Estimation of expected minimum paths in dynamic and stochastic traffic networks

For most in-vehicle route guidance systems (RGS) currently under development, the optimal route between an origin and destination is defined as the one with the minimum expected travel time. This optimal route is calculated by applying standard shortest path algorithms to the network where the link travel times are modeled as deterministic rather than as stochastic. The drawback to this method is that while it is computationally tractable, it may, in fact, generate a sub-optimal solution. Conversely, when the stochastic nature of link travel times are explicitly modeled, an optimal algorithm can become computationally inefficient for use within an actual application. The objective of this paper is to develop a new shortest path algorithm which takes into account the stochastic nature of link travel times without significantly increasing the overall computation time. The dynamic and stochastic shortest path problem (DSSPP) is first defined and the properties associated with this problem are discussed. A heuristic algorithm based on the k-shortest path algorithm is subsequently proposed. The trade-off between solution quality and computational efficiency of the proposed algorithm will be demonstrated on a network from Edmonton, Alberta, Canada.