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ScienceDirect Procedia - Social and Behavioral Sciences 111 (2014) 498 – 507

EWGT2013 – 16th Meeting of the EURO Working Group on Transportation

Calibration and validation of a dynamic assignment model in emergency conditions from real-world experimentation Giuseppe Musolinoa,*, Antonino Vitettaa a Università Mediterranea di Reggio Calabria DIIES-Dipartimento di ingegneria dell’Informazione, delle Infrastrutture e dell’Energia Sostenibile Feo di Vito, 89100 Reggio Calabria - Italy

Abstract Calibration and validation of dynamic assignment models to simulate urban road transport systems in ordinary conditions are still an open issue. This problem is further emphasized in the case of transport systems analysis in emergency conditions, as there are no standardised methods and there is a lack of experience of real-world applications. The paper presents a DA model and a procedure able to simulate transport supply and transport supply – travel demand interaction of an urban road transport system in emergency conditions. The transport supply models are calibrated and validated through traffic data observed during a real-world evacuation experiment conducted in the town of Melito di Porto Salvo (Italy). The DA model has been applied in order to reproduce the observed real-world evacuation experiment and a set of indicators for testing the performance of a road network in emergency conditions is estimated. We think that the findings reported in the paper represent a contribution in the field of transportation systems analysis in emergency conditions at urban scale. The specified and calibrated DA model and the applied set of indicators can be a useful tool to support the planning and management of road networks and mobility in emergency conditions. © 2013 The The Authors. Authors.Published Publishedby byElsevier ElsevierLtd. Ltd. © 2013 Selection and/or peer-review peer-reviewunder underresponsibility responsibilityofofScientific ScientificCommittee Committee. Selection and/or Keywords: dynamic assignment models; cost functions; path choice; calibration and validation; evacuation; urban area.

1. Introduction The paper focuses on Dynamic Assignment (DA) models to support evacuation planning and it is motivated by the consideration that, although the market and research literature offer a large variety of DA models developed in recent years (some of them present very advanced specifications from a theoretical point of view), there is a

* Corresponding author. Tel.: +39-0965-875272; fax: +39-0965-875247. E-mail address: [email protected]

1877-0428 © 2013 The Authors. Published by Elsevier Ltd.

Selection and/or peer-review under responsibility of Scientific Committee doi:10.1016/j.sbspro.2014.01.083

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lack of experience concerning calibration and validation in evacuation conditions. This is due to two reasons. The first is operational: collecting field data is both burdensome and costly, because it is not possible to monitor human behaviour in real evacuations and because it is expensive to set-up a real-world evacuation experiment. The second is conceptual: human behaviour in a evacuation experiment is not the same as that in a real evacuation, because, in the first case, people are aware that there is no real disaster approaching. There is a debate about the validity of field data collected in real-world evacuation experiments; however, our opinion is that DA models need to be calibrated and validated against field data, even if they come from a real-world evacuation experiment. A comprehensive literature review leads us to the following consideration. Available DA models (see as example Papageorgiou, 1990; Akamatsu, 2001; Peeta and Ziliaskopoulos, 2001) present very advanced specifications containing a sizeable number of parameters. This makes calibration and validation possible only in some particular contexts in the sphere of ordinary conditions, but, extremely hard in emergency conditions such as those that may be forecasted in some disaster scenarios. The paper presents a DA model able to simulate supply and supply-demand interaction of a road transport system in ordinary and emergency conditions. The model is specified in its components which are link and node models and path choice model. Models are calibrated and validated using field data observed during a real-world evacuation experiment performed in the town of Melito di Porto Salvo (Italy). The specification is valid for ordinary and emergency conditions, the calibration and validation is in emergency condition. The work is part of a research project, titled SICURO, carried out by the Laboratory for Transport Systems Analysis (LAST) of Università Mediterranea di Reggio Calabria (Italy). The general objective of SICURO was risk reduction in urban areas in terms of exposure through the definition and implementation of evacuation procedures (Russo and Rindone, 2007). The results concern the development of models, procedures and guidelines for evacuation travel demand simulation (Russo and Chilà, 2007), for transport supply and demandsupply interaction simulation (Vitetta et al., 2009, Musolino and Vitetta, 2011), for path design of emergency vehicles (Vitetta and Quattrone, 2011). The paper is structured into five sections. In section 2 the literature review concerning DA models for urban road transport systems analisys in emergency conditions is presented. Section 3 describes the DA models system. Section 4 describes field data acquisition and presents calibrated model parameters. Conclusions are reported in the last section. 2. State of the art Several DA models for emergency conditions are available on the market or have been developed as research prototypes. Many of them were originally developed to simulate transportation systems in ordinary conditions and then adapted to the above purpose (Di Gangi et al., 2003; Vitetta et al., 2009). DA models for emergency conditions started to be developed in USA after the partial meltdown of the reactor at the Three Mile Island nuclear power plant in 1979. In the 1980s a first generation of models for supporting evacuation planning was developed. There have been continuous advancements in the research on DA models during the last two decades, which has led to a large number of models being implemented to support operative transport planning in ordinary conditions. After 9/11, great efforts were made not only to adapt existing models but also to develop dedicated models to simulate transportation systems in emergency conditions in order to support evacuation planning. The applications of DA models in emergency conditions may be classified according to three purposes which are demand management, network design and simulation of an evacuation plan. Demand management applications concern departure time definition in order to reduce congestion phenomena and minimize evacuation time. Demand management for evacuation of nuclear plants and an arms depot in executed in (Goldblatt, 1996). Several demand time profiles are defined, simulated through DA models and compared with the simultaneous departures scenario in urban areas (Sbayti and Mahmassani, 2006; Liu Yue et al., 2008). Network design applications concern path optimization and management in emergency conditions

