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Finding an optimal core on a tree network with M/G/c/c state-dependent queues

Author

Listed:
  • Mehrdad Moshtagh

    (Shahrood University of Technology)

  • Jafar Fathali

    (Shahrood University of Technology)

  • James MacGregor Smith

    (University of Massachusetts)

  • Nezam Mahdavi-Amiri

    (Sharif University of Technology)

Abstract

We consider the stochastic queue core problem on a tree network. Our aim is to find an optimal path on a tree network subject to the average travel time of particles moving along the tree for service given by a server traversing along the optimal path. We assume that particles originating at a node on a tree network request their demands for service randomly and the server is modeled first by an M/M/1 and then by an M/G/1 queue using the FIFO discipline. We consider that all paths along which the particles travel are modeled with an M/G/c/c state-dependent queue with the particles being independent of each other having demands according to the Poisson distribution. Two algorithms are developed for computing the optimal path on a tree network along with the M/M/1 and the M/G/1 queues. The computational complexity of the algorithms and illustrative numerical results obtained by implementations of the algorithms in MATLAB software environment are given.

Suggested Citation

  • Mehrdad Moshtagh & Jafar Fathali & James MacGregor Smith & Nezam Mahdavi-Amiri, 2019. "Finding an optimal core on a tree network with M/G/c/c state-dependent queues," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(1), pages 115-142, February.
    • Handle: RePEc:spr:mathme:v:89:y:2019:i:1:d:10.1007_s00186-018-0651-3
    DOI: 10.1007/s00186-018-0651-3
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    References listed on IDEAS

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