Temporal Expansion of a Transportation Network—II

The problem of optimal timing of investments in the capacity of transportation networks that was developed in Part I has been extended, under the assumption that all costs and usage-capacity relations are linear, to include an equilibrium relation between usage and capacity. It is shown that unique equilibrium usages can be computed by inverting a certain matrix whose dimension equals the number of arcs of the network. Simple rules are given that solve the optimal timing problem in which limits on the change in capacity per period and budgetary constraints are imposed. These procedures do not appear to place serious restrictions on the size of the networks that may be considered in applications.