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(Russo and Vitetta, 2000). As regards path optimization design, there are several applications related both to buildings (Sisiopiku et al., 2004) and urban areas (Yuan et al., 2006; Cova and Johnson, 2003). Some papers focused on supply management through operations like contraflow (Tuydes and Ziliaskopoulos, 2004; Theodoulou and Wolshon, 2004) and ramp metering (Gomes and May, 2004) in order to improve network capacity during evacuation. DA models are applied to quantify the effectiveness of evacuation plans both for urban areas (McGhee and Grimes, 2007; Pel and Bliemer, 2008) and for industrial areas (Jha et al., 2004). Some experiences of calibration of traffic flow models parameters in dynamic context are reported in: Tavana and Mahamassani (2000) for macroscopic models; Kunde (2002) for mesoscopic models; Park and Won (2006) for microscopic models. 3. Model The dynimc assignment model estimates the time-varying flow profile vector, f(t), on the links of the network. Given an origin-destination pair rs, the generalized cost of path k is wk. The travel demand flow on rs pair, drs, and the probability of choosing path k, pk, change for each departure time interval m defined in the time interval Γm, characterized by an instant time τm ∈ Γm. In particular, the probability of choosing path k at time instant τm, pk,τm, depends on the path cost, wk,τm, forecasted by the user before departing from the origin, for all the path perceived. At each departure time interval τm, (pre-trip) path choices made by users are estimated assuming that they anticipate future traffic conditions to be faced during the trip, by introducing the concept of experienced travel times (Huang and Lam, 2002) on the network (those experienced during the trip). At τm, the travel demand flow on path k, hk,τm, is given by the product: hk,τm = pk,τm drs,τm

(1)

The (pre-trip) path choice model estimates the probability pk,τm of choosing path k at time instant τm: pk,τm = ȈIτm pk°Iτm ǜ pIτm

(2)

with • Iτm, the perceived choice set at time instant τm; • pIτm, the probability of choosing the choice set Iτm; • pk°Iτm, the conditional probability of the generic path k given the choice set Iτm. The path choice model of the assignment model is pre-trip and probabilistic. The travel demand flow hk,τm along path k departing at time instant τm is distributed at a subsequent instant t (t • τm) on the links belonging to path k. It is possible to define the quantity: qijk(t°τm)

(3)

as the probability of travelling on link ij belonging to path k at the time instant t conditional upon departing at time instant, τm. The probability qijk(t°(τm)) depends on traffic conditions on the network or on the link costs (experienced travel times) belonging to path k at time t (t • τm). The sum of probabilities qijk(t°τm) for all links belonging to path k, for a fixed τm, calculated at time instant t, is equal to one: Σij∈k qijk(t°τm) = 1

