X. Zhou, [email protected]. Transportation Research Record: Journal of the Transportation Research Board, No. 2254, Transportation Research Board of the National Academies, Washington, D.C., 2011, pp. 112–121. DOI: 10.3141/2254-12

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Jia, Zhou, Li, Rouphail, and Williams

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constant road capacity, and the variability sources considered in those models are limited to route and departure time choices. To enhance the operational realism of dynamic traffic network simulation, this paper aims to address the following: • How to integrate stochastic capacity elements seamlessly into traveler behavior model and networkwide vehicular flow simulation and • How to model travelers’ route choice under a stochastic capacity environment. On the basis of a mesoscopic dynamic traffic simulator, namely DYNASMART-P, this research enhances a number of key modeling components to meet the above challenges (3). The enhancements include stochastic capacity generation for freeway bottlenecks and signalized arterial links and a new set of day-to-day learning and route choice rules under the resulting stochastic travel time variations. A case study performed on a real-world network is used to present the modeling capability of the enhanced simulator, and simplifying assumptions are made to make the proposed model practically operational. This paper is organized as follows. The next section introduces the underlying stochastic capacity and queue discharge functional forms. That is followed by the conceptual route choice mechanism designed to respond to the stochastic travel time variations and a detailed simulation implementation procedure. The paper concludes with a case study for the real-world network and overall conclusions.

FIGURE 1 Cumulative distribution of prebreakdown headway for freeway bottlenecks.

STOCHASTIC CAPACITY AND QUEUE DISCHARGE MODEL A mesoscopic DTA simulator typically has two key capacity inputs (as constraints on flow propagation): maximum service flow rates at freeway bottlenecks and saturation flow rate at signalized intersections. In addition, at each simulation interval, queued vehicles are transferred to downstream links according to queue discharge rates. This section presents the key components for the proposed simulation framework, namely, the stochastic capacity and queue discharge models.

Stochastic Capacity Model Consistent with the current practice, the flow rates just preceding the breakdown condition are used to analyze the stochastic capacity for the freeway bottlenecks. On the basis of the sensor data aggregated at 15-min intervals, Jia et al. found that prebreakdown headways followed a shifted lognormal distribution with the following probability density function (11): f x ( x μ, σ ) =

1

2π ( x − c) σ

−

e

[ ln( x − c)− μ ]2 2 σ2

x>c

(1)

where x= c= μ= σ=

average prebreakdown headway (s) for 15-min interval, minimum prebreakdown headway (s), mean of prebreakdown headway’s natural logarithm, and standard deviation of prebreakdown headway’s natural logarithm.

On the basis of traffic measurement data from the Performance Measurement System (PeMS) (17) and TransGuide (18) systems, the corresponding parameters for Equation 1 are calibrated as c = 1.5 s, μ = −0.97, and σ = 0.68 by using the maximum likelihood method. The cumulative probability distribution of prebreakdown headways for freeway bottlenecks is illustrated in Figure 1. The shift value of 1.5 s for the above lognormal distribution represents headways associated with the upper envelope of 15-min segment capacity. This minimum headway is equivalent to 2,400 pc/h/ln, which is consistent with capacity values suggested by the HCM. Therefore, the freeway data calibration results indicate that the HCM capacity levels are more representative of the upper tail of the capacity observations and conversely are not representative of expected segment capacity values. Turning to signalized intersections, traffic engineers have long known that saturation flow rates fluctuate over time and that this fluctuation can be observed even from cycle to cycle at the same intersection. Similar to the calibration procedure for the prebreakdown headway distribution on freeway bottlenecks, a stochastic model was developed for predicting saturation headways at signalized intersections. The model was based on a saturation headway database developed by the Florida Department of Transportation (19). Extensive investigation of candidate distributions revealed that the shifted lognormal probability distribution model again provides an acceptable fit to the empirical data. Based on the maximum likelihood method, the corresponding fitted probability density function is f x ( x μ, σ ) =

1

2 π ( x − 1.9 ) × 0.2

−

e

[ ln( x −1.9)−1.14 ]2 2 2( 0.2 )

x > 1.9

(2)

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Transportation Research Record 2254

