The n/g/l finite capacity queue

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Abstract
In this paper, we study a single server queue with finite capacity where the arrival process is Neuts' versatile Markovian point process (the N-process). Many arrival processes are special cases of this iV-process, such as the Markov modulated Poisson process, the renewal process of phase-type and others. The service times are generally distributed. We obtain recursive formulas for the joint distribution of the length of the busy period and the number of customers served during such a period. The queue length distribution, both at departure instants and at an arbitrary time instant are derived. The Laplace-Stielt jes transform of the virtual waiting time distribution is also obtained. This result generalizes Lavenberg's formula for the M/G/l finite capacity queue to the present model.

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