Bottlenecks and Congestion in Evacuation Scenarios: AMicroscopic Evacuation Simulation for Large-Scale

Disasters

Gregor LämmelTransport Systems Planning

and Transport Telematics(VSP)

TU Berlin, Salzufer 17-19,Sekr. SG 12, 10587 Berlin,

Germanylaemmel@vsp.tu-

berlin.de

Marcel RieserTransport Systems Planning

and Transport Telematics(VSP)

TU Berlin, Salzufer 17-19,Sekr. SG 12, 10587 Berlin,

Germanyand

Institute for Transport Planningand Systems (IVT)

ETH Zurich, 8093 Zurich,Switzerland

rieser@vsp.tu-berlin.de

Kai NagelTransport Systems Planning

and Transport Telematics(VSP)

TU Berlin, Salzufer 17-19,Sekr. SG 12, 10587 Berlin,

Germanynagel@vsp.tu-berlin.de

ABSTRACTMulti Agent Simulation has increasingly been used for trans-portation simulation in recent years. With current tech-niques, it is possible to simulate systems consisting of severalmillion agents. Such Multi Agent Simulations have been ap-plied to transportation simulation for whole cities and evenlarge regions. In this paper we demonstrate how to adapt anexisting multi agent transportation simulation framework tolarge-scale pedestrian evacuation simulation. The underly-ing �ow model simulates the tra�c based on a simple queuemodel where only free speed and bottleneck capacities aretaken into account. The queue simulation, albeit simple,captures the most important aspects of evacuations such asthe congestion e�ects of bottlenecks and the time needed toevacuate the endangered area. During the simulation, eachevacuee optimizes his/her personal evacuation route to �ndthe fastest escape route. At this point two di�erent routingsolutions are considered:An �empty network� routing solution, where every evacueefollows the path that would be fastest in an empty network.A �Nash equilibrium� approach, where, via iterations everyevacuating person attempts to �nd a route that is optimalfor him/herself under the given circumstances.Both approaches can be considered as benchmarks: the �rstas one where congestion e�ects are not taken into accountin the path choice; the second one as one which might beachieved by appropriate training or guidance while main-taining acceptability in the sense that no person could gainby deviating from this solution. The results from the simu-lation give an estimate of the time it could take to evacuatethe endangered area. We applied the system to a hypothet-ical scenario, namely a dam-break of the Sihlsee dam near

Cite as: Title, Author(s), Proc. of 7th Int. Conf. on Au-tonomous Agents and Multiagent Systems (AAMAS 2008),Padgham, Parkes, Müller and Parsons (eds.), May, 12-16., 2008, Estoril,Portugal, pp. XXX-XXX.Copyright© 2008, International Foundation for Autonomous Agents andMultiagent Systems (www.ifaamas.org). All rights reserved.

Zurich, which would lead to an inundation of large parts ofthe city of Zurich within two hours. We show how well bothapproaches perform with respect to evacuation time and theout�ow rate of evacuees. It is planned to eventually applythe system to the Indonesian city of Padang. The criticalquestion is under which conditions the warning time beforethe arrival of a Tsunami wave will be su�cient to evacuateup to a million people.

Keywordsmulti agent simulation, large-scale evacuation simulation

1. INTRODUCTIONThe evacuation of whole cities or even regions is an im-

portant problem, as demonstrated by recent events such asevacuation of Houston in the case of Hurricane Rita or theevacuation of coastal cities in the case of Tsunamis. A ro-bust and �exible simulation framework for such large-scaledisasters helps to predict the evacuation process. Further-more, it is possible to recognize bottlenecks in advance, sothat an elimination of those bottlenecks is possible. Thisshould lead to a better preparedness for an event of evac-uation for cities or regions that face a high risk of naturaldisasters.

