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

Hiroyuki Masuyama ()
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Hiroyuki Masuyama: Tokyo Metropolitan University

Queueing Systems: Theory and Applications, 2022, vol. 102, issue 1, No 9, 175-217

Abstract: Abstract 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.

Keywords: Subexponential asymptotics; Upper block-Hessenberg (UBH) Markov chain; Asymptotically block-Toeplitz structure; Retrial queue; Balking queue; 60J10; 60K25 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11134-022-09857-5

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