Flows over Time with Load-Dependent Transit Times

More than forty years ago, Ford and Fulkerson studied maximum s-t-flows over time (also called `dynamic' flows) in networks with fixed transit times on the arcs and a fixed time horizon. Here, flow on arcs may change over time and transit times specify the amount of time it takes for flow to travel through a particular arc. Ford and Fulkerson proved that there always exists an optimal solution which sends flow on certain s-t-paths at a constant rate as long as there is enough time left for the flow along a path to arrive at the sink; a flow over time featuring this simple structure is called `temporally repeated'