Routing in a Stochastic Network with Nonrecurrent Incidents: Behavioral Interpretation of Dynamic Traffic Assignment

Abstract

In an advanced traveler information system (ATIS), this study examines how to map a driver’s time constraints and risk-taking behavior to real-time routing in a probabilistic time-dependent network (or stochastic network). Accounting for en route delays and alternate routings, ATIS networks are shown to exhibit other than the first-in first-out property (FIFO) behavior: drivers who depart earlier may not arrive ahead of those who depart later. In this paper, the term FIFO is used well beyond the traditional connotation of a single queue or a single path; it applies toward multiple routes. It is used to describe a well-recognized phenomenon in dynamic traffic assignment, wherein a commuter who delays their departure time may arrive at work earlier than one who takes off earlier. Given a network with full spatiotemporal information, a wait-time search algorithm is employed to account for the best-planned delays at the origin or en route. The algorithm elicits the bottlenecks in the network and obtains the optimal wait times a driver needs to avoid these bottlenecks, given their tolerance for risk. The herein defined routing policy makes decision at every network node—based on the current states—to determine the optimal wait time (if any) and the next-hop node. The model also valuates a driver’s risk tolerance by imputing the worth of safety as a cost metric. Empirical results were obtained from a central Arkansas highway network based on incident reports obtained from the state police between the years 2000 to 2003. Solidly founded on Bellman’s optimality condition, the fundamental diagram of traffic flow, and multiattribute utility theory, the algorithm is shown to be operationally feasible for real-time applications.