Discrete Dynamics in Nature and Society

Volume 2015 (2015), Article ID 958052, 10 pages

http://dx.doi.org/10.1155/2015/958052

## Proactive Traffic Information Control in Emergency Evacuation Network

^{1}Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China^{2}School of Transportation, Southeast University, Nanjing 210096, China

Received 2 April 2014; Accepted 24 September 2014

Academic Editor: Zbigniew Leśniak

Copyright © 2015 Zhengfeng Huang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Traffic demand in emergency evacuation is usually too large to be effectively managed with reactive traffic information control methods. These methods adapt to the road traffic passively by publishing real-time information without consideration of the routing behavior feedback produced by evacuees. Other remedy measures have to be prepared in case of nonrecurring congestion under these methods. To use the network capacity fully to mitigate near-future evacuation traffic congestion, we propose proactive traffic information control (PTIC) model. Based on the mechanism between information and routing behavior feedback, this model can change the route choice of evacuees in advance by dissipating strategic traffic information. Generally, the near-future traffic condition is difficult to accurately predict because it is uncertain in evacuation. Assume that the value of traffic information obeys certain distribution within a range, and then real-time traffic information may reflect the most-likely near-future traffic condition. Unlike the real-time information, the proactive traffic information is a selection within the range to achieve a desired level of the road network performance index (total system travel time). In the aspect of the solution algorithm, differential equilibrium decomposed optimization (D-EDO) is proposed to compare with other heuristic methods. A field study on a road network around a large stadium is used to validate the PTIC.

#### 1. Introduction

For the natural or man-made disasters, the surrounding road network should be fully utilized to evacuate the affected people. Otherwise, stochastic evacuation flows may induce nonrecurring traffic congestion. Therefore, optimizing the operation of evacuation flows to improve emergency evacuation efficiency is one of the main goals of the disaster relief. From the perspective of behavior, how to adjust evacuees’ route-choice result to mitigate congestion in advance is a critical point. In other words, we should consider evacuees’ routing behavior feedback in the evacuation management.

Compared to general transportation network management, routing behavior feedback is less considered in the evacuation condition. Unlike the widely applied cases in the former condition, such as street capacity optimization [1] and signal optimization [2], only few studies are found in the latter condition, that is, Xie and Turnquist [3] in the planning of lane reversals and intersection crossings mitigation, Chiu and Mirchandani [4], and Paz and Peeta [5] in the dynamic choice of information-publishing routes.

Traffic information control can be a feasible evacuation management. However, decision makers usually passively published real-time information to evacuees whose route-choice result is not being optimized. Thus, the performance index of evacuation network can be improved only to a limited extent. Generally, the real-time information can solely reflect the near-future traffic condition with the maximum probability because this condition is uncertain in evacuation. At the current time interval, the value of near-future traffic information may emerge to be a probabilistic distribution within a range. Selecting any of them may lead to varied route-choice results of evacuees; thus, we need to develop a method to choose the appropriate value instead of the real-time value as the information provision to improve evacuation efficiency.

To design traffic information considering behavior feedback, the mapping between traffic information and evacuation flows should be addressed. Under specific information, the mapping is generated by two intermediate processes, the route choice and traffic loading. This is also the routing behavior feedback of evacuees, through which the decision maker can design the information to optimize the system performance. We define such optimization as proactive traffic information control (PTIC). Thus, this type of information optimization is akin to network design problem, which belongs to Stackelberg game. Because of the non-closed-form of traffic-loading simulation steps involved in this application, the general operations research methods used for nonlinear planning cannot be applied. The useful methods are heuristic, such as equilibrium decomposed optimization algorithm [6], linear approximation algorithm [7], and intelligent algorithm [8]. The last algorithm can have the potency of global convergence because the searching process is akin to enumeration. However, it is imperfect for its low efficiency. The first method is a numerical method which uses one-dimensional search to reduce the solution range, but the global solution may be ignored at the initial iterations with large step size and also we cannot ensure the convergence of the solutions in the whole operation. The main idea of the second method is to use Taylor expansion to change the objective to a linear function to solve drop direction and golden selection method to solve step size, such as Frank-Wolfe (F-W) algorithm. The only note is that the derivative or difference of objective with respect to decision variable should be provided in the generated subproblem. However, this method may converge to a local optimum near the initial solution because the drop direction and step size are too accurate to jump out of the local trap.

