Second-order bounds for the M/M/s queue with random arrival rate

Wouter J. E. C. Eekelen (), Grani A. Hanasusanto, John J. Hasenbein and Johan S. H. Leeuwaarden
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Wouter J. E. C. Eekelen: University of Chicago
Grani A. Hanasusanto: University of Illinois Urbana-Champaign
John J. Hasenbein: The University of Texas at Austin
Johan S. H. Leeuwaarden: Tilburg University

Queueing Systems: Theory and Applications, 2025, vol. 109, issue 1, No 3, 31 pages

Abstract: Abstract Consider an M/M/s queue with the additional feature that the arrival rate is a random variable of which only the mean, variance, and range are known. Using semi-infinite linear programming and duality theory for moment problems, we establish for this setting tight bounds for the expected waiting time. These bounds correspond to an arrival rate that takes only two values. The proofs crucially depend on the fact that the expected waiting time, as function of the arrival rate, has a convex derivative. We apply the novel tight bounds to a rational queueing model, where arriving individuals decide to join or balk based on expected utility and only have partial knowledge about the market size.

Keywords: Second-order bounds; Rational queueing; M/M/s queue; Poisson mixture model; Parametric uncertainty; 60K30; 66K25; 90B22 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11134-024-09931-0

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