Author:
Asmussen Søren,Thorisson Hermann
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.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Cited by
6 articles.
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