Two-stage queueing network models for quality control and testing

Shaul K. Bar-Lev, Onno Boxma, Wolfgang Stadje, Frank A. Van der Duyn Schouten, Christoph Wiesmeyr

Research output: Contribution to journalArticlepeer-review


We study sojourn times in a two-node open queueing network with a processor sharing node and a delay node, with Poisson arrivals at the PS node. Motivated by quality control and blood testing applications, we consider a feedback mechanism in which customers may either leave the system after service at the PS node or move to the delay node; from the delay node, they always return to the PS node for new quality controls or blood tests. We propose various approximations for the distribution of the total sojourn time in the network; each of these approximations yields the exact mean sojourn time, and very accurate results for the variance. The best of the three approximations is used to tackle an optimization problem that is mainly inspired by a blood testing application.

Original languageEnglish
Pages (from-to)859-866
Number of pages8
JournalEuropean Journal of Operational Research
Issue number3
StatePublished - 1 Nov 2009

Bibliographical note

Funding Information:
The authors are grateful for the constructive comments of a referee which led to an improved exposition. The research of Onno Boxma was supported by the BSIK/BRICKS project. A visitor grant for Shaul Bar-Lev from the Dutch Science Foundation NWO is gratefully acknowledged.


  • Blood testing
  • Feedback
  • Queueing
  • Sojourn time

ASJC Scopus subject areas

  • General Computer Science
  • Modeling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management


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