Fluid limit explained

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]

Notes and References

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