Abstract
Two major sources of uncertainty in evacuation modeling are randomness in evacuation demand and roadway capacity. This paper takes these two sources of uncertainty into account in proposing an analytical system-optimal dynamic traffic assignment model with probabilistic demand and capacity constraints. The problem is modeled on the basis of two stochastic modeling approaches considering the problem's constraints, namely, individual chance constraints and joint chance constraints. The probability distributions of random demands and capacities are assumed to be discrete. A solution method customized for stochastic programming models with random discrete right-hand sides is used. The differences in reliability between the two models are discussed with the help of a numerical example. Although use of the proposed stochastic dynamic traffic assignment is not confined to evacuation modeling, it provides an important probabilistic modeling and analysis framework for evacuation modeling in which the demand and capacity uncertainties are vital. Overall, the proposed model enables evacuation planners to obtain results that can be interpreted through well-understood reliability measures instead of deterministic point estimates of the highly stochastic evacuation process.