Stochastic Queue Discharge Model

Conceptual Framework

Similar to the conventional definition of capacity in the HCM, the queue discharge flow rate is also typically characterized in a deterministic manner. However, the empirical study by Lorenz and Elefteriadou has clearly demonstrated that the queue discharge flow rate at freeway bottlenecks is also stochastic in nature (8). Dong and Mahmassani suggested and calibrated a linear relationship between queue discharge rates and prebreakdown flow rates (20). In the most recent study, Jia et al. concluded that the queue discharge rate series is strongly time correlated and developed the following recursive queue discharge model (11):

The day-to-day learning framework proposed by Hu and Mahmassani (13) and Jha et al. (15) provides a promising path for seamlessly integrating stochastic capacity models in the DTA simulator for large-scale networks. Generally speaking, the learning behavior in such a day-to-day learning framework is determined by each vehicle’s historical traveling experiences, the traveler information obtained before and during the trip, as well as newly experienced travel times on the current day. Conceptually, the proposed model includes three components: Traffic flow assignment model:

Ct = Ct −1 + γ ( uc − Ct −1 ) + δ t

t ≥1

(3)

f d +1 = A ( f d , T d , w d )

(4)

where Ct = queue discharge rate at time interval t (pc/h/ln), γ = linear parameter that models the strength of regression to the mean, μc = average discharge rate (pc/h/ln), and δt ∼ N(0, σ2 ) = random error. When t = 1, C0 is the prebreakdown flow rate. Calibrated with the sensor data from a study site on I-880 in the Bay Area of California, the fitted parameters for Equation 2 are γ = 0.2, μc = 1,850 pc/h/ln, and σ = 100 pc/h/ln.

DAY-TO-DAY TRAVELER LEARNING AND ROUTE CHOICE MODEL As stated previously, conventional traffic assignment methods assume static, deterministic road capacity. Therefore, the travel time of a path depends only on the flow pattern on that path. In other words, for a fixed networkwide path flow pattern, the corresponding path travel times do not change. However, real-world road capacities vary with time over a certain range, and a driver’s traveling experience on a single day can be dramatically affected by the underlying realized capacity values on that particular day. In other words, travelers will experience different travel times on the same path during different days even for the same path flow pattern because of the inherent travel time variability introduced by stochastic capacity. As a result, conventional within-day or iterative route choice methods for reaching user equilibrium, such as the method of successive averaging, may not enable drivers to recognize and appropriately respond to the travel time variability and unreliability resulting from capacity fluctuation. A theoretically rigorous and practically useful traveler route choice model is crucially needed to capture adaptively the stochastic day-to-day travel time evolution process and also to maintain robustness under disruptions due to stochastic capacity reductions. To that end, a new route choice mechanism is proposed to simulate the drivers’ route choice behavior under stochastic traffic process noise. By comparison, conversional stochastic assignment models focus on traveler perception errors under a deterministic traffic environment. The proposed mechanism includes two key components: a route choice learning module and a route choice decision module. In addition, different user classes, which receive and perceive different types of traffic information at different decision points along trips, are further investigated in this study.

Stochastic traffic system simulation process: t d = S ( f d ) + wd

(5)

Travel time perception model: T d = t d + ⑀d

(6)

where f d = assigned route flow pattern on day d, determined by traffic assignment model and function A(䡠); t d = true travel time on day d, determined by dynamic assignment and simulation function S(䡠); wd = system noise introduced by the stochastic capacity; T d = observed travel time by a traveler; and ⑀d = traveler perception error associated with perceived travel time in the network, introduced by the sampling error associated with personal experience and quality of information. Most existing day-to-day learning models are implemented with stable road capacity and assume no system noise, that is, w d = 0, so the travel time t d is a deterministic vector for a given set of route flows, f d, in Equation 5. Accordingly, the focus in the previous research has been on how to reach the deterministic steady state conditions and how to construct realistic learning and updating models for the travel time perception error term ⑀d related to Equation 6. In this study a dynamic traffic flow simulator, namely, DYNA SMART-P, is enhanced to describe a traffic simulation process with day-to-day varying system noise, wd, in Equation 5. Corresponding to the traffic flow assignment model, Equation 4, a day-to-day learning module is presented to describe adaptive traveler behavior across multiple days in a stochastic traffic evolution environment. The essential idea for the learning module is to enable certain users to use their historical traveling experiences to construct their estimates and make decisions under uncertain system travel times (introduced by the system noise wd). To simplify the route choice rules, ⑀d = 0 is assumed in the following discussion. As a result, the proposed model does not involve the use of a probit or logit model to assign traffic flows and does not require a travel perception error updating process.


