Stability and instability of fluid models for reentrant lines

J. G. Dai, G. Weiss

Research output: Contribution to journalArticlepeer-review


Reentrant lines can be used to model complex manufacturing systems such as wafer fabrication facilities. As the first step to the optimal or near-optimal scheduling of such lines, we investigate their stability. In light of a recent theorem of Dai (1995) which states that a scheduling policy is stable if the corresponding fluid model is stable, we study the stability and instability of fluid models. To do this we utilize piecewise linear Lyapunov functions. We establish stability of First-Buffer-First-Served (FBFS) and Last-Buffer-First-Served (LBFS) disciplines in all reentrant lines, and of all work-conserving disciplines in any three buffer reentrant lines. For the four buffer network of Lu and Kumar we characterize the stability region of the Lu and Kumar policy, and show that it is also the global stability region for this network. We also study stability and instability of Kelly-type networks. In particular, we show that not all work-conserving policies are stable for such networks; however, all work-conserving policies are stable in a ring network.

Original languageEnglish
Pages (from-to)115-134
Number of pages20
JournalMathematics of Operations Research
Issue number1
StatePublished - Feb 1996


  • Fluid models
  • Harris recurrence
  • Multiclass queueing networks
  • Piecewise linear Lyapunoc functions
  • Reentrant lines
  • Scheduling policies
  • Stability
  • Unstable networks

ASJC Scopus subject areas

  • General Mathematics
  • Computer Science Applications
  • Management Science and Operations Research


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