Reliability Analysis of Evacuation Routes Under Capacity Uncertainty of Road Links

In this paper, we present a reliability based evacuation route planning model that seeks to find the relationship between the clearance time, number of evacuation paths and congestion probability during evacuation. Most of the existing models for network evacuation assume deterministic capacity estimates for road links without taking into account the uncertainty in capacities induced by myriad external conditions. Only a handful of models exist in the literature that account for capacity uncertainty of road links. We extend the dynamic network based evacuation model with probabilistic arc capacity constraints and formulate a minimum cost network flow problem for finding a lower bound on clearance time within the framework of chance constrained programming technique. We also use the concept of network breakdown minimization principle of traffic flow for evacuation planning problem and formulate a path based evacuation routing and scheduling model. Given the horizon time for evacuation, model selects the evacuation paths and finds flows on the selected paths that result in minimum congestion in the network and finds the reliability of the evacuation plan. Numerical examples are presented and we discuss the effectiveness of the stochastic models in evacuation planning. It is shown that the reliability based evacuation plan is conservative as compared to plans made using a deterministic model. Stochastic models guarantee that congestion can be avoided with greater confidence level at the cost of increased clearance time.