PARALLEL IMPLEMENTATION OF THE SOCIAL FORCES MODEL

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1 PARALLEL IMPLEMENTATION OF THE SOCIAL FORCES MODEL Michael J. Quinn 1, Ronald A. Metoyer 1, and Katharine Hunter-Zaworski 2 1 School of Electrical Engineering and Computer Science 2 Department of Civil, Construction, and Environmental Engineering Oregon State University Corvallis, OR USA ABSTRACT We demonstrate how the use of a multicomputer can greatly accelerate the speed of a pedestrian movement simulator based on the social forces model. Our objective is to develop a simulator that updates the position of every pedestrian in real time; that is, 30 times a second. We have achieved this goal through the use of multiple processors. We describe the design of our parallel pedestrian movement model and present benchmark results demonstrating that 11 processors can update the positions of 10,000 pedestrians in about 1/50 th of a second. The parallel algorithm is highly scalable, meaning that adding processors will enable the simulation of even larger crowds. INTRODUCTION The importance of pedestrian motion simulation for facilitating the creation of pedestrian friendly urban environments has been recognized for several years. Furthermore, in today's climate of terrorism alert, accurate simulations of pedestrian motion and the behaviors of heterogeneous populations can provide valuable information for building evacuation studies and for training emergency personnel. In order to create effective simulations, we must answer several important questions. First, how do we create pedestrian motion that is realistic enough to be useful to designers and to suspend disbelief in training simulators? Second, how do we create large simulations (> 50,000 pedestrians) that run and render in real time? Third, how do we design tools that leverage the large body of existing pedestrian motion simulators? Lastly, how do we build simulation systems with intuitive interfaces for complex scenario content creation? This paper focuses on the second question. We have begun construction of a software tool that will enable engineers, architects, and government agencies to improve the safety of buildings and transportation facilities (Figure 1). The tool will take as input a building description and a description of the emergency scenario (which includes information about the people inside the building). At the heart of the tool is a microscopic model of pedestrian 1

2 motion. Every person is represented individually, allowing them to have unique sizes, movement characteristics, destinations, and planned routes. 2D interactive desktop interface AutoCAD 2D rendering engine Architect/ Engineer Building description Scenario description Pedestrian movement model Position of each person at each point in time 3D rendering engine Scenario builder User tracking Emergency planning team 3D immersive environment Figure 1: Components of a pedestrian movement simulator to support the design of safer facilities and the training of emergency personnel. A two-dimensional (2D) rendering engine will provide overhead views of the simulated crowd movement. Engineers, architects, and emergency management and transportation agencies will be able to use this information to test building designs for both typical pedestrian traffic as well as emergency evacuation situations. The system will also serve as a training tool for emergency management personnel. In its early stages, it will provide these people with a 2D, overhead view of the building to be evacuated and help them understand how various actions they take (such as erecting barriers or opening up stairwells) improve or hinder pedestrian flow. In its later stages, emergency personnel (such as paramedics or police officers) will be immersed in a virtual, three-dimensional (3D) world. They will have the ability to move about the environment and take actions that affect pedestrian movement. RELATED WORK Microsimulation models of pedestrian behavior can be put into three categories: cellular automata models, AI-based models, and behavioral force models. Helbing et al. 12 have produced an extensive bibliography of work in this area. Many computer simulations focusing on evacuation have been developed [Burstedde 3, Drager 7, Ebihara 8, Hamacher 10,11, Helbing 12, Ketchell 13, Klupfel 14, Lovas 20, Okazaki 26, 2

