Path comparisons for a priori and time-adaptive decisions in stochastic, time-varying networks

Travel times in congested transportation networks are time-varying quantities that can at best be known a priori probabilistically. In such networks, the arc weights (travel times) are represented by random variables whose probability distribution functions vary with time. These networks are referred to herein as stochastic, time-varying, or STV, networks. The determination of “least time” routes in STV networks is more difficult than in deterministic networks, in part because, for a given departure time, more than one path may exist between an origin and destination, each with a positive probability of having the least travel time. In this paper, measures for comparing time-varying, random path travel times over a time period are given for both a priori optimization and time-adaptive choices (where a driver may react to revealed arrival times at intermediate nodes). The resulting measures are central to the development of methodologies for determining “optimal” paths in STV networks.