Hostname: page-component-7dd5485656-gs9qr Total loading time: 0 Render date: 2025-10-31T08:25:02.489Z Has data issue: false hasContentIssue false
  • English
  • Français

Rates of convergence for queues in heavy traffic. II: Sequences of queueing systems

Published online by Cambridge University Press:  01 July 2016

Douglas P. Kennedy
Douglas P. Kennedy*
Affiliation:
University of Sheffield
Get access Rights & Permissions [Opens in a new window]

Abstract

Estimates are given for the rates of convergence in functional central limit theorems for the queue length process in a sequence of general multiple channel queues. The situation is considered where the traffic intensity in the nth. queue, ρn , tends to ρ ≧ 1 as n approaches infinity. This extends previous work by the author, [6], in which the traffic intensity was fixed ≧ 1.

Keywords

RATES OF CONVERGENCEERROR TERMSWEAK CONVERGENCEFUNCTIONAL LIMIT THEOREMSHEAVY TRAFFICMULTIPLE CHANNEL QUEUESQUEUES

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 4 , Issue 2 , August 1972 , pp. 382 - 391
Copyright
Copyright © Applied Probability Trust 1972 

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.)

Article purchase

Temporarily unavailable

References

[1] Billingsley, P. (1968) Convergence of Probability Measures. John Wiley, New York.Google Scholar
[2] Dharmadhikari, S. W., Fabian, V. and Jogdeo, K. (1968) Bounds on the moments of martingales. Ann. Math. Statist. 39, 1719–1723.Google Scholar
[3] Heyde, C. (1969) On extended rate of convergence results for the invariance principle. Ann. Math. Statist. 40, 2178–2179.CrossRefGoogle Scholar
[4] Iglehart, D. L. and Whitt, W. (1970) Multiple channel queues in heavy traffic. I. Adv. Appl. Prob. 2, 150–177.CrossRefGoogle Scholar
[5] Iglehart, D. L. and Whitt, W. (1970) Multiple channel queues in heavy traffic. II: sequences, networks and batches. Adv. Appl. Prob. 2, 355–369.CrossRefGoogle Scholar
[6] Kennedy, D. P. (1972) Rates of convergence for queues in heavy traffic. I. Adv. Appl. Prob. 4.Google Scholar
[7] Rosenkrantz, W. A. (1967) On rates of convergence for the invariance principle. Trans. Amer. Math. Soc. 129, 542–552.CrossRefGoogle Scholar
[8] Skorokhod, A. V. (1965) Studies in the Theory of Random Processes. Addison-Wesley, Reading, Massachusetts. (English translation).Google Scholar
[9] von Bahr, B. and Essen, C. G. (1965) Inequalities for the rth absolute moment of a sum of random variables, 1 ≦ r ≦ 2. Ann. Math. Statist. 36, 299–303.CrossRefGoogle Scholar
[10] Whitt, W. (1970) Multiple channel queues in heavy traffic. III: random server selection. Adv. Appl. Prob. 2, 370–375.Google Scholar