Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-20T02:22:03.828Z Has data issue: false hasContentIssue false
  • English
  • Français

Heavy traffic limit theorems for a queueing system in which customers join the shortest line

Published online by Cambridge University Press:  01 July 2016

Zhang Hanqin  and
Wang Rongxin
Zhang Hanqin*
Affiliation:
Hebei Institute of Technology
Wang Rongxin*
Affiliation:
Xian Jiaotong University
*
∗Postal address: Teaching and Research Section of Mathematics, Hebei Institute of Technology, Tianjin, The People's Republic of China.
∗∗Postal address: Department of Mathematics, Xian Jiaotong University, Xian, The People's Republic of China.
Get access Rights & Permissions [Opens in a new window]

Abstract

The queueing system considered in this paper consists of r independent arrival channels and s independent service channels, where, as usual, the arrival and service channels are independent. In the queueing system, each server of the system has his own queue and arriving customers join the shortest line in the system. We give functional central limit theorems for the stochastic processes characterizing this system after appropriately scaling and translating the processes in traffic intensity ρ > 1.

Keywords

WEAK CONVERGENCEQUEUE LENGTH PROCESSLOAD PROCESSWAITING TIME PROCESS
Type
Research Article
Information
Advances in Applied Probability , Volume 21 , Issue 2 , June 1989 , pp. 451 - 469
Copyright
Copyright © Applied Probability Trust 1989 

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

[1] Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.Google Scholar
[2] Chow, Y. S. and Teicher, H. (1978) Probability Theory. Springer-Verlag, New York.CrossRefGoogle Scholar
[3] Iglehart, D. L. and Whitt, W. (1970) Multiple channel queues in heavy traffic I. Adv. Appl. Prob. 2, 150–177.CrossRefGoogle Scholar
[4] Prohorov, Yu. (1956) Convergence of random processes and limit theorems in probability. Theory Prob. Appl. 1, 157–214.Google Scholar
[5] Whitt, W. (1968) Weak Convergence Theorems for Queues in Heavy Traffic. , Stanford University.Google Scholar