3 Schneider 29, Still 30, Thompson 33 ]. Daamen et al. 6 have worked with Holland Railconsult to develop a simulation tool that estimates the mean and variance of walking times of passengers and the paths they take inside transit stations. Recently, crowd simulation has gained popularity in the 3D graphics arena. One area of research has been the design of simulation environments for generating realistic, directible crowds [Farenc 9, Musse 23,24, Tecchia 31 ]. Several researchers in the graphics area have focused specifically on generating individual 3D pedestrian behaviors such as navigation planning and natural locomotion [Choi 4, Ko 15, Kuffner 17,18, Noser 25, Reich 28 ]. Few of these approaches have generated motion as natural as that produced with motion capture data. Recent research has led to algorithms for sequencing motion capture data to produce natural transitions under user constraints such as desired paths or key poses [Arikan 1, Kovar 16, Lee 19, Metoyer 21 ]. A closely related research project is CROSSES (Crowd Simulation System for Emergency Simulations). The goal of the work is develop an immersive environment that can be used to train people to respond to outdoor urban emergency situations [Ulicny 35,36 ]. However, this system cannot render large crowds in real time. MODEL SELECTION Previously reported work with cellular automata (CA) demonstrates that CA models running on single processors can update the positions of tens of thousands of pedestrians in 1/30 th of a second [Meyer-Konig 22 ]. However, CA models divide the world into discrete cells, typically 40 cm on a side. Our 3D rendering software requires more precise location information in order to generate a realistic representation of human motion that can suspend disbelief (Figure 2). Figure 2. Given a path of point masses, the rendering engine constructs a realistic portrayal of a pedestrian following that path. In contrast, the social forces model generates the precise locations of each simulated pedestrian at each time interval. Hence it can provide the 3D rendering engine with the continuous paths it needs in order to generate realistic-looking motion. Various experiments have demonstrated that the social forces model can simulate many effects 3

4 seen in the real world, such as jamming at exits, spontaneous lane formation when pedestrians are traveling in opposite directions, and virtual roundabouts where hallways intersect. The disadvantage of the social forces model is that updating the position of a pedestrian takes much longer than in a CA model. Our experiments suggest that the social forces model is about 100 times slower than a CA model, when simulating the same number of pedestrians. Fortunately, parallel computing is a way to accelerate the performance of a simulation based on the social forces model. Parallel computers constructed out of commodity microprocessors have relatively low cost and are widely available. DESIGN In this section we describe the design of a parallel program that implements the pedestrian movement model of Figure 1. We have chosen to use the manager/worker paradigm to organize the processes (Figure 3). The manager process is responsible for communication with the other components of the software system. It reads the building layout and broadcasts it to the workers. It also receives the scenario information (including information about the pedestrians) and sends information about each pedestrian to the appropriate worker process. At each time step the manager process gathers data about the locations of the pedestrians from the worker processes and passes this information along to the appropriate rendering engine. The worker processes organize themselves into a 2D virtual grid. Each worker gets building layout information from the manager process, as well as information about pedestrians in its portion of the building. Every worker is responsible for updating the positions of the pedestrians in its portion of the building each time step. When the new locations have been determined, the workers send the locations of the pedestrians to the manager process. Manager process Worker processes Figure 3. The parallel implementation uses a manager/worker organization. Each worker process is responsible for simulating pedestrian movement within a rectangular region of the building. 4

5 In the social forces model, every pedestrian can exert a repulsive or an attractive force on every other pedestrian. In practice, a pedestrian is barely influenced by pedestrians more than a few meters away, because the social force decreases exponentially with distance. The performance of the program is improved significantly if we limit the number of social force interactions we compute. For these reasons we divide the building into zones. When computing social forces, we only consider other pedestrians in the same zone or a horizontally, vertically, or diagonally adjacent zone. The size of each zone is an easily modified parameter. In our current implementation, we have chosen our zone size to be 2 meters (Figure 4). According to the transportation literature, inter-person spacing greater than 1.2 meters is considered level of service A [TRB 34 ]. Hence ignoring social forces from pedestrians more than 2 meters away is a reasonable assumption. When computing the social forces on a particular pedestrian, the system considers all pedestrians in the same zone and the eight zones surrounding it. Examination of every pedestrian in these nine zones guarantees the computation of social forces generated by every pedestrian within 2 meters and some pedestrians as far as 5.26 meters away, depending upon the position of the subject pedestrian in the central zone. Figure 4: When computing social forces acting on a particular pedestrian (shown in gray), we only consider pedestrians in the same zone or one of the eight surrounding zones, guaranteeing consideration of all pedestrians within one zone diameter of the subject. With this optimization, execution time is bounded by a linear function of the number of pedestrians. Since the number of pedestrians that can physically fit into a zone is a constant, the maximum execution time of our algorithm increases linearly with the number of pedestrians. The social forces model also takes into account wall and obstacle avoidance. We generate a fine grid, 0.1 meters on a side, and map all walls and obstacles onto this grid. Before the simulation begins, the model pre-computes, for each grid point corresponding to a location in the building, the social forces produced by walls and obstacles. Hence during the execution of the simulation, these forces can be determined quickly through table lookup. 5

