zbMATH — the first resource for mathematics

A Markov modulated, nearly completely decomposable M/M/1 queue. (English) Zbl 0862.60086
Stewart, William J. (ed.), Computations with Markov chains. Proceedings of the 2nd international workshop on the numerical solution of Markov chains, Raleigh, NC, USA, January 16–18, 1995. Boston, MA: Kluwer Academic Publishers. 39-48 (1995).
Summary: We consider a positive recurrent M/M/1 queue in a slowly varying Markovian environment, such that in some environments, the arrival rate may be higher than the service rate. The system therefore may oscillate between stable and unstable modes of behaviour. We investigate the limiting distribution as the expected sojourn times in the various environments increase to infinity. We show that the limiting behaviour of the stationary distribution is significantly different when there are unstable environments.
For the entire collection see [Zbl 0940.00042].

60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research