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Keywords:

  • pedestrian dynamics;
  • real-time simulation;
  • evacuation;
  • cellular automata;
  • continuous models

ABSTRACT

  1. Top of page
  2. ABSTRACT
  3. 1 INTRODUCTION
  4. 2 MODELING AND SIMULATION
  5. 3 RUNTIME OPTIMIZATION
  6. 4 RESULTS
  7. 5 CONCLUSION
  8. ACKNOWLEDGEMENTS
  9. REFERENCES
  10. Biographies

To improve safety at mass events, an evacuation assistant that supports security services in case of emergencies is developed. One central aspect is forecasting the emergency egress of large crowds in complex buildings. This requires realistic models of pedestrian dynamics that can be simulated faster than real-time by using methods applied in high performance computing. We give an overview of the project and present the actual results. We also describe the modeling approaches used thereby focusing on the runtime optimization and parallelization concepts. Copyright © 2012 John Wiley & Sons, Ltd.

1 INTRODUCTION

  1. Top of page
  2. ABSTRACT
  3. 1 INTRODUCTION
  4. 2 MODELING AND SIMULATION
  5. 3 RUNTIME OPTIMIZATION
  6. 4 RESULTS
  7. 5 CONCLUSION
  8. ACKNOWLEDGEMENTS
  9. REFERENCES
  10. Biographies

Multifunctional buildings in combination with a wide range of large-scale public events present new challenges for the quality of security concepts [1]. Previous works have demonstrated simulations in this context [2-8]. Prescriptive construction and planning regulations ensure, in general, that in case of an emergency, everyone present is able to quickly leave the danger zone by specifying, for example, minimal width and maximal length of escape routes. In the event of loss of rescue routes because of fire or other risks, however, dangerously high crowd densities and bottlenecks can occur. To prevent such critical situations, optimal crowd management needs accurate and up-to-date information about the current status. Usually in complex buildings, the decision makers miss information, for example, the number of people in the danger zone. They are often confronted with imponderabilities such as where dangerous congestions with long waiting times will occur in the course of the evacuation or how the loss of escape routes influences the evacuation time. The evacuation assistant, developed within the Hermes project [9] and outlined in this contribution, will close this gap and support the decision makers to rate the actual danger, to decide on a successful evacuation strategy, and to optimally employ the security staff. The project is funded by the German Government (Federal Ministry of Education and Research), and its goal is the development of an evacuation assistant for mass events. The ESPRIT arena in Düsseldorf (Germany) provides a venue for testing the evacuation assistant. The example of this multifunctional arena with a capacity of 60 000 spectators will show how crowds of people at big events can be guided also considering the current risk situation. The evacuation assistant has been tested in the mentioned facility in the period from April to November 2011.

Figure 1 shows the functional layout of the evacuation assistant. With the use of automated counting of persons at entrances and doors, the present distribution of people in the building is delivered to the decision makers and the simulation cores. The safety and security management system provides information about escape routes blocked because of smoke, locked doors, or other dangers. With the use of the actual data about the distribution of people and the availability of rescue routes, a parallel computer generates faster than real-time simulations to predict the movement of all people during the next 15 minutes and updates it at 1-minute intervals. The simulations can be performed using either a cellular automata (CA) or a force-based model. Both models have different requirements regarding the geometry and the simulation step size for instance. They have been successfully integrated as simulation cores in the evacuation assistant. The simulation results include, for example, potential dangerous congestion areas or evacuation times. Moreover, a macroscopic network model is used to calculate the optimal distribution of occupants on the available routes. A communication module provides this information to the emergency teams on site. Various universities, industrial partners, and users cooperate in this project. For an overview, we refer to [10, 9].

image

Figure 1. Schematic diagram of the evacuation assistant.

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The basic structure of the evacuation assistant in action is shown schematically in Figure 2. Different types of information are actually displayed, for instance, real-time information such as the spatial distribution of the pedestrians as well as the states of the different doors and areas. The simulation results are shown using different level of services (LOS) [11]. LOS is a measure used in traffic to determine the effectiveness of elements of transportation infrastructure, for instance, pathways. The LOS of the areas are displayed in three colors: red, yellow, and green. Red stands for high density and green for low density.

image

Figure 2. The evacuation assistant showing the results of a simulation. The congestion areas are displayed.

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The organization of this paper is as follows. The two modeling approaches used in the evacuation assistant are described in Section 2. Runtime optimization methods are discussed in Section 3. An analysis of the runtime results is presented in Section 4. Concluding remarks are given in Section 5.

2 MODELING AND SIMULATION

  1. Top of page
  2. ABSTRACT
  3. 1 INTRODUCTION
  4. 2 MODELING AND SIMULATION
  5. 3 RUNTIME OPTIMIZATION
  6. 4 RESULTS
  7. 5 CONCLUSION
  8. ACKNOWLEDGEMENTS
  9. REFERENCES
  10. Biographies

The models for pedestrian dynamics fall into two main categories: microscopic and macroscopic models. Microscopic models can further be categorized into CA, force-based models, rule-based models, agent-based models, and hybrid models. For further details, we refer to [12] where different extensions of CA are presented. More details about the advantages and drawbacks of the different models can be found in [13]. For other various pedestrian-modeling techniques and specially behavioral agent-based models, we refer to [14] and the references therein.

In the evacuation assistant, different modeling strategies are combined to obtain reliable predictions from the simulations and achieve an optimal performance. One approach uses CA, and the other is a spatially continuous force-based model. Both approaches have advantages and drawbacks, and we refer to [13] for a deeper discussion. A crucial point in the application of these models to security sensitive tasks within the Hermes project is their quantitative verification and calibration. Regarding the reliability of forecasts based on simulations of these models, we are still at the beginning, see for example [15]. This lack is because of the contradictory experimental database for model testing [13] and an open discussion about the principles of validation and calibration, see Section 2.1 in [16]. In the following, we introduce the basics of the modeling approaches applied in the Hermes project.

