In: Queueing Systems Theory and Applications, Vol. 8, No. 2, pages 111-127. April 1991.
Abstract: The paper considers queueing systems in which the server occasionally takes a vacation of random duration. The vacation can be used to do additional work; it can also be a rest period. Several models of this problem have been analyzed in the past assuming that the population of the system is infinite. Similarly, it is generally assumed that the capacity of the system is infinite. In the paper the authors show how the finite-population system can be modeled by the stochastic Petri net. They also extend the model to the finite-capacity system.
Keywords: stochastic net (analysis of) finite-population vacation queueing systems; finite-capacity system.