The virtual waiting time in a finite-buffer queue with a single vacation policy
ASMTA'12 Proceedings of the 19th international conference on Analytical and Stochastic Modeling Techniques and Applications
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A finite-buffer queueing system with batch Poisson arrivals is considered. A system of integral equations for the distribution function of the number of customers h(t) served before t, conditioned by the initial state of the system, is built. A compact formula for probability generating function of the Laplace transform of distribution of h(t) is found using the potential technique. From this representation the mean of h(t) can be effectively calculated numerically using one of the inverse Laplace transform approximation algorithms. Moreover a limit behavior of departure process as the buffer size tends to infinity is investigated. Numerical examples are attached as well.