A unified approach for large queue asymptotics in a heterogeneous multiserver queue. (17th March 2017)

• Record Type: Journal Article
• Authors: Miyazawa, Masakiyo
• Is Part Of: Advances in applied probability. Volume 49:Number 1(2017)
• Page Start: 182
• Page End: 220
• Publication Date: 2017-03-17
• Subjects: Piecewise-deterministic Markov process, -- martingale, -- heterogeneous server, -- queue length process, -- stationary distribution, -- tail asymptotics, -- large variance, -- heavy-traffic approximation; Primary 60K25, -- Secondary 60J27, -- 60K37; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/apr.2016.84
• Languages: English
• ISSNs: 0001-8678

Abstract

Abstract: We are interested in a large queue in a GI/G/ k queue with heterogeneous servers. For this, we consider tail asymptotics and weak limit approximations for the stationary distribution of its queue length process in continuous time under a stability condition. Here, two weak limit approximations are considered. One is when the variances of the interarrival and/or service times are bounded, and the other is when they become large. Both require a heavy-traffic condition. Tail asymptotics and heavy-traffic approximations have been separately studied in the literature. We develop a unified approach based on a martingale produced by a good test function for a Markov process to answer both problems.