2.1 Cellular Automata

In CA, space, time, and state variables are discrete. One of their attractive properties is that they allow for an intuitive definition of the dynamics in terms of simple rules. In CA models of pedestrian dynamics, the space is discretized into small cells that can be occupied by at most one pedestrian (exclusion principle). The cell size corresponds to the space requirement of a person in a dense crowd. A typical density of 6  persons∕m2 then yields to a cell size of 40 × 40cm2. Time is also discrete, and the pedestrians move synchronously in each time step, which is then identified with the reaction time of a pedestrian. Thus, one time step corresponds to a few tenths of a second in real time.

Most models represent pedestrians by particles without any internal degrees of freedom. Models that yield realistic pedestrian behavior are usually based on stochastic rules. Particles move to one of the neighboring cells with transition probabilities that are determined by three factors: (i) the desired direction of motion (e.g., given by origin and destination); (ii) interactions with other pedestrians; and (iii) interactions with the infrastructure (walls, doors, etc.). In the simplest models, the latter two factors are only taken into account through an exclusion principle, that is, occupied or wall cells are not accessible. More sophisticated approaches such as the floor field model try to model these interactions in more detail that leads to more realistic results, especially for collective effects and self-organization phenomena [16].

Figure 3 illustrates the definition of the transition probabilities pij for a particle representing a pedestrian located at (0,0) to one of the neighbor cells (including the current position). Here, sometimes, diagonal steps are also allowed.

image

Figure 3. Definition of the transition probabilitiespij for a particle.

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One of the most popular models used in pedestrian dynamics is the floor field model developed in [17-20]. Its dynamics, that is, the choice of the transition probabilities pij, takes inspiration from nature, especially the process of chemotaxis used by ants [21] for communication. This allows translating the effects of longer-ranged interactions into purely local ones by introducing a kind of memory.

The transition probabilities are determined by the three contributions (i)–(iii) mentioned earlier. The contributions (ii) and (iii) are incorporated via floor fields. These act like virtual chemotaxis by enhancing transitions in the direction of stronger fields. Mainly, the transition probabilities are determined by the preferred walking direction of the pedestrians. This information is encoded in the so-called matrix of preference. Its matrix elements Mij are directly related to observable quantities, namely the average velocity and its fluctuations [17].

The probabilities are modified by the interaction with two discrete floor fields, D and S. The field strengths Dij and Sij at site (i,j) are interpreted as the numbers of D and S-particles present at that site (Dij, Sij = 0,1,2, … ). D and S modify the transition probabilities in such a way that a movement in the direction of higher fields is preferred. The dynamic floor field D represents a virtual trace left by moving pedestrians. The virtual trace may be interpreted as representation of the path of others in the mind of a pedestrian. Similar to the process of chemotaxis, this trace has its own dynamics (diffusion and decay). Two parameters α ∈ [0,1] and δ ∈ [0,1] control the broadening and dilution of the trace. Every moving pedestrian creates a D-particle at its origin cell. The static floor field does not change in time. It reflects the surrounding infrastructure. In the case of the evacuation processes, the static floor field describes the shortest distance to an exit door. It is calculated for each lattice site by using some distance metric. The field value increases in the direction of the exit such that it is the largest for door cells. The static floor field can even be used to incorporate the information usually contained in the matrix of preference.

Then, for each pedestrian, the transition probabilities pij for a move to a neighbor cell (i,j) (see Figure 3) are given by

  • display math(1)

The relative influence of the fields D and S is controlled by sensitivity parameters kS and kD, which are nonnegative. The occupation number is nij = 0 for an empty cell and nij = 1 for an occupied cell where the occupation number of the cell currently occupied by the considered particle is taken to be n00 = 0. The obstacle number is ζij = 0 for forbidden cells, for example, walls, and ζij = 1 otherwise, and the factor N ensures the normalization inline image of the probabilities. A more detailed description of the update rules can be found in [17, 19].

In contrast to most force-based models that are based on repulsive forces, the floor field model is characterized by attractive interactions. However, this is an interaction between a density and the velocity field created by the other pedestrians. In contrast, the force-based models usually have a repulsive density–density interaction that reflects the private sphere of each persons. This is also included in the floor field model in a short-ranged form through the exclusion principle.

The floor field model has been applied to various situations. It is not only able to reproduce collective effects such as lane formation or oscillations at bottlenecks [17, 20] but also gives realistic results for evacuation scenarios [17, 18, 22]. The realism of the floor field model can further be improved by taking into account various modifications [12], for example, transitions beyond nearest neighbors [23], friction effects [18], or smaller cells [23]. There are other extensions of the floor field model where repulsive forces between the pedestrians are introduced. These are, for instance, models using proxemic floor field [24] or vector-based particle field [25].

2.2 Generalized Centrifugal Force Model

The generalized centrifugal force model (GCFM) [26] is a spatially continuous force-based model. It expresses mathematically the idea that the movement of pedestrians can be understood in terms of fields or forces [27-29]. The acceleration inline image of a pedestrian i results from the superposition of forces acting on him or her at a certain moment. In analogy to Newtonian mechanics, the dynamics of pedestrian i is determined by the equation of motion

  • display math(2)

where inline image is the driving force of pedestrian i to move towards a desired destination, inline image is the repulsive force emerging from pedestrian j to i, and inline image is the force between the pedestrian i and walls or other stationary obstacles. The sets inline image and inline image are, respectively, the sets of all pedestrians and walls that influence pedestrian i at a given moment. In the next section, we discuss methods to define inline image and inline image for each pedestrian i.

