Stochastic Traffic Equilibrium Based on Travel Time Robust Reliability

Abstract An assumption that pervades the current reliable traffic equilibrium problem is that probability distributions of the origin-destination (O-D) demand or/and link capacities are known explicitly. However, these distributions are difficult to be accurately obtained. This paper relaxes this assumption. It only needs to know the first m moments of travel demand (where m is a positive integer associated with the formulation of link cost function), and then applies two worse-case Value-at-Risk (WVaR) and Conditional value-at-risk (CVaR) risk measures to define robust percentile travel time (RPTT) and robust mean-excess travel time (RMETT) and prove that this two kinds travel time is equal under general distribution. By incorporating the defined travel time and travelers' perception error, the robust percentile stochastic user equilibrium (RPSUE) or robust mean-excess stochastic traffic equilibrium model (RMESTE) is proposed, which is formulated as an equivalent route-based variational inequality. Conditions are established guaranteeing existence of this equilibrium. A heuristic solution problem is introduced to solve the variational inequalities problem. A numerical example is used to illustrate the applications of the proposed model and the solution algorithm.

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