On a BMAP/G/1 G-queue with Setup Times and Multiple Vacations  

作　　者：Yi PENG Xiang-qun YANG 

机构地区：[1]School of Mathematical Science and Computing Technology, Central South University, Changsha 410075, Hunan, China [2]College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, China

出　　处：《Acta Mathematicae Applicatae Sinica》2011年第4期625-638,共14页应用数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (No. 10871064)

摘　　要：In this paper, we consider a BMAP/G/1 G-queue with setup times and multiple vacations. Arrivals of positive customers and negative customers follow a batch Markovian arrival process （BMAP） and Markovian arrival process （MAP） respectively. The arrival of a negative customer removes all the customers in the system when the server is working. The server leaves for a vacation as soon as the system empties and is allowed to take repeated （multiple） vacations. By using the supplementary variables method and the censoring technique, we obtain the queue length distributions. We also obtain the mean of the busy period based on the renewal theory.In this paper, we consider a BMAP/G/1 G-queue with setup times and multiple vacations. Arrivals of positive customers and negative customers follow a batch Markovian arrival process （BMAP） and Markovian arrival process （MAP） respectively. The arrival of a negative customer removes all the customers in the system when the server is working. The server leaves for a vacation as soon as the system empties and is allowed to take repeated （multiple） vacations. By using the supplementary variables method and the censoring technique, we obtain the queue length distributions. We also obtain the mean of the busy period based on the renewal theory.

关 键 词：G-queues batch Markovian arrival process （BMAP） setup times multiple vacations censoring technique Markov chains 

分 类 号：O226[理学—运筹学与控制论] TP311.12[理学—数学]