The driving force is defined by

  • display math(3)

with the desired velocity of pedestrian i, the current velocity, and τ a time constant. The repulsive force is given by

  • display math(4)

where

  • display math(5)

and

  • display math(6)

inline image is the distance between the intersection points of the line joining the centers of i and j and the borders of the ellipses, see Figure 4 (left).

image

Figure 4. The repulsive force acting on the center of the ellipse-representing pedestrian i (left). Interpolation of the repulsive force between pedestrians i and j with respect to their distance (right). The constants inline image,Reps, and s0 are interpolation specific parameters.

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vij is the projection of the relative velocity of pedestrians i and j onto the direction of the vector connecting their centers, see Figure 4 (left). inline image is the distance between pedestrians i and j. The polar radius of pedestrian i is denoted by ri. The coefficient kij reduces the action field of the repulsive force to 180° in the direction of movement. Pedestrians are modeled as ellipses with velocity-dependent semi-axes. This is motivated by the observation that, on the one hand, faster pedestrians require more space in their walking directory than slower pedestrians. On the other hand, slower pedestrians sway laterally stronger than faster pedestrians. This model is based on modifications of the centrifugal force model introduced in [30]. Further details are given in [26, 31]. The strength of the repulsive force decreases with increasing distance between two pedestrians. Nevertheless, the range of the repulsive force is infinite. This is unrealistic for interactions between pedestrians. Therefore, we introduce a cutoff radius Rc for the force limiting the interactions to adjacent pedestrians solely. To guarantee robust numerical integration, a two-sided Hermite interpolation of the repulsive force is implemented. The interpolation guarantees that the norm of the repulsive force decreases smoothly to zero for inline image . For R[RIGHTWARDS ARROW] 0 + , the interpolation avoids an increase of the force to infinity, see Figure 4 (right). The limitation of the range of the force to Rc is important for the runtime optimization by means of neighbor list methods discussed in the next section.

The initial value problem (see Equation (2)) was solved using a Euler scheme with fixed-step size Δt. To make a compromise between stability and run time, we choose Δt = 0.01 second. The desired speeds of pedestrians are Gaussian distributed with mean μ = 1.34m∕s and standard deviation σ = 0.26m∕s. Other parameter specifications and numerical details can be found in [26].

By proceeding in three steps, we validate systematically the GCFM. The following setups are simulated:

  1. One single movement (close boundary): In this scenario, pedestrians move in a corridor without overtaking. The fundamental diagram is measured and compared with empirical data.
  2. Movement in wide corridors (close boundary): In this scenario, pedestrians are allowed to move in both directions. Here, again, we measure the fundamental diagram.
  3. Bottleneck: Pedestrians move through a bottleneck by varying its width. We measure the flow and compare its values with empirical data.

Figure 5 shows the fundamental diagram in one dimension in comparison with experimental data [32]. In the second phase, the fundamental diagram in corridors of a length of 20 m and different widths is measured. The shape of the resulting velocity density relation is in good agreement with the empirical data [33-36], see Figure 6 (left). Furthermore, the flow of pedestrians through a bottleneck as described in [37] was simulated and compared with experimental data [37, 38], see Figure 6 (right). After an adequate calibration of the free parameters, the model describes quantitatively well the dynamics of pedestrians in bottlenecks and wide corridors.

image

Figure 5. One dimensional fundamental diagram in narrow corridor (25 × 1 m) in comparison with empirical data [32].

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image

Figure 6. Fundamental diagram in wide corridor (20 × 2 m) in comparison with empirical data (left). Flow through bottleneck for different widths (right).

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3 RUNTIME OPTIMIZATION

  1. Top of page
  2. ABSTRACT
  3. 1 INTRODUCTION
  4. 2 MODELING AND SIMULATION
  5. 3 RUNTIME OPTIMIZATION
  6. 4 RESULTS
  7. 5 CONCLUSION
  8. ACKNOWLEDGEMENTS
  9. REFERENCES
  10. Biographies

Even if previous experience shows that current CA models need less computational effort than actual spatially continuous models, general comparative statements about the runtime of implementations are difficult to make. The runtime depends on the spatial and temporal resolution of the model, the situation modeled, the implementation, and the underlying hardware as well as other parameters. A reliable comparative statement would need at least a definition of a scenario together with the phenomena the model has to reproduce and specific implementations of these models on the same hardware. In the next section, we discuss general aspects influencing the runtime of CA and spatially continuous force-based models, and we present the results of different optimization approaches.

3.1 Runtime Factors for Cellular Automata

Because of their discreteness, CA models are well suited for large-scale computer simulations. Except for the transition probabilities in the case of stochastic dynamics, they require only integer algebra. Furthermore, the simulations are free of additional approximations (if no averages are calculated) because the dynamical rules already take the discreteness into account. However, the discreteness, especially in space, becomes a problem in applications. Usually, a spatial resolution of 40 cm is not sufficient. Therefore, smaller cells have to be used, which decreases the computational efficiency. Because smaller cell sizes usually also require modifications of the dynamics, the precise effect on the runtime is difficult to estimate, as the following discussion shows. Rescaling the cell length by 1 ∕ b increases the total number of cells by a factor of b2. In addition, the time step is rescaled by 1 ∕ b[23], which yields an estimated factor of b3 in computational complexity. However, this strongly depends on the details of the dynamics. If, for example, the interaction range is increased at the same time, the timescale can be left unchanged [23]. On the other hand, a larger interaction range can increase the computational demand substantially. Furthermore, the asymptotic scaling behavior could be irrelevant for practical purposes. Starting from 40-cm cells, rescaling five times with b = 2 already yields a length scale of about 1 cm, which seems sufficient for application. If the runtime scales as abα for a model, it can be expected that for high values of a, the behavior in the cases of interest is not determined by the scaling exponent α

3.2 Runtime Factors for Force-based Models

The advantages of force-based models regarding the representation of space lead, on the other hand, to a high computational demand because of small time steps (usually ≤ 0.01 second)) needed to enable an accurate integration. Moreover, the nonlocal interactions between pedestrians cause problems, see Equation (2). A straightforward implementation (brute force method) of the repulsive forces requires the calculation of (N − 1) × N terms, leading to a complexity of O(N2). In the next sections, we introduce neighbor list approaches to reduce the runtime of force-based models and an appropriate parallelization strategy on a small cluster.

