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Analysis of a two-phase queueing system with a fixed-size batch policy

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  • Park, Hyun-Min
  • Kim, Tae-Sung
  • Chae, Kyung C.

Abstract

We consider a single-server, two-phase queueing system with a fixed-size batch policy. Customers arrive at the system according to a Poisson process and receive batch service in the first-phase followed by individual services in the second-phase. The batch service in the first-phase is applied for a fixed number (k) of customers. If the number of customers waiting for the first-phase service is less than k when the server completes individual services, the system stays idle until the queue length reaches k. We derive the steady state distribution for the system's queue length. We also show that the stochastic decomposition property can be applied to our model. Finally, we illustrate the process of finding the optimal batch size that minimizes the long-run average cost under a linear cost structure.

Suggested Citation

  • Park, Hyun-Min & Kim, Tae-Sung & Chae, Kyung C., 2010. "Analysis of a two-phase queueing system with a fixed-size batch policy," European Journal of Operational Research, Elsevier, vol. 206(1), pages 118-122, October.
    • Handle: RePEc:eee:ejores:v:206:y:2010:i:1:p:118-122
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    References listed on IDEAS

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    1. Sennott, Linn I. & Van Oyen, Mark P. & Iravani, Seyed M.R., 2006. "Optimal dynamic assignment of a flexible worker on an open production line with specialists," European Journal of Operational Research, Elsevier, vol. 170(2), pages 541-566, April.
    2. Kim, Tae-Sung & Park, Hyun-Min, 2003. "Cycle analysis of a two-phase queueing model with threshold," European Journal of Operational Research, Elsevier, vol. 144(1), pages 157-165, January.
    3. Ronald W. Wolff, 1982. "Poisson Arrivals See Time Averages," Operations Research, INFORMS, vol. 30(2), pages 223-231, April.
    4. S. W. Fuhrmann & Robert B. Cooper, 1985. "Stochastic Decompositions in the M / G /1 Queue with Generalized Vacations," Operations Research, INFORMS, vol. 33(5), pages 1117-1129, October.
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    Cited by:

    1. Hanukov, Gabi, 2022. "Improving efficiency of service systems by performing a part of the service without the customer's presence," European Journal of Operational Research, Elsevier, vol. 302(2), pages 606-620.

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