In queueing theory, a discipline within the mathematical theory of probability, a fluid queue (fluid model,[1]fluid flow model[2] or stochastic fluid model[3]) is a mathematical model used to describe the fluid level in a reservoir subject to randomly determined periods of filling and emptying. The term dam theory was used in earlier literature for these models. The model has been used to approximate discrete models, model the spread of wildfires,[4] in ruin theory[5] and to model high speed data networks.[6] The model applies the leaky bucket algorithm to a stochastic source.
The model was first introduced by Pat Moran in 1954 where a discrete-time model was considered.[7][8][9] Fluid queues allow arrivals to be continuous rather than discrete, as in models like the M/M/1 and M/G/1 queues.
^Mitra, D. (1988). "Stochastic Theory of a Fluid Model of Producers and Consumers Coupled by a Buffer". Advances in Applied Probability. 20 (3): 646–676. doi:10.2307/1427040. JSTOR1427040.
^Cite error: The named reference anick was invoked but never defined (see the help page).
^Hohn, N.; Veitch, D.; Papagiannaki, K.; Diot, C. (2004). "Bridging router performance and queuing theory". Proceedings of the joint international conference on Measurement and modeling of computer systems - SIGMETRICS 2004/PERFORMANCE 2004. p. 355. CiteSeerX10.1.1.1.3208. doi:10.1145/1005686.1005728. ISBN978-1581138733. S2CID14416842.
^Gani, J. (1969). "Recent Advances in Storage and Flooding Theory". Advances in Applied Probability. 1 (1): 90–110. doi:10.2307/1426410. JSTOR1426410.
^Ramaswami, V. Smith, D.; Hey, P (eds.). "Matrix analytic methods for stochastic fluid flows". Teletraffic Engineering in a Competitive World (Proceedings of the 16th International Teletraffic Congress). Elsevier Science B.V.