Generalized maximum flow over time with intermediate storage

We consider two classical network flow problems. First, it is possible to store excess flow in the intermediate nodes to improve the total amount of flow that can be transported through the network. Second, we consider lossy network, where each arc has certain gain factor along with capacity and some portion of the flow is lost while traversing through such arcs. While both extensions have been considered separately in the literature, this will be the first time that they are considered simultaneously, which requires new mathematical model, analysis and solution methods. We consider that intermediate nodes have sufficient holding capacity and the excess flow is stored in the priority order within their capacity. We introduce the generalized maximum static and dynamic flow problems with intermediate storage in lossy network and present efficient algorithms and FPTAS for the solutions. Furthermore, notion of the generalized maximum dynamic flow with excess flow storage is extended to contraflow technique with symmetric and asymmetric arc travel times.