Joint Queue-Length Distribution for the Non-Preemptive Multi-Server Multi-Level Markovian Priority Queue

Josef Zuk; David Kirszenblat

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arXiv · 2311.01641

Joint Queue-Length Distribution for the Non-Preemptive Multi-Server Multi-Level Markovian Priority Queue

Josef Zuk·David Kirszenblat

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Abstract

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.

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BibTeX RIS

Josef Zuk, David Kirszenblat. 2023-11-02. Joint Queue-Length Distribution for the Non-Preemptive Multi-Server Multi-Level Markovian Priority Queue. https://arxiv.org/abs/2311.01641

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