∀ k | t, τm (t • τm)

(4)

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Traffic flow on link ij at time instant t is given by the sum, on all pairs rs, on all paths containing link ij and on all departure times τm belonging to the [t0, t] interval, of the products between qijk(t°τm) and hk,τm: fij(t) = Σk : ij∈k Στm∈[t0, t] qijk(t°(τm,)) pk,τm drs,τm

∀ ij

(5)

In the model, given the travel demand, three main class of models have to be specified, calibrated and validated: link, node and route choice models. 3.1. Supply components: link model specification The travel time on link a, ca, is assumed as: ca = la/va(ka; ua)

(6)

where • la, length of link a; • va, speed on link a that is dependent on the density ka and the available width ua. The speed on link is estimated using the following mesoscopic model (the notation ij for each link is omitted) (Van Aerde, 1997; Rakha and Arafeh, 2010): h=h(x(β β, u); v)

(7)

where h is the spatial headway between two vehicles travelling on the link; β = [β1 β2 β3 β4]T is a vector of parameters to be calibrated; u is the available width of the link, x=[kJ v0 vCR C]T is a vector of functions of variables that identify the fundamental diagram related to the link, with kJ, jam density; v0, free-flow speed; vCR, critical speed; C, capacity: kJ = β1 v0 = β2 u vCR = β3β2 u C = β4 u

(8) (9) (10) (11)

For simplicity’s sake, four background variables are introduced (Van Aerde, 1997): δ1 = (2 vCR - v0) / (v0 - vCR)2 δ2 = (1 / kJ)(1 / (δ1 + 1 / v0)) δ 3 = δ1 δ 2 δ4 = (-δ3 + v0 / C - (δ2 / (v0 - vCR)))/vCR

(12) (13) (14) (15)

Hence the specification of eq (7) becomes: h = h(x(β β,u); v) = δ3 + [δ2 / (v0 – v)] + δ4 v

(16)

From eq (16) and given that spatial headway h is the reciprocal of density k, a speed-density and speed-flow relationships may be derived:

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v = v(x(β β, u); k) v = v(x(β β, u); f)

(17) (18)

Eqs (16), (17) and (18) are plotted in Figure 1 for three values of available width (u=3.5 m; 4.0 m; 5.0 m). 200

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Fig. 1. Plots of eqs 16, 17 and 18 for values of available width: u =3.5 m; 4.0 m; 5.0 m.

3.2. Supply components: node model specification The node model (gap-acceptance/rejection) is a relationship between the accepted (rejected) gap, G, and the time spent searching for a gap in the priority vehicle stream to execute the manoeuvre, T: Gacc(rej) = G(T)

(19)

As regards gap-acceptance model it is important to highlight that the critical gap GCR is not an observable variable. On the contrary accepted and refused gaps are observable variables. So gap-acceptance and gap-rejection models were specified and calibrated by means of observed data. The models were distinguished for straight through and right turning manoeuvres. The gap-acceptance model has the following equation: Gacc = γ0 + γ1T Gacc = γ2 + γ3T

straight through manoeuvres right turning manoeuvres

(20) (21)

where • T is the waiting time; • Gacc is the accepted gap; • γ0, γ1, γ2, γ3 are parameters to be calibrated. The gap-rejection model has the following equation: Grej = γ4 + γ5T Grej = γ6 + γ7T

straight through manoeuvres right turning manoeuvres

where γ4, γ5, γ6, γ7, are parameters to be calibrated.

(22) (23)

Giuseppe Musolino and Antonino Vitetta / Procedia - Social and Behavioral Sciences 111 (2014) 498 – 507

3.3. Demand component: path choice model specification The route choice model is specified in two steps: • definition of a path choice set with a selective approach, which considers a path admissible if it satisfies a defined criterion; • generation of k-paths by means of utilities estimated with an attribute (congested time, distance, ….) associated to the above criterion. The choice probability pk,rs, relative to path k connecting the pair rs, is given by Manski (1977), reported in eq. (2). Given the present costs at time instant τm for each origin-destination pair rs, the choice set Iτm is the perceived choice set at time instant τm. In this paper the monoset approach is considered and the perceived paths are generated with a K-PATHS algorithm. In broad terms, alternative paths which are candidate to enter in the K-set may be evaluated according to some criteria such as: minimum route length; minimum route travel time; minimum route monetary cost; minimum route with high levels of road accidents. The set is generated according to a model of perceived paths calibrated in Quattrone and Vitetta (2011). Given that in a monoset approach one set is perceived, pIτm, is equal to 1. The conditional probability of the generic path k given the choice set Iτm, pk°Iτm, is evaluated with a logit model: pk°Iτm = exp(vk)/ Σu ∈ Iu,rs exp(vu)