2. RELATED WORKDisaster and evacuation planning has become an impor-

tant topic in science and politics. In principle there are twodi�erent situations: evacuation of buildings, ships and air-planes or the like on the one hand, or evacuation of wholecities or even regions on the other hand. The former involvesnormally the evacuation of pedestrians, where the latter israther associated with the evacuation by car.In the area of pedestrian evacuation simulation, there has

been done considerable research in the last 20 years. A goodoverview about models and software for pedestrian evacua-tion simulation can be found in the proceedings of the con-

ference �Pedestrian and Evacuation Dynamics� [32, 10, 11].Corresponding to the two di�erent types of problems, thereare two di�erent basic approaches for simulating the tra�c�ow:(1) Methods of dynamic tra�c assignment (DTA) have

been applied to evacuation simulation on the city or regionalscale. Some examples are: MITSIM [18], Dynasmart [20] orVISSIM [15]. The DTA approach is based on the analogybetween tra�c and hydrodynamic characteristics of �uids.That means DTA is a macroscopic approach and reducesthe problem of evacuation dynamics to a well known phys-ical problem. On state of the art hardware it is possibleto handle even large-scale scenarios with this approach. �However, in DTA it is not straight forward to deal withthe inhomogeneity of a population. For this, a microscopicsimulation is needed, where all people are simulated as in-dividuals.(2) Microscopic simulations are often based on Cellular

Automata (CA) [26, 27, 17]. In CA models each evacueeis designed as an individual therefore it would be possi-ble to simulate also complex population structures wherepeople have di�erent speeds, ranges and especially complexbehavior. The modeling of a complex behavior in evacua-tion simulation has become important in recent years. Peo-ple could for example ignore warnings or might not choosethe nearest emergency exit, furthermore people tend to fol-low others (herd behavior) [16, 21]. Agent oriented researchgroups have modelled such behavior [25, 28]. In general it isexpected that complex behavior leads to longer evacuationtimes, consequently a simulation that ignores such behaviorpatterns is probably optimistic.It is planned to apply this evacuation simulation to the

city of Padang at the west coast of Sumatra. In case of aTsunami evacuation hundreds of thousands people could bea�ected. A standard CA-based approach is not applicablehere: The area of approx. 7km × 32km would need about109 cells, leading to rather long computing times. In con-trast, a DTA approach, as pointed out earlier, is not able tohandle complex individual behavior. One possible approachto deal with such large-scale scenarios but to retain per-sons as individual agents is based up on a modi�ed queuingmodel [12, 33]. The queuing model simpli�es streets to edgesand crossings to nodes; the di�erence to standard queue-ing theory is that agents (particles) are not dropped butspill back, causing congestion. This graph-oriented model isde�ned by lengths/widths, free speed and �ow capacity ofthe edges. This simpli�cation leads to a major speedup ofthe simulation while keeping results realistic. For example,the simulation of the whole (motor) tra�c of Switzerland(approx. 5 million trips) takes less then 5 minutes for 24hreal time [30]. In this work the adaptation of the existingmulti agent transportation simulation framework to large-scale pedestrian evacuation simulation is described.

3. MULTI AGENT SIMULATIONOur simulation is constructed around the notion of agents

that make independent decisions about their actions. Inthis case study, each evacuee is modeled as an individualagent in our simulation. In the simulation the agents tryto �nd the best (in terms of time) escape route, wherebythe real world is modeled as a network constructed of nodes(intersections) and links (roadway between intersections).The overall approach consists of three important pieces:

• Each agent independently generates a so-called planwhich encodes its intended escape route.

• All agents' plans are simultaneously executed in thesimulation of the physical system. This is also calledthe tra�c �ow simulation or mobility simulation.

• There is a mechanism that allows agents to learn. Inour implementation, the system iterates between plansgeneration and tra�c �ow simulation (i.e. system-atic relaxation [19, 5]). The system remembers severalplans per agent, and scores the performance of eachplan. Agents normally chose the plan with the high-est score, sometimes re-evaluate plans with bad scores,and sometimes obtain new plans. Further details willbe given below.

The simulation approach is the same as in many of ourprevious papers (e.g. [31, 4]) on the same subject. Theresults of this paper are based on a re-implementation ofthe MATSim framework in Java [23]. Since not all elementsof MATSim are important for an evacuation simulation, thefollowing exposition is a shortened and simpli�ed descriptionof key elements.A plan contains the itinerary of activities the agent wants

to perform during the day, plus the intervening trip legs theagent must take to travel between activities. An agent'splan details the order, type, location, duration and othertime constraints of each activity, and the mode, route andexpected departure and travel times of each leg. This paperconcentrates on �home� and �evacuated� as the only activi-ties, and �walk� as the only mode.A plan can be modi�ed by the router module: The

router is implemented as a time-dependent Dijkstra algo-rithm. It calculates link travel times from the output of thetra�c �ow simulation. The link travel times are encoded invariable-sized time bins, so they can be used as the time-dependent weights of the links in the network graph.The tra�c �ow simulation executes all agents' plans

