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Join-Idle-Queue system with general service times: Large-scale limit of stationary distributions

Published: 11 October 2017 Publication History

Abstract

A parallel server system with n identical servers is considered. The service time distribution has a finite mean 1/μ, but otherwise is arbitrary. Arriving customers are to be routed to one of the servers immediately upon arrival. Join- Idle-Queue routing algorithm is studied, under which an arriving customer is sent to an idle server, if such is available, and to a randomly uniformly chosen server, otherwise. We consider the asymptotic regime where n→∞ and the customer input flow rate is λn. Under the condition λ/μ < 1/2, we prove that, as n → ∞, the sequence of (appropriately scaled) stationary distributions concentrates at the natural equilibrium point, with the fraction of occupied servers being constant equal λ/μ. In particular, this implies that the steady-state probability of an arriving customer having to wait for service vanishes.

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Cited By

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  • (2020)A Proficient Approach for Load Balancing in Cloud Computing-Join Minimum Loaded QueueInternational Journal of Information System Modeling and Design10.4018/IJISMD.202001010211:1(12-36)Online publication date: Jan-2020
  • (2018)Asymptotics of insensitive load balancing and blocking phasesQueueing Systems: Theory and Applications10.1007/s11134-017-9559-588:3-4(243-278)Online publication date: 1-Apr-2018

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Published In

cover image ACM SIGMETRICS Performance Evaluation Review
ACM SIGMETRICS Performance Evaluation Review  Volume 45, Issue 2
Setember 2017
131 pages
ISSN:0163-5999
DOI:10.1145/3152042
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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 11 October 2017
Published in SIGMETRICS Volume 45, Issue 2

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Cited By

View all
  • (2020)A Proficient Approach for Load Balancing in Cloud Computing-Join Minimum Loaded QueueInternational Journal of Information System Modeling and Design10.4018/IJISMD.202001010211:1(12-36)Online publication date: Jan-2020
  • (2018)Asymptotics of insensitive load balancing and blocking phasesQueueing Systems: Theory and Applications10.1007/s11134-017-9559-588:3-4(243-278)Online publication date: 1-Apr-2018

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