On Two Interacting Markovian Queueing Systems

Valeriy A. Naumov, Yuliya V. Gaidamaka and Konstantin E. Samouylov
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Valeriy A. Naumov: Service Innovation Research Institute, 8 A Annankatu, Helsinki 00120, Finland
Yuliya V. Gaidamaka: Department of Applied Informatics and Probability, Peoples’ Friendship University of Russia (RUDN University), Miklukho-Maklaya St. 6, Moscow 117198, Russian
Konstantin E. Samouylov: Department of Applied Informatics and Probability, Peoples’ Friendship University of Russia (RUDN University), Miklukho-Maklaya St. 6, Moscow 117198, Russian

Mathematics, 2019, vol. 7, issue 9, 1-12

Abstract: In this paper, we study a Markovian queuing system consisting of two subsystems of an arbitrary structure. Each subsystem generates a multi-class Markovian arrival process of customers arriving to the other subsystem. We derive the necessary and sufficient conditions for the stationary distribution to be of product form and consider some particular cases of the subsystem interaction for which these conditions can be easily verified.

Keywords: Markovian arrival process; multi-class arrival processes; product form (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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