Fast Augmentation Algorithms for Maximising the Flow in Repairable Flow Networks After a Component Failure

Abstract

The paper discusses new, very efficient augmentation algorithms and theorems related to maximising the flow in single-commodity and multi-commodity networks. For the first time, efficient algorithms with linear average running time O(m) in the size m of the network, are proposed for restoring the maximum flow in single-commodity and multi-commodity networks after a component failure. The proposed algorithms are particularly suitable for discrete-event simulators of repairable production networks whose analysis requires generating thousands of simulation histories, each including hundreds of component failures. In this respect, a new, very efficient augmentation method with linear running time has been proposed for restoring the maximum output flow of oil in oil and gas production networks, after a component failure. Another important application of the proposed algorithms is in networks controlled in real time, where upon failure, the network flows need to be redirected quickly in order to maintain a maximum output flow.