Optimal Control of Oversaturated Store-and-Forward Transportation Networks

A general method is developed for the dynamic optimization of multi-commodity flows in an oversaturated, store-and-forward transportation network. The network is characterized by time-varying inputs, and the existence of queues in front of certain nodes where the incoming flows exceed the capacity to discharge them, during a certain period of oversaturation. The method consists of discretizing in time and solving a linear programming (LP) problem, in order to obtain the order of exhaustion of the various queues and an approximation to their, optimum time variation. The LP solution may be refined to any degree of desired accuracy, or used as a first step in a two-step procedure, where the order of exhaustion of the queues of the LP solution is used in a variational scheme to obtain the exact solution. The method is demonstrated by optimizing the operation of a two-node, four-queue network.