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Fluid queue information


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.

Fluid queues have been used to model the performance of a network switch,[10] a router,[11] the IEEE 802.11 protocol,[12] Asynchronous Transfer Mode (the intended technology for B-ISDN),[13][14] peer-to-peer file sharing,[15] optical burst switching,[16] and has applications in civil engineering when designing dams.[17] The process is closely connected to quasi-birth–death processes, for which efficient solution methods are known.[18][19]

  1. ^ 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. JSTOR 1427040.
  2. ^ Ahn, S.; Ramaswami, V. (2003). "Fluid Flow Models and Queues—A Connection by Stochastic Coupling" (PDF). Stochastic Models. 19 (3): 325. doi:10.1081/STM-120023564. S2CID 6733796.
  3. ^ Elwalid, A. I.; Mitra, D. (1991). "Analysis and design of rate-based congestion control of high speed networks, I: Stochastic fluid models, access regulation". Queueing Systems. 9 (1–2): 29–63. doi:10.1007/BF01158791. S2CID 19379411.
  4. ^ Stanford, David A.; Latouche, Guy; Woolford, Douglas G.; Boychuk, Dennis; Hunchak, Alek (2005). "Erlangized Fluid Queues with Application to Uncontrolled Fire Perimeter". Stochastic Models. 21 (2–3): 631. doi:10.1081/STM-200056242. S2CID 123591340.
  5. ^ Remiche, M. A. (2005). "Compliance of the Token-Bucket Model with Markovian Traffic". Stochastic Models. 21 (2–3): 615–630. doi:10.1081/STM-200057884. S2CID 121190780.
  6. ^ Kulkarni, Vidyadhar G. (1997). "Fluid models for single buffer systems" (PDF). Frontiers in Queueing: Models and Applications in Science and Engineering. pp. 321–338. ISBN 978-0-8493-8076-1.
  7. ^ Moran, P. A. P. (1954). "A probability theory of dams and storage systems". Aust. J. Appl. Sci. 5: 116–124.
  8. ^ Phatarfod, R. M. (1963). "Application of Methods in Sequential Analysis to Dam Theory". The Annals of Mathematical Statistics. 34 (4): 1588–1592. doi:10.1214/aoms/1177703892.
  9. ^ Gani, J.; Prabhu, N. U. (1958). "Continuous Time Treatment of a Storage Problem". Nature. 182 (4627): 39. Bibcode:1958Natur.182...39G. doi:10.1038/182039a0. S2CID 42193342.
  10. ^ Cite error: The named reference anick was invoked but never defined (see the help page).
  11. ^ 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. CiteSeerX 10.1.1.1.3208. doi:10.1145/1005686.1005728. ISBN 978-1581138733. S2CID 14416842.
  12. ^ Arunachalam, V.; Gupta, V.; Dharmaraja, S. (2010). "A fluid queue modulated by two independent birth–death processes". Computers & Mathematics with Applications. 60 (8): 2433–2444. doi:10.1016/j.camwa.2010.08.039.
  13. ^ Norros, I.; Roberts, J. W.; Simonian, A.; Virtamo, J. T. (1991). "The superposition of variable bit rate sources in an ATM multiplexer". IEEE Journal on Selected Areas in Communications. 9 (3): 378. doi:10.1109/49.76636.
  14. ^ Rasmussen, C.; Sorensen, J. H.; Kvols, K. S.; Jacobsen, S. B. (1991). "Source-independent call acceptance procedures in ATM networks". IEEE Journal on Selected Areas in Communications. 9 (3): 351. doi:10.1109/49.76633.
  15. ^ Gaeta, R.; Gribaudo, M.; Manini, D.; Sereno, M. (2006). "Analysis of resource transfers in peer-to-peer file sharing applications using fluid models". Performance Evaluation. 63 (3): 149. CiteSeerX 10.1.1.102.3905. doi:10.1016/j.peva.2005.01.001.
  16. ^ Yazici, M. A.; Akar, N. (2013). "Analysis of continuous feedback Markov fluid queues and its applications to modeling Optical Burst Switching". Proceedings of the 2013 25th International Teletraffic Congress (ITC). pp. 1–8. doi:10.1109/ITC.2013.6662952. hdl:11693/28055. ISBN 978-0-9836283-7-8. S2CID 863180.
  17. ^ Gani, J. (1969). "Recent Advances in Storage and Flooding Theory". Advances in Applied Probability. 1 (1): 90–110. doi:10.2307/1426410. JSTOR 1426410.
  18. ^ 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.
  19. ^ Govorun, M.; Latouche, G.; Remiche, M. A. (2013). "Stability for Fluid Queues: Characteristic Inequalities". Stochastic Models. 29: 64–88. doi:10.1080/15326349.2013.750533. S2CID 120102947.

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