V. N. Sobolev, A. E. Kondratenko, “On the stationary distributions in some queueing systems”, Vestnik TVGU. Ser. Prikl. Matem. [Herald of Tver State University. Ser. Appl. Math.], 2021, Issue 4,Pages <nobr>5

Theory of Probability and Mathematical Statistics

On the stationary distributions in some queueing systems

V. N. Sobolev^a, A. E. Kondratenko^b

^a Laboratory of TVP, Moscow
^b Lomonosov Moscow State University, Moscow

Abstract: This paper deals with two queuing system: $M_{\lambda}|G|n|\infty$ and $GI_{\lambda}^{\nu}|M_{\mu}|1|\infty$. The purpose is to find the steady-state results in terms of the probability-generating functions.

Keywords: queueing system, batch arrivals, probability generating functions, embedded Markov chain, renewal process.

UDC: 519.872, 519.217.2, 519.113.3

MSC: 60K25

Received: 11.11.2021
Revised: 02.12.2021

DOI: 10.26456/vtpmk626