A Scalable Algorithm for the Minimum Expected Cost Restorable Flow Problem

We introduce a model for the computation of a multicommodity flow together with back-up flows for each commodity after any of a given set of failure states occurs in a network. We call such a total routing strategy a restorable multicommodity flow. One advantage of restorable flows over classical network protection methods, such as disjoint paths, is that the commodities may effectively share capacity in the network for their back-up flows. We consider the problem of finding a minimum expectedcost restorable flow, under a given probability distribution on network element failures. The underlying stochastic optimization problem can be modelled as a large-scale linear programming (LP) problem that explicitly incorporates the network failure scenarios. The size of the LPs grows swiftly, however, in the size of network and number of failure states. Our focus is on developing a scalable combinatorial algorithm for this problem. This leads us to specialize the problem to the case where traffic flows for each commodity are restricted to a (pre-computed) collection of disjoint paths. This restriction also makes it easier to restore traffic after network failures; specifically, restoration can be performed by the commodity’s endpoints without rerouting any of the traffic which was not disturbed by the network failure. In this setting, devise an approximation scheme for the feasibility problem that is based only on repeatedly pushing flow along cheapest pairs of paths. The algorithms are easily described and readily implementable. We give computational results relating how our approach scales for large networks in comparison with general-purpose LP solvers. An earlier version of this paper, with identical results, appeared in [9].