An M-[X]/G/1 Retrial G-queue with Single Vacation Subject to the Server Breakdown and Repair

作者：Yang, Shu-ping^*; Wu, Jin-biao; Liu, Zai-ming

来源：Acta Mathematicae Applicatae Sinica-English Series, 2013, 29(3): 579-596.

DOI：10.1007/s10255-013-0237-z

• Batch arrivals in a compound poisson process
• G-queues
• retrial queues
• single vacation
• reliability

An M-[X]/G/1 retrial G-queue with single vacation and unreliable server is investigated in this paper. Arrivals of positive customers form a compound Poisson process, and positive customers receive service immediately if the server is free upon their arrivals; Otherwise, they may enter a retrial orbit and try their luck after a random time interval. The arrivals of negative customers form a Poisson process. Negative customers not only remove the customer being in service, but also make the server under repair. The server leaves for a single vacation as soon as the system empties. In this paper, we analyze the ergodical condition of this model. By applying the supplementary variables method, we obtain the steady-state solutions for both queueing measures and reliability quantities.

• 出版日期2013
• 单位中南大学