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]


  1. ^ 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.
  2. ^ 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.
  3. ^ 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.