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<p>In the finite capacity queueing system, a single server provides service in the form of groups, where customers utilize the Batch Markovian Arrival Process (BMAP) for entering the system. Group of various batch sizes are served, and it is expected that the service durations follow a phase-type distribution. The service rate accelerates to rapid service when the buffer size is greater than some threshold value, and it returns to its normal rate after the current service is finished. The batch arrival customer may balk at the idle time of the server. The server undergoes the setup process during the completion of each service. The matrix analytic method is used to analyze the steady-state conditions for this queueing model. Performance measures based on regular splitting are presented, and numerical examples are discussed.</p>

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Analysis of BMAP/PH/ 1/K Queueing Model with Controllable Group Service, Setup Time and Balking

  • 期刊论文

  • 发表日期：

    2026年8月1日

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  • A. Melikov,
  • S. Navendhan,
  • G. Ayyappan

摘要

In the finite capacity queueing system, a single server provides service in the form of groups, where customers utilize the Batch Markovian Arrival Process (BMAP) for entering the system. Group of various batch sizes are served, and it is expected that the service durations follow a phase-type distribution. The service rate accelerates to rapid service when the buffer size is greater than some threshold value, and it returns to its normal rate after the current service is finished. The batch arrival customer may balk at the idle time of the server. The server undergoes the setup process during the completion of each service. The matrix analytic method is used to analyze the steady-state conditions for this queueing model. Performance measures based on regular splitting are presented, and numerical examples are discussed.