Computing the probability mass function of the maximum flow through a reliable network

In this paper we propose a fast state-space enumeration based algorithm called TOP-DOWN capable of computing the probability mass function of the maximum s-t flow through reliable networks. The algorithm computes the probability mass function in the decreasing order of maximum s-t flow values in the network states. This order of enumeration makes this algorithm attractive for commonly observed reliable networks, e.g., in telecommunication networks where link reliabilities are high. We compare the performance of the TOP-DOWN algorithm with a path-based exact algorithm and show that the TOP-DOWN algorithm solves problem much faster and is able to handle much larger problems than existing algorithms.

Evaluating Downside Risks in Reliable Networks

Reliable networks are those in which network elements have a positive probability of failing. Conventional performance measures for such networks concern themselves either with expected network performance or with the performance of the network when it is performing well. In reliable networks modeling critical functions, decision makers are often more concerned with network performance when the network is not performing well. In this paper, we study the single-source single-destination maximum flow problem through reliable networks and propose two risk measures to evaluate such downside performance. We propose an algorithm called COMPUTE-RISK to compute downside risk measures, and report our computational experience with the proposed algorithm.