3.3 Neighbor List Methods for Force-based Models

The cutoff radius Rc of the force, introduced previously, allows for reducing the number of interactions that has to be calculated, by remembering all neighboring pedestrians in a list. Two of these neighbor list concepts that are widely used in molecular dynamics simulations with short-range forces are tested. One is the Linked-Cell algorithm [39, 40], and the second is the Verlet-List algorithm [39, 41].

The concept of the Verlet-List algorithm is sketched in Figure 7 (left). For each person, the neighbors in the region with radius Rc + Rs are saved in a list. Rc gives the cutoff radius of the interaction force, whereas Rs is the skin radius determining the size of the reservoir. In each time step, only interactions with pedestrians in the list have to be calculated. The list must be updated in time intervals given by Rs and the maximal speed of the pedestrians. This leads to a total complexity of O(N2) with a small coefficient. A drawback of the Verlet-List algorithm is the amount of memory needed for the neighbor lists.

image

Figure 7. Sketch of the Verlet-List method (left) and the Linked-Cell method (right). For the Linked-Cell methods, Lc = Rc.

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In case of the Linked-Cell algorithm, the space is decomposed in cells of size Rc × Rc as illustrated in Figure 7 (right). It is convenient to choose the cell size equal to the cutoff radius. Only the interactions with pedestrians in adjacent cells have to be considered, reducing the complexity to O(N). The complexity here is relative to the neighborhood search of a pedestrian. For each pedestrian, at most 9 × Pmax distance, computations have to be performed. Pmax is the maximum number of pedestrians that fit in a cell. In each time step of the simulation, the pedestrians are reassigned to their particular cells. Opposed to the Verlet-List algorithm, the memory complexity is of order O(N). The indirect addressing that is caused by managing the cells and the corresponding pedestrians in two lists might be a drawback because of possible cache misses and thus, a loss of performance.

Aside from further parameters, the efficiency of the methods mentioned earlier depends on the local distribution of the pedestrians and the range of the repulsive force. For example, the runtime of a simulation using the Linked-Cell method will not differ from the brute force method when all pedestrians are located in one cell. Thus, we analyzed the dependency of the performance gain on the degree of congestion, the system size, and the range of the interaction force. For this purpose, we introduce the speedup

  • display math(7)

given by the runtime of the brute force method tBF divided by the runtime of the respective neighbor-list method tNL.

We investigated the performance gain by using two different test scenarios: a homogeneous and an inhomogeneous distribution of pedestrians (see Figure 8). For both cases, the speedup was determined by measuring the corresponding runtime in relation to an increasing number of pedestrians. In the homogeneous case despite the number of pedestrians, the density ρ and the size of the room Aroom can be varied where

  • display math(8)

By assuming that the runtime mainly consists of the calculations of the interaction forces, the expected speedup can be approximated in advance. Therefore, with Equations (7) and (8) it follows that

  • display math(9)
image

Figure 8. Examples for a homogeneous (left) and an inhomogeneous (right) distribution of 500 pedestrians at t = 100s. The speedup reachable using the Linked-Cell or Verlet-List method depends on the degree of congestion. The blue circle (right) shows the cutoff radius Rc of the force.

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Obviously for a constant density, the speedup goes to infinity for an increasing number of pedestrians, which can also be concluded from Equation (9). Looking at the behavior of the speedup for a constant room size and an increasing number of pedestrians is more interesting because it will probably be a frequently applied scenario especially in the context of evacuations. As can be seen from Equation (9) in this case, the speedup converges to a constant. This also reveals the dependence of the speedup on the cutoff radius Rc and allows to calculate the speedup in advance (independent of the number of pedestrians). Simulations proved these results as shown in Figure 9 (left) where the convergence of the speedup can be seen in case of the homogeneous scenario.

image

Figure 9. Speedup of the homogeneous (left) and inhomogeneous (right) distribution of pedestrians. For 2500 pedestrians, a speedup of more than 35 could be reached. The speedup for the inhomogeneous distribution is smaller than for the homogeneous. For the latter case with constant density of 3m − 2, the speedup reaches 80 for 10 000 pedestrians.

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Experimentally, the speedup was determined by measuring the corresponding runtime in relation to an increasing number of pedestrians. For the tests, a simulation time of 100 seconds and a room size of 35 × 50 m were chosen. The time interval Δt = 0.01s for integrating the equations of motion (see Equation  (2)) results in 104 iteration steps. Runtime measurements were performed using the operating system openSUSE 10.2 and an Intel Pentium D Processor (Pro-data service GmbH, Grevenbroich, Germany) with 3.40 GHz, a L2 Cache of 2048 KB and 2048 MB of random access memory.

