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

Abstract

The paper discuses new, very efficient augmentation algorithms and theorems related to maximising the flow in singlecommodity and multi-commodity networks. For the first time, efficient algorithms with linear average running time ) (m O 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.

The Dual Network Theorem for Static Flow Networks and Its Application for Maximising the Throughput Flow

“…It is important to note, that the definition of excess nodes and deficit nodes given in Todinov [18] (equations (7) and 8)is different from the definition of excess and deficit nodes given in Dong et al [6] (equations (1) and 2). The definition given by (1) and 2is based on the capacities of the ingoing and outgoing edges while the definition given by (7) and 8is based on the actual ingoing and outgoing flows of a node.…”

“…Here, we need to point out that the node-balancing theorem as a way of maximising the throughput flow in repairable flow networks, has already been stated explicitly in Todinov [18,19] where the redistribution of flow along paths connecting excess and deficit nodes has also been used. The node-balancing theorem has also been rigorously proved in Todinov [17,21] and this proof is valid for both, repairable and static flow networks.…”

The Throughput Flow Constraint Theorem and its Applications

“…In the case of a single edge failure, a method for reoptimising the flows has already been outlined in [13]. However, the critical question related to eliminating the overloading and congestion along branches of a flow network, with minimum generation shedding,was not discussed in Ref.…”

“…However, the critical question related to eliminating the overloading and congestion along branches of a flow network, with minimum generation shedding,was not discussed in Ref. [13]. Finally, Ref.…”

“…Finally, Ref. [13] treats only the special case where the throughput flow in the network is the maximum possible throughput flow. In communication networks, electrical networks and transportation networks however, the throughput flow is rarely the maximum possible throughput flow.…”