Continuous-Time Flows in Networks

We consider a class of maximum flow problems formulated in a directed network where the arc flows vary as Lebesgue-measurable functions of time, and storage is allowed at the nodes of the network. A max flow-min cut result of Anderson, Nash and Philpott [1] is extended to cover the case where each arc has a traversal time. The ideas of the paper are then applied to derive some simple results on emptying networks at least cost.