Skip to main content

Stability of Queueing Networks

  • Chapter
  • 847 Accesses

Part of the Lecture Notes in Mathematics book series (LNMECOLE,volume 1950)

The approach we employ in this chapter to study the stability of queueing networks employs fluid limits and fluid models. Fluid models were discussed briefly in Section 1.3; we will examine both fluid limits and fluid models in detail here. Employing these tools, one can reduce the study of queueing networks to their simpler deterministic analogs. The basic theory is given here; applications will be given in Chapter 5.

Independently, [St95] and [Da95] developed criteria for the stability of queueing networks, in terms of the stability of limits of rescaled solutions of the network. (In the terminology of this chapter, [St95] used fluid limits and [Da95] used both fluid limits and fluid models.) [St95] assumed exponential distributions for the interarrival and service times; [Da95] considered more general distributions, but at the price of requiring the use of Markov processes with general state space. Applications illustrating this approach are given in [Da95].

The material in this chapter is based on the approach taken in [Da95]. The main theorem of the chapter, Theorem 4.16, corresponds to Theorem 4.2 in [Da95]. Our approach here is a modification of that in [Br98a]. Care has been taken to give a detailed presentation of the material, including that cited in [Da95]. As a consequence, the chapter is quite long; in the remainder of the introduction, we summarize its contents.

Keywords

  • Markov Process
  • Service Time
  • Interarrival Time
  • Queueing Network
  • Strong Markov Property

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   49.95
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Rights and permissions

Reprints and Permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

(2008). Stability of Queueing Networks. In: Stability of Queueing Networks. Lecture Notes in Mathematics, vol 1950. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68896-9_4

Download citation