On the insensitivity of the stationary distribution of the limited resources queuing system with state-dependent arrival and service rates

E. S. Sopin^ab, V. A. Naumov^c, K. E. Samouylov<sup>ab

a</sup> Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Str., Moscow 117198, Russian Federation
^b Institute of Informatics Problems, Federal Research Center “Computer Sciences and Control” of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
^c Service Innovation Research Institute (PIKE), 8A Annankatu, Helsinki 00120, Finland

Abstract: The authors consider further generalization of the queuing systems, in which customers require not only a server but also a certain amount of limited resources. In the considered queuing system, arrival and serving intensities depend on the statе of the system. The authors assume an arbitrary distribution of the service time. The authors prove that the stationary distribution of the system has product form in the case of Poisson arrivals. On the insensitivity of the stationary distribution of the limited resources queuing system with state-dependent arrival Moreover, it was shown that the steady-state probability distribution of number of customers in the system and volumes of occupied resources depends on the service time distribution only through its mean.

Keywords: queueing system; limited resources; insensitivity; service time.

Received: 15.06.2018

DOI: 10.14357/19922264180306

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