Fluid approximations for a processor-sharing queue

Hong Chen*, Offer Kella, Gideon Weiss

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


In this paper a fluid approximation, also known as a functional strong law of large numbers (FSLLN) for a GI/G/1 queue under a processor-sharing service discipline is established and its properties are analysed. The fluid limit depends on the arrival rate, the service time distribution of the initial customers, and the service time distribution of the arriving customers. This is in contrast to the known result for the GI/G/1 queue under a FIFO service discipline, where the fluid limit is piecewise linear and depends on the service time distribution only through its mean. The piecewise linear form of the limit can be recovered by an equilibrium type choice of the initial service distribution.

Original languageAmerican English
Pages (from-to)99-125
Number of pages27
JournalQueueing Systems
Issue number1-2
StatePublished - Dec 1997


  • Fluid approximation
  • Functional strong law of large numbers
  • GI/G/1 queue
  • Processor-sharing discipline


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