The Pht/Pht/∞ queueing system: Part I - The single node

Barry L. Nelson*, Michael R. Taaffe

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


We develop a numerically exact method for evaluating the time-dependent mean, variance, and higher-order moments of the number of entities in a Ph t/Pht/∞ queueing system. We also develop a numerically exact method for evaluating the distribution function and moments of the virtual sojourn time for any time t; in our setting, the virtual sojourn time is equivalent to the service time for virtual entities arriving to the system at that time t. We include several examples using software that we have developed and have put in downloadable form in the Online Supplement to this paper on the journal's website.

Original languageEnglish (US)
Pages (from-to)266-274
Number of pages9
JournalINFORMS Journal on Computing
Issue number3
StatePublished - Jun 2004


  • Algorithms
  • Infinite server
  • Nonstationary processes
  • Phase-type distribution
  • Queues

ASJC Scopus subject areas

  • Software
  • Information Systems
  • Computer Science Applications
  • Management Science and Operations Research


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