Steady-state analysis of load-balancing algorithms in the sub-Halfin-Whitt regime

Xin Liu, Lei Ying

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


We study a class of load-balancing algorithms for many-server systems (N servers). Each server has a buffer of size with, i.e. a server can have at most one job in service and jobs queued. We focus on the steady-state performance of load-balancing algorithms in the heavy traffic regime such that the load of the system is for [CDATA[0 which we call the sub-Halfin-Whitt regime (and 0,] is the so-called Halfin-Whitt regime). We establish a sufficient condition under which the probability that an incoming job is routed to an idle server is 1 asymptotically (as) at steady state. The class of load-balancing algorithms that satisfy the condition includes join-the-shortest-queue, idle-one-first, join-the-idle-queue, and power-of-d-choices with (r a positive integer). The proof of the main result is based on the framework of Stein's method. A key contribution is to use a simple generator approximation based on state space collapse.

Original languageEnglish (US)
Pages (from-to)578-596
Number of pages19
JournalJournal of Applied Probability
Issue number2
StatePublished - Jun 1 2020


  • Keywords: Many-server systems
  • Stein's method
  • asymptotic zero delay
  • heavy traffic
  • load balancing
  • mean-field model
  • state space collapse
  • steady state

ASJC Scopus subject areas

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


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