A note on the event horizon for a processor sharing queue

Robert C. Hampshire, William A. Massey

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

In this note we identify a phenomenon for processor sharing queues that is unique to ones with time-varying rates. This property was discovered while correcting a proof in Hampshire, Harchol-Balter and Massey (Queueing Syst. 53(1-2), 19-30, 2006). If the arrival rate for a processor sharing queue has unbounded growth over time, then it is possible for the number of customers in a processor sharing queue to grow so quickly that a newly entering job never finishes. We define the minimum size for such a job to be the event horizon for a processor sharing queue. We discuss the use of such a concept and develop some of its properties. This short article serves both as errata for Hampshire, Harchol-Balter and Massey (Queueing Syst. 53(1-2), 19-30, 2006) and as documentation of a characteristic feature for some processor sharing queues with time varying rates.

Original languageEnglish (US)
Pages (from-to)185-190
Number of pages6
JournalQueueing Systems
Volume59
Issue number3-4
DOIs
StatePublished - Aug 1 2008

All Science Journal Classification (ASJC) codes

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

Keywords

  • Diffusion limits
  • Dynamical queueing systems
  • Fluid limits
  • Processor sharing queues
  • Sojourn times
  • Transient behavior
  • Uniform acceleration
  • Virtual customers

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