simultaneously on the network, and provides output describ-ing what happened to each individual agent during the exe-cution of its plan. The tra�c �ow simulation is implementedas a queue simulation, which means that each street (link)is represented as a FIFO (�rst-in �rst-out) queue with tworestrictions [13, 6]. First, each agent has to remain for a cer-tain time on the link, corresponding to the free speed traveltime. Second, a link storage capacity is de�ned which limitsthe number of agents on the link. If it is �lled up, no moreagents can enter this link.The outcome of the tra�c �ow simulation (e.g. conges-

tion) depends on the planning decisions made by the decision-making modules (in this case, the router). However, thosemodules can base their decisions on the output of the tra�c�ow simulation (e.g. knowledge of congestion) using feed-back from the multi-agent simulation structure [19, 5]. Thissets up an iteration cycle which runs the tra�c �ow simula-tion with speci�c plans for the agents, then uses the planningmodules to update the plans, these changed plans are againfed into the tra�c �ow simulation, etc., until consistencybetween modules is reached.The feedback cycle is controlled by the agent database,

which also keeps track of multiple plans generated by eachagent, allowing agents to reuse those plans at will. The repe-tition of the iteration cycle coupled with the agent database

Figure 1: Inundation map provided by the Zurichcivil defense o�ce

enables the agents to learn how to improve their plans overmany iterations. This circle continues until the system hasreached a relaxed state. At this point, there is no quantita-tive measure of when the system is �relaxed�; we just allowthe cycle to continue until the outcome seems stable.In order to compare plans, it is necessary to assign a quan-

titative score to the performance of each plan. In principle,arbitrary scoring schemes can be used (e.g. prospect theory[3]). In this work the agents are only interested in minimiz-ing their individual evacuation time. That's why the utilityof a plan is determined by the negative of the time neededto reach the save area.

3.1 Scenario SetupIn this approach a hypothetical event of a dam-break of

the Sihlsee dam was chosen. This would lead to an inunda-tion of large parts of the city of Zurich. According to thecivil defense o�ce there will be an advance warning time ofabout 110 minutes until the inundation will reach the citycenter. The civil defense o�ce also provides an instructionsheet [2] with an inundation map of the area at risk (shownin �gure 1).

3.2 Data BasisThere are two main inputs that have to be provided to

the simulation framework. At �rst the simulation needs anetwork. We extracted the evacuation network by project-ing the inundation map from the civil defense o�ce onto thenetwork of Switzerland provided by NAVTEQ1. The origi-nal NAVTEQ network of Switzerland consists of about 400knodes and 880k links. After cropping, the resulting networkconsist of 3037 nodes and 6120 links. It is shown in �gure 2.The other important input to the simulation framework

1NAVTEQ is a provider of digital maps for in-vehicle navi-gation systems (see also http://www.navteq.com/)

Figure 2: Emtpy evacuation network

is a so-called �plans �le�, containing information about peo-ple and their plans, including home and work locations. Asynthetic population for the area of Zurich was generatedby [24] and provided to us. The population was generatedusing data from the Swiss census for the year 2000 [14] andinformation about facilities in the city center. Every per-son in this synthetic population obtains one complete dayplan, describing all activities the person performs during aday. The �rst work location appearing in a plan of eachagent was extracted to build the agents' initial locations forthe evacuation. In the end, there were 165571 agents with awork activity within the endangered area. This set of agentsand locations builds our start setup for the evacuation; thismeans we will simulate a break of the Sihlsee dam duringregular working hours.

3.3 Calibration of the Queuing ModelSince the underlying simulation framework is mainly de-

signed for the simulation of motorized transportation, sev-eral adaptations are necessary. At �rst it is obvious thatthe evacuees do not care about the opposite carriageway.So we allowed all links in the street network to be used inboth directions. This will lead to correct results as long asno oncoming tra�c occurs � which is not expected duringan evacuation. Given the link length, the queuing model isdescribed be three parameters for each link. The parame-ters are: �ow capacity, storage capacity and free �owspeed. These parameters had to be calibrated to achieve anappropriate �ow dynamic for pedestrians. In literature the�ow dynamic of pedestrians is often described by fundamen-tal diagrams [34, 29]. These diagrams show the velocity asa function of the density of pedestrians. Weidmann pointedout that the relation between density and velocity is ade-quate captured by the so-called Kladek-formula [34]:

vF,hi = vF,hf × [1− e−γ×( 1

D− 1

Dmax)]

Figure 3: Weidmann's fundamental diagram com-pared to queuing model

With:

• vF,hi the velocity at a particular density [m/s],

• vF,hf the velocity at free �ow [m/s],

• γ a free parameter [persons/m2],

• D the actual density [persons/m2] and

• Dmax the density at which no �ow disrupt [persons/m2].