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T(P vd−1) = travel time on path P vd−1; and Pvd−1 = path traveled by vehicle v on day d − 1.

Route Choice Utility Function and Simplified Route Switching Rule This research adapts a behaviorally sound route choice utility function, proposed and calibrated by Brownstone and Small (21) and Lam and Small (22), to consider the stochastic nature of traffic systems. VOR TOLL TOLL × TSD + = T + β × TSD + VOT VOT VOT

GT = T +

(7)

where GT T TSD β

= = = =

generalized travel time, expected travel time for traveler, perceived travel time variability, reliability ratio [computed as ratio of value of reliability (VOR) and value of time (VOT)], and TOLL = road toll charge, which is assumed to be zero in the following discussions because no toll-related strategies will be evaluated in this paper. It has been well recognized that travel time variability and reliability are important measures of service quality for travelers. In the above utility function, Equation 7, the travel time standard deviation (TSD) is used to measure system travel time variability associated with the underlying stochastic traffic process. This measurement contrasts with the perception error variance in a deterministic assignment model. For a single traveler v, the route choice decision is made by comparing the generalized travel time of habitual path, GTvh, and that of the alternate path, GTva. GTvh > GTva

(8)

where v = traveler index, h = index for habitual path, and a = index for potential alternative path. According to Equation 7, if the generalized travel time of the habitual path, GTvh, is greater than that of the alternate path, GTva, as shown in Equation 8, a vehicle should switch its route from the habitual path to the alternative path. The resulting decision rule could be derived as Tvh − Tva > β ( TSD av − TSD hv )

(9)

– In this study, T hv is equal to T vd−K,d−1 as calculated in Equation 10. To take a traveler’s multiday travel time experience into account, T va is calculated by using the estimated travel time on the shortest path. The calculation of T va varies for different user classes, which will be discussed later.

Tvd − K , d −1 =

T (P

d−K v

) + T (P

d − K +1 v

K

) + . . . + T ( Pvd −1 )

The right side of Equation 9 can be viewed as the minimum acceptable absolute tolerance needed for a route switch decision. This value arises from three components: the reliability ratio β, the standard deviation of travel time on the habitual path TSDvh, and the standard deviation of travel time on the alternative path TSDva. The calibration study from Noland et al. indicated a reliability ratio value of β = 1.27 on the basis of survey data from more than 700 commuters in the Los Angeles region in California (23). The setting of parameter K depends on the signal-to-noise ratio in the traffic system. Specifically, the more stable the travel time process, the smaller K can be and still yield a reliable mean travel time estimate. In general, K must be large enough to filter out the process noise from the stochastic traffic system. The travel time variability measure, TSDhv, for the habitual path can be calculated from multiday travel times experienced by the traveler. The remaining challenge is how to estimate the standard deviation of travel time on the alternative path, TSDva, in cases in which the traveler has little or no experience on this path. When there is no external pretrip or en route information available, TSDav needs to be calculated from the traveler’s previous experience. To the authors’ knowledge, there is no widely accepted method to calibrate the standard deviation of perceived travel times on alternative paths for travelers without access to advanced traveler information systems and relying on previous knowledge only. In this research it is assumed that TSDva is significantly larger than TSDvh because of the lack of precise information and the high level of uncertainty associated with the perceived alternative travel time. The calibration of the minimum acceptable absolute tolerance was beyond the scope of this study. Therefore, this research uses a simplified, single-term model, β(TSDva − TSDvh), to represent the minimum acceptable absolute tolerance needed for a route switch decision. This simple model is intuitively sound, and using it eliminates the need for extensive calibration efforts. In this study a bounded rationality model, which states that a driver’s decision depends on his or her desired satisfaction level, is adopted to make the route choice comparison. The bounded rationality concept is used because there has been growing attention [starting from the early work by Mahmassani and Herman (24)] to bounded rationality since Simon (25) pointed out that perfectly rational decisions are often not feasible given the limits of human cognition. Based on the minimum acceptable absolute tolerance and the relative acceptable tolerance, a set of bounded rationality rules, shown in Equation 11, are used to describe users’ route switching behavior. As opposed to the optimization theory in which users select the best option from all possible decisions, in the bounded rationality approach users perform limited searches, accepting the first satisfactory decision. ⎧ ⎪1 δ=⎨ ⎪ ⎩0

if Tvd − K , d −1 − Tva > max ⎡⎣α, λ × Tvh ⎤⎦

(11)

otherwise

where (10)

where d = day index; K = number of days in learning memory window; – T vd−K,d−1 = traveling experience (i.e., average travel time) for traveler v from day d − K to day d − 1, on a particular path;

