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Exact transient solution of a discrete time queue with state-dependent rates. (English) Zbl 1244.90068
Summary: Exact expressions are obtained in closed form for the time-dependent system size probabilities of a discrete queue with state-dependent arrival and service rates. The underlying difference equations of systems size probabilities is converted into a continued fraction which is then expressed as a power series. As a special case we derive a Geo/Geo/1 queue. Numerical illustrations are presented.

MSC:
90B22 Queues and service in operations research
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