Initial Location Assignment and Dynamic Reassignment Optimization for Urban Evacuation Guiders Jing-Xian Tang, Student Member, IEEE, Qing-Shan Jia, Senior Member, IEEE, Zhiling Liu, Student Member, IEEE, Ning Ding, Xiao-Dong Liu, Hui Zhang Abstract— Urban evacuation is of great significance in saving human lives when disasters strike major cities. Comparing with the large population to evacuate, the number of evacuation guiders is much smaller. Since the location of evacuation guiders can greatly influence the evacuation process, it is crucial to identify the most critical locations to assign guiders. The assignment optimization for evacuation guiders usually suffers from partial information, partial control, uncertainty of individual behaviors and ever-changing traffic conditions during an evacuation. We divide this important problem into two parts: initial location assignment optimization and dynamic reassignment optimization. Both of them are considered in this paper and the major contributions are as follows. First, we mathematically model the assignment optimization problem using Markov decision process (MDP) framework. Second, we make a comparison among three methods that can be applied in initial location assignment optimization. Third, a simulation-based policy improvement method is developed to obtain optimal reassignment policies. Forth, some numerical examples are presented to demonstrate the performance of our methods. We hope this work sheds insight on evacuation guider assignment optimization problem in more general situations. Index Terms— Emergency evacuation, discrete time dynamic system, location assignment, simulation-based policy improvement
I. INTRODUCTION With worldwide urbanization and drastic global climate change, it can be predicted that natural and man-made disasters (e.g. earthquake, tsunami, nuclear radiation accidents, etc.) are going to happen with increasing potentiality and greater effects. As an intuitive and effective way to protect people’s safety of lives and property against hazardous situations, evacuation has long been used and received more and more attention in recent years. This work is supported in part by the National Key R&D Program of China (2017YFC0704100), the National Natural Science Foundation of China under grants (Nos. 61673229, 61174072, 61222302, 91646201, 91124008, and U1301254), the Tsinghua National Laboratory for Information Science and Technology (TNLIST) for Excellent Young Scholar, the 111 International Collaboration Program of China (No.B06002), the Basic Research Program of People’s Public Security University of China (No. 2016JKF01307), and the Program for New Star of Science and Technology in Beijing (No. xx2014B056). J.-X. Tang, Q.-S. Jia and Z. Liu are with the Center for Intelligent and Networked Systems, Department of Automation, Tsinghua University, Beijing, 100084, China (email:
[email protected],
[email protected],
[email protected]). N. Ding is with the School of Criminal Investigation and Counterterror, People’s Public University of China, Beijing, China. X.-D. Liu and H. Zhang are with the Institute of Public Safety Research, Department of Engineering Physics, Tsinghua University, Beijing, 100084, China (email:
[email protected],
[email protected]). Q.-S. Jia is corresponding author.
,(((
During a large-scale urban emergency evacuation, a notwell management can cause serious traffic jams, great delays to the evacuation process, and eventually severe losses. Evacuation guiders, as first responders, play important roles in offering efficient traffic managements along with control strategies. However, there are very likely not enough personnel to be assigned under those emergency situations. Thus an effective assignment policy for the evacuation guiders is of great importance to achieve the best system performance. This is the location assignment optimization problem for evacuation guiders studied in the paper, which includes the initial location assignment before evacuation starts and dynamic reassignment as the evacuation process goes on. We assume that road map does not change during the evacuation process; there are enough time for guiders to arrive at their guiding locations; and guiders are always assigned to intersections so as to collect local information and provide guidance more efficiently. Our concern is to minimize the total clearance time. The challenges of this work are as follows. First, partial information. An evacuation guider can only observe the real time traffic conditions of his surroundings in a limited range. It is infeasible for him to acquire the global information of the evacuation process. Second, partial control. Evacuees usually have a lack of information about, and a lack of experience with the emergency situation, and they act out of a user-optimal instead of system-optimal thinking. They are uncontrollable unless they pass by a guider. Third, uncertainty of individual behaviors. People’s behaviors can be affected dramatically by their psychological status which brings great uncertainty to evacuation process. Besides, the decision making can be quite different among individuals even under the same circumstance. We can hardly model evacuees to give an accurate prediction of their actions and decisions. Forth, identifying the most crucial intersections dynamically. As the evacuation process goes on, the set of most critical intersections keeps changing, which requires us to make reassignments for evacuation guiders online. There are many existing works related to the evacuation problem. Yamada [1] considered a static network flow model for the evacuation and used a shortest path algorithm to obtain the evacuation guidance for each node. Chalmet et al. [2] used a dynamic network flow model to formulate the evacuation process. They modeled the traffic network as a static directed graph first and expanded it on discrete time, which is a pure mathematical model. Though it captures more details than static models, it is still deterministic and
