On busy periods of the critical GI/G/1 queue and BRAVO


          

刊名：Queueing systems: Theory and applications
作者：Nazarathy, Yoni（Wroclaw Univ Sci & Technol）
Palmowski, Zbigniew（Wroclaw Univ Sci & Technol）
刊号：513LB020
ISSN：0257-0130
出版年：2022
年卷期：2022, vol.102, no.1/2
页码：219-225
总页数：7
分类号：O13
关键词：Busy period；BRAVO；Single server queue；Asymptotics；TAIL ASYMPTOTICS；MOMENTS
参考中译：
语种：eng
文摘：We study critical GI/G/1 queues under finite second-moment assumptions. We show that the busy-period distribution is regularly varying with index half. We also review previously known M/G/1/ and M/M/1 derivations, yielding exact asymptotics as well as a similar derivation for GI/M/1. The busy-period asymptotics determine the growth rate of moments of the renewal process counting busy cycles. We further use this to demonstrate a Balancing Reduces Asymptotic Variance of Outputs (BRAVO) phenomenon for the work-output process (namely the busy time). This yields new insight on the BRAVOeffect. Asecond contribution of the paper is in settling previous conjectured results about GI/G/1 and GI/G/sBRAVO. Previously, infinite bufferBRAVOwas generally only settled under fourth-moment assumptions together with an assumption about the tail of the busy period. In the current paper, we strengthen the previous results by reducing to assumptions to existence of 2 + epsilon moments.



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