This paper establishes a dynamic stochastic route choice model for evacuation to simulate the propagation process of traffic flow and estimate the stochastic route choice under evacuation situations. The model contains a lane-group-based cell transmission model (CTM) which sets different traffic capacities for links with different turning movements to flow out in an evacuation situation, an actual impedance model which is to obtain the impedance of each route in time units at each time interval and a stochastic route choice model according to the probit-based stochastic user equilibrium. In this model, vehicles loading at each origin at each time interval are assumed to choose an evacuation route under determinate road network, signal design, and OD demand. As a case study, the proposed model is validated on the network nearby Nanjing Olympic Center after the opening ceremony of the 10th National Games of the People's Republic of China. The traffic volumes and clearing time at five exit points of the evacuation zone are calculated by the model to compare with survey data. The results show that this model can appropriately simulate the dynamic route choice and evolution process of the traffic flow on the network in an evacuation situation.
Evacuation is one of the most important measures adopted in emergency response to protect masses and to avoid both physical and property damages. Reflecting dynamic propagation characteristics of evacuation traffic flow appropriately is the core theory problem in estimating the evacuation time and evaluating evacuation plans reasonably.
In the studies throughout the world that focus on the evacuation route choice problem, modeling methods include static traffic assignment and dynamic network traffic flow theory. The dynamic models can reflect the propagation process of evacuation traffic flow more effectively than the static method. The core problem of the dynamic method is describing the dynamic propagation and stochastic characteristics of evacuation traffic flow.
The urban dynamic network traffic flow theory under normal conditions has been developed for nearly 20 years with the evolution of intelligent transportation systems, and the macrosimulation model in static traffic flow has been imported into the dynamic flow theory. The cell transmission model (CTM) is one of the dynamic traffic performance models. CTM was first proposed by Daganzo to simulate the traffic flow on highways [
Based on previous studies on the DTA problem, the dynamic propagation characteristics of traffic flow in an evacuation situation were researched further. Tuydes and Ziliaskopoulos [
However, during evacuation, road users are not bound to choosing their routes according to the optimum system. To address this problem, some existing models assumed that drivers’ route choices were based on current road and traffic conditions. The NETVAC1 model allowed drivers to choose a turning movement at each intersection at each time interval based on the anterior traffic conditions, while the CEMPS model followed the shortest path-based mechanism [
Different assumptions of the estimated term generate different SUE models under normal conditions, in which the multinomial logit (MNL) model and Multinomial Probit (MNP) model are the most widely applied. With further study of the SUE problem, the dynamic stochastic user optimal problem (DSUO), which is an extension of the static stochastic user equilibrium problem, was proposed by Daganzo and Sheffi [
Generally speaking, on one hand, previous models of the dynamic evacuation route choice problem did not consider the characteristic of the evacuation traffic flow. In an evacuation situation, the large density of traffic flow makes it difficult for drivers to exchange lanes, while the minimum headway diminishes compared with normal conditions [
Therefore, the objective of this paper is to simulate the evolution process of the traffic flow on the network and the stochastic route choice in an evacuation situation under determinate road network, signal design, and OD demand. The model contains three parts: the lane-group-based cell transmission model (CTM) which sets different traffic capacities for links with different turning movements to flow out, the actual impedance model which is to obtain the impedance of each route in time units at each time interval, and the stochastic route choice model according to the probit-based stochastic user equilibrium. It can be applied to estimate the real-time evacuation traffic condition and provide the basis for evaluating the performance of evacuation plans developed in response to the possibility of an event or a disaster.
The dynamic stochastic route choice model for evacuation contains three parts, the CTM model, the actual impedance model, and the stochastic route choice model, which is applied to simulate a dynamic propagation process, estimate actual impedance in time units of routes, and simulate route choice of vehicles, respectively. The logistic relationships among the three parts and the structure of the synthesis model are shown in Figure
Flow chart of the model.
The traditional CTM model divides one direction of each street on the network into small homogeneous segments, called cells, while the lane-group-based CTM model divides every link into cells to simulate the evolution process of traffic flow. Drivers cannot change lanes easily in evacuation situations given the large traffic density and car-following phenomenon. Hence, it is assumed that each vehicle considers the desired link fully when the vehicle enters into the roadway.
Based on the transmission mechanism of the traditional CTM model, the traffic propagation rule at intersections can be reflected through different constraints of the first and last cells of the link: the first cell may be an ordinary cell or a merging cell [
The equation of traffic flow propagation can be expressed as
In particular, the number of vehicles in the source cell can be acquired by loading values and outflows at each time interval. Thus, when the first cell of a link is connected with the source cell
The sink cell can be considered as a storeroom with infinite capacity. When the last cell of a link is connected with the sink cell
The equation of traffic flow propagation of a merging link is
In particular, for a merging link that not only connected with links but also with a source cell, it is supposed that the vehicles in the links have priority over the source cell.
