Two major sources of uncertainty in evacuation modeling are randomness inevacuation demand and roadway capacity. This paper proposes an analyticalsystem optimal dynamic traffic assignment model with probabilistic demandand capacity constraints to take these two sources of uncertainty into account. The problem is modeled based on two different stochastic modeling approaches in terms of its 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-sidesis employed. The differences of two different models in terms of model reliability are discussed with the help of a numerical example. Although theuse of 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 capacityuncertainties have a vital importance. 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.
Abstract