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On the steady-state queue size distribution of the discrete-time \(\text{Geo}/G/1\) queue with repeated customers. (English) Zbl 0840.60085
The author investigates the steady-state queue-size distribution of the discrete-time \(\text{Geo}/G/1\) retrial queue. He derives analytic formulas for the generating functions of the joint distribution of the number of customers in the system and the residual service times and shows that the stochastic decomposition law holds. He develops recursive formulas for the steady-state probabilities and illustrates their use through numerical examples. This model has applications in the slotted non-persistent CSMA when the traffic load is relatively light and the collision probability is negligible small.

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