| Article ID: | iaor20101631 |
| Volume: | 64 |
| Issue: | 3 |
| Start Page Number: | 253 |
| End Page Number: | 265 |
| Publication Date: | Mar 2010 |
| Journal: | Queueing Systems |
| Authors: | Bae Jongho, Kim Sunggon |
| Keywords: | GI/M/1 queues |
We consider a GI/M/1 queue in which the patience time of the customers is constant. The stationary distribution of the workload of the server, or the virtual waiting time, is derived by the level crossing argument. To this end, we obtain the expected downcrossings of a level in the workload process during a busy cycle and then the expected length of a busy cycle. For both the expectations, we use the dual property between the M/G/1 and GI/M/1 queue.