Optimal routing policy problems in stochastic time-dependent networks. I. Framework and taxonomy

We present optimal routing policy (ORP) problems in stochastic and time-dependent networks where general travel costs are used as the optimization criterion. The presentation is an extension to the authors' previous work on ORP problems where travel times are considered as travel costs. Routing problems are at the heart of dynamic traffic assignment models, and are also fundamental network optimization problems for a wide variety of transportation and telecommunication applications. The problems to be studied can be viewed as counterparts of the minimum cost path problems in deterministic networks. A stochastic time-dependent network is a network where link travel times and link travel costs are random variables with time-dependent distributions. A routing policy is defined as a decision rule that specifies what node to take next at each decision node based on the realized link travel times, link travel costs and the current time. We extend the framework for minimum expected travel time routing policy problems to minimum expected travel cost problems. This framework includes a general description of a stochastic time-dependent network, a decision process, a minimization problem, and a generic optimality condition for the minimization problem. We then give a taxonomy and a discussion of variants of the general problem.