6 Each worker process is responsible for pedestrians within a rectangular region of zones (Figure 5). The positions of the pedestrians in the interior zones (white squares of Figure 5a) can be updated without any communication among processes, because the surrounding zones are available locally. However, the positions of the pedestrians in the border zones (gray squares of Figure 5a) cannot be updated without getting information about pedestrians in adjacent zones. We surround the rectangular region of zones controlled by a process with ghost zones (striped cells of Figure 5b). These zones contain copies of pedestrians controlled by other processes. (a) (b) (c) Figure 5. Processes must exchange pedestrian information. (a) A process cannot update gray border zones without getting information from other processes. (b) Ghost zones (striped cells) contain duplicate information about pedestrians controlled by neighboring processes. (c) A process exchanges information about pedestrians in its border zones with a neighboring process. Received information is put in ghost zones. Before computing the new positions of its pedestrians, each worker process exchanges information about pedestrians in its border zones with its neighbors in the virtual 2D grid of processes. For example, Figure 5c illustrates the data exchanged between two neighboring processes. Each process fills its ghost wrapper with information about pedestrians in its neighbor's border zones. Depending on its position in the virtual process grid, a process may have as many as eight neighbors (N, NE, E, SE, S, SW, W, NW). Pedestrians move from zone to zone. If a pedestrian moves between zones controlled by the same process, the process can update the appropriate data structures without communicating with another process. However, if a pedestrian moves from a zone controlled by process A to a zone controlled by process B, process A must hand over the pedestrian to process B. Figure 6 contains the pseudocode for a worker process. One message-passing optimization is noteworthy. The messages to fill the ghost zones are generated before the processes compute the new locations of the pedestrians. The messages about 6

7 pedestrians crossing between different processes' zones are generated after the processes compute the new pedestrian locations. We can cut the number of message exchanges between neighboring processors from two to one each iteration by combining the zone-crossing messages (generated in step 5f of one iteration) with ghost-zone-filling messages (generated in step 5a of the subsequent iteration). Worker Process 1. Receive building plan from manager process 2. Organize with other worker processes into virtual 2-D grid 3. Receive portion of pedestrians from manager process 4. Set lengths of all outgoing message buffers to zero 5. Repeat a. For each pedestrian in a border zone i. Put pedestrian in appropriate outgoing message buffer b. For each neighboring process i. Send appropriate outgoing message buffer to that process c. For each neighboring process B i. Receive message from process B ii. Empty buffer of pedestrians, putting each pedestrian in correct zone d. Set lengths of all outgoing message buffers to zero e. Move pedestrians in zones this process controls f. For each pedestrian that has moved from zone (i,j) to zone (k,m) i. Detach process from zone (i,j) ii. If this process controls zone(k,m) then 1. Attach pedestrian to zone (k,m) iii. Else 1. Add process to outgoing message buffer associated with process controlling zone (k,m) Figure 6. Algorithm executed by worker processes. Since communication overhead reduces the speedup achievable by the parallel program, reducing communication overhead is an important goal. Increasing the ratio between the total number of zones controlled by a process and the number of border zones it controls increases the computation-to-communication ratio. We do this by making each process's region of zones as square as possible. The dimensions of the virtual grid of processes depends on the dimensions of the building being modeled. In the next section we describe the simulation of an airport terminal. Because the terminal is long and narrow, the best organization of processes is a one-dimensional grid. IMPLEMENTATION AND BENCHMARKING We have implemented our design as a C program with calls to the Message Passing Interface (MPI) library. MPI is the most popular message-passing library standard for parallel programming [Quinn 27 ]. It is available on most commercial parallel 7

8 computers, and free versions are available to those constructing multicomputers out of commodity components. Writing our program using MPI ensures its portability across a wide range of platforms. To benchmark our parallel implementation, we have developed an airport evacuation case study. The building is roughly modeled after Terminal 1 at O'Hare International Airport in Chicago (see Figures 7 and 8). We populated the terminal with 10,000 randomly dispersed, heterogeneous pedestrians. Using data collected by Teknomo 32, the pedestrians have mean velocity 1.38 m/sec with standard deviation of 0.37 m/s, while their mean acceleration is 0.68 m/sec 2. We have simulated the first minute of an orderly exit of these pedestrians from the terminal (1800 iterations). Figure 7. Overview of our model s simulation of an orderly evacuation of 10,000 pedestrians from a large airport terminal (1.05 km long). Figure 8. Close-up view of the airport evacuation simulation. The pedestrians are evacuating through the corridor on the right. We have benchmarked our parallel implementation of the social forces model on SWARM, a Linux-based multicomputer at Oregon State University consisting of 2.4 GHz Intel Xeon CPUs connected by a gigabit Ethernet switch. Figure 9 illustrates the performance of the parallel model in terms of updates per second as a function of number of worker processors. (An additional processor executes the manager process.) The performance scales well as processors are increased. With 10 worker processors (11 processors overall) the system is able to update the positions of the 10,000 simulated pedestrians nearly 50 times per second. 8

