This paper studies the problem of finding a priori optimal paths to guarantee a maximum likelihood of arriving on-time in a stochastic time-varying transportation network. The reliable path can help travelers better plan their trip by measuring the risk of late under uncertain conditions. We first identify a set of mathematical relationships between the on-time arrival probability, mean and var...

In a companion paper (Godfrey and Powell 2002) we introduced an adaptive dynamic programming algorithm for stochastic dynamic resource allocation problems, which arise in the context of logistics and distribution, fleet management, and other allocation problems. The method depends on estimating separable nonlinear approximations of value functions, using a dynamic programming framework. That pa...

Heavy and uncertain traffic conditions exacerbate the commuting experience of millions of people across the globe. When planning important trips, commuters typically add an extra buffer to the expected trip duration to ensure on-time arrival. Motivated by this, we propose a new traffic assignment model that takes into account the stochastic nature of travel times. Our model extends the traditio...

The classical Wardrop user equilibrium (UE) assignment model assumes traveller choices are based on fixed, known travel times, yet these times are known to be rather variable between trips, both within and between days; typically, then, only mean travel times are represented. Classical stochastic user equilibrium (SUE) methods allow the mean travel times to be differentially perceived across th...

ÐThe dynamic and stochastic shortest path problem (DSSPP) is de®ned as ®nding the expected shortest path in a trac network where the link travel times are modeled as a continuous-time stochastic process. The objective of this paper is to examine the properties of the problem and to identify a technique that can be used to solve the DSSPP given information that will be available in networks wit...

In this paper we discuss stochastic optimal path problems where the goal is to find a path that has minimal expected cost and at the same time is less risky (in terms of travel time) than a given benchmark path. The model is suitable for a risk-averse traveler, who prefers a path with a more guaranteed travel time to another path which could be faster but could also be slower. Such risk attitud...