Diffusion approximation for an overloaded X model via a stochastic averaging principle

Ohad Perry*, Ward Whitt

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


In previous papers we developed a deterministic fluid approximation for an overloaded Markovian queueing system having two customer classes and two service pools, known in the call-center literature as the X model. The system uses the fixed-queue-ratio-with-thresholds (FQR-T) control, which we proposed as a way for one service system to help another in face of an unexpected overload. Under FQR-T, customers are served by their own service pool until a threshold is exceeded. Then, one-way sharing is activated with customers from one class allowed to be served in both pools. The control aims to keep the two queues at a pre-specified fixed ratio. We supported the fluid approximation by establishing a functional weak law of large numbers involving a stochastic averaging principle. In this paper we develop a refined diffusion approximation for the same model based on a many-server heavy-traffic functional central limit theorem.

Original languageEnglish (US)
Pages (from-to)347-401
Number of pages55
JournalQueueing Systems
Issue number4
StatePublished - Apr 2014


  • Averaging principles
  • Diffusion limits
  • Functional central limit theorem
  • Heavy-traffic limits
  • Many-server queues
  • Overload control

ASJC Scopus subject areas

  • Statistics and Probability
  • Computer Science Applications
  • Management Science and Operations Research
  • Computational Theory and Mathematics


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