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Queueing Systems
Published in: Queueing Systems 3-4/2015

01-04-2015

A law of iterated logarithm for multiclass queues with preemptive priority service discipline

Authors: Yongjiang Guo, Yunan Liu

Published in: Queueing Systems | Issue 3-4/2015

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Abstract

A law of iterated logarithm (LIL) is established for a multiclass queueing model, having a preemptive priority service discipline, one server and \(K\) customer classes, with each class characterized by a renewal arrival process and i.i.d. service times. The LIL limits quantify the magnitude of asymptotic stochastic fluctuations of the stochastic processes compensated by their deterministic fluid limits. The LIL is established in three cases: underloaded, critically loaded, and overloaded, for five performance measures: queue length, workload, busy time, idle time, and number of departures. The proof of the LIL is based on a strong approximation approach, which approximates discrete performance processes with reflected Brownian motions. We conduct numerical examples to provide insights on these LIL results.
previous article The stability of the deterministic Skorokhod problem is undecidable
next article Heavy-traffic asymptotics for networks of parallel queues with Markov-modulated service speeds

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Appendix
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Metadata
Title
A law of iterated logarithm for multiclass queues with preemptive priority service discipline
Authors
Yongjiang Guo
Yunan Liu
Publication date
01-04-2015
Publisher
Springer US
Published in
Queueing Systems / Issue 3-4/2015
Print ISSN: 0257-0130
Electronic ISSN: 1572-9443
DOI
https://doi.org/10.1007/s11134-014-9419-5

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