lose stochastic features of an evacuation process. Numerous simulation models have been developed and tested also, such as cellular automata [3], multi-agent model[4], cell transmission model (CTM) [5] and particle hopping model [6]. The basic idea of CTM is to convert links into homogeneous cells that could be traversed in a unit of time interval at freeflow speed, it can accurately describe the traffic condition and capture the dynamics such as traffic jam. Liu et al. [7] and Liu [8] proposed a control strategy optimization model using CTM at both the network level and the corridor level. However, location assignment optimization for evacuation guiders is rarely studied in network emergency evacuation problems. On the other hand, some research has been done in finding critical intersections to allocate traffic control devices and emergency service facilities. For example, static covering location model was first proposed by Toregas C. et al. [9] in 1971, and Maxwell M. et al. [10] developed a dynamic programming model in 2009 based on Toregas’s work. Zhang et al. [11] proposed a mixed integer nonlinear programming model (MINLP) for emergency evacuation. But they still suffer from losing dynamics and stochastic features. In this paper, we use a CTM-based simulation framework to describe the detailed process of an urban evacuation, with which we can get accurate performance estimations of methods and policies. Now the problem can be converted to simulation-based optimization. Bertsekas et al. developed the rollout method for combinatorial optimization [15] and extend to discrete time stochastic optimization [16]. Rollout is a form of sequential optimization that originated in dynamic programming, the basic idea is to estimate the cost of actions in the action space by running simulation under a base policy, and pick the action that can minimize the cost to obtain an improved policy. When the simulation replication close to infinity, rollout algorithm is guaranteed to improve the performance of the base policy. Four major contributions are made in this paper. First, we formulate the location assignment problem based on Markov decision process framework and develop a simulation model to show detailed process of evacuation. Second, we make a comparison among three methods in solving the initial location assignment problem. Third, a simulation-based policy improvement method is developed to obtain optimal dynamic reassignment policies. Forth, the performance of our methods are evaluated by some numerical examples. The rest of this paper is organized as follows. Section II formulates the problem and develops a mathematical model. Section III presents the solution methodologies for both initial location assignment and dynamic reassignment optimization problems. Some numerical results are given in Section IV, and Section V provides brief conclusions of this work. II. PROBLEM FORMULATION To capture the dynamic and stochastic features of an urban evacuation process, we use Markov decision process (MDP) method to mathematically model the problem. MDP provides
a general framework for many state-based control, decisionmaking and optimization problems. First of all, we model the traffic network as an undirected graph G(V, E), where V = {1, 2, ..., |V |} is the node set representing intersections, and E = {(i, j)|i, j ∈ V } is the edge set representing roads. Safe nodes are intersections located in safe areas, an evacuee is considered to be evacuated successfully if and only if he arrived at a safe node. The set of safe nodes is denoted as VS . At the beginning of the evacuation process, there are N evacuees numbered from 1 to N and M evacuation guiders numbered from 1 to M . Note that in this model, an evacuee is either on a road or at an intersection while an evacuation guider can only stand at an intersection. The system state at time t is defined as St = (Ct (1), ..., Ct (N ), Gt (1), ..., Gt (M ), Xt ) ∈ S,
(1)
where S denotes the state space, Ct (i) and Gt (j) denotes the state of the ith evacuee and the jth evacuation guider at time t, respectively. Xt is the total amount of evacuees that have not reached the safe nodes at time t. Ct (i) and Gt (j) are defined as follows: Ct (i) = (et (i), dt (i), st (i)),
(2)
where et (i) ∈ E denotes the serial number of the road where the ith evacuee is on at time t, dt (i) denotes the serial number of the intersection where the ith evacuee is going to reach after he travels to the end of road et (i), and st (i) denotes the current speed of the ith evacuee at time t. Gt (j) = (vt (j), ft (j), pt (j)),
