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State Dependent Models of Material Handling Systems in Closed Queueing Networks

Author

Listed:
  • Laoucine Kerbache

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

  • J. Macgregor Smith

    (Department of Mechanical and Industrial Engineering [UMass] - UMass Amherst - University of Massachusetts [Amherst] - UMASS - University of Massachusetts System)

Abstract

A comprehensive algorithmic analysis of finite state-dependent queueing models and exponentially distributed workstations is formulated and presented. The material handling system is modeled with finite state-dependent queueing network M/G/c/c models and the individual workstations are modeled with exponentially distributed single and multi-server M/M/c queueing models. The coupling of these queueing models is unique via the material handling structure. The performance modeling of the systems for series, merge, and split and other complex network topologies are included so as to demonstrate the type of topological network design that is possible with these incorporated material handling systems. Of some importance, it is shown that these integrated M/M/c and M/G/c/c networks have a product form when the population arriving at the M/G/c/c queues is controlled. Numerous experimental results demonstrate the efficacy of our approach for a variety of contexts and situations.

Suggested Citation

  • Laoucine Kerbache & J. Macgregor Smith, 2012. "State Dependent Models of Material Handling Systems in Closed Queueing Networks," Post-Print hal-00796338, HAL.
    • Handle: RePEc:hal:journl:hal-00796338
    DOI: 10.1080/00207543.2010.535041
    as

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    Citations

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    Cited by:

    1. James MacGregor Smith, 2018. "Simultaneous buffer and service rate allocation in open finite queueing networks," IISE Transactions, Taylor & Francis Journals, vol. 50(3), pages 203-216, March.
    2. Ruzelan Khalid & Mohd Kamal M. Nawawi & Luthful A Kawsar & Noraida A Ghani & Anton A Kamil & Adli Mustafa, 2013. "A Discrete Event Simulation Model for Evaluating the Performances of an M/G/C/C State Dependent Queuing System," PLOS ONE, Public Library of Science, vol. 8(4), pages 1-9, April.
    3. Amjath, Mohamed & Kerbache, Laoucine & Smith, James MacGregor & Elomri, Adel, 2022. "Fleet sizing of trucks for an inter-facility material handling system using closed queueing networks," Operations Research Perspectives, Elsevier, vol. 9(C).
    4. J. Smith, 2015. "Optimal workload allocation in closed queueing networks with state dependent queues," Annals of Operations Research, Springer, vol. 231(1), pages 157-183, August.

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