| Article ID: | iaor20001858 |
| Country: | Netherlands |
| Volume: | 112 |
| Issue: | 3 |
| Start Page Number: | 646 |
| End Page Number: | 653 |
| Publication Date: | Feb 1999 |
| Journal: | European Journal of Operational Research |
| Authors: | Field A.J., Harrison P.G. |
| Keywords: | Sojourn times, M/M/1 queues |
We consider an equilibrium M/M/1 queue in which customers arrive at a random position, both for the preemptive and non-preemptive cases. The Laplace–Stieltjes transforms of their sojourn time distributions are derived and in the latter case it is verified that the result is that of an M/M/1 queue where the server chooses the next task to serve at random.