A Markov chain approach to periodic queues
- 1 March 1987
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 24 (1) , 215-225
- https://doi.org/10.2307/3214072
Abstract
We consider GI/G/1 queues in an environment which is periodic in the sense that the service time of the nth customer and the next interarrival time depend on the phase θ n at the arrival instant. Assuming Harris ergodicity of {θ n} and a suitable condition on the traffic intensity, various Markov chains related to the queue are then again Harris ergodic and provide limit results for the standard customer- and time-dependent processes such as waiting times and queue lengths. As part of the analysis, a result of Nummelin (1979) concerning Lindley processes on a Markov chain is reconsidered.Keywords
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