Empirical studies showed the best results with γ = 1.913persons/m2, vF,hf = 1.34 m/s and Dmax = 5.4 person/m2.Our queueing model, however, generates a speed-density

relationship of the form v = min[vmax, 1/D] [33]. Thereforea complete agreement is not possible. However, as shown in�gure 3, the �ow dynamic produced by our queue model isnot too far away from Weidmanns's fundamental diagram.The details of the calibration are explained in the followingparagraphs.As the above mentioned NAVTEQ network is designed for

transport simulation, we had to adjust the networks param-eters accordingly. In the original network �le, there is onlyinformation about number of lanes but not the width of thestreet, so we had to estimate it. According to the hand-book Strassenprojektierung [7] the lane width on streets inSwitzerland has to be 2.20-3.00 m for automobiles and 3.10-3.90 m for trucks. Taking this information, we set the widthof all lanes in the network to 3.50 m. For pedestrian evac-uation the �ow capacity is assigned in persons per meterper second, but it depends on the actual density of persons.According to Weidmann [34] the maximum �ow capacity isabout 1.3 persons/(m·s) on a density of 2 persons/m2. TheSFPE Handbook of Fire Protection Engineering [9] supportsthese values. Together with the lane width we got the �owcapacity of 4.55 persons/(lane · s).Another parameter for the queue simulation is the storage

capacity of the links. Not to contradict the �ow rate in Wei-dmann's fundamental diagram we set the storage capacityto 2 persons/m2.The free �ow speed was set to 1.666m/s. This value is

slightly higher then the 1.34m/s recommended in literature,but the values presented by Weidmann re�ect the pedestrian�ow under normal conditions and not in a case of emergency.Before we can apply this approach to �real world� scenarios

Figure 4: Sketch of the modi�ed evacuation network

we have to verify all parameters and check if they are real-istic.Overall, there are 101 links that lead out of the evacuation

area. Most of them have one or two lanes. The aggregatedcapacity of all these �escape links� is 787.15 persons/s. How-ever, this capacity is a theoretical value since it is unlikelythat the evacuees will �nd a way to distribute themselvesin such a smooth way over the network. Rather it is ex-pected that this out�ow rate has a much lower value at theinitial iteration, where all evacuees proceed on the assump-tion that the network is empty and there is free speed on alllinks. With the optimization of the evacuation procedurethe out�ow rate is expected to increase as the evacuees willmake better use of all roads.

3.4 Initial RoutingInitial plans use the shortest path (according to free speed

travel time) out of the evacuation area for all agents. Withinthe MATSim framework a shortest path router based onDijkstra's shortest path algorithm [8] has been implemented.This router �nds the shortest path in a weighted graph fromone node to any other, whereby the actual weights for a linkare de�ned by a time-dependent cost function. Since wewant to evacuate the city as fast as possible, the weightsrepresents the (expected) travel time2.There is, however, no particular node as the target of the

shortest path calculation, as the evacuees have more thanone safe place to run to. Instead, in the underlying domainevery node outside the evacuation area is a possible desti-nation for an agent that is looking for an escape route. Toresolve this, the standard approach (e.g. [22]) is to extendthe network in the following way: All links which lead out ofthe evacuation area are connected, using virtual links within�nite �ow capacity and zero length, to a special �evacu-ation node� (see �gure 4). Doing so, Dijkstra's algorithm

2For the initial evacuation plans the expected travel time isdetermined by free travel speed.

Figure 5: Evacuation time vs. iteration number

will always �nd the shortest route from any node inside theevacuation area to this evacuation node.