In the inhomogeneous scenario, the speedup scales differently for an increasing number of pedestrians as shown in Figure 9 (right). Looking at the development of the speedup, the local maximum for a simulation with 200 persons after a strong increase and followed by a decrease until about 500 persons is quite remarkable. This can be explained as follows: For few pedestrians, no congestions occur, and the speedup increases because of fewer calculations of interaction forces. The congestion areas grow with an increasing number of pedestrians, and as soon as the size of the congestion areas is in the order of Rc, most interaction forces are located within this area, thus, reducing the performance gain obtained by the neighbor list methods, see Figure 7 (right). When the majority of pedestrians are located in the congestion areas, we obtain a distribution of a quasi-constant density and the speedup scales as in the homogeneous case. Because for an increasing number of pedestrians the inhomogeneous distribution converges to a homogeneous distribution in the limit case, the speedup is expected to converge to a constant.

3.4 Parallelization of Forced-based Models

The evacuation assistant should perform a faster than real-time computation. This is a particular challenge for the force-based models as each step includes computationally intensive arithmetic operations such as computing the forces between the pedestrians, the forces to the obstacles, the new velocities, and positions. Each of which comprises several trigonometric and square root functions. Detailed information about the operations and performance are found in [42].

3.4.1 Simulation Area

The simulation domain (part of the arena) with an initial configuration of pedestrians is presented in Figure 10. It is logically subdivided into 15 sections, which are also mapped into the detection areas of the automatic person-counting systems. This division is also used as domain decomposition technique for the parallelization as explained in the next section.

image

Figure 10. Simulation area divided into 15 sections. The initial configuration prior to a simulation is represented by the number of pedestrians inside the sections. These are real input data coming from the automated person-counting system. Camera teams, for instance, are also accounted to the pedestrians in the playing field area.

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3.4.2 Parallelization Technique

The Message Passing Interface [43] and the Open Multi-Processing [44] application programming interfaces are used for this purpose. The most suitable parallelization strategy for an application is usually coupled to the underlying hardware architecture. Some techniques on graphics processing units are presented in [45], and results on the cell broadband engine are presented in [46]. More general techniques for particles in molecular dynamics are found in [47] and especially for pedestrian dynamics in [48, 49]. Independently of the underlying hardware architecture, there are several parallelization techniques with different complexities in the computation, the memory required, and the communication, respectively, the data exchange between the processors. One technique is the replicated data approach [50]. Each processor keeps a copy of all data in its memory but works only on the portion it is responsible of. This method has a large communication complexity. At each step, all processors have to update their data. For P processors and N pedestrians, this algorithm achieves a parallel complexity of the order O(N ∕ P) (N thanks to the linked-cells) for the CPU time, but its communication and memory complexities are of the order O(N). The replicated data approach does not scale with P, and the total runtime is dominated by the communication.

Another approach is parallelization by data partitioning. Here, each processor only stores the data of the pedestrians required during the computation. These are the N ∕ P pedestrians that are assigned to the processors in the parallel computation and the other pedestrians that interact with those pedestrians, that is, the pedestrians in the neighborhood (see Equation (2)). The data-partitioning method scales as O(N ∕ P) for computation and communication as long as P is so small that latency is negligible.

A similar approach to the data partitioning is achieved by static domain decomposition [51, 52]. The main goal here is to limit the communication between the processors. For that purpose, the simulation domain is decomposed into subdomains, and each processor is assigned a subdomain. The data are partitioned and distributed to processors in such a way that as little communication as possible is needed. In each communication step, only the pedestrians from neighboring subdomains have to be communicated. With the use of the linked-cells, this number of neighboring pedestrians can be further reduced using the so-called ghost areas. In this way, the number of pedestrians for which data have to be received or sent decreases to inline image. The complexity of the entire computation is of the order O(N ∕ P). One should note that this applied only when the pedestrians are uniformly distributed.

In the case where the pedestrians are not uniformly distributed, dynamic decompositions [53-55] might be required to ensure an almost uniform distribution of the N pedestrians on the P processors.

A major difference to general particle simulation in molecular dynamics or in N-body systems, in general, is that the pedestrian stream and direction of movement are predictable, in the sense that at a certain time in the simulation, the pedestrians will gather at exits. In addition, the results of the simulation, that is, the trajectories of the pedestrians are written with respect to those areas, which means that each processor can perform input/output operations without any need of synchronization with others. The best suitable choice was a static decomposition on the geometry presented in Figure 10 not only because of its relatively low communication requirements but also because of the natural partitions given by the person-counting system. This partitioning is indeed performed to achieve as less interactions as possible between the subdomains. A method is to choose the boundaries between the domains, which are also the counting lines for the system, as small as possible, thus, mainly at doors. In addition, we can assume an initial uniform distribution of the pedestrians in the simulation area. In the routing strategy used, pedestrians observe their surrounding and take decisions on the basis of their observations [56]. With this static domain decomposition, all information necessary for a route choice are available on the same processor.

4 RESULTS

  1. Top of page
  2. ABSTRACT
  3. 1 INTRODUCTION
  4. 2 MODELING AND SIMULATION
  5. 3 RUNTIME OPTIMIZATION
  6. 4 RESULTS
  7. 5 CONCLUSION
  8. ACKNOWLEDGEMENTS
  9. REFERENCES
  10. Biographies

The results computed by the assistant are presented in Figure 2. The congestion areas are displayed. The assistant interface is web based making it flexible and location independent. The CA model and the GCFM have different requirements, concerning the geometry for instance. CA uses a discretized geometry, whereas the GCFM needs a continuous geometry. Also, the information needed from the geometry is model specific. This has been a major issue in the integration process as some compromises had to be taken. Two representations of the arena-containing model specific information are passed to the models at runtime. The integration with the automatic person-counting system, to obtain the initial distribution of pedestrians and with the safety and security management system, to obtain the states of the exits and rooms was performed through web services.