(3)
where vt (j) ∈ V denotes the serial number of the node where the jth evacuation guider is at time t, ft (j) ∈ N ∗ is the degree of node vt (j). pt (j) is the traffic control strategy used by the jth guider at time t, which is a ft (j)-dimensional vector. It can be regard as a probability distribution and is defined as follows: f (j)
pt (j) = (kt1 , kt2 , ..., kt t ft (j)
)
(4)
ktq = 1, 0 ≤ ktq ≤ 1
(5)
q=0
We define the action for the ith guider at time t as At (i) = (Vt+1 (i), Pt+1 (i)), where Vt+1 (i) denotes the node where the ith guider will be at time t + 1 (stay or move to the neighbor node), and Pt+1 (i) is the control strategy he will use at time t + 1. To simplify the problem, the traveling time for evacuation guiders is not taken into account. In another word, they make decisions at time t and make it at time t+1. Our goal in this paper is to minimize the total clearance time, which is the time until the last evacuee reaches the safe area. Thus the cost function is defined as: 0, if Xt = 0 g(St , At ) = (6) 1, otherwise
and the long-run average performance of policy L is shown below: ∞ J(L, S0 ) = E[ g(St , At )|S0 ] (7) t=0
j∈Γ(i)
III. SOLUTION METHODOLOGY
xij = kij (
A. Initial Location Assignment Optimization The initial location assignment should be done when an emergency condition is predicted or has already occurred but has not arrived at the area of interest (AoI) yet. Since we cannot predict the traffic conditions during the evacuation before it starts, it is more practical to identify the most crucial locations to assign evacuation guiders based on some priori knowledge of AoI, e.g. topology of the traffic network, daily vehicular traffic, population distribution. As we model the traffic network of AoI as a graph and we have the assumption that all the guiders are assigned to intersections, centrality measures on graph theory can offer reference to us in finding crucial nodes. Holme [12] designed some simulation experiments of traffic flow on complex networks and found that nodes (intersections) with high centrality are more likely to suffer from congestions. We regard these nodes as crucial nodes and use the following two methods to identify them. 1) Betweenness centrality (BC) [13] Betweenness centrality is based on shortest paths. It represents the degree of which nodes stand between each other and was applied to a large range of problems in network theory. The betweenness centrality of node v is defined as: σst (v) σst
(8)
s=v=t
where σst is the total amount of shortest paths from node s to node t, and σst (v) is the amount of those paths that pass through node v. 2) Closeness centrality (CC) [14] Closeness centrality indicates the capacity of a node to reaching all the rest nodes in graph. The more central a node is, the closer it is to all other nodes. The closeness centrality is given by the following equation: CC (v) =
1 y=x d(y, x)
xpi + di ), ∀(i, j) ∈ L
(13) (14)
0 ≤ kij ≤ 1, ∀(i, j) ∈ L
(15)
xij ≥ 0, ∀(i, j) ∈ L
(16)
Ai ∈ {0, 1}, ∀i ∈ N
(17)
where xij is the traffic flow on link (i, j), tij is the travel time on link (i, j), N denotes the set of all nodes, NS denotes the set of safe nodes, L denotes the set of all links from node i to node j, i, j ∈ N , Γ(i) denotes the set of successor nodes to node i, Γ−1 (i) denotes the set of predecessor nodes to node i, Ai is a binary variable indicating whether there is a guider at node i ∈ N (1 for yes and 0 for no), m is the total number of guiders, rij and gij are the traffic distribution factor at intersection i to link (i, j) according to drivers’ previous experience and guider’s control strategy. kij is the actual traffic distribution factor at intersection i to link (i, j), di is the evacuation demand at node i. B. Dynamic Reassignment Optimization During an evacuation process, the traffic conditions keep changing, which might brings about changes for the set of the most crucial locations too. Thus it is necessary to make use of real-time traffic information and reassign evacuation guiders dynamically as the evacuation goes on. Different from most MDP problems, evacuation process is a transient state process with huge state space, during which we can hardly observe the same state twice or more. But with the help of simulation, we can estimate the performance of different actions online, making it practical to use simulationbased policy improvement methods to find an optimal policy. We use a simulation-base rollout method in this paper to optimize the dynamic reassignment for evacuation guiders. Let Q(s, a) denote the long-run performance of action a when the system is at state s. It can be defined as: Q(s, a) = E{g(X0 , A0 )+
(i,j)
(12)
p∈Γ−1 (i)
(9)
where d(y, x) denotes the length of the shortest path between node y and node x. Apart from centrality, static mathematical model can also be used here to find a solution. Inspired by the MINLP model proposed by Zhang et al. [11], we also propose a MINLP model below. 3) MINLP model The objective function is: minz = xij tij (10)
(11)
i∈N
kij = gij Ai + rij (1 − Ai ) kij = 1, ∀i ∈ N \NS
the objective function is minL J(L, S0 ).
