Evacuation Simulation Using a Combination of Computational Fluid Dynamics and Agent-Based Modeling
A time accurate CFD simulation of aerosol contaminant transport over a section of a major U.S. city was combined with an agent-based evacuation model to demonstrate a new method to study and possibly ameliorate the problems inherent in reducing casualties following the release of toxic agents in a crowded urban environment. The agents leaving the buildings were randomly assigned one of three possible destinations which the agents try to reach by the shortest possible route. State variables within each agent track its exposure to the contaminant until it exits the simulation. The exposure history of every agent in the simulation was used to populate a Postgres database. Various mitigation strategies such as stay-in-place directives, car pooling, evacuation staging and traffic routing were simulated and compared on the basis of a specific cost metric. The objective of this study was to show that fairly simple agent rules could be enough to identify the largest bottlenecks in the evacuation process. This would then enable the design and evaluation of mitigation strategies and policies and even provide real-time guidance when backed with sufficient computational power and model refinements.
CFD Simulation of Plume Transport
The simulation of the contaminant transport, modeled as a neutrally buoyant gas, was performed using a RANS/ DES from the Tenasi[ 1] CFD suite with an unstructured grid of the city section with 18 million nodes. The precondition solver used a node-centered finite-volume implicit scheme with 2 nd and 3 rd order temporal and spatial discretizations respectively. Since the buildings are bluff bodies with large regions of flow separation on their leeward sides, a Detached Eddy Simulation ( DES)[ 2] approach was considered superior to a purely RANS simulation. Further details of the CFD simulation can be found in [ 3]. Node locations and concentration of the contaminant were written out every 10 time steps and were post-processed to generate transport history files for the agent-based model. CFD simulation of the plume required approximately 2 days on 100 Intel Xeon 3.0 Ghz processors.
The object-oriented programming paradigm lends itself particularly well to the implementation of agent models in that the agents are codes as instances of a base agent class. Agent behavior which deviates from the base class can be elegantly handled either through state variables or a derived class when the deviation is substantial.
The agent model was initialized with agents that populate the buildings and roads. All agents remain active until they exit the simulation domain. Agents in buildings exit onto the open space around buildings at a fixed specified rate. The agents then navigate towards specified entry points to the roads in the vicinity while avoiding other agents and any buildings in their path. Once they access the road, they are transformed into road agents which execute a simple car-following algorithm which is explained in the following section. In open spaces, the agent uses an underlying Cartesian grid and potentials defined at the grid nodes for navigation.
Car-Following Traffic Model
On the road, the agent is in one of 3 modes:
Mode 0 : Free flow
Mode 1 : Close to the preceding car but not dangerously close
Mode 2 : Dangerously close
In mode 0 the agent will accelerate until it reached the maximum allowable speed on the road segment unless it changes modes. In mode 1, the agent decelerates gently if the preceding agent is going slower. Otherwise it accelerates to maximum segment velocity. In mode 2, the agent brakes hard if the preceding car is slower or continues at constant velocity. . In mode 1 & 2, the agent will brake hard if the agent preceding it does the same. The agents can have variable safe following distances, accelerations, and decelerations (both soft & hard) to account for vehicle heterogeneity and variations in driver behavior. However in the simulations discussed here, an averaged value was used for all agents
Figure 1. Flow-density plot showing capacity drop and hysteresis
The effects of building permeability on the exposure of agents were computed during the post-processing stage by using separate state variables for summing up exposure within and outside buildings. Building permeability can then be treated as a variable when computing the cost functions using SQL commands to retrieve data from the Postgres database. Building permeability will have to be handled within the agent model if compliance to SIP directives were to be modeled as a function of permeability.
Agents are routed using the Floyd-Warshall algorithm. Routing can be done to minimize distance travelled or time travelled. Mimimization of travel time can be done on the basis of posted road segment speed limits or instantaneous actuals from the simulation.
The transient behavior of the model was tested using the simulation of a ring road [ 9] with a circumference of 1080m. The agents are assumed to have a length of 6m and the maximum allowable travel speed is 30m/s. Cars enter and exit the road at regular intervals. The ring road was represented by 20 straight line segments which were also used as detectors to measure vehicle density (defined as the number of vehicles/segment length) and vehicle speed (average speed of vehicles on segment). The flow is then computed as the product of vehicle density and vehicle speed. The flow density plot averaged over all the road segments (Figure 1) displays both the so-called capacity drop and hysteresis phenomena observed experimentally.
Cost Mitigation Measures
Exposure mitigation measures implemented in the agent code include:
- Variable Building Permeability
- Stay-In-Place Directives with variable compliance
- Improved Routing
A hundred percent compliance with the SIP directive and buildings with 0% permeability to the contaminant yields the lowest cost which is confined to the agents that were already on the roads at the time of the release event. This scenario was however highly unrealistic and a number of other interventions to reduce the effects of traffic congestion were modeled.
For this simulation, each agent leaving a building and getting onto the road was modeled as a car containing 4 individuals. As expected, congestion was drastically reduced with increased average traffic velocity. However, the total cost of exposure increased up due to more agents driving through the plume from unaffected parts of the city at an early stage of the plume dispersal when it was still highly concentrated. This is likely to be a transient effect which will be reversed if the city evacuation is simulated to completion.
A minimum travel time routing based on instantaneous average traffic speeds on the roads segments was used for each agent at the moment it exited a building. Average traffic speed increased along with a decrease in the degree of gridlock. However, the improvement was either too small or was overshadowed by the effect seen in car-pooling such that the cost curves showed no significant difference.
SIP directives were removed from building which were within the bounding box of the expanding plume. This was found to be a very effective strategy since it rapidly removed the agents which were most at risk of contamination.
In simulations involving thousands of highly mobile agents, animations are a useful tool for debugging and analysis. An interactive animation tool was developed to read in the time history file of each agent. Using this tool the animation can be slowed down, frozen and reversed to detect anomalous agent behavior. During simulations, the agents can also output files containing POVRay statements which can be used to generate very realistic ray-traced animations.
The toll of a contaminant release in a crowded urban environment is a complex function of myriad factors which are not easily amenable to conventional analyses. Even obvious mitigation measures might have adverse non-intuitive results. Combined CFD-ABM simulations offer one possible way to explore the space of mitigation measures and to select a set of measures which succeed with minimum sensitivity to prevailing conditions.
- Briley, W.R., Taylor, L.K., and Whitfield, D.L., “High-Resolution Viscous Flow Simulations at Arbitrary Mach Number,” Journal of Computational Physics, Vol. 184, 2003, pp 79-105.
- Strelets, M., “Detached Eddy Simulation on Massively Separated Flow,” AIAA Paper 01-0879, 2001, 39th AIAA Aerospace Sciences Meeting and Exhibit, 8-11 January 2001, Reno NV.
- Nichols, D.S., Mitchell, B. J., Sreenivas, K., Taylor, L.K., Briley, W.R., and Whitfield, D.L., “Aerosol Propagation in an Urban Environment,” 2006, 36th AIAA Fluid Dynamics Conference and Exhibit, 5-8 June 2006, San Francisco, California.
- Marmot, A.F., and Eley, J., “Office Space Planning: Designs for Tomorrow’s Workplace,” McGraw-Hill Professional, 2000.
- Epstein, J. and R. Axtell. 1996. Growing Artificial Societies MIT Press.
- Epstein, J. 2006. Generative Social Science Princeton Press.
- Zhang, H.M., and Kim, T., “A car-following theory for multiphase vehicular traffic flow,” Transportation Research Part B, Volume 39, Issue 5 June 2005, Pages 385-399.