The simulations are performed on a cluster consisting of 15 PowerEdge M610 (Avnet Technology Solutions GmbH, Leinfelden-Echterdingen, Germany) blade servers. Each server features two 6-core Intel(R) Xeon(R) CPU X5670 clocked at 2.93 GHz. The results presented in this section are obtained with the GCFM. Figure 11 shows the runtime achieved using different numbers of processors. The runtime applies to a complete simulation, that is, all pedestrians have left the facility. The simulation is performed with 22 500 pedestrians. The evacuation time provided by this simulation is 817 seconds. One should note that an evacuation scenario was simulated in this case. It means that there is no direct way of validating the obtained evacuation time. The times measured during a routine clearing (after a concert is over for instance) are usually bigger. This is because of the fact that people might spend more time in the facility, at the fan shops for instance.

image

Figure 11. Runtime using different numbers of processors. The simulation is performed with 22 500 pedestrians. The evacuation time is about 817 s.

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The runtime measurements take into account the linked-cells and the hybrid parallelization described earlier. Still, a closer look at the simulation with appropriate debugging tools of the Scalasca toolset [57] shows that the communication between the processors offers further possibilities of optimization. The simulation cluster supports hyper-threading allowing up to 360 virtual processors. However, this has been shown to be very inefficient in this case.

5 CONCLUSION

  1. Top of page
  2. ABSTRACT
  3. 1 INTRODUCTION
  4. 2 MODELING AND SIMULATION
  5. 3 RUNTIME OPTIMIZATION
  6. 4 RESULTS
  7. 5 CONCLUSION
  8. ACKNOWLEDGEMENTS
  9. REFERENCES
  10. Biographies

An evacuation assistant for mass events providing results in real-time has been presented in this contribution. The assistant is currently absolving a test phase in the facilities of the ESPRIT Arena in Düsseldorf. The different tiers of the system have been described. A focus has been set on the modeling approaches and on the runtime optimization. Two classes of pedestrian models are integrated in the system, and the use of different optimization techniques have enabled a real-time simulation and processing of the results. Future works include the analysis of the data generated by the system. For instance, the data generated by the automated person-counting system could give more information about pedestrian route choice in the facility. Another class of CA models with smaller cell size is also being investigated.

ACKNOWLEDGEMENTS

  1. Top of page
  2. ABSTRACT
  3. 1 INTRODUCTION
  4. 2 MODELING AND SIMULATION
  5. 3 RUNTIME OPTIMIZATION
  6. 4 RESULTS
  7. 5 CONCLUSION
  8. ACKNOWLEDGEMENTS
  9. REFERENCES
  10. Biographies

This work has been performed within the program “Research for Civil Security” in the field “Protecting and Saving Human Life” funded by the German Government, Federal Ministry of Education and Research. The project is supported under the grant nos. 13N9952 and 13N9960.

