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

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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.

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Acknowledgements

The first and second authors are thankful to Shahrood University of Technology and the fourth author thanks Sharif University of Technology for supporting this work.

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Authors and Affiliations

  1. Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran

    Mehrdad Moshtagh & Jafar Fathali

  2. Department of Mechanical and Industrial Engineering, University of Massachusetts, Amherst, MA, 01003, USA

    James MacGregor Smith

  3. Faculty of Mathematical Sciences, Sharif University of Technology, Tehran, Iran

    Nezam Mahdavi-Amiri

Authors
  1. Mehrdad Moshtagh
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  2. Jafar Fathali
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  3. James MacGregor Smith
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  4. Nezam Mahdavi-Amiri
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Correspondence to Jafar Fathali.

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Moshtagh, M., Fathali, J., Smith, J.M. et al. Finding an optimal core on a tree network with M/G/c/c state-dependent queues. Math Meth Oper Res 89, 115–142 (2019). https://doi.org/10.1007/s00186-018-0651-3

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  • DOI: https://doi.org/10.1007/s00186-018-0651-3

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