Nonlinear Accumulating Priority Queues with Equivalent Linear Proxies

Na Li (), David A. Stanford (), Peter Taylor () and Ilze Ziedins ()
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Na Li: Statistical and Actuarial Sciences, University of Western Ontario, London, Ontario N6A 3K7, Canada; McMaster Centre for Transfusion Research, McMaster University, Hamilton, Ontario L8S 4L8, Canada
David A. Stanford: Statistical and Actuarial Sciences, University of Western Ontario, London, Ontario N6A 3K7, Canada
Peter Taylor: Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia
Ilze Ziedins: Statistics, University of Auckland, Auckland 1142, New Zealand

Operations Research, 2017, vol. 65, issue 6, 1712-1721

Abstract: In 1964, Kleinrock proposed a queueing discipline for a single-server queue in which customers from different classes accumulate priority as linear functions of their waiting time. At the instant that a server becomes free, it selects the waiting customer with the highest accumulated priority, provided that the queue is nonempty. He developed a recursion for calculating the expected waiting time for each class. In 2014, Stanford, Taylor, and Ziedins reconsidered this queue, which they termed the accumulating priority queue (APQ), and derived the waiting time distribution for each class. Kleinrock and Finkelstein in 1967 also studied an accumulating priority system in which customers’ priorities increase as a power-law function of their waiting time. They established that it is possible to associate a particular linear APQ with such a power-law APQ, so that the expected waiting times of customers from all classes are preserved. In this paper, we extend their analysis to characterise the class of nonlinear APQs for which an equivalent linear APQ can be found, in the sense that, for identical sample paths of the arrival and service processes, the ordering of all customers is identical at all times in both the linear and nonlinear systems.

Keywords: key performance indicator; linear proxy; waiting times (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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