REFERENCES

  1. Top of page
  2. ABSTRACT
  3. 1 INTRODUCTION
  4. 2 MODELING AND SIMULATION
  5. 3 RUNTIME OPTIMIZATION
  6. 4 RESULTS
  7. 5 CONCLUSION
  8. ACKNOWLEDGEMENTS
  9. REFERENCES
  10. Biographies
  • 1
    Schadschneider A.I'm a football fan… get me out of here.Physics World2010;21.
  • 2
    Galea ER, Gwynne S, Lawrence PJ, Filippidis L, Blackspields D, Cooney D.buildingEXODUS V 4.0 – User Guide and Technical Manual, (2004).www.fseg.gre.ac.uk.
  • 3
    TraffGo HT GmbH.Handbuch PedGo 2, PedGo Editor 2, (2005).www.evacuation-simulation.com.
  • 4
    Korhonen T, Hostikka S, Heliövaara S, Ehtamo H.FDS+Evac: an agent based fire evacuation model, In Proceedings of the 4th International Conference on Pedestrian and Evacuation Dynamics,2008.
  • 5
    Raney B, Nagel K.An improved framework for large-scale multi-agent simulations of travel behavior.Towards Better Performing European Transportation Systems2006:305347.
  • 6
    Thompson PA, Marchant EW.A computer model for the evacuation of large building populations.Fire Safety Journal1995;24:131148.
  • 7
    I.S.T. Integrierte Sicherheits-Technik GmbH, Frankfurt/Main.Referenzhandbuch Aseri, Version 4.6, (2008).
  • 8
    Tavares R. M., Galea ER.Evacuation modelling analysis within the operational research context: a combined approach for improving enclosure designs.Building and Environment2009;44(5):10051016.
  • 9
    Holl S, Seyfried A.Hermes – an evacuation assistant for mass events.inSiDe2009;7(1):6061.
  • 10
    Hermes Project. http://www.fz-juelich.de/jsc/hermes. Accessed [January 2012].
  • 11
    Fruin JJ.Pedestrian Planning and Design.Elevator World,New York,1971.
  • 12
    Schadschneider A, Chowdhury D, Nishinari K.Stochastic Transport in Complex Systems from Molecules to Vehicles.Elsevier,Amsterdam/Oxford,2011.
  • 13
    Schadschneider A, Klingsch W, Kluepfel H, Kretz T, Rogsch C, Seyfried A.Encyclopedia of Complexity and System Science, chapter Evacuation dynamics: empirical results, modeling and applications, pages 31423176, Vol.  5. Springer, Berlin, Heidelberg,2009.
  • 14
    Thalmann D, Musse SR.Crowd Simulation.Springer,London,2007.
  • 15
    Rogsch C, Seyfried A, Klingsch W.Comparative investigations of the dynamical simulation of foot traffic flow. InPedestrian and Evacuation Dynamics 2005, Waldau N, Gattermann P, Knoflacher H, Schreckenberg M (eds).Springer,Berlin, Heidelberg,2007;357362.
  • 16
    Schadschneider A, Seyfried A.Empirical results for pedestrian dynamics and their implications for cellular automata models. In Pedestrian Behavior: Data Collection and Applications, chapter 2, Harry Timmermans (ed.), 1st edition.Emerald Group Publishing Limited,Bingley, UK,2009;2743.
  • 17
    Burstedde C, Klauck K, Schadschneider A, Zittartz J.Simulation of pedestrian dynamics using a two-dimensional cellular automaton.Physica A2001;295:507525.
  • 18
    Kirchner A, Schadschneider A.Simulation of evacuation processes using a bionics-inspired cellular automaton model for pedestrian dynamics.Physica A2002;312:260276.
  • 19
    Schadschneider A.Cellular automaton approach to pedestrian dynamics – theory, InPedestrian and Evacuation Dynamics, Schreckenberg M, Sharm SD (eds).Springer,Berlin/Heidelberg,2002;7586.
  • 20
    Burstedde C, Kirchner A, Klauck K, Schadschneider A, Zittartz J.Cellular automaton approach to pedestrian dynamics – applications. InPedestrian and Evacuation Dynamics, Schreckenberg M, Sharm SD (eds).Springer,Berlin/Heidelberg,2002;8798.
  • 21
    Kirchner A, Nishinari K, Schadschneider A.Friction effects and clogging in a cellular automaton model for pedestrian dynamics.Physical Review E2003;67:056122.
  • 22
    Kirchner A, Klüpfel H, Nishinari K, Schadschneider A, Schreckenberg M.Simulation of competitive egress behavior: comparison with aircraft evacuation data.Physica A2003;324:689697.
  • 23
    Kirchner A, Klüpfel H, Nishinari K, Schadschneider A, Schreckenberg M.Discretization effects and the influence of walking speed in cellular automata models for pedestrian dynamics.Journal of Statistical Mechanics2004;10:P10011.
  • 24
    Ezaki T, Yanagisawa D, Ohtsuka K, Nishinari K.Simulation of space acquisition process of pedestrians using proxemic floor field model.Physica A: Statistical Mechanics and its Applications2012;391(12):291299.
  • 25
    Henein CM, White T.Macroscopic effects of microscopic forces between agents in crowd models.Physica A: Statistical Mechanics and its Applications2007;373(0):694712.
  • 26
    Chraibi M, Seyfried A, Schadschneider A.Generalized centrifugal force model for pedestrian dynamics.Physical Review E2010;82:046111.
  • 27
    Lewin K (ed.).Field Theory in Social Science,Greenwood Press,Connecticut,1951.
  • 28
    Helbing D, Molnár P.Social force model for pedestrian dynamics.Physical Review E1995;51:42824286.
  • 29
    Molnár P.Modellierung und Simulation der Dynamik von Fußgängerströmen, Dissertation, Universität Stuttgart, 1995.
  • 30
    Yu WJ, Chen LY, Dong R, Dai SQ.Centrifugal force model for pedestrian dynamics.Physical Review E2005;72(2):026112.
  • 31
    Chraibi M, Kemloh U, Seyfried A, Schadschneider A.Force-based models of pedestrian dynamics.Networks and Heterogeneous Media2011;6(3):425442.
  • 32
    Seyfried A, Chraibi M, Kemloh U, Mehlich J, Schadschneider A.Runtime optimization of force based models within the Hermes project, InPedestrian and Evacuation Dynamics 2010.Springer,Springer US,2011;363373.
  • 33
    Mori M, Tsukaguchi H.A new method for evaluation of level of service in pedestrian facilities.Transp Res1987;21A(3):223234.
  • 34
    Helbing D, Johansson A, Al-Abideen HZ.Dynamics of Crowd Disasters: An Empirical Study, Vol.75,2007.
  • 35
    Oeding D.Verkehrsbelastung und Dimensionierung von Gehwegen und anderen Anlagen des Fußgängerverkehrs, 1963. Forschungsbericht 22, Technische Hochschule Braunschweig.
  • 36
    Hankin BD, Wright RA.Passenger flow in subways.Operational Research Quarterly1958;9:8188.
  • 37
    Seyfried A, Passon O, Steffen B, Boltes M, Rupprecht T, Klingsch W.New insights into pedestrian flow through bottlenecks.Transportation Science2009;43(3):395406.
  • 38
    Kretz T, Grünebohm A, Schreckenberg M.Experimental study of pedestrian flow through a bottleneck.J. Stat. Mech.2006;10:P10014.
  • 39
    Sutmann G, Stegailov V.Optimization of neighbor list techniques in liquid matter simulations.Journal of Molecular Liquids2006;125(2-3):197203.
  • 40
    Allen MP, Tildesley DJ.Computer Simulation of Liquids, Vol. 18.Oxford University Press,1989.
  • 41
    Verlet L.Computer “experiments” on classical fluids. I. Thermodynamical properties of Lennard–Jones molecules.Physical Review1967;159(1):98103.
  • 42
    Steffen B, Kemloh Wagoum AU, Chraibi M, Seyfried A.Parallel real time computation of large scale pedestrian evacuations, In The Second International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering,2011.
  • 43
    Message P Forum.Mpi: A message-passing interface standard. Technical Report Technical Report, Knoxville, TN, USA, 1994.
  • 44
    Chandra R, Dagum L, Kohr D, Maydan D, McDonald J, Menon R.Parallel Programming in OpenMP.Morgan Kaufmann Publishers Inc,San Francisco, CA, USA,2001.
  • 45
    Richmond P, Romano D.A high performance framework for agent based pedestrian dynamics on GPU hardware, In Proceedings of EUROSIS ESM 2008 (European Simulation and Modelling),2008.
  • 46
    Reynolds C.Big fast crowds on PS3, In Proceedings of the 2006 ACM SIGGRAPH Symposium on Videogames,2006.
  • 47
    Griebel M, Knapek S, Zumbusch G.Numerical Simulation in Molecular Dynamics: Numerics, Algorithms, Parallelization, Applications, 1st edition.Springer Publishing Company, Incorporated,2007.
  • 48
    Quinn MJ, Metoyer RA, Hunter-Zaworski K.Parallel implementation of the social forces model, In Proceedings of the Second International Conference in Pedestrian and Evacuation Dynamics,2003;6374.
  • 49
    Pettré J, Ciechomski PdH, Maïm J, Yersin B, Laumond J-P, Thalmann D.Real-time navigating crowds: scalable simulation and rendering.Computer Animation and Virtual Worlds2006;17:445455.
  • 50
    Janak JF, Pattnaik PC.Protein calculations on parallel processors. ii. Parallel algorithm for the forces and molecular dynamics.Journal of Computational Chemistry1992;13(9):10981102.
  • 51
    Hanxleden RV, Clark TW, Mccammon JA, Scott LR.Parallelizing molecular dynamics using spatial decomposition, In Scalable High Performance Computing Conference,1993;95102. IEEE Computer Society Press.
  • 52
    Plimpton S, Hendrickson B.Parallel molecular dynamics algorithms for simulation of molecular systems. InParallel Computing in Computational Chemistry, Mattson TG (ed.).American Chemical Society,Washington D.C.,1995;114136.
  • 53
    Hegarty D, Kechadi M, Dawson K.Dynamic domain decomposition and load balancing for parallel simulations of long-chained molecules. InApplied Parallel Computing Computations in Physics, Chemistry and Engineering Science, Vol. 1041, Jack Dongarra, Kaj Madsen, Jerzy Wasniewski (eds),Lecture Notes in Computer Science,1996;303312.
  • 54
    Baiardi F, Bonotti A, Ferrucci L, Ricci L, Mori P.Load balancing by domain decomposition: the bounded neighbour approach, In Proceedings of 17th European Simulation Multiconference,2003;911.
  • 55
    Wang S, Armstrong MP.A quadtree approach to domain decomposition for spatial interpolation in grid computing environments.Parallel Computing2003;29:14811504.
  • 56
    Kemloh Wagoum AU, Seyfried A, Holl S.Modelling dynamic route choice of pedestrians to assess the criticality of building evacuation.Advances in Complex Systems2011;arXiv:1103.4080. (To appear).
  • 57
    Geimer M, Wolf F, Wylie BJN, Ábrahám E, Becker D, Mohr B.The scalasca performance toolset architecture.Concurrency and Computation: Practice and Experience2010;22(6):702719.

