The Discrete Time Geom/Geom/1 Repairable Queuing System with Pseudo-Fault and Multiple Vacations

摘要

In this paper, we study a new class of the discrete time Geom/Geom/1 repairable queuing system with pseudo-fault and multiple vacations. We assume that the system may become disabled only when it is in operation. Service interruption is caused by two kinds of factors of pseudo-fault and breakdown. And they will result in different effects on the system. Using the quasi birth and death chain and matrix-geometric solution method, we may gain the distribution of the stationary queue length. Furthermore, the distribution of systems reliability and the number of customers and the waiting time of a customer in the system in steady state are researched. Finally, some numerical examples are given for analyzing the effect of parameters on the performance of the system.