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Further results for the M/M(a, ∞)/N batch-service system

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Abstract

A multi-server Markovian queueing system is considered such that an idle server will take the entire batch of waiting customers into service as soon as their number is as large as some control limit. Some new results are derived. These include the distribution of the time interval between two consecutive commencements of service (including itsrth moment) and the actual service batch size distribution. In addition, the average customer waiting time in the queue is derived by a simple combinatorial approach.

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Author notes

  1. S. H. Sim

    Present address: Ontario Hydro Research Division, 800 Kipling Avenue, M8Z 5S4, Toronto, Canada

Authors and Affiliations

  1. Department of Industrial Engineering, University of Toronto, M5S 1A4, Toronto, Canada

    S. H. Sim & J. G. C. Templeton

Authors
  1. S. H. Sim
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  2. J. G. C. Templeton
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Additional information

This is an expanded version of “Combinatorial analysis of batch-service queues” which was presented at the ORSA/TIMS meeting, Orlando, Florida, November 1983.

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Sim, S.H., Templeton, J.G.C. Further results for the M/M(a, ∞)/N batch-service system. Queueing Syst 6, 277–286 (1990). https://doi.org/10.1007/BF02411478

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  • DOI: https://doi.org/10.1007/BF02411478

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