CB (v) =
the model is subject to the following constraints: Ai = m
∞
g(Xl , Al )|X0 = s, A0 = a}
l=1
(18) Q(s, a) is evaluated by simulating the clearance time after action a is taken when the initial system state is s. We make sequential decisions every τ simulation time interval until the evacuation simulation ends. Let a∗t denote the optimal action at time t, it is defined as: a∗t = arg min {Q(St , a)}, a∈At
(19)
the kth decision can be obtained by xk = ak·τ . Finally the rollout method can find us an optimal policy (x1 , x2 , ..., xN ).
Note that the base policy is all the guiders stand still at every decision-making time. The simulation-based rollout method can be summarized as Algorithm 1. Algorithm 1 Simulation-based Rollout Method 1: Start evacuation simulation with initial system state 2: k = 1 3: for t = 1 : inf do 4: Run simulation 5: if t mod τ = 0 then 6: Pause simulation 7: for all a ∈ At do 8: Evaluate Q(St , a) 9: end for 10: a∗t = arg mina∈At {Q(St , a)} 11: xk = a∗t , continue simulation 12: k =k+1 13: end if 14: if all evacuees have arrived at safe area then 15: return Clearance time t 16: return Sequential decisions (x1 , ..., xk ) 17: end if 18: end for
Fig. 1.
Example traffic network
The simulation size is 60 seconds and the free-flow speed is set to be 60km/h, thus the length of each cell is 1km. The number of vehicles in each cell is updated at every simulation time interval and restricted to flow conservation equations. B. System Performance Curve
In this section, some numerical examples are presented to: (1)make comparisons on solving the initial location assignment optimization problem among three methodologies mentioned in part III.A (BC, CC and MINLP); (2)illustrate the application of simulation-based rollout method in finding an optimal dynamic reassignment policy for evacuation guiders. Assume that there is only one guider available, and we use 100 replications of simulation to estimate total clearance time under different situations. A. Description of Traffic Network and Simulation Framework The example traffic network, adopted and revised from Nguyen and Dupuis(1984) network[17], is shown in Fig.1. Many researchers have used this network in the past to demonstrate solution techniques to solve transportation related problems. The traffic network has 13 nodes and 20 links. The origins are nodes 1 and 4(grey), the destinations are nodes 2 and 3(green). To capture as many dynamics and stochastic features as possible without consuming too much computing time and resources, we develop a CTM-based simulation framework in which roads are converted into a set of connected cells. Each road has a capacity limit proportional to its length. We assume that all the evacuees take vehicles and make their own way to safe area based on their experiences or instructions unless they pass by an evacuation guider. Depending on the degree of panic, the evacuee listens to the guidance with probability when he/she encounter a guider.
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IV. NUMERICAL RESULTS
Cumulative evacuation curve is widely used to describe evacuation process. The x axis is time and the y axis is cumulative number of vehicles evacuated. Let’s denote system performance curve(SPC) as cumulative evacuation curve of a system without evacuation guider in it. The shapes of SPCs may vary with some factors, e.g. topology of traffic network and behavior of evacuees. But there are 4 basic shapes as shown in Fig. 2, with which complex curves can be formed. We name them early single peak, late single peak, double peak and fluent, respectively. We consider fluent as the most ideal shape.
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/DWH6LQJOH3HDN 7LPH
Fig. 2.
4 basic shapes of system performance curves
Through changing the population distribution and the distribution of evacuation instructions, we did some simulation experiments on example traffic network, during which 3 basic shapes are observed as shown in Fig 3,4,5. Note that the works below are based on early-single-peak curve and double-peak curve. C. Initial Location Assignment Optimization According to BC, CC and MINLP, it can be found that the most crucial nodes in the example network to allocate the guider are node 6, 10 and 12, respectively, as is shown in Table I. In the following subsections, two cases are presented to make comparisons among three methodologies.
