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A multiserver queue with markovian arrivals and group services with thresholds

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  • S. Chakravarthy
  • Attahiru Sule Alfa

Abstract

We consider a multiserver queueing system in which arrivals are governed by a Markovian arrival process. The system is attended by K identical exponential servers. Under a dynamic probabilistic service rule which depends on two threshold parameters, this model is studied as a Markov process. The steady‐state probability vector is shown to be of (modified) matrix‐geometric type. Efficient algorithmic procedures for the computation of the steady‐state probability vector and some key performance measures of the system are developed. Some numerical examples are discussed. © 1993 John Wiley & Sons, Inc.

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  • S. Chakravarthy & Attahiru Sule Alfa, 1993. "A multiserver queue with markovian arrivals and group services with thresholds," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(6), pages 811-827, October.
    • Handle: RePEc:wly:navres:v:40:y:1993:i:6:p:811-827
    DOI: 10.1002/1520-6750(199310)40:63.0.CO;2-R
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    References listed on IDEAS

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    1. Marcel F. Neuts & R. Nadarajan, 1982. "A Multiserver Queue with Thresholds for the Acceptance of Customers into Service," Operations Research, INFORMS, vol. 30(5), pages 948-960, October.
    2. Powell, Warren B. & Simão, Hugo P., 1986. "Numerical simulation of transient bulk queues with general vehicle dispatching strategies," Transportation Research Part B: Methodological, Elsevier, vol. 20(6), pages 477-490, December.
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    Cited by:

    1. Sergei Dudin & Olga Dudina, 2023. "Analysis of a Multi-Server Queue with Group Service and Service Time Dependent on the Size of a Group as a Model of a Delivery System," Mathematics, MDPI, vol. 11(22), pages 1-20, November.

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