Ergodic Theorem for a Queue with Unreliable Server

S. Zh. Aibatov

Lomonosov Moscow State University

Abstract: A single server queue with unreliable server is considered. The server breakdown probability depends on the state of a random medium described by a Markov chain. An ergodic theorem is proved for this system.

Keywords: regenerative flow, unreliable server, ergodicity, limit theorems, Markov chain, random medium.

UDC: 519.218.84

Received: 16.05.2014
Revised: 26.10.2014

DOI: 10.4213/mzm10491

 English version: Mathematical Notes, 2015, 97:6, 821–830

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