Each vehicle chooses a route between the OD pair when loaded at the origin and then propagate to the diverging link of the route after some time. Therefore, the proportion of vehicles moving from the diverging link to each downstream link in time interval
In particular, it is assumed that when the source cell is diverged, vehicles in the source cell follow a uniform distribution to flow into the downstream links of the source cell. The equation can be expressed as
The equation of traffic flow propagation of ordinary cells within the link is almost the same as the traditional CTM model.
Due to the restrictions of the traffic capacity of the first and last cells of a link, the inflow of a link during time interval
The routes between OD pairs are composed of links. Therefore, based on the impedance of links, the actual impedance in time units of route
As mentioned previously, drivers perceive the route impedance differently. To treat this problem, let the perceived route impedance consist of two parts: the actual impedance and an error term. Assume that
The covariance between the perceived impedance of two routes with overlapping links is expressed as follows:
In summary, the perceived route impedance in time units of path
Each evacuated driver estimates impedance of all routes between the OD pair at the time interval loading at the origin and chooses the route for which the impedance is perceived to be the least of all the optional routes. Hence, the probability
Furthermore, on the basis of normal distribution properties, it can be calculated as follows:
If the routes between OD pair
A Monte Carlo simulation can be applied to estimate the probability of each route between each OD pair chosen by drivers.
Based on the probability, the traffic volume of route
The stochastic route choice problem is equivalent to finding vectors
Calculate the free-flow impedance in time units of each route to find the shortest one of each OD pair and assign all of the traffic demands of the corresponding origins on them in each time interval. Record the initial traffic volume of route
The number of iterations is
Update the actual impedance in time units of route
Calculate the probability of route
If convergence is attained, stop, and
Convergence criterion:
Based on the distribution of parking lots and the road network data,we calculated the evacuation traffic volumes and clearing time of each exit point of the evacuation zone after the opening ceremony of the 10th National Games of China to compare with survey data to verify the model’s effectiveness.
The 10th National Games of China, which were held in Nanjing Olympic Sports Center, led to many traffic needs. According to the usage data supplied by Traffic Administration Bureau, streets on the northern side of the Olympic Center were used for inside driveway parking lots, which parked 1100 vehicles; it also provided two inside driveway parking lots on the eastern side, which parked 465, 385 vehicles separately, and there was an underground parking on the southern side that was not only for the audience but also for players and servicers, which had been used in 439 parking spaces.
The managers conducted some traffic management such as contraflow in the evacuation zone nearby the Olympic Sports Center to handle the large-scale demand of short-term traffic evacuation. All roads within the region applied one-way access during evacuation to compose a closed area allowing traffic to flow out only. Thus, the parking lots are set as origins for evacuation, and the exit links of the northern side and eastern side are assumed to connect to a virtual sink cell separately, which means the whole evacuation network has two destinations. The evacuation network with origins and destinations is shown in Figure
(a) Evacuation network and (b) OD demand table and dynamic loading condition.
Cell representation of the evacuation network.
Specific information of each link is listed in Table
Basic information of the links.
Link | Amount of cells | Amount of lanes |
---|---|---|
|
4 | 5 |
|
6 | 10 |
|
14 | 4 |
|
4 | 4 |
|
3 | 8 |
|
12 | 4 |
|
4 | 4 |
|
4 | 4 |
|
20 | 8 |
|
4 | 5 |
|
14 | 6 |
|
14 | 3 |
|
4 | 8 |
|
3 | 8 |
|
12 | 4 |
|
4 | 4 |
|
6 | 8 |
|
20 | 6 |
|
8 | 5 |
|
14 | 5 |
|
14 | 3 |
|
4 | 4 |
|
12 | 6 |
|
12 | 3 |
|
4 | 8 |
|
10 | 10 |
|
12 | 6 |
|
8 | 5 |
|
14 | 4 |
|
4 | 4 |
|
4 | 4 |
|
12 | 5 |
|
12 | 3 |
|
4 | 4 |
|
11 | 10 |
Based on the exiting studies [
Length of time interval | 5 s |
Jam density | 0.2 veh/m |
Free-flow speed | 54 km/h (i.e., 15 m/s) |
Backward propagation speed | 6 m/s |
Straight-through capacity of a cell | 2160 veh/h/lane (i.e., 3 veh/interval/lane) |
Left-turn capacity of a cell | 2.4 veh/interval/lane |
Right-turn capacity of a cell | 2.7 veh/interval/lane |
Merging capacity of a cell | 2.7 veh/interval/lane |
Length of a cell | 75 m |
Carrying capacity of cell | 15 veh/lane |
|
0.5 |
The solution algorithm presented previously is coded in Microsoft visual C++ and run on a desktop personal computer with CPU of Intel Core(TM)2 2.2 GHz and RAM of 2 GB. The computing time to converge is about 16.9 minutes. The long computing time can be reduced by diminishing sampling size for Monte Carlo simulation. When the traffic demand gets larger, the computing time will not elongate obviously unless the loading time intervals become more.
