Skip to main content Accessibility help
×
Home
Hostname: page-component-684bc48f8b-4z9h4 Total loading time: 0.322 Render date: 2021-04-11T14:02:54.505Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }

Universality of load balancing schemes on the diffusion scale

Published online by Cambridge University Press:  09 December 2016

Debankur Mukherjee
Affiliation:
Eindhoven University of Technology
Sem C. Borst
Affiliation:
Eindhoven University of Technology and Nokia Bell Labs
Johan S. H. van Leeuwaarden
Affiliation:
Eindhoven University of Technology
Philip A. Whiting
Affiliation:
Macquarie University
Corresponding
E-mail address:

Abstract

We consider a system of N parallel queues with identical exponential service rates and a single dispatcher where tasks arrive as a Poisson process. When a task arrives, the dispatcher always assigns it to an idle server, if there is any, and to a server with the shortest queue among d randomly selected servers otherwise (1≤dN). This load balancing scheme subsumes the so-called join-the-idle queue policy (d=1) and the celebrated join-the-shortest queue policy (d=N) as two crucial special cases. We develop a stochastic coupling construction to obtain the diffusion limit of the queue process in the Halfin‒Whitt heavy-traffic regime, and establish that it does not depend on the value of d, implying that assigning tasks to idle servers is sufficient for diffusion level optimality.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2016 

Access options

Get access to the full version of this content by using one of the access options below.

References

[1] Badonnel, R.and Burgess, M. (2008).Dynamic pull-based load balancing for autonomic servers. In Network Operations and Management Symposium, NOMS 2008, pp. 751754.Google Scholar
[2] Bramson, M.,Lu, Y. and Prabhakar, B. (2012).Asymptotic independence of queues under randomized load balancing.Queueing Systems 71,247292.CrossRefGoogle Scholar
[3] Ephremides, A.,Varaiya, P. and Walrand, J. (1980).A simple dynamic routing problem.IEEE Trans. Automatic Control 25,690693.CrossRefGoogle Scholar
[4] Eschenfeldt, P. and Gamarnik, D. (2015).Join the shortest queue with many servers. The heavy traffic asymptotics. Preprint. Available athttps://arxiv.org/abs/1502.00999v2.Google Scholar
[5] Gupta, V.,Harchol-Balter, M.,Sigman, K. and Whitt, W. (2007).Analysis of join-the-shortest-queue routing for web server farms.Performance Evaluation 64,10621081.CrossRefGoogle Scholar
[6] Halfin, S. and Whitt, W. (1981).Heavy-traffic limits for queues with many exponential servers.Operat. Res. 29,567588.CrossRefGoogle Scholar
[7] Jonckheere, M. (2006).Insensitive versus efficient dynamic load balancing in networks without blocking.Queueing Systems 54,193202.CrossRefGoogle Scholar
[8] Lu, Y. et al. (2011).Join-idle-queue: a novel load balancing algorithm for dynamically scalable web services.Performance Evaluation 68,10561071.CrossRefGoogle Scholar
[9] Mitzenmacher, M. (2001).The power of two choices in randomized load balancing.IEEE Trans. Parallel Distributed Systems 12,10941104.CrossRefGoogle Scholar
[10] Pang, G.,Talreja, R. and Whitt, W. (2007).Martingale proofs of many-server heavy-traffic limits for Markovian queues.Prob. Surveys 4,193267.CrossRefGoogle Scholar
[11] Sparaggis, P. D.,Towsley, D. and Cassandras, C. G. (1994).Sample path criteria for weak majorization.Adv. Appl. Prob. 26,155171.CrossRefGoogle Scholar
[12] Stolyar, A. L. (2015).Pull-based load distribution in large-scale heterogeneous service systems.Queueing Systems 80,341361.CrossRefGoogle Scholar
[13] Towsley, D. (1995).Application of majorization to control problems in queueing systems. In Scheduling Theory and Its Applications, eds P. Chrétienne et al.,John Wiley,Chichester.Google Scholar
[14] Towsley, D.,Sparaggis, P. D. and Cassandras, C. G. (1992).Optimal routing and buffer allocation for a class of finite capacity queueing systems.IEEE Trans. Automatic Control 37,14461451.CrossRefGoogle Scholar
[15] Vvedenskaya, N. D.,Dobrushin, R. L. and Karpelevich, F. I. (1996).Queueing system with selection of the shortest of two queues: an asymptotic approach.Prob. Peredachi Inf. 32,2034.Google Scholar
[16] Weber, R. R. (1978).On the optimal assignment of customers to parallel servers.J. Appl. Prob. 15,406413.CrossRefGoogle Scholar
[17] Whitt, W. (1986).Deciding which queue to join: some counterexamples.Operat. Res. 34,5562.CrossRefGoogle Scholar
[18] Winston, W. (1977).Optimality of the shortest line discipline.J. Appl. Prob. 14,181189.CrossRefGoogle Scholar

Altmetric attention score

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 114 *
View data table for this chart

* Views captured on Cambridge Core between 09th December 2016 - 11th April 2021. This data will be updated every 24 hours.

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Universality of load balancing schemes on the diffusion scale
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Universality of load balancing schemes on the diffusion scale
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Universality of load balancing schemes on the diffusion scale
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *