Approximating earliest arrival flows with flow-dependent transit times Original Research Article

For the earliest arrival flow problem one is given a network image with capacities image and transit times image on its arcs image, together with a source and a sink vertex image. The objective is to send flow from s to t that moves through the network over time, such that for each time image the maximum possible amount of flow up to this time reaches t. If, for each image, this flow is a maximum flow for time horizon image, then it is called earliest arrival flow. In practical applications a higher congestion of an arc in the network often implies a considerable increase in transit time. Therefore, in this paper we study the earliest arrival problem for the case that the transit time of each arc in the network at each time image depends on the flow on this particular arc at that time image.