An M-X/G/1 G-Queue With Single Vacation, Setup Times And Working Breakdown

An M-X/G/1 G-queue with single vacation, setup times and working breakdown is analyzed in this paper. In a normal busy period, the positive customer being served is taken away by the negative customer who arrives. And the system malfunctioned by reason of the arrival of negative customers. During the repair time, the server is maintained without stopping the service. If the system is not idle at the end of the repair or the vacation, the system starts a new busy period. Otherwise, the system turns off. And the system starts the setup when the positive customers arrive. By applying the matrix-analytic theory, the probability generating functions(PGF) for queue length are obtained. The key performance indicators about the system are also expatiated. In addition, the sensitivity analysis and cost analysis of the queueing model are demonstrated by numerical examples.