Fluid limit of a PS-queue with multistage service

Maria Frolkova (Corresponding author), Bert Zwart (Corresponding author)

Research output: Contribution to journalArticleAcademicpeer-review


We consider a variation of the processor-sharing (PS) queue, inspired by freelance job websites where multiple freelancers compete for a single job. We develop fluid limit approximations for the overloaded PS-model with multiple (possibly infinitely many) service stages. Based on this approximation, we estimate what proportion of freelancers get the job they apply for. In addition, the PS model studied here is an instance of PS with routing and impatience, for which no Lyapunov function is known, and we suggest some partial solutions.

Original languageEnglish
Pages (from-to)1-27
Number of pages27
JournalProbability in the Engineering and Informational Sciences
Issue number1
Publication statusPublished - 2019


  • fluid limits
  • freelance job websites
  • Lyapunov functions
  • processor-sharing
  • routing

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