Law of large numbers limits for many-server queues

68Citations
Citations of this article
22Readers
Mendeley users who have this article in their library.

Abstract

This work considers a many-server queueing system in which customers with independent and identically distributed service times, chosen from a general distribution, enter service in the order of arrival. The dynamics of the system are 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 characterized 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, when the arrival process is time-homogeneous, the measure-valued component of 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. © Institute of Mathematical Statistics, 2011.

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Cite

CITATION STYLE

APA

Kaspi, H., & Ramanan, K. (2011). Law of large numbers limits for many-server queues. Annals of Applied Probability, 21(1), 33–114. https://doi.org/10.1214/09-AAP662

Readers' Seniority

Tooltip

PhD / Post grad / Masters / Doc 11

61%

Professor / Associate Prof. 4

22%

Lecturer / Post doc 2

11%

Researcher 1

6%

Readers' Discipline

Tooltip

Computer Science 4

27%

Mathematics 4

27%

Engineering 4

27%

Business, Management and Accounting 3

20%

Save time finding and organizing research with Mendeley

Sign up for free