Skip to main content
SpringerLink
Log in

Distribution of the Time Between Processing Starts

  • Chapter
  • First Online:
Performance Analysis of Closed Queueing Networks

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 663))

  • 757 Accesses

Abstract

The two previous chapters focused on the calculation of the first-moment performance measures. In the following, the calculation of the exact distribution of the time between processing starts, denoted by TBPS, is presented. This distribution concerns processes that take place at the instant of a processing-start.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The calculation of these is described in Chap. 5.

  2. 2.

    See Werner (2010, p. 184f).

  3. 3.

    See http://www.siegfeld.com/picflow/milkrun.jpg,03.04.2012

  4. 4.

    See Werner (2010, p. 184f).

  5. 5.

    See Lean Enterprise Institute (2003, p. 60).

  6. 6.

    Note that this assignment is unambiguous. A non-active state might have several active predecessors, however, only one predecessor from an active state can finish after phase ph. This is because for any given state s, there is only one transition possibility to enter the particular non-active state u when requiring that the transition is induced by station i.

  7. 7.

    See Property 5.3 on page 94.

  8. 8.

    See page 93.

  9. 9.

    See Property 5.4 on page 95.

  10. 10.

    For the theoretical background on the transition rate matrix, see Sect. 5.5.1.

  11. 11.

    See Stewart (2009, p. 168ff).

References

  • Lean Enterprise Institute. (2003). Lean lexicon: A graphical glossary for lean thinkers. Brookline: Lean Enterprise Institute.

    Google Scholar 

  • Neuts, M. F. (1982). Explicit steady-state solution to some elementary queueing models. Operations Research, 30(3), 480–489.

    Article  Google Scholar 

  • Stewart, W. J. (2009). Probability, Markov chains, queues, and simulation. Princeton: Princeton University Press.

    Google Scholar 

  • Werner, H. (2010). Supply chain management: Grundlagen, Strategien, Instrumente und Controlling. Wiesbaden: Gabler.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Supply Chain Management and Production, University of Cologne, Cologne, Germany

    Svenja Lagershausen

Authors
  1. Svenja Lagershausen
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Lagershausen, S. (2013). Distribution of the Time Between Processing Starts. In: Performance Analysis of Closed Queueing Networks. Lecture Notes in Economics and Mathematical Systems, vol 663. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32214-3_6

Download citation

Publish with us

Policies and ethics

Search

Navigation