Optimal Time-Varying Flows on Congested Networks

Abstract

This paper develops a well-behaved convex programming model for least-cost flows on a general congested network on which flows vary over time, as for example during peak/off-peak demand cycles. The model differs from static network models and from most work on multiperiod network models because it treats the time taken to traverse each arc as varying with the flow rate on the arc. We develop extensions of the model to handle multiple destinations and multiple commodities, though not all of these extensions yield convex programs. As part of its solution, the model yields a set of nonnegative time-varying optimal flow controls for each arc. We determine and discuss sufficient conditions under which some or all of these optimal flow controls will be zero-valued. These conditions are consistent with computational experience. Finally, we indicate directions for further research.