δ = 1, switch to an alternative path; = 0, remain on the habitual or current path; λ = relative acceptable tolerance (i.e., relative improvement threshold); α = minimum acceptable absolute tolerance needed for a switch; and α = β ( TSD av − TSD hv )

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Multiple User Classes Three types of user classes are considered in this study: pretrip information users, en route information users, and unequipped users. The different user classes have access to different types of travel information to help them make their route choice decisions. Pretrip information is acquired by pretrip users before departure through the Internet, TV, radio, and cell phone. En route information that describes the estimated time of arrival is provided to en route users during the trip by Global Positioning System navigation devices, radio channels, and variable message signs. The personal posttrip information acquired by unequipped users typically is based on a commuter’s experienced travel time, in addition to potential external information sources from television and newspaper reports. In this heterogeneous information environment, each user class has different ways to estimate travel time on the alternative path T av and different decision-making locations and times. The pretrip users estimate T va on the basis of the network real-time snapshot conditions just before their departure and make the route choice decision at the departure time. The en route users make route choice decisions each time they reach a node where alternative routes are available and estimate T va on the basis of the network real-time snapshot conditions. The unequipped users determine whether to change their habitual path on day d at the end of day d − 1, when all trips are completed, and estimate the travel time on the shortest path on the basis of average path travel times on day d − 1. In reality, many people are creatures of habit and unlikely to make route changes right away, if ever. Moreover, the information quality could vary for different user classes. Thus, the following assumptions are made about how different user classes receive information and how this information triggers route switching considerations: 1. Pretrip and en route users are always willing to switch their routes, 2. Only a certain percentage (p) of unequipped users have access to posttrip information and are willing to switch their routes, and 3. Pretrip and en route users receive the information with higher quality than unequipped users. The value of p also requires a site-specific calibration effort. For example, Haselkom et al. found that 20.06% of drivers are willing to switch their routes in the study area in Washington State (26); Abdel-Aty et al. indicated that 15.50% of drivers are willing to switch routes in Los Angeles (27).

CONCEPTUAL SIMULATION FRAMEWORK AND SYSTEM IMPLEMENTATION The system evolution-modeling simulation framework for the enhanced version of DYNASMART-P is illustrated in Figure 2. In the proposed modeling framework, static demand (i.e., the same number of vehicles with fixed departure times) is simulated over different days. The four critical inputs (illustrated in the input boxes in Figure 2) that should be prespecified by users in the conceptual simulation framework are listed as follows: • Time-dependent traffic demand; • Bottleneck locations;


• Percentage of unequipped, pretrip, and en route users; and • Parameters of the bounded rationality rule. Figure 2 demonstrates the entire conceptual simulation framework currently implemented in DYNASMART-P. However, the two key components, stochastic capacity generation on freeway bottlenecks and signalized arterial and route choice mechanism, are not illustrated in detail. Because of their significance, the implementation frameworks of the capacity generation and route choice models are demonstrated in Figure 3 and Figure 4, respectively.

CASE STUDY The proposed simulation frameworks are applied to a real-world subarea network in the Portland, Oregon, metropolitan area to demonstrate the model applicability and usefulness. The subarea network selected for this purpose is illustrated in Figure 5. It is relatively large and therefore represents a good opportunity to test scaling issues associated with the method applications. The above network includes 858 nodes, 2,000 links, and 208 origin–destination zones. Among the 858 nodes, 169 of them are modeled as signalized intersections with actuated control and the rest are modeled at uncontrolled nodes with capacity constraints. In this case study the percentage of vehicles assigned to each of three available user classes was as follows: 98% of drivers were assumed to have no access to real-time information about network conditions (referred to as the “unequipped” user class), 1% were assumed to access pretrip information only (referred to as the pretrip user class), and 1% were assumed to have access to continuous en route information (referred to as the en route user class). Among the unequipped users, the percentage of drivers who are willing to make a route change in any given day was set to 15%. The number of days in the learning window was set to K = 5. Therefore the mean travel time was calculated from the experience of day d − 5 to day d − 1. This mean travel time represents each driver’s historical traveling experience. The calibrated parameters of the stochastic models described previously were applied to generate stochastic capacity and queue discharge flow rates for freeway bottlenecks (i.e., on-ramp and lane-drop segments) and saturation flow rates for signalized arterials. For simplicity, the minimum acceptable absolute tolerances used in the bounded rationality rule are 5 min for unequipped users and 2 min for pretrip and en route users. The default value of the relative switching threshold is set to 20% in this study. In the case study, the simulation run was performed for 100 days of simulated time to effectively generate realistic results. Figure 6 shows the networkwide average travel time and route switching rate of total vehicles segmented in three time regimes. In this study, for example, during the baseline stabilization period (Regime I in Figure 6) 50 days are simulated to achieve a stable baseline scenario. The average travel time diminishes significantly during the first 40 days and stabilizes afterward. After the baseline stabilization period was completed, the operational or construction strategies, or both, to be evaluated were introduced into the network, and the simulation process was carried out for an additional 30 days to allow driver adjustments and achieve stable conditions under the new scenario. This period is referred to as the strategy stabilization period and is illustrated as Regime II. Following immediately on this 30-day period was a simulation of an additional 20 days (Regime III in Figure 6) that formed the basis for the summary results output associated with the particular strategy being investi-