To better mitigate near-future congestion for emergency evacuation network, we propose PTIC to provide the traffic information strategically according to routing behavior feedback. The minimal total system travel time (TSTT) is set as the objective, which is composed of total evacuation time, arrival time penalty, and congestion cost. A corresponding differential equilibrium decomposition optimization (D-EDO) algorithm is proposed and demonstrated to be advantageous in the accuracy.

In what follows, the PTIC model and solving steps of D-EDO are introduced. Then, the theoretical method is applied in the field case of evacuation network around Nanjing Olympic Stadium in China.

#### 2. Method

##### 2.1. PTIC Model

The following constraints (1–8) and the minimal TSTT objective (9) are designed to formulate PTIC model. The constraints are in accord with one-shot stochastic dynamic traffic assignment, composed of stochastic route choice and one-shot traffic loading. The reason for adopting a nonequilibrium model is that no historic travel experience can help evacuees make a game decision; the reason for adopting stochastic model is that evacuees cannot know the* a priori* flow condition in the nonrecurring event.

###### 2.1.1. Route-Choice Utility

There are some exogenous route-related variables influencing evacuees on the route choice. The determination of exogenous variables mainly depends on two criteria (evacuation time and information reliability). As for evacuation time, it is no doubt that people prefer to choose shorter routes. Besides, Wardman et al. [9] concluded, using a stated preference (SP) survey, that delay time is more useful than travel time in the route choice. With respect to information reliability, risk aversion will emerge in travelers’ mind when unreliable information is provided. Hua et al. [10] showed that the disseminated delay-time reliability is a significant factor influencing route choice. Therefore, exogenous variables of route length, delay time, and disseminated delay-time reliability are chosen as the route-choice explanatory variables. For easy recognition, these three explanatory variables corresponding to route at an information-updating interval are represented as (m), (min), and (%) in sequence. The utility value of route at the information-updating interval can be calculated by

In formula (1), the evacuees are assumed to be homogeneous, so use constant to represent the utility value of endogenous attributes of evacuees. We can lose this term “commensurable and can be removed” in the discrete choice model. To consider the overlap line problem, the* C*-logit model [11], a type of multinomial logit model, is usually adopted as the discrete choice model because of its simple form and easy calibration. The variable is the commonality factor in the utility of* C*-logit model. The variable is the proportional weight (often represented as a length ratio) of the overlap section between path and another route of the same OD pair. The set includes all the overlap sections related to route . The variable is the number of routes, connecting the same OD pair with , which share the overlap section . The explanatory-variable coefficients , , , and need to be calibrated using SP survey.

###### 2.1.2. Analytical Route-Choice Probability Function

According to the* C*-logit model, the analytical route-choice probability for choosing route from origin cell to destination at an information-updating interval can be determined by
where is the route set from cell to destination. Because the destination of evacuation network is normally set as a virtual node, the index for destination can be eliminated to reduce notation complexity. The destination is known implicitly through the route index.

###### 2.1.3. One-Shot Traffic Loading

Daganzo’s [12] cell transmission model (CTM) can load traffic dynamically and successfully embedded in simulation software VISTA. But this basic cell cannot extract congestion information. In the following, we propose an enhanced CTM to overcome this shortcoming. The following variables at each (loading) interval are defined* a priori*:: set of cells succeeding cell , : set of cells preceding cell , : maximal number of vehicles that can flow into or out of cell at interval , : maximal number of vehicles that can be present inside a cell at interval , : demand from source cell at interval , : vehicle occupancy of cell at interval , : flow outflowing from cell at interval , : flow from cell to cell at interval *.*It is noted that the unit time interval for traffic loading is shorter than the information-updating time interval.

Assuming the time-varying demands and route-choice ratios are provided, we can turn to the procedure of the enhanced CTM (shown in Figure 1) to simulate the flow. Regarding the proposed varied length cell, each link in our model is divided into three types of cells composed of 1 tail cell, 1 head cell, and a few approach cells (its number is based on the number of stream directions). Head cell and tail cell are used to capture the intersection queue length and traffic spillback separately. The latter two indexes could serve the representation of congestion cost in the PTIC objective. For example, we can let the length of approach cell be equal to unit time first and set the length of head cell to be equal to a threshold value required by decision maker to penalize the intersection queue and give the remaining length to tail cell to check the queue spillback for penalization.