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<p>The asymptotic behavior of the almost surely extreme values of the queue length and queueing time for queueing systems is analyzed. First, one general limit theorem on the asymptotics of extreme values of regenerative processes is considered. Further, based on this theorem applied to queueing systems <i>M</i> |<i>G</i>|1 and <i>GI</i> |<i>M</i>|1, the law of the repeated logarithm for lim sup and the law of the triple logarithm for lim inf, as well as some of their refinements, are formulated.</p>

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Asymptotic Behavior of the Extreme Values of Queue Length and Waiting Time in M|G|1 and GI |M|1 Systems

  • 期刊论文

  • 发表日期：

    2025年1月1日

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  • I. K. Matsak,
  • S. M. Krasnitskiy

摘要

The asymptotic behavior of the almost surely extreme values of the queue length and queueing time for queueing systems is analyzed. First, one general limit theorem on the asymptotics of extreme values of regenerative processes is considered. Further, based on this theorem applied to queueing systems M |G|1 and GI |M|1, the law of the repeated logarithm for lim sup and the law of the triple logarithm for lim inf, as well as some of their refinements, are formulated.