This article is cited in 14 papers

Multichannel queueing systems with regenerative input flow

L. G. Afanasyeva^a, A. V. Tkachenko<sup>b

a</sup> M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
^b National Research University "Higher School of Economics"

Abstract: We consider the multichannel queueing system with nonidentical servers and regenerative input flow. The necessary and sufficient condition for ergodicity is established, and functional limit theorems for high and ultra-high load are proved. As a corollary, the ergodicity condition for queues with unreliable servers is obtained. Suggested approaches are used to prove the ergodic theorem for systems with limitations. We also consider the hierarchical networks of queueing systems.

Keywords: multichannel queueing system; regenerative flow; ergodicity; stochastic boundedness.

MSC: 60

Received: 15.11.2012

DOI: 10.4213/tvp4504

 English version: Theory of Probability and its Applications, 2014, 58:2, 174–192

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