This article is cited in 3 papers

Limit Theorems for an Infinite-Server Queuing System

E. Chernsvakaya

Lomonosov Moscow State University

Abstract: We consider an infinite-server queuing system with a doubly stochastic Poisson input flow. Assuming that the service time does not have expectation, we prove limit theorems for the number of occupied servers. As a consequence, we obtain limit theorems for systems in which the input flow intensity is a regenerative process.

Keywords: infinite-server queuing system, doubly stochastic Poisson flow, regenerative process, limit theorem.

UDC: 517

Received: 02.07.2014

DOI: 10.4213/mzm10533

 English version: Mathematical Notes, 2015, 98:4, 653–666

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