Law of Large Numbers Limits for Many Server Queues
| dc.creator | Kaspi, Haya | |
| dc.creator | Ramanan, Kavita | |
| dc.date | 2007-08-07 | |
| dc.date.accessioned | 2026-07-07T08:22:36Z | |
| dc.date.available | 2026-07-07T08:22:36Z | |
| dc.description | This work considers a many-server queueing system in which customers with i.i.d., generally distributed service times enter service in the order of arrival. The dynamics of the system is represented in terms of a process that describes the total number of customers in the system, as well as a measure-valued process that keeps track of the ages of customers in service. Under mild assumptions on the service time distribution, as the number of servers goes to infinity, a law of large numbers (or fluid) limit is established for this pair of processes. The limit is characterised as the unique solution to a coupled pair of integral equations, which admits a fairly explicit representation. As a corollary, the fluid limits of several other functionals of interest, such as the waiting time, are also obtained. Furthermore, in the time-homogeneous setting, the fluid limit is shown to converge to its equilibrium. Along the way, some results of independent interest are obtained, including a continuous mapping result and a maximality property of the fluid limit. A motivation for studying these systems is that they arise as models of computer data systems and call centers. | |
| dc.description | 57 pages | |
| dc.identifier | https://arxiv.org/abs/0708.0952 | |
| dc.identifier | http://arxiv.org/abs/0708.0952 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135706 | |
| dc.subject | Probability | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 60F17, 60K25, 90B22; 60H99, 35D99 | |
| dc.title | Law of Large Numbers Limits for Many Server Queues | |
| dc.type | text |