Network routing problems in stochastic-state networks
Network Routing problems focus on exploiting the network-based struc- ture of a mathematical optimization problem to establish e cient solutions that are tailored to the problem at hand. The topic of this dissertation relates to a speci c class of network routing problems, those in which the properties of the nodes and/or links in the network can be represented as instances of a particular network-state realization, where the set possible network-state can be represented by a discrete probability distribution. The main contribution of this research is to formalize the de nition of such families of network-states, a construct we de ne as Stochastic-State Networks (SSN), and show that certain properties of such networks can allow for the systematic development of exact and heuristic solution procedures for a speciric class of network routing problems. The class of network problems considered are those in which dynamic routing decisions are seeked, and where information about the network can only be gathered through direct observation of the instantiation of the stochastic elements of the network. Two speci c instances of routing problems are considered: a dynamic instance of a Traveling Salesman Problem, and a routing problem in the presence of stochastic link failures. Exact methods and heuristics are developed by exploiting the underlaying stochastic-state network formulation and numerical results are presented.