A stochastic network under proportional fair resource control - Diffusion limit with multiple bottlenecks

Hengqing Ye, David D. Yao

Research output: Journal article publicationJournal articleAcademic researchpeer-review

15 Citations (Scopus)


We study a multiclass stochastic processing network operating under the so-called proportional fair allocation scheme, and following the head-of-the-line processor-sharing discipline. Specifically, each server's capacity is shared among the job classes that require its service, and it is allocated, in every state of the network, among the first waiting job of each class to maximize a log-utility function. We establish the limiting regime of the network under diffusion scaling, allowing multiple bottlenecks in the network, and relaxing some of the conditions required in prior studies. We also identify the class of allocation schemes among which the proportional fair allocation minimizes a quadratic cost objective function of the diffusion-scaled queue lengths, and we illustrate the limitation of this asymptotic optimality through a counterexample.
Original languageEnglish
Pages (from-to)716-738
Number of pages23
JournalOperations Research
Issue number3
Publication statusPublished - 1 May 2012

ASJC Scopus subject areas

  • Computer Science Applications
  • Management Science and Operations Research

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