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A unified approach for large queue asymptotics in a heterogeneous multiserver queue

  • Masakiyo Miyazawa (a1)
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.

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* Postal address: Department of Information Sciences, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510, Japan. Email address: miyazawa@rs.tus.ac.jp
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Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
  • URL: /core/journals/advances-in-applied-probability
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