Queue-and-idleness-ratio controls in many-server service systems

Itay Gurvich*, Ward Whitt

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

65 Scopus citations


Motivated by call centers, we study large-scale service systems with multiple customer classes and multiple agent pools, each with many agents. We propose a family of routing rules called queue-and-idleness-ratio (QIR) rules. A newly available agent next serves the customer from the head of the queue of the class (from among those he is eligible to serve) whose queue length most exceeds a specified state-dependent proportion of the total queue length. An arriving customer is routed to the agent pool whose idleness most exceeds a specified state-dependent proportion of the total idleness. We identify regularity conditions on the network structure and system parameters under which QIR produces an important state-space collapse (SSC) result in the quality-and-efficiency-driven (QED) many-server heavy-traffic limiting regime. The SSC result is applied here to prove stochastic-process limits and in subsequent papers to solve important staffing and control problems for large-scale service systems.

Original languageEnglish (US)
Pages (from-to)363-396
Number of pages34
JournalMathematics of Operations Research
Issue number2
StatePublished - May 2009


  • Control of queueing systems
  • Diffusion limits
  • Halfin-Whitt regime
  • Heavy-traffic
  • QED regime
  • State-space collapse

ASJC Scopus subject areas

  • General Mathematics
  • Computer Science Applications
  • Management Science and Operations Research


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