## Law of large number limits for many-server queues (2007)

Citations: | 17 - 2 self |

### BibTeX

@MISC{Kaspi07lawof,

author = {Haya Kaspi and Kavita Ramanan},

title = {Law of large number limits for many-server queues},

year = {2007}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. 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 measurevalued 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