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

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  • Sharma, Megha
  • Ghosh, Diptesh

Abstract

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.

Suggested Citation

  • Sharma, Megha & Ghosh, Diptesh, 2009. "Computing the probability mass function of the maximum flow through a reliable network," IIMA Working Papers WP2009-10-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    • Handle: RePEc:iim:iimawp:8338
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    References listed on IDEAS

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    1. J. Scott Provan & Michael O. Ball, 1984. "Computing Network Reliability in Time Polynomial in the Number of Cuts," Operations Research, INFORMS, vol. 32(3), pages 516-526, June.
    2. Sharma, Megha & Ghosh, Diptesh, 2009. "Evaluating Downside Risks in Reliable Networks," IIMA Working Papers WP2009-09-02, Indian Institute of Management Ahmedabad, Research and Publication Department.
    3. Megha Sharma & Ghosh, Diptesh, 2009. "Speeding Up the Estimation of Expected Maximum Flows Through Reliable Networks," IIMA Working Papers WP2009-04-05, Indian Institute of Management Ahmedabad, Research and Publication Department.
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