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- Title
Analytic approach to the non-pre-emptive Markovian priority queue.
- Authors
Zuk, Josef; Kirszenblat, David
- Abstract
A new approach is developed for the joint queue-length distribution of the two-level non-pre-emptive M/M/c (i.e. 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, which 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.
- Subjects
GENERALIZATION; PROBABILITY theory
- Publication
Queueing Systems, 2024, Vol 107, Issue 1/2, p159
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-024-09912-3