Explicit results for the distributions of queue lengths for a non-preemptive two-level priority queue

Explicit results are derived using simple and exact methods for the joint and marginal queue-length distributions for the M/M/ c queue with two non-preemptive priority levels. Equal service rates are assumed. Two approaches are considered. One is based on numerically robust quadratic recurrence rela...

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Bibliographic Details
Published in:Annals of operations research 2024-10, Vol.341 (2-3), p.1223-1246
Main Authors: Zuk, Josef, Kirszenblat, David
Format: Article
Language:English
Subjects:
Business and Management
Combinatorics
Exact solutions
Operations research
Operations Research/Decision Theory
Original Research
Preempting
Probability
Queues
Robustness (mathematics)
Theory of Computation
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Summary:Explicit results are derived using simple and exact methods for the joint and marginal queue-length distributions for the M/M/ c queue with two non-preemptive priority levels. Equal service rates are assumed. Two approaches are considered. One is based on numerically robust quadratic recurrence relations. The other is based on a complex contour-integral representation that yields exact closed-form analytical expressions, not hitherto available in the literature, that can also be evaluated numerically with very high accuracy.
ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-024-06237-5