# Fluid limit

In queueing theory, a discipline within the mathematical theory of probability, a **fluid limit**, **fluid approximation** or **fluid analysis** of a stochastic model is a deterministic real-valued process which approximates the evolution of a given stochastic process, usually subject to some scaling or limiting criteria.

Fluid limits were first introduced by Thomas G. Kurtz publishing a law of large numbers and central limit theorem for Markov chains.^{[1]}^{[2]} It is known that a queueing network can be stable, but have an unstable fluid limit.^{[3]}

## References

- ↑ Pakdaman, K.; Thieullen, M.; Wainrib, G. (2010). "Fluid limit theorems for stochastic hybrid systems with application to neuron models".
*Advances in Applied Probability*.**42**(3): 761. arXiv:1001.2474. doi:10.1239/aap/1282924062. - ↑ Kurtz, T. G. (1971). "Limit Theorems for Sequences of Jump Markov Processes Approximating Ordinary Differential Processes".
*Journal of Applied Probability*. Applied Probability Trust.**8**(2): 344–356. JSTOR 3211904. - ↑ Bramson, M. (1999). "A stable queueing network with unstable fluid model".
*The Annals of Applied Probability*.**9**(3): 818. doi:10.1214/aoap/1029962815. JSTOR 2667284.

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