117

Bottleneck Identification Vehicle Path Loading

Traffic Demand Loading

Signalized Arterial & Freeway On-ramp/ Lane-drop Bottlenecks

Stochastic Capacity Generation

Updated Path Flow Pattern

DTA Simulator

No

Dynamic Mesoscopic Traffic Simulator

Experienced Travel Time on Day d for Each Vehicle

Stochastic Link Travel Time Performance Stability Checking

% of Unequipped/ Pre-trip/En-route Users

Update Mean Travel Time from day d-K to day d

Parameters of Bounded Rationality Rule

Route Choice Decision & Habitual Path Updating

Alternative Route Generation

Route Choice Mechanism

Day d++

Input Parameters

FIGURE 2

Algorithmic Module

Internal Data Interface

Traffic MOE Database

Comprehensive conceptual simulation framework.

gated. In Regime III, although the average travel time or switching rate is relatively stable, there are still obvious day-to-day fluctuations because the travel time experience on a single day can be dramatically affected by the underlying stochastic capacity features. Therefore, evaluation of network performance based only on the last simulation day (last iteration) is not recommended and new reliability-oriented system performance measures should be applied to take multiple days into account. In this study, for example, the simulation results from the last 20 days were used to report the network performance. In this experimental study various capacity-enhancing construction and operational strategies were evaluated on the Portland subarea network. These strategies are discussed in detail as follows: • Baseline scenario. Scenario 0. Baseline condition without any strategies

• Construction strategy scenarios: – Scenario 1. Construct a new through lane on Tualatin Valley Highway (each direction). – Scenario 2. Construct a new through lane on OR-217 northbound. • Operational strategy scenarios: – Scenario 3. Increase the percentage of users who access pretrip information from 1% to 10%. – Scenario 4. Increase the percentage of users who access en route information from 2% to 10%. Each of the four improvement strategies identified above, in addition to a “no change” baseline scenario, was analyzed. Table 1 summarizes the performance at networkwide level of the above five scenarios in regard to average networkwide travel time, standard

118


Initialization

Bottleneck Identification

Signalized Arterial

Freeway Bottlenecks

Saturation Headway Distribution

Pre-Breakdown Headway Distribution

Generate stochastic saturation flow rate

Generate stochastic capacity for next 15 minute interval

Calculate stochastic capacity

Queue at the end of 15 minute interval?

NO

Recursive Queue Discharge Model

YES End of cycle? Calculate queue discharge rate for 15 min interval

YES

Queue at the end of 15 minute interval?

NO

YES

FIGURE 3

Implementation framework of stochastic capacity generation.

deviation (SD) of travel time, and buffer index (BI). For comparison purposes, the corresponding results under deterministic capacity condition were also summarized. All of the results are calculated on the 20-day simulation basis. The BI is defined as follows:

BI =

TT95th − TTavg TTavg

(12)

where TT95th is the 95th percentile travel time from among 20-day simulation results and TTavg is the average travel time of 2-day simulation results. As expected, all of the strategies improve the network performance in regard to average travel time with the stochastic capacity or deterministic capacity simulation settings. However, average net-

work travel time (min), SD, and BI in the stochastic capacity environment are consistently higher than their counterparts in the deterministic capacity environment. This pattern is consistent with the previous assertion that deterministic network modeling platforms are likely to underrepresent the traffic operational impact of freeway system bottlenecks. Therefore, the proposed simulation framework, which incorporates stochastic capacity models and a compatible route choice mechanism, holds the promise of providing a more realistic and robust representation of network performance under various alternative scenarios. In the stochastic capacity environment, network performance benefited the most from increasing the percent of drivers who make use of pretrip and en route information on average travel time and travel time reliability. In contrast, in the deterministic capacity environment, the network performance benefited the most from the physical capacity additions.


