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On a Poisson queue with random idle period. (English) Zbl 0902.60082
Summary: The differential-difference equation technique has been applied to study an M/M/1 queue with random idle period, wherein an idle period of random length begins each time after the system becomes empty. Various probability generating functions required for deriving the queue length distribution and Laplace-Stieltjes transform of waiting time distribution have been derived under steady state condition with a view to providing system performance measure for the model. Further, the probability distribution of the queue length for Markovian idle period is also presented along with some simple numerical illustration as a special case of such M/M/1 model.
60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)