Cumulative number of vehicles evacuated/vehicle
Cumulative number of vehicles evacuated/vehicle
But there is an interesting discovery that the top two assignments for the guider are node 8 and node 13, which both neighbor to a safe node. The clearance time is clipped by 147 and 142 minutes, respectively.
Time/min
Time/min
Late-single-peak
Fig. 4.
Double-peak
Cumulative number of vehicles evacuated/vehicle
Fig. 3.
Case 2 In this case, the shape of SPC is double-peak. We run simulations on both small-scale and large-scale, in which the total evacuation demand are set to be 800 and 3200 vehicles. The traffic control strategy for the guider is obtained through rollout algorithm. The simulation results are shown in Table III. TABLE III AVERAGE CLEARANCE TIME UNDER DIFFERENT SITUATIONS (II)
Time/min
Fig. 5.
Early-single-peak TABLE I
Initial location assignment
Average clearance time (800 vehicles)/min
Average clearance time (3200 vehicles)/min
No guider Node 6 Node 10 Node 12
180 130 161 171
472 468 421 430
I NITIAL LOCATION ASSIGNMENTS FOR THE GUIDER
BC CC MINLP
Node 6 Node 10 Node 12
Case 1 In this case, the shape of SPC is early-single-peak. The total evacuation demand is set to be 800 vehicles, and the traffic control strategy for the guider is: all the vehicles passing through him are guided to his neighbor node which is on the shortest path to safe nodes. We estimate the clearance time under 10 different situations, the results are shown in Table II. According to the results, betweenness centrality is the highest performing among three methodologies when deciding which node should the guider be assigned to, reducing the clearance time from 388min to 286min. TABLE II AVERAGE CLEARANCE TIME UNDER DIFFERENT SITUATIONS (I)
Initial location assignment
Average clearance time/min
Variance
No guider Node 5 Node 6 Node 7 Node 8 Node 9 Node 10 Node 11 Node 12 Node 13
388 349 286 299 241 262 336 273 380 246
10.1 9.7 9.2 9.2 7.2 8.4 8.7 7.6 8.6 7.2
When dealing with the small-scale evacuation, assigning the guider to node 6 based on BC is a practical method, bringing a 27.8% improvement compared to the situation where there is no guider. But when facing the large-scale evacuation, the results show little improvement of BC. To see exactly what happened during the large-scale evacuation process, we paint the cumulative evacuation curves when the guider is at node 6 on both small and large scale, as is shown in Fig 6. 800 vehicles
Time/min
Fig. 6.
3200 vehicles
Cumulative numbers of vehicles evacuated/vehicle
Selected Node
Cumulative numbers of vehicles evacuated/vehicle
Methodology
Time/min
Cumulative evacuation curves on small and large scale
Compared to the SPC (Fig 4), the guider at node 6 do help a lot in reducing traffic jam in both situations, and make the process smoothly on small scale. But when facing a large scale evacuation, the traffic congestion happens again soon, which is beyond the guider’s control, resulting in what is shown in Tab III. Nevertheless we can consider node 6 as the optimal initial location assignment for the guider, and what we are going to do is putting up with a dynamic location reassignment policy to deal with the second congestion, or even prevent it from happening. From what have been discussed above, we can draw the conclusion that it is practical to use betweenness centrality
when finding an optimal initial location assignment policy for evacuation guiders. Also, if the shape of SPC is earlysingle-peak, it can be an effective way to assign guiders to the nodes neighboring to safe nodes. D. Dynamic Reassignment Optimization Through the following two cases, we are going to show the necessity of changing guiders’ location dynamically during an evacuation process and to illustrate that our simulationbased rollout method performs well in dynamic location reassignment optimization. Case 3 In this case, the simulation conditions are as same as those in Case1. Based on BC, we choose node 6 as the initial location assignment for the guider, and the decision-making time interval is set to be 40 minutes. The simulation results are shown in Table IV. TABLE IV
Location of the guider
0 40 80 120 160 200 240
Node Node Node Node Node Node Node
TABLE V I MPROVEMENT ON CLEARANCE TIME Clearance time
Initial assignment
Dynamic reassignment No Yes
Node 8
Node 6
241 ± 7.2 241 ± 7.2
288 ± 9.2 248 ± 7.4
Case 4 In this case, the simulation conditions are as same as those in Case2. Based on BC, we choose node 6 as the initial location assignment for the guider, and the decision-making time interval is set to be 50 minutes. During a small-scale evacuation (800 vehicles), the dynamic location reassignment policy obtained by rollout method is shown in Table VI. Node 6 is a good enough guiding location under this circumstance, and there is no need for the guider to change location during the evacuation process.