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Day d-1

Day d

Travel Experience on Day d-1 for each Vehicle

Habitual Path Loading on Day d

Updated Path Flow Pattern

Update Mean Travel Time from day d-K to day d

Pre-Trip/En-Route Users

Unequipped Users

Shortest Path Calculation (Network Snapshot)

Shortest Path Calculation (All Complete Trips)



Bounded Rationality Rule

Habitual Path Update

Bounded Rationality Rule

Switch to Alternative Route

Switch to Alternative Route

FIGURE 4

Implementation framework of route choice mechanism.

CONCLUSIONS In this study methodological and analytic enhancements to existing dynamic traffic simulation models have been proposed for the purpose of increasing the realism and sensitivity of the models in simulating a real-world network and the effects of strategy applications. The particular focus is on how to seamlessly integrate stochastic capacity models and compatible route choice models in a stochastic capacity environment. These enhancements have been prototyped and tested through a mesoscopic DTA simulator, DYNASMART-P, and could be easily incorporated into other dynamic traffic simulation and analysis models as well. The study described in this paper provides the following contributions to existing DTA models:

FIGURE 5

Portland network study area.

• Innovative simulation platform incorporating stochastic road capacity for freeway and arterial links, which enables reasonable and realistic modeling of travel time; • New set of day-to-day learning and route choice models, which enable a realistic representation of drivers’ route selection process and effectively stabilize overall network flow under stochastic capacity conditions; and • Practical modeling guidelines that are effective for the enhanced DTA model to simulate various capacity-enhancing design, operational, and technological strategies.

120


17

25 Baseline Travel Time 20

Strategy Travel Time

15

Baseline Switching %

13 11

15

9 10

6

Switching %

Travel Time

Strategy Switching %

4 5

0 0

FIGURE 6 TABLE 1

10

20

30

40

50 Days

60

2

Regime III

Regime II

Regime I

70

80

0 100

90

Networkwide simulation results. Networkwide Travel Time Characteristics of Alternative Improvement Strategies Stochastic Capacity (Enhanced DYNASMART-P)

Deterministic Capacity (Original DYNASMART-P)

Scenario

TTavg

Improvement (%)

SD

BI

TTavg

Improvement (%)

SD

BI

0 1 2 3 4

11.50 11.03 9.98 9.87 9.58

— 4 13 14 17

1.43 1.36 1.21 1.21 1.20

0.25 0.23 0.21 0.20 0.18

10.12 9.53 8.58 9.45 9.17

— 6 15 7 9

0.63 0.60 0.52 0.58 0.58

0.11 0.09 0.09 0.10 0.09

NOTE: — = data not applicable; SD = standard deviation.

In a future study, real-world data sets will be used to quantify the modeling needs for incorporating stochastic capacity and to develop a more sophisticated day-to-day learning model to consider the resulting travel time variability. ACKNOWLEDGMENTS This research was conducted under the sponsorship of SHRP 2 as part of C05, Understanding the Contribution of Operations, Technology, and Design to Meeting Highway Capacity Needs. The authors thank the Transportation Research Board of the National Academies for the opportunity to participate in this research and for the permission to share this modeling framework with the research community. The authors also thank other members of the research team, whose contributions and insight made this research project possible. REFERENCES 1. Cambridge Systematics, Inc. Traffic Congestion and Reliability: Trends and Advanced Strategies for Congestion Mitigation. FHWA, U.S. Department of Transportation, 2005. 2. Peeta, S., and A. Ziliaskopoulos. Foundations of Dynamic Traffic Assignment: The Past, the Present, and the Future. Networks and Spatial Economics, Vol. 1, 2001, pp. 233–265. 3. Mahmassani, H. S. Dynamic Network Traffic Assignment and Simulation Methodology for Advanced System Management Application. Networks and Spatial Economics, Vol. 1, 2001, pp. 267–292.

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The Transportation Demand Forecasting Committee peer-reviewed this paper.