∀ rs

(24)

where • vk = -θ wk, the systematic utility of path k connecting pair rs; • θ, path choice to be calibrated. 4. Experimentation 4.1. Data acquisition The experimentation is done on the base of a real-world exercise of evacuation. A forthcoming disaster in a portion of the town of Porto Salvo (Reggio Calabria, Italy) is simulated during the morning rush-hour of a working day in accordance with the emergency plan drawn up by the Civil Protection Department. Melito Porto Salvo is a town in the province of Reggio Calabria, in the south of Italy with 35.30 km2, 10483 inhabitants and 2432 employees. The evacuation area is about 0.04 km2 with 57 buildings, 255 residents, 65 households and 225 employees. Evacuation was observed and recorded through a system of video cameras. Data for the calibration were extracted in the laboratory from traffic scenes recorded by video cameras. The observed traffic flow variables were: • on link o vehicle running time, calculated as time spent by a vehicle crossing through two predefined road sections at known fixed distance along the link; o vehicle speed (vobs), as the ratio of distance between the two road sections to vehicle running time; o traffic flow (fobs), as the number of vehicles travelling on a predefined road section in a time unit; o density (kobs), as the ratio between f obs and v obs; • on node o manoeuvre type (right turning, straight through and left turning); o arrival time of vehicle at the node; o accepted gap; o refused gap;

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o o o

refused gap count (integer), as the sum of the refused gaps before the vehicle starts its manoeuvre; greatest refused gap; maximum waiting time for vehicle n starting from t', after which the vehicle starts the manoeuvre.

4.2. Models calibration and validation Parameters calibration was carried out with the Least Squares Method that has the property of minimizing total square differences between estimated values and values provided by the model whose parameters have to be known. For the calibration of the speed, the specification (18) v = v(x(β β, u); f) is considered with: β, u); f) )2 objective: Minimum ¦i = 1…N (vi,obs – v i (x(β T calibrated variables: β = [β1 β2 β3 β4] where • N is the number of observations; • vi,obs is the value of observed speed for the generic vehicle i; β, u); f) is the value of speed provided by the the model for the generic vehicle i. • vi(x(β Model calibration was performed on the 75% of the observed data (455 observations). Model validation was performed on the 25% of the observed data (114 observations) applying it on the three selected links. Validation is executed through the following statistical indicators: • informal tests on calibrated parameter signs; • MSE = (¦i=N (vi,obs – vi)2)/N • RMSE% = 100⋅((¦i=N (vi,obs – vi)2)/N)1/2/(¦i=N vi,obs /N) In table 1 the values of calibrated parameters and statistical indicators MSE and RMSE% are presented. Starting from the calibrated parameters, in relation to the link width, the values of the kJ, jam density; v0, free-flow speed; vCR, critical speed; C, capacity can be evaluated. For the parameters calibration of the gap acceptance models, the specifications (19), (20) and (21) is considered with: objective: Minimum ¦i = 1…N (Gi,obs – G i,(T) )2 calibrated variables: γ = [γ0 γ1 γ2 γ3 γ4 γ5 γ6 γ7]T where • Gi,obs is the value of observed gap for the generic vehicle i; • Gi(T) is the value of gap provided by the the model for the generic vehicle i. In tables 2, 3 and 4 the values of calibrated parameters and statistical indicators MSE and RMSE% are presented. The parameter θ of route choice model specified in eq. (24) is calibrated by means of: objective: Minimum ¦i = 1…N (fi,obs – f i,(θ) )2 calibrated variables: θ where • fi,obs is the value of observed flow for the generic link and time interval i; • fi(θ) is the value of flow provided by the the model for the generic link and time interval i. The value of the calibrated parameter is θ = 0,042 [1/sec]. An aggregate validation of the models systems is executed considering the vehicular flow variable in two cases: • simulated vehicular flows vs observed vehicular flows on some selected links of the road network (Figure 2);

