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Asymptotics of waiting time distributions in the accumulating priority queue

Joris Walraevens (joris.walraevens@ugent.be), Thomas Giel, Stijn Vuyst and Sabine Wittevrongel
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Joris Walraevens: Ghent University
Thomas Giel: Ghent University
Stijn Vuyst: Ghent University
Sabine Wittevrongel: Ghent University

Queueing Systems: Theory and Applications, 2022, vol. 101, issue 3, No 2, 244 pages

Abstract: Abstract We analyze the asymptotics of waiting time distributions in the two-class accumulating priority queue with general service times. The accumulating priority queue was suggested by Kleinrock in the 60s—he coined it time-dependent priority—to diversify waiting time objectives of different classes in a paramaterized way. It also avoids the typical starvation problem of regular priority queues. All customers build up priority linearly while waiting in the queue but at a class-dependent rate. At a service opportunity epoch, the customer with highest priority present is served. Stanford and colleagues recently calculated the Laplace–Stieltjes Transform (LST) of the waiting time distributions of the different classes, but only invert these LSTs numerically. In this paper, we analytically calculate the asymptotics of the corresponding distributions from these LSTs. We show that different singularities of the LST can play a role in the asymptotics, depending on the magnitude of service differentiation between both classes.

Keywords: Accumulating priority; Dominant singularity analysis; 60K25; 90B22 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s11134-022-09839-7

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