Geodesic
Sufficient condition for primary queues stationary distribution existence in a tandem of queuing systems
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2018), pp. 49-74

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A tandem of two queuing systems is under consideration. Customers having been serviced in the first system are non-instantaneously transferred to the second system. Each system has primary input flow generated by an environment. Besides the second system besides has input flow of customers that were serviced by the first system. A mathematical model is constructed in the form of a multidimensional denumerable discrete-time Markov chain defined on an explicitly built probability space. The Markov chain describing service dynamics and primary input flows queues fluctuations is investigated. A sufficient condition for the chain stationary distribution existence is found.
Keywords: stationary distribution, controlling queueing system, conflicting flows, multidimensional denumerable discrete-time Markov chain.
Mots-clés : cyclic algorithm with prolongations 
@article{VTPMK_2018_2_a2,
     author = {V. Kocheganov and A. V. Zorine},
     title = {Sufficient condition for primary queues stationary distribution existence in a tandem of queuing systems},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {49--74},
     publisher = {mathdoc},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2018_2_a2/}
}
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V. Kocheganov; A. V. Zorine. Sufficient condition for primary queues stationary distribution existence in a tandem of queuing systems. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2018), pp. 49-74. http://geodesic.mathdoc.fr/item/VTPMK_2018_2_a2/