DYNAMIC REASSIGNMENT FOR THE GUIDER (I)
Time/min
during the whole evacuation process), which performs best in case1. From what is shown in Table V, we learn that although node 6 is not the best initial location assignment policy for the guider, we can reduce the clearance time by reassigning his location dynamically and rollout method provide us a good enough solution to the dynamic location reassignment optimization problem. But it would be better to make the best assignment at first (node 8).
6 6 7 7 8 8 8
Compared to the situation without a guider (388 minutes) and the situation where the guider stands still at node 6 (286 minutes), the total clearance time is reduced to 248 minutes, which makes a remarkable improvement. The cumulative evacuation curves under these three situations are shown in Fig 7, in which the tail of SPC is considerably shorten by dynamic location reassignment.
TABLE VI DYNAMIC REASSIGNMENT FOR THE GUIDER (II)
Time/min 0 30 60 90 120
Location of the guider Node Node Node Node Node
6 6 6 6 6
800
Cumulative numbers of vehicles evacuated/vehicle
700
During a large-scale evacuation(3200 vehicles), the dynamic location reassignment policy is shown in Table VII. Compared to the situation without a guider (472minutes) and
600 500 400
TABLE VII DYNAMIC REASSIGNMENT FOR THE GUIDER (III)
300 200 No guider(SPC) Guider stands still at node 6 Guider change location dynamically
100 0 0
50
100
150
200
250
300
350
400
Time/min
Fig. 7.
Cumulative evacuation curves
By changing the initial location assignment for the guider and running simulations, we find that wherever the guider is assigned at first, he ends up standing at node 8 (if the initial location assignment is node 8, the guider stands still
Time/min
Location of the guider
0 50 100 150 200 250 300
Node 6 Node6 Node 6 Node 6 Node 6 Node 10 Node 10
the situation where the guider stands still at node 6 (468
minutes), the clearance time is reduced to 340 minutes, which makes a dramatic improvement. Two cumulative evacuation curves are painted below in Fig 8 to show what can dynamic location reassignment bring to the evacuation process. 3500
Cumulative numbers of vehicles evacuated/vehicle
3000
Guider moves to node 10 at the 250th minute
2500 2000 1500
and mixed integer nonlinear programming) that can be applied in solving the initial location assignment optimization problem. Third, we use a simulation-based rollout method for dynamic reassignment optimization problem. Forth, we demonstrate the performance of our methods by presenting some numerical results. The results show that betweenness centrality and rollout method propose effective solutions to these two problems. As for the future work, we will improve the rollout method to overcome its short-sighted feature. We hope this work brings insight on evacuation guider assignment optimization problems in general. R EFERENCES
1000 500
Guider stands still at node 6 Guider changes location dynamically
0 0
100
200
300
400
500
Time/min
Fig. 8.
Cumulative evacuation curves on large scale
As is shown in the blue curve, a second congestion happens again soon and is beyond the guider’s control. If we reassign the guider’s location every 50 minutes, as we can learn from the orange curve, the assignment at the 250th minute that changes the guider’s location to node 10 prevent the second congestion from happening, making the evacuation process smoothly. By changing the evacuation demand and repeating the simulation experiments, we find that there is no need to reassign guiders’ location during a small-scale evacuation and during a large-scale evacuation, we can obtain an optimal policy based on rollout method which brings considerable improvement compared to base policy. The larger the scale of the evacuation is, the greater the improvement of total clearance time is. The results are shown in Table VIII. TABLE VIII P ERFORMANCE OF ROLLOUT ALGORITHM
Evacuation demand
Clearance time (base policy)/min
Clearance time (optimal policy)/min
Improvement/%
800 1000 1500 2000 2500 3200
130 151 212 344 397 468
131 151 210 302 319 340
0 0 0.9 12.2 19.6 27.4
V. CONCLUSIONS In this paper, we consider both the initial location assignment and dynamic reassignment optimization problems for urban evacuation guiders and make the following major contributions. First, we propose a mathematical model using MDP method to formulate the location assignment optimization problem and construct a simulation framework based on CTM. Second, we make comparative studies on three methods (betweenness centrality, closeness centrality
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