Abstract
In the paper the M X /G/1-type queueing system with the N-policy and multiple vacations is considered. The output process, counting successive departures, is studied using the approach consisting of two main stages. Firstly, introducing an auxiliary model with the N-policy and multiple vacations, and applying the formula of total probability, the analysis is brought to the case of the corresponding system without restrictions in the service process, on its first busy cycle. Next, defining a delayed renewal process of successive vacation cycles, the general results are obtained. The explicit formula for the probability generating function of the Laplace transform of the distribution of the number of packets completely served before a fixed moment t is derived and written using transforms of “input” distributions of the system, and components of the Wiener-Hopf-type factorization identity connected with them. Moreover, illustrative numerical results are presented.
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