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We consider a queuing problem in which both the service rate of a finite-buffer queue and its rate of arrivals are functions of the same partially observed Markov chain. Basic performance indices of this device, such as long term throughput and loss rates, are expressed in terms of an invariant measure over a suitable finite-dimensional simplex. In this paper we prove the existence of that invariant measure.
Seyed Mohammadhossein Tabatabaee
Jean-Yves Le Boudec, Ehsan Mohammadpour