Large-scale join-idle-queue system with general service times

S. Foss, A. L. Stolyar

Research output: Contribution to journalArticle

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 routed to one of the servers immediately upon arrival. The join-idle-queue routeing 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 at λ / μ. In particular, this implies that the steady-state probability of an arriving customer waiting for service vanishes.

Original languageEnglish (US)
Pages (from-to)995-1007
Number of pages13
JournalJournal of Applied Probability
Volume54
Issue number4
DOIs
StatePublished - Dec 1 2017

Keywords

  • Large-scale service system
  • asymptotic optimality
  • fluid limit
  • join-idle-queue
  • load balancing
  • pull-based load distribution
  • stationary distribution

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

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