Services within a busy period of an M/M/1 queue and Dyck paths
| dc.creator | Draief, Moez | |
| dc.creator | Mairesse, Jean | |
| dc.date | 2007-07-27 | |
| dc.date.accessioned | 2026-07-07T08:20:44Z | |
| dc.date.available | 2026-07-07T08:20:44Z | |
| dc.description | We analyze the service times of customers in a stable M/M/1 queue in equilibrium depending on their position in a busy period. We give the law of the service of a customer at the beginning, at the end, or in the middle of the busy period. It enables as a by-product to prove that the process of instants of beginning of services is not Poisson. We then proceed to a more precise analysis. We consider a family of polynomial generating series associated with Dyck paths of length 2n and we show that they provide the correlation function of the successive services in a busy period with (n+1) customers. | |
| dc.identifier | https://arxiv.org/abs/0707.4124 | |
| dc.identifier | http://arxiv.org/abs/0707.4124 | |
| dc.identifier | Queueing Systems / Queueing Systems Theory Appl 49, 1 (2005) 73-84 | |
| dc.identifier | doi:10.1007/s11134-004-5556-6 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135155 | |
| dc.subject | Discrete Mathematics | |
| dc.title | Services within a busy period of an M/M/1 queue and Dyck paths | |
| dc.type | text |