Sengupta's invariant relationship and its application to waiting time inference

Hiroshi Toyoizumi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


This paper presents a new proof of Sengupta's invariant relationship between virtual waiting time and attained sojourn time and its application to estimating the virtual waiting time distribution by counting the number of arrivals and departures of a G/G/1 FIFO queue. Since this relationship does not require any parametric assumptions, our method is non-parametric. This method is expected to have applications, such as call processing in communication switching systems, particularly when the arrival or service process is unknown.

Original languageEnglish
Pages (from-to)795-799
Number of pages5
JournalJournal of Applied Probability
Issue number3
Publication statusPublished - 1997 Sept
Externally publishedYes


  • Attained sojourn time
  • Communication switching system
  • G/G/1 Queue
  • Queue inference
  • Sengupta's invariant relationship
  • Virtual waiting time

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty


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