Abstract
This paper studies the probability distribution of the number of cycles completed in a single-server queueing system with Poisson arrivals, exponential service times and having a limited capacity. The expressions for the number of cycles completed in the time interval (0, t] and the distribution of the number of busy periods completed in time interval (0, t] are obtained explicitly. These distributions are contemplated through the joint probability distribution of the number of customers in the system at time t and the number of times the system reaches its extreme state in the interval (0, t].
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