A simple formula for mean multiplexing delay for independent regenerative sources

Hervé Dupuis, Bruce Hajek

Research output: Contribution to journalArticlepeer-review


Simple expressions are given for the mean delay, mean waiting time, and mean busy period length in a multiplexer. Data streams with active periods having a general distribution are permitted, and the data rate during the active periods can be random. Data can also arrive in batches. The key restrictions of the model are that the sources are independent, idle periods are exponentially distributed, and a source generates at least enough data during an active period to keep the server busy throughout the period. The exact formulas allow evaluation of the error in approximations such as a heavy traffic diffusion approximation. Both continuous and discrete time models are considered. The discrete-time model includes that studied by Viterbi and subsequently generalized by Neuts. The Pollaczek-Khinchine formula for the mean amount of work in an M/GI/1 queue is retrieved as a limiting case.

Original languageEnglish (US)
Pages (from-to)195-239
Number of pages45
JournalQueueing Systems
Issue number3-4
StatePublished - Sep 1 1994


  • Queueing
  • diffusion approximation
  • fluid model
  • multiplexing
  • renewal processes

ASJC Scopus subject areas

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


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