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Analytic Approach to the Non-Preemptive Markovian Priority Queue
  • Josef Zuk ,
  • David Kirszenblat
Josef Zuk

Corresponding Author:[email protected]

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David Kirszenblat
Defence Science and Technology Group


A new approach is developed for the joint queue-length distribution of the two-level non-preemptive Markovian priority queue that allows explicit and exact results to be obtained. Marginal distributions are derived for the general multi-level problem. The results are based on a representation of the joint queue-length probability mass function as a single-variable complex contour integral, that reduces to a real integral on a finite interval arising from a cut on the real axis. Both numerical quadrature rules and exact finite sums, involving Legendre polynomials and their generalization, are presented for the joint and marginal distributions. A high level of accuracy is demonstrated across the entire ergodic region. Relationships are established with the waiting-time distributions. Asymptotic behaviour in the large queue-length regime is extracted.
29 Jan 2024Submitted to TechRxiv
08 Feb 2024Published in TechRxiv