Subexponential asymptotics of asymptotically block-Toeplitz and upper block-Hessenberg Markov chains


          

刊名：Queueing systems: Theory and applications
作者：Masuyama, Hiroyuki（Tokyo Metropolitan Univ）
刊号：513LB020
ISSN：0257-0130
出版年：2022
年卷期：2022, vol.102, no.1/2
页码：175-217
总页数：43
分类号：O13
关键词：Subexponential asymptotics；Upper block-Hessenberg (UBH) Markov chain；Asymptotically block-Toeplitz structure；Retrial queue；Balking queue；STATIONARY PROBABILITY VECTORS；LIGHT-TAILED ASYMPTOTICS；QUEUING-PROCESSES；M/G/1-TYPE；DISTRIBUTIONS；LENGTH
参考中译：
语种：eng
文摘：This paper studies the subexponential asymptotics of the stationary distribution vector of an asymptotically block-Toeplitz and upper block-Hessenberg (atUBH) Markov chain in discrete time. The atUBH Markov chain is a kind of the upper block-Hessenberg (UBH) one and is a generalization of the M/G/1-type one. The atUBH Markov chain typically arises from semi-Markovian retrial queues, as the queue-length process, its embedded process, or appropriately time-scaled versions of these processes. In this paper, we present subexponential and locally subexponential asymptotic formulas for the stationary distribution vector. We then extend the locally subexponential asymptotic formula to a continuous-time version of the atUBH Markov chain by uniformization and change of time scale. This extension expands the applicability of the locally subexponential asymptotic formula.



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