Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-24T01:39:19.707Z Has data issue: false hasContentIssue false
  • English
  • Français

On the GA/G/∞ queue

Published online by Cambridge University Press:  01 July 2016

Thomas Kuczek
Thomas Kuczek*
Affiliation:
Rutgers University
*
∗Postal address: Department of Statistics, P.O. Box 231, Cook College, Rutgers University, New Brunswick, NJ 08903, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

A particular queue, the general arrival, general service-time, infinite-server queue (GA/G/∞), is introduced and certain of its properties studied. Motivated by a life situation in which the interarrival times for service converge to 0, a different sort of regularity condition (involving a tail property of random measures) is imposed on the arrival process to prove various limit theorems. There are similarities to heavy-traffic theory.

Keywords

GENERAL ARRIVALGENERAL SERVICE TIMEINFINITE SERVERRANDOM MEASUREHEAVY-TRAFFIC THEORY
Type
Research Article
Information
Advances in Applied Probability , Volume 15 , Issue 2 , June 1983 , pp. 444 - 459
Copyright
Copyright © Applied Probability Trust 1983 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Borovkov, A. A. (1967) On limit laws for service processes in multichannel systems. Siberian Math. J. 8, 746–763.Google Scholar
Cohn, H. (1982) Norming constants for the supercritical Bellman-Hams process. Z. Wahrscheinlichkeitsth. Google Scholar
Grandell, J. (1977) Point processes and random measures. Adv. Appl. Prob. 9, 502–526.Google Scholar
Jagers, P. (1975) Branching Processes with Biological Applications. Wiley, New York.Google Scholar
Jagers, P. and Nerman, O. (1982) Limit theorems for sums determined by branching and other exponentially growing processes. Stoch. Proc. Appl. Google Scholar
Kuczek, T (1980). On Some Results in Branching Processes and GA/G/8 Queue with an Application to Biology. , Purdue University.Google Scholar
Nerman, O. (1982) On the convergence of supercritical general (C-M-J) branching processes. Z. Wahrscheinlichkeitsth. 57, 365–395.Google Scholar
Teicher, H. (1980) Almost certain behaviour of row sums of double arrays. Conf. Analytic Methods for Probability Theory, Oberwolfach, Springer-Verlag, Berlin.Google Scholar