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Discrete-time queues with correlated arrivals and constant service times. (English) Zbl 0941.90022

Summary: A discrete-time single-server finite-capacity queue with correlated arrivals and constant service times of arbitrary length is investigated in this paper. Cells are generated by a bursty on/off source, with geometrically distributed lengths of the on-periods and the off-periods. The performance of the system is evaluated by means of an analytical technique, based on generating functions, whose computational complexity does not depend on the buffer space. As a result of the analysis, closed-form expressions are obtained for the cell loss ratio, the steady-state probability generating functions of the queue length, the unfinished work and the cell delay and the joint probability generating function of two consecutive interdeparture times at the output of the queue. Some numerical examples illustrate the results.

MSC:

90B22 Queues and service in operations research
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