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Queues with slowly varying arrival and service processes. (English) Zbl 0713.60105
Summary: We examine a generalisation of the M/G/1 queue. The arrival and service processes are governed by a Markov chain which determines the rate of arrival and the service time distribution from a finite set. This Markov chain is assumed to vary “slowly”, so that we are able to derive analytical results for the stationary distribution of the queue length using an approach based on decomposability. The practical interest of this model stems from the numerous applications where the parameters of queueing systems are time varying, such as inventory models, telephone systems, time-sharing systems, computer networks with bursty traffic, etc. We also show how this approach can be extended to arbitrary networks of queues and in particular to those with product form solution.

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