Many-Sources Delay Asymptotics with Applications to Priority Queues

Authors:
Sanjay Shakkottai;R. Srikant
Affiliations:
Coordinated Science Laboratory and Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, USA shakkott@uiuc.edu;Coordinated Science Laboratory and Department of General Engineering, University of Illinois at Urbana-Champaign, 1308 W. Main Street, Urbana, IL 61801, USA rsrikant@uiuc.edu
Venue:
Queueing Systems: Theory and Applications
Year:
2001

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Abstract

In this paper, we study discrete-time priority queueing systems fed by a large number of arrival streams. We first provide bounds on the actual delay asymptote in terms of the virtual delay asymptote. Then, under suitable assumptions on the arrival process to the queue, we show that these asymptotes are the same. As an application of this result, we then consider a priority queueing system with two queues. Using the earlier result, we derive an upper bound on the tail probability of the delay. Under certain assumptions on the rate function of the arrival process, we show that the upper bound is tight. We then consider a system with Markovian arrivals and numerically evaluate the delay tail probability and validate these results with simulations.