3.5 Re-Planning and LearningAt the end of each iteration, every agent scores the per-

formed plan. In this study the scoring function is simplythe negative of the travel time. After an agent has updatedthe score of its actual plan, it will be selected with a proba-bility of 10% for re-routing. The replanning probability is acon�gurable parameter; 10% is a good compromise betweentoo slow convergence and over-reaction of the system. In there-routing procedure the Dijkstra router is again applied to�nd the fastest escape route for the particular agent. Theonly di�erence to the initial routing is that the weights forthe links are no longer based on free speed travel times buton the experienced travel times from the last iteration. It isobvious that the travel time on a link varies with the time-of-day within one iteration. Therefore the travel times ofall links are recorded and averaged into bins. The size ofthese bins is con�gurable; for the present study, a size of15 mins was used. If no tra�c for a particular time bin andlink occurs, free speed travel time is assumed for this timebin and link. For agents that have not been chosen for re-planning the plan with the highest scores (i.e. the plan withthe fastest escape route) will be selected for the next itera-tion. Indeed, the score of such a former performed plan willnot necessarily be consistent with the actual status of thesystem. So, plans can perform worse even if they got a highscore in former iterations. However, this is not a problemsince those plans will get a low score after the next iterationand then the probability for being chosen decreases. Re-peating this iteration cycle successively, the agent behaviorwill move towards a Nash equilibrium.

4. RESULTSThe simulation run was performed on a dual core CPU

at 2.33 GHz with 2 GB of RAM. The computer runs JAVAjdk1.5_012 on Linux. The evacuation simulation has beenstopped after 100 re-planning cycles. The average runtimefor an iteration was 123 seconds and the overall runtime was3 hours and 24 minutes. The simulation consumed up to1393MB of RAM. Besides the evacuation time, the out�owrate of the evacuation area has been recorded, too. As ex-pected, the evacuation time decreases signi�cantly with theiterations. Especially within the early iterations, it drops

Figure 6: Evacuation progress

Iteration max mean median

0 127 22.98 51 129 24.32 55 139 34.78 1010 139 50.26 46100 148 59.94 68

Table 1: Statistics of the out�ow rate (persons/s)

very fast. A diagram that represents this process is shownin �gure 5. The evacuation takes 7205 seconds at the initialiteration. Beginning with iteration 15 there are only smallchanges and it �uctuates randomly around 2676 seconds.These values show only how long the overall evacuation

takes but it tells nothing about the evacuation process itself.Therefore we evaluated the evacuation process for iteration0, 1, 5, 10 and 100 in detail. Figure 6 shows the results.The initial iteration results in a steep gradient (high out-

�ow) at the beginning but it �attens very fast. As the it-erations progress the initial gradient gets even steeper andbecomes more linear.Some statistics of the out�ow of evacuees for the discussed

iterations are given in table 1. Overall the results are asexpected. Nevertheless, there are some interesting details.One interesting aspect is the low value for the median ofthe initial or 5th iteration. A possible reason for this phe-nomenon is that many agents try to perform the same escaperoute. If this happens they will line up in a few long queues,which will result in a low constant out�ow rate.The comparison of the snapshots for iteration 0 and 100

in �gure 7 supports this hypothesis. Both snapshots weretaken after 30 minutes of evacuation. The escape directionsare indicated by black arrows. In iteration 0 there are con-siderably more evacuees at this point then in iteration 100.In the latter, the agents take advantage of six evacuationpoints (indicated by the red circles). This is much more ef-fective then the behavior in the initial iteration, where onlyfour evacuation points are used. Bottlenecks can also be de-tected. Figure 8 depicts this issue. In this �gure the links arecolored dependent on congestions. A green color indicatesthat the agents travel with free �ow speed and as the colormoves to red the �ow speed decreases. That these conges-tions emerge at bridges is not surprising, but the snapshot istaken after 100 iterations of learning and that means: there

Figure 7: Comparison of two snapshots

seems to be no better solution for the individual agent thento queue up on these bridges.3

5. CONCLUSIONSWe introduced a microscopic pedestrian simulation frame-

work for large-scale evacuations. It is implemented as aMulti Agent Simulation, where every agent tries to opti-mize its individual evacuation plan in an iterative way. Thesimulation framework is demonstrated through a case studybased on a hypothetical dam-break of the Sihlsee dam nearZurich. The runtime performance shows that this approachis well suited for large scale scenarios. With state of the arthardware it should be no problem to simulate much largerscenarios with over one million agents. Despite of the un-derlying behavioral model being quite simple the simula-tion gives plausible results regarding the predicted evacua-tion time and bottlenecks. Besides applying the simulationframework to larger scenarios, the improvement of the be-havioral model will be the topic on future work.

6. ACKNOWLEDGMENTSThis project was funded in part by the German Ministry

for Education and Research (BMBF), under grant number03G0666E ("last mile").

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