Figure
Convergent trend for the evacuation network.
According to the proposed model, the evacuation route choice result and other important calculations are as follows.
This is defined as the evacuating time from when the opening ceremony finishes to when the last evacuees arrive at a virtual sink cell. This indicator is the most important one to reflect the performance of evacuation and to evaluate the evacuation plans. Figures
Clearing time of each exit.
Exit link | Exit | Evacuation time (5 s) |
---|---|---|
|
D1 | 543 |
|
D2 | 576 |
|
D2 | 553 |
|
D2 | 548 |
|
D1 | 512 |
|
D1 | 588 |
The evacuation route choice result at each time interval can deduce the total traffic volume of each route during the whole evacuation period which is shown in Table
Traffic volume of each route.
Route | Point | Traffic volume (veh) |
---|---|---|
|
1 | 223 |
|
2 | 97 |
|
4 | 38 |
|
5 | 234 |
|
1 | 8 |
|
3 | 118 |
|
4 | 88 |
|
5 | 1 |
|
1 | 385 |
|
3 | 1100 |
|
4 | 94 |
|
5 | 3 |
We can obtain the number of vehicles in each cell and outflow of each cell at each time interval by solving
Comparison of model calculation and survey data of time-sharing traffic volume.
We compare the Previous computed results with the field survey data to verify the validity of the dynamic stochastic route choice model.
The survey collected traffic volumes of the exit points (1~5) of the evacuation zone from 22:00–23:30. The distribution of these points is shown in Figures
Comparison of model calculation and survey data of traffic volume.
Point | Destination | Traffic volume | Model calculation |
Survey data |
Error |
---|---|---|---|---|---|
1 | D1 | 713 | 616 | 616 | 0 |
2 | 97 | 97 | |||
| |||||
3 | 1218 | 1180 | |||
4 | D2 | 1676 | 220 | 258 | 2.27% |
5 | 238 | 238 | |||
| |||||
Total | 2389 | 2.27% |
In Table
The dynamic stochastic evacuation route choice model is established to simulate the evolution process of the traffic flow on the network and the stochastic route choice in an evacuation situation under determinate road network, signal design, and OD demand. It contains three parts: the lane-group-based CTM model, the actual impedance model, and the stochastic route choice model.
Considering the large traffic density which makes it difficult for vehicles to exchange lanes in an evacuation situation, this paper established a lane-group-based CTM model, which detailed the propagation process of the traffic flow with different flowing-out turning movements on the basis of the car-following phenomenon in an evacuation situation. This part obtains the inflow and outflow of each cell. Because evacuation in an instant time is of the essence, a realistic model of traffic network performance under a dynamic load is necessary.
Based on the lane-group-based CTM model for evacuation, the piecewise function was established to obtain the actual impedance of each link at each time interval and the dynamic route impedance; then, combined with the principle of stochastic user equilibrium, we confirmed the error term of the route impedance and acquired the perceived impedance which is taken to be the main criterion for the decision of evacuation route choice.
To verify the effectiveness of this model, this paper applies the proposed model to calculate the evacuation traffic volumes and clearing time of each exit point of the evacuation zone after the opening ceremony of the 10th National Games of China based on the distribution of parking lots and traffic data of the road network. The comparison between the computed results of the proposed model and field survey data proves that this model can reflect the dynamic propagation characteristics of evacuation traffic flow appropriately.
In an emergency evacuation, the OD demand table is not known a priori. Traffic route choice model needs to reflect the emergency circumstances; therefore the estimation of OD demand should be constructed as part of the modeling effort—a subject for further research.
Further studies in the calibration for each parameter in the proposed model under different familiarity of drivers to evacuation network and different levels of emergency evacuation situation are necessary. Design and development of the user interface of this model could simplify the cellular process of the traffic networks and enhance the practicality and operability of the model.
Set of discrete time intervals
Set of source cell (origin)
Set of sink cell (destination)
Set of links, a link equivalent to a link with a unique turning movement at intersection
Maximum number of vehicles that can flow out (traffic capacity) of cell
Traffic capacity of the end cell of a through link/left-turn link/right-turn link at time interval
Traffic capacity of merging cell
Ratio of the free-flow speed and backward speed of cell
Set of successor cells
Set of predecessor cells to cell
Maximum number of vehicles in cell
Signal and priority control parameter of link
Evacuation demand generated from source cell
Evacuation demand of path
Number of lanes of link
Number of vehicles in cell
Number of vehicles in link
Number of vehicles moving from cell
Number of vehicles moving from link
Number of vehicles moving out of link
Number of vehicles moving into at time interval
Accumulative number of vehicles moving out of link
Proportion of vehicles moving from link
The average impedance in time units of a link
The actual impedance in time units of route
The perceived impedance in time units of route
A random error term of impedance of route
This research is supported by the National Natural Science Foundation of China (no. 51078086) and (no. 51278101). The authors appreciate the Jiangsu Provincial Key Laboratory of Transportation Planning and Management of Southeast University.