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Maximizing throughput in finite-source parallel queue systems

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  • Delasay, Mohammad
  • Kolfal, Bora
  • Ingolfsson, Armann

Abstract

Motivated by the dispatching of trucks to shovels in surface mines, we study optimal routing in a Markovian finite-source, multi-server queueing system with heterogeneous servers, each with a separate queue. We formulate the problem of routing customers to servers to maximize the system throughput as a Markov Decision Process. When the servers are homogeneous, we demonstrate that the Shortest Queue policy is optimal, and when the servers are heterogeneous, we partially characterize the optimal policy and present a near-optimal and simple-to-implement policy. We use the model to illustrate the substantial benefits of pooling, by comparing it to the permanent assignment of customers to servers.

Suggested Citation

  • Delasay, Mohammad & Kolfal, Bora & Ingolfsson, Armann, 2012. "Maximizing throughput in finite-source parallel queue systems," European Journal of Operational Research, Elsevier, vol. 217(3), pages 554-559.
    • Handle: RePEc:eee:ejores:v:217:y:2012:i:3:p:554-559
    DOI: 10.1016/j.ejor.2011.09.041
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    References listed on IDEAS

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    1. Wartenhorst, Pieter, 1995. "N parallel queueing systems with server breakdown and repair," European Journal of Operational Research, Elsevier, vol. 82(2), pages 302-322, April.
    2. Susan H. Xu & Rhonda Righter & J. George Shanthikumar, 1992. "Optimal Dynamic Assignment of Customers to Heterogeneous Servers in Parallel," Operations Research, INFORMS, vol. 40(6), pages 1126-1138, December.
    3. Ki Ching, Wai, 2001. "Machine repairing models for production systems," International Journal of Production Economics, Elsevier, vol. 70(3), pages 257-266, April.
    4. Lola Coleman Goheen, 1977. "On the Optimal Operating Policy for the Machine Repair Problem When Failure and Repair Times Have Erlang Distribution," Operations Research, INFORMS, vol. 25(3), pages 484-492, June.
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    Citations

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    Cited by:

    1. Brooks, James D. & Kar, Koushik & Mendonça, David J., 2016. "Allocation of flows in closed bipartite queueing networks," European Journal of Operational Research, Elsevier, vol. 255(2), pages 333-344.
    2. Dmitry Efrosinin & Natalia Stepanova & Janos Sztrik, 2021. "Algorithmic Analysis of Finite-Source Multi-Server Heterogeneous Queueing Systems," Mathematics, MDPI, vol. 9(20), pages 1-24, October.
    3. Zhao, Yaping & Xu, Xiaoyun & Li, Haidong & Liu, Yanni, 2016. "Prioritized customer order scheduling to maximize throughput," European Journal of Operational Research, Elsevier, vol. 255(2), pages 345-356.
    4. Ta, Chung H. & Ingolfsson, Armann & Doucette, John, 2013. "A linear model for surface mining haul truck allocation incorporating shovel idle probabilities," European Journal of Operational Research, Elsevier, vol. 231(3), pages 770-778.
    5. Dmitry Efrosinin & Natalia Stepanova, 2021. "Optimal Open-Loop Routing and Threshold-Based Allocation in TWO Parallel QUEUEING Systems with Heterogeneous Servers," Mathematics, MDPI, vol. 9(21), pages 1-18, October.

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