Join-idle-queue with service elasticity

Debankur Mukherjee, Alexander Stolyar

Research output: Contribution to journalConference articlepeer-review


We consider the model of a token-based joint auto-scaling and load balancing strategy, proposed in a recent paper by Mukherjee, Dhara, Borst, and van Leeuwaarden [4] (SIGMETRICS'17), which oers an efficient scalable implementation and yet achieves asymptotically optimal steady-state delay performance and energy consumption as the number of servers N ! 1. In the above work, the asymptotic results are obtained under the assumption that the queues have fixed-size finite buers, and therefore the fundamental question of stability of the proposed scheme with infinite buers was left open. In this paper, we address this fundamental stability question. The system stability under the usual subcritical load assumption is not automatic. Moreover, the stability may not even hold for all N. The key challenge stems from the fact that the process lacks monotonicity, which has been the powerful primary tool for establishing stability in load balancing models. We develop a novel method to prove that the subcritically loaded system is stable for large enough N, and establish convergence of steady-state distributions to the optimal one, as N ! 1. The method goes beyond the state of the art techniques - it uses an induction-based idea and a “weak monotonicity” property of the model; this technique is of independent interest and may have broader applicability.

Original languageEnglish (US)
Pages (from-to)18-20
Number of pages3
JournalPerformance Evaluation Review
Issue number2
StatePublished - Jan 17 2019
Event2018 Workshop on MAthematical Performance Modeling and Analysis, MAMA 2018 and Workshop on Critical Infrastructure Network Security, CINS 2018 - Irvine, United States
Duration: Jun 1 2018 → …


  • Auto-scaling
  • Fluid limit
  • Join-Idle-Queue
  • Load balancing
  • Many-server asymptotics
  • Mean-field limit
  • Stability

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Computer Networks and Communications


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