Biographies

  1. Top of page
  2. ABSTRACT
  3. 1 INTRODUCTION
  4. 2 MODELING AND SIMULATION
  5. 3 RUNTIME OPTIMIZATION
  6. 4 RESULTS
  7. 5 CONCLUSION
  8. ACKNOWLEDGEMENTS
  9. REFERENCES
  10. Biographies
  • Image of creator

    Armel Ulrich Kemloh Wagoum received his graduate engineer degree (Diplom-Ingenieur) in Computer Engineering from the Hamburg University of Technology, Hamburg, Germany, in 2008. He is currently a PhD candidate in the Jülich Supercomputing Centre at the German Research Centre Forschungszentrum Jülich GmbH. His research interests are in the areas of pedestrian dynamics and high performance computing with emphasis on mathematical modeling of pedestrian route choice and performance optimization.

  • Image of creator

    Mohcine Chraibi received his graduate engineer degree (Diplom- Ingenieur) in Computer Engineering from the Hamburg University of Technology, Hamburg, Germany, in 2008. He is currently a PhD candidate in the Jülich Supercomputing Centre at the German Research Centre Forschungszentrum Jülich GmbH. His research interests are in the areas of pedestrian dynamics with emphasis on mathematical modeling of pedestrian dynamics.

  • Image of creator

    Jonas Mehlich received his Bachelor of Science degree in Scientific Programming from the Aachen University of Applied Sciences, Aachen, Germany, in 2007. During his subsequent master's program in Technomathematics, he was part of the pedestrian dynamics team at the Jülich Supercomputing Centre of the Forschungszentrum Jülich. Within the context of his master's thesis, he examined the runtime optimization of simulations in pedestrian dynamics. In 2009, he completed his Master of Science at the Aachen University of Applied Sciences, Aachen, Germany.

  • Image of creator

    Armin Seyfried studied theoretical physics at the Bergische Universität Wuppertal from 1988 to 1996. In the course of his diploma project and PhD thesis, which he finished in 1998, he focused on many particle systems, high energy physics, and parallel computing. After his PhD, he specialized in the fire safety field. Since 2004, he has been establishing a new research group for pedestrian dynamics and fire simulations at the Jülich Supercomputing Centre of the Forschungszentrum Jülich. In 2010, he became a professor for computer simulations for fire safety and pedestrian traffic at the Bergische Universität Wuppertal.

  • Image of creator

    Andreas Schadschneider is a professor for theoretical physics at the University of Cologne. He has studied physics in Cologne and received his PhD in 1991 working in the area of theoretical solid state physics. After a postdoctoral stay at the State University of New York in Stony Brook, he returned to the University of Cologne working in Statistical Mechanics focusing on interdisciplinary applications, for example, to vehicular traffic, pedestrian dynamics, biology, and economics. After his habilitation in 1999, he became an associate professor in 2000. In 2006, he was appointed as professor at the Institute for Theoretical Physics. Since 2008, he is also at the Institute for Physics Education of Cologne University.