Dynamics of Two Interacting Queues

A.A. Yambartsev, A.A. Zamyatin

2001, v.7, №2, 301-324

ABSTRACT

We consider Markov chains that describe the evolution of two interacting queues of symbols. The transitions of the Markov chain depend only on the last symbols of both queues, and the lengths of the queues at subsequent moments of time cannot differ by more than 1. The main goal of the present paper is to prove transience and ergodicity conditions for Markov chains under consideration.

Keywords: Markov chain,queue,string,invariant measure,ergodicity,transience,induced chain,drift vector

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