| Article ID: | iaor2010216 |
| Volume: | 52 |
| Issue: | 4 |
| Start Page Number: | 377 |
| End Page Number: | 401 |
| Publication Date: | Dec 2009 |
| Journal: | Journal of the Operations Research Society of Japan |
| Authors: | Takine Tetsuya, Masuyama Hiroyuki, Lui Bin |
| Keywords: | BMAP/G/1 queues |
This paper considers the stationary queue length and waiting time distributions in a FIFO BMAP/GI/1 queue with heavy-tailed service times and that with heavy-tailed batch sizes. In each case, we provide sufficient conditions under which the stationary queue length and waiting time distributions are subexponential. Furthermore, we obtain asymptotic relationships between the tail distributions of the stationary queue length and waiting time.