caa a22 4500 445830972 CHVBK 20180317145314.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s10255-011-0052-3 doi (NATIONALLICENCE)springer-10.1007/s10255-011-0052-3 On a BMAP/G/1 G-queue with setup times and multiple vacations [Elektronische Daten] [Yi Peng, Xiang-qun Yang] 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. Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg, 2011 G-queues nationallicence batch Markovian arrival process (BMAP) nationallicence setup times nationallicence multiple vacations nationallicence censoring technique nationallicence Markov chains nationallicence Peng Yi School of Mathematical Science and Computing Technology, Central South University, 410075, Changsha, Hunan, China aut Yang Xiang-qun College of Mathematics and Computer Science, Hunan Normal University, 410081, Changsha, China aut Acta Mathematicae Applicatae Sinica, English Series Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 27/4(2011-10-01), 625-638 0168-9673 27:4<625 2011 27 10255 https://doi.org/10.1007/s10255-011-0052-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10255-011-0052-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Peng Yi School of Mathematical Science and Computing Technology, Central South University, 410075, Changsha, Hunan, China aut NATIONALLICENCE 700 1- Yang Xiang-qun College of Mathematics and Computer Science, Hunan Normal University, 410081, Changsha, China aut NATIONALLICENCE 773 0- Acta Mathematicae Applicatae Sinica, English Series Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 27/4(2011-10-01), 625-638 0168-9673 27:4<625 2011 27 10255 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer