| Article ID: | iaor20105855 |
| Volume: | 26 |
| Issue: | 1 |
| Start Page Number: | 141 |
| End Page Number: | 163 |
| Publication Date: | Jan 2010 |
| Journal: | Stochastic Models |
| Authors: | Leeuwaarden J S H van, Lopker A H, Janssen A J E M |
| Keywords: | M/D/1 queues, renewal processes |
We consider the length of a busy period in the M/D/∞ queue and show that it coincides with the sojourn time of the first customer in an M/D/1 processor-sharing queue. We further show that the busy period is intimately related with the stationary waiting time in the M/D/1 first-come-first-served queue. We present three characterizations for the distribution function of the busy period and an asymptotic expression for its tail distribution. The latter involves complex-valued branches of the Lambert W function.