Transient flows in queueing systems via closure approximations

C. Roger Glassey, Sridhar Seshadri

Research output: Contribution to journalArticlepeer-review


We present a method for obtaining approximations to the distribution of flow times of customers in arbitrary queueing systems. We first propose approximations for uni-variate and multi-variate distributions of non-negative random variables. Then using a closure approximation, we show that the distribution of flow time can be calculated recursively. Computational results for the single server, multi-server and tandem queues are encouraging, with less than 5%average error in the mean flow time in most cases. The average error in the variance of flow times is found to be less than 10% for the more regular distributions.

Original languageEnglish (US)
Pages (from-to)177-201
Number of pages25
JournalQueueing Systems
Issue number1-2
StatePublished - Mar 1993
Externally publishedYes


  • Approximation of distributions
  • closure approximation
  • queueing network
  • sojourn time
  • transient analysis

ASJC Scopus subject areas

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


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