Giuseppe Musolino and Antonino Vitetta / Procedia - Social and Behavioral Sciences 111 (2014) 498 – 507 • simulated vehicular flows vs observed vehicular flows incoming in the refuge area (Figure 3). In the first case, the scatterplot shows an acceptable adaptation of the simulated flows to the observed ones with a ratio between simulated and observed flows equal to 1,1255. In the second case, the comparison is executed between observed and simulated incoming flow in the refuge area. The results of the simulaton are related to the transport system with the parameters calibrated from real data. Table 1. Calibrated parameters and of statistical indicators for the car-following model

β1 [vehic/km] 180

β2 [km/(h m)] 7.50

β3 0.85

MSE [sec2] 30.09

β4 [vehic/(h m)] 317.00

RMSE % 19.37

Table 2. Calibrated parameters for the gap-acceptance model. Straight through manoeuvres

γ0 [sec] 8.432

MSE [sec2] 0.92

γ1 -0.422

RMSE % 16.19

Table 3. Calibrated parameters for the gap-acceptance model. Right turning manoeuvres

γ3 -0.332

γ2 [sec] 6.436

MSE [sec2] 0.98

Table 4. Calibrated parameters for the gap-rejection model

Straight through γ5 [sec] -0.11

γ6 1,57 ϭϬϬ

Right turning γ7 [sec] -0,08

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RMSE % 18.39

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5. Conclusions The paper presents a DA model able to simulate supply and supply-demand interaction of a road transport system in emergency conditions. The DA model is specified in the supply, travel demand and assignment (demand-supply interaction) components. The specified supply components are the link (car-following) and node (for non-signalized intersections) models, while the specified travel demand component is the path choice model. The link (car-following) model is a simplified multi-regime headway-speed relationship, that allows the model to be calibrated against aggregate field data related to traffic flow and link geometry, that are relatively easy to collect. The same considerations hold for the node model, which is currently linear in the waiting time. Not-linear specifications will allow in the future to capture driver behaviour for longer waiting times, where zero gaps might become possible. The link and node models do not consider vehicle mix, lane-changing behaviour or behavioural differences amomg drivers. The path choice model is a pre-trip stochastic model, which overcomes the problems of the logit structures. The dispersion parameter is calibrated by means of data provided by the real-world experimentation. Great effort was focused on calibrating and validating link and node models against field data; which required a complex preliminary set-up of the test site for the real-world experimentation of the evacuation. 6. References Akamatsu, T. (2001). An efficient algorithm for dynamic traffic equilibrium assignment with queues. Transportation Science, 35(4), 389-404. Cova, T. J., & Johnson, J. P. (2002) Microsimulation of neighborhood evacuations in the urban-wildland interface. Environmental Planning B: Plan. Des., 34, 2211–2229. Di Gangi, M., Musolino, G., Russo, F., Velonà, P., & Vitetta, A. (2003) Analysis and comparison of several urban road transportation assignment models in emergency conditions. Sustainable World, 8, 247-257. Goldblatt, R. (1996) Development of Evacuation Time Estimates for the Blue Grass Army Depot. Transportation Research, 326. Gomes, G., & May, A. (2004) A microsimulation of a congested freeway using VISSIM. In TRB Annual Meeting Compendium of Papers, Washington, D.C. Huang, H.-J., & Lam, W.H.K. (2004) Modeling and solving the dynamic user equilibrium route and departure time choice problem in network with queues. Transportation Research B, 36(3), 253-273. Kunde K. (2002). Calibration of mesoscopic traffic simulation models for dynamic traffic assignment. Master thesis, Massachusetts Institute of Technology. Jha, M., Moore, K., & Pashaie, B. (2004) Emergency evacuation planning with microscopic traffic simulation. Transportation Research Record (1886), Washington, D.C., 40–48. Liu Yue, G.L. Chang, & Li, Y. (2008) A corridor-based emergency evacuation system for Washington D.C.: system development and case study. In TRB 87th Annual Meeting Compendium of Papers, Washington, D.C.

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