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Queueing Systems

Erschienen in:

08.01.2020

Stationary distributions and convergence for M/M/1 queues in interactive random environment

verfasst von: Guodong Pang, Andrey Sarantsev, Yana Belopolskaya, Yuri Suhov

Erschienen in: Queueing Systems | Ausgabe 3-4/2020

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Abstract

A Markovian single-server queue is studied in an interactive random environment. The arrival and service rates of the queue depend on the environment, while the transition dynamics of the random environment depend on the queue length. We consider in detail two types of Markov random environments: a pure jump process and a reflected jump diffusion. In both cases, the joint dynamics are constructed so that the stationary distribution can be explicitly found in a simple form (weighted geometric). We also derive an explicit estimate for the exponential rate of convergence to the stationary distribution via coupling.

Vorheriger Artikel Algorithms for the upper bound mean waiting time in the GI/GI/1 queue

Nächster Artikel Analysis of the infinite server queues with semi-Markovian multivariate discounted inputs

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Titel: Stationary distributions and convergence for M/M/1 queues in interactive random environment
verfasst von: Guodong Pang
Andrey Sarantsev
Yana Belopolskaya
Yuri Suhov
Publikationsdatum: 08.01.2020
Verlag: Springer US
Erschienen in: Queueing Systems / Ausgabe 3-4/2020
Print ISSN: 0257-0130
Elektronische ISSN: 1572-9443
DOI: https://doi.org/10.1007/s11134-019-09644-9

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