Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-28T06:13:42.484Z Has data issue: false hasContentIssue false
  • English
  • Français

On berry–esseen rate for queue length of the GI/G/K system in heavy traffic

Published online by Cambridge University Press:  14 July 2016

Xing Jin
Xing Jin*
Affiliation:
Anhui University
*
∗ Postal address: Department of Mathematics, Anhui University, Hefei City, Anhui Province, People's Republic of China.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper provides Berry–Esseen rate of limit theorem concerning the number of customers in a GI/G/K queueing system observed at arrival epochs for traffic intensity ρ > 1. The main method employed involves establishing several equalities about waiting time and queue length.

Keywords

WAITING TIMEIDLE PERIODKINGMAN MODELRATE OF CONVERGENCE
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 3 , September 1988 , pp. 596 - 611
Copyright
Copyright © Applied Probability Trust 1988 

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] Chow, Y. S. and Teicher, H. (1978) Probability Theory. Springer-Verlag, Berlin.Google Scholar
[2] Xing, Jin (1986) On the Berry–Esseen type theorems of GI/G/K system. To appear.Google Scholar
[3] Xing, Jin and Rongxing, Wang (1986) On Berry–Esseen rate for the waiting time of GI/G/1 system in heavy traffic. Acta Math. Sinica 29, 651–657.Google Scholar
[4] Kennedy, D. P. (1972) Rates of convergence for queue in heavy traffic, I. Adv. Appl. Prob. 4, 357–391.Google Scholar
[5] Nagaev, S. V. (1970) On the speed of convergence in a boundary problem, I and II. Theory Prob. Appl. 15, 179–199; 419–441.Google Scholar
[6] Petrov, P. P. (1975) Sums of Independent Random Variables. Springer-Verlag, Berlin.Google Scholar
[7] Sawyer, S. (1972) Rates of convergence for some functionals in probability. Ann. Math. Statist. 43, 273–284.Google Scholar