9 Updates per second Worker processes Figure 9. Frequency at which the positions of 10,000 pedestrians are updated, as a function of number of worker processes. Each worker executes on one CPU. One additional CPU is allocated to the manager process. FUTURE WORK In our current implementation every processor is given responsibility for roughly the same number of zones. If the pedestrians are evenly distributed among these zones, the workload is well balanced among the processors. However, when the pedestrians are concentrated in one area of the building, some processors will require much longer than others to complete one time step. Since the parallel execution time is determined by the time required by the processor finishing last, an unbalanced workload can reduce or even eliminate the performance benefit of adding processors. The solution to this problem is to balance the workloads among the processors at run time. We have organized the processors into a virtual 2D grid. To keep the communications among these processors straightforward, we want to partition the matrix of zones into orthogonal blocks. Our goal is to find a partitioning that minimizes the maximum amount of work required by a single processor. This well-known problem is called finding the general block distribution of a matrix. Because the problem is NP-hard, research has focused on finding good approximations to the optimal solution [Aspvall 2 ]. In order to use our 2D models to validate architectural designs and help emergency personnel plan for catastrophic events, we must provide a simple and natural means for interacting with the large-scale 2D simulations. We are developing a system that allows users to use graspable icons to interact with a 2D virtual environment projected onto a large table. For example, the planner could manipulate a figurine as a stamp to deposit pedestrians in the scene. Likewise, the architect or engineer could manipulate obstacles by physically moving actual blocks representing these objects in the scene. The architect or engineer could observe the real-time simulation to evaluate the new design. Emergency planning personnel could evaluate crowd responses in a stadium by manipulating roadblocks and gates. 9

10 We are currently implementing algorithms for the generation of natural 3D character motion in real time. Once this portion of the work is complete, we will explore various options for the real-time visualization of the 3D motion in an immersive environment. We have collaborators within the National Center for Supercomputing Applications who have access to the CAVE system [Cruz-Neira 5 ]. The CAVE infrastructure will allow us to place individuals in the 3D emergency scene, track their motion, and observe their performance in crowd control tasks. SUMMARY We are developing a software tool capable of simulating and rendering the motion of tens of thousands of pedestrians in real time. The social forces model has been implemented as a parallel program written in C with calls to the MPI library. Benchmarking this parallel program on a commodity cluster of high-performance PCs demonstrates the system s ability to generate in real time the coordinates needed by the rendering engine. ACKNOWLEDGEMENT We thank Saurabh Sethia for directing us to the literature on the general block distribution of a matrix. REFERENCES 1. Arikan, O., and Forsyth, D. A., Interactive Motion Generation from Examples, Proceedings of SIGGRAPH 2002, Aspvall, B., Halldorsson, M. M., and Manne, F., Approximations for the General Block Distribution of a Matrix, Theoretical Computer Science 262, 1/2, 2001, pp Burstedde, C., Kirchner, A., Klauck, K., Schadschneider, A., and Zittartz, J., Cellular Automaton Approach to Pedestrian Dynamics Applications, in Pedestrian and Evacuation Dynamics, Springer, Berlin, 2002, pp Choi, M. G., Lee, J., and Shin, S. Y., Planning Biped Locomotion Using Motion Capture Data and Probabilistic Roadmaps, ACM Transactions on Graphics 22, 2 (to appear). 5. Cruz-Neira, C., Sandin, D. J., DeFanti, T. A., Kenyon, R. V., and Hart, J. C., The CAVE: AudioVisual Experience Automatic Virtual Environment, Communications of the ACM 35, 6, 1992, pp Daamen, W., Bovy, P. H. L., and Hoogendoorn, S. P., Modelling Pedestrians in Transfer Stations, in Pedestrian and Evacuation Dynamics, Springer, Berlin, 2002, pp

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