M/M/c Queue with Two Priority Classes

Jianfu Wang (), Opher Baron () and Alan Scheller-Wolf ()
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Jianfu Wang: Nanyang Business School, Nanyang Technological University, Singapore, 639798
Opher Baron: Rotman School of Management, University of Toronto, Toronto, Ontario M5S 3E6, Canada
Alan Scheller-Wolf: Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213

Operations Research, 2015, vol. 63, issue 3, 733-749

Abstract: This paper provides the first exact analysis of a preemptive M/M/c queue with two priority classes having different service rates. To perform our analysis, we introduce a new technique to reduce the two-dimensionally infinite Markov chain (MC), representing the two class state space, into a one-dimensionally infinite MC, from which the generating function (GF) of the number of low-priority jobs can be derived in closed form . (The high-priority jobs form a simple M/M/c system and are thus easy to solve.) We demonstrate our methodology for the c = 1, 2 cases; when c > 2, the closed-form expression of the GF becomes cumbersome. We thus develop an exact algorithm to calculate the moments of the number of low-priority jobs for any c ≥ 2. Numerical examples demonstrate the accuracy of our algorithm and generate insights on (i) the relative effect of improving the service rate of either priority class on the mean sojourn time of low-priority jobs; (ii) the performance of a system having many slow servers compared with one having fewer fast servers; and (iii) the validity of the square root staffing rule in maintaining a fixed service level for the low-priority class. Finally, we demonstrate the potential of our methodology to solve other problems using the M/M/c queue with two priority classes, where the high-priority class is completely impatient.

Keywords: multiserver queue; multiclass; preemptive priority; different service rates (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (6)

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