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Fluid Models of Queueing Networks

  1. David Gamarnik

Published Online: 15 FEB 2011

DOI: 10.1002/9780470400531.eorms0329

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Gamarnik, D. 2011. Fluid Models of Queueing Networks. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. Operations Research Center and Sloan School of Management, MIT, Cambridge, Massachusetts

Publication History

  1. Published Online: 15 FEB 2011


Fluid models are a powerful approximation technique for studying important dynamic properties of queueing networks. The model is typically derived from an underlying queueing system by replacing a stochastic discrete model with a continuous deterministic model, using a certain law of large numbers type of rescaling. The obtained process reveals a lot of fundamental dynamic structures in the underlying system. This article introduces basics of fluid models and illustrates them with a lot of examples. We begin with an informal construction to be followed by rigorous definitions and basic properties. A particular focus is given to the notions of stability of fluid models and methods of stability analysis such as the Lyapunov function technique. Examples of stable fluid models are given as well as some counterexamples, illustrating subtle issues in stability analysis. The formality of connections between fluid models and underlying stochastic queueing systems is discussed at a very high level, since the underlying techniques are highly involved and fall outside of the scope of the article. Instead we point the reader to a rich literature on this subject.


  • queueing;
  • law of large numbers;
  • fluid models;
  • Lyapunov function;
  • stability