Evacuation time estimate for a total pedestrian evacuation using queuing network model and volunteered geographic information

Estimating city evacuation time is a nontrivial problem due to the interaction between thousands of individual agents, giving rise to various collective phenomena, such as bottleneck formation, intermittent flow, and stop-and-go waves. We present a mean field approach to draw relationships between road network spatial attributes, the number of evacuees, and the resultant evacuation time estimate (ETE). Using volunteered geographic information, we divide 50 United Kingdom cities into a total of 704 catchment areas (CAs) which we define as an area where all agents share the same nearest exit node. 90% of the agents are within approximate to 6,847 m of CA exit nodes with approximate to 13,778 agents/CA. We establish a characteristic flow rate from catchment area attributes (population, distance to exit node, and exit node width) and a mean flow rate in a free-flow regime by simulating total evacuations using an agent based "queuing network" model. We use these variables to determine a relationship between catchment area attributes and resultant ETEs. This relationship could enable emergency planners to make a rapid appraisal of evacuation strategies and help support decisions in the run up to a crisis.