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<p>Explicit results are obtained using simple and exact methods for the joint queue-length distribution of the M/M/<i>c</i> queue with an arbitrary number of non-preemptive priority levels. This work is the first to provide explicit results for the joint probability generating function and joint probability mass function for a general number of priority levels. A fixed-point iteration is developed for the stationary balance equations, which enables direct computation of the joint queue-length distribution. A multi-variate probability generating function is also derived, from which the joint probability mass function can be computed by means of a multi-dimensional fast Fourier transform method.</p>

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Joint queue-length distribution for the non-preemptive multi-server multi-level Markovian priority queue

  • 期刊论文

  • 发表日期：

    2026年3月6日

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  • Josef Zuk,
  • David Kirszenblat

摘要

Explicit results are obtained using simple and exact methods for the joint queue-length distribution of the M/M/c queue with an arbitrary number of non-preemptive priority levels. This work is the first to provide explicit results for the joint probability generating function and joint probability mass function for a general number of priority levels. A fixed-point iteration is developed for the stationary balance equations, which enables direct computation of the joint queue-length distribution. A multi-variate probability generating function is also derived, from which the joint probability mass function can be computed by means of a multi-dimensional fast Fourier transform method.