Skip to main content
SpringerLink
Log in

Fluid Models in Performance Analysis

  • Chapter
Book cover Formal Methods for Performance Evaluation (SFM 2007)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 4486))

Abstract

Stochastic fluid models have been applied to model and evaluate the performance of many important real systems. The automatic analysis tools to support of fluid models are still not as improved as the ones for discrete state Markov models, but there is a wide range of models which can be effectively described and analyzed with fluid models. Also the model support of hybrid models from various performance evaluation tools improves continuously.

The aim of this work is to summarize the basic concepts and the potential use of Markov fluid models. The factors which determine the limits of solvability of fluid models are also discussed. Practical guidelines can be extracted from these factors to determine the applicability of fluid models in practical modeling examples. The work is supported by an example where Fluid Models, derived from an higher level modeling language (Fluid Stochastic Petri Nets), have been exploited to study the transfer time distribution in Peer-to-Peer file sharing applications.

This work is partially supported by the Italian-Hungarian R&D project 9/2003 and by the OTKA K61709 grant.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Agapie, M., Sohraby, K.: Algorithmic solution to second order fluid flow. In: Proc. of IEEE Infocom, Anchorage, Alaska, Usa (Apr. 2001)

    Google Scholar 

  2. Ahn, S., Ramaswami, V.: Matrix-geometric algorithms for stochastic fluid flows. In: SMCtools ’06: Proceeding from the 2006 workshop on Tools for solving sturctured Markov chains, Pisa, Italy, p. 11. ACM Press, New York (2006), doi:10.1145/1190366.1190376

    Chapter  Google Scholar 

  3. Ajmone Marsan, M., Balbo, G., Bobbio, A., Chiola, G., Conte, G., Cumani, A.: The effect of execution policies on the semantics and analysis of stochastic Petri nets. IEEE Transactions on Software Engineering 15(7), 832–846 (1989)

    Article  MathSciNet  Google Scholar 

  4. Ajmone Marsan, M., Balbo, G., Conte, G., Donatelli, S., Franceschinis, G.: Modelling with Generalized Stochastic Petri Nets. John Wiley & Sons, Chichester (1995)

    MATH  Google Scholar 

  5. Alla, H., David, R.: Continuous and Hybrid Petri Nets. Journal of Systems Circuits and Computers 8(1) (1998)

    Google Scholar 

  6. Ang, E.-J., Barria, J.: The markov modulated regulated brownian motion: A second-order fluid flow model of a finite buffer. Queueing Systems 35, 263–287 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  7. Anick, D., Mitra, D., Sondhi, M.M.: Stochastic Theory of a Data-Handling System. Bell Sys. Tech. J. 61(8), 1871–1894 (1982)

    MathSciNet  Google Scholar 

  8. Chen, D.-Y., Hong, Y., Trivedi, K.S.: Second order stochastic fluid flow models with fluid dependent flow rates. Performance Evaluation 49(1-4), 341–358 (2002)

    Article  MATH  Google Scholar 

  9. Ciardo, G., Nicol, D.M., Trivedi, K.S.: Discrete-event Simulation of Fluid Stochastic Petri Nets. In: Proc. 7th Int. Workshop on Petri Nets and Performance Models (PNPM’97), Saint Malo, France, June 1997, pp. 217–225. IEEE Computer Society Press, Los Alamitos (1997)

    Google Scholar 

  10. Ciardo, G., Nicol, D.M., Trivedi, K.S.: Discrete-event Simulation of Fluid Stochastic Petri Nets. IEEE Transactions on Software Engineering 2(25), 207–217 (1999)

    Article  Google Scholar 

  11. Czachorski, T., Pekergin, F.: Diffusion approximation as a modelling tool. In: Tutorial Papers of the ATM & IP 2000, Ilkley, UK, Jul. 2000, pp. 18/1–18/40 (2000)

    Google Scholar 

  12. de Souza e Silva, E., Gail, R.: An algorithm to calculate transient distributions of cummulative rate and impulse based reward. Commun. in Statist. – Stochastic Models 14(3), 509–536 (1998)

    Article  MATH  Google Scholar 

  13. Elwalid, A.I., Mitra, D.: Statistical Multiplexing with Loss Priorities in Rate-Based Congestion Control of High-Speed Networks. IEEE Transaction on Communications 42(11), 2989–3002 (1994)

    Article  Google Scholar 

  14. Gaeta, R., Gribaudo, M., Manini, D., Sereno, M.: Analysis of resource transfers in peer-to-peer file sharing applications using fluid models. Perform. Eval. 63(3), 149–174 (2006), doi:10.1016/j.peva.2005.01.001

    Article  Google Scholar 

  15. German, R.: Performance Analysis of Communication Systems: Modeling with Non-Markovian Stochastic Petri Nets. John Wiley & Sons, Chichester (2000)

    MATH  Google Scholar 

  16. German, R., Gribaudo, M., Horváth, G., Telek, M.: Stationary analysis of FSPNs with mutually dependent discrete and continuous parts. In: International Conference on Petri Net Performance Models – PNPM 2003, Urbana, IL, USA, Sept. 2003, pp. 30–39. IEEE Computer Society Press, Los Alamitos (2003)

    Chapter  Google Scholar 

  17. German, R., Lindemann, C.: Analysis of Stochasitc Petri Nets by the Method of Supplementary Variables. Performance Evaluation 20, 317–335 (1994)

    Article  MathSciNet  Google Scholar 

  18. Gribaudo, M., German, R.: Numerical solution of bounded fluid models using matrix exponentiation. In: Proc. 11th GI/ITG Conference on Measuring, Modelling and Evaluation of Computer and Communication Systems (MMB), Aachen, Germany, Sep. 2001, VDE, Berlin (2001)

    Google Scholar 

  19. Gribaudo, M., Sereno, M., Bobbio, A.: Fluid Stochastic Petri Nets: An Extended Formalism to Include non-Markovian Models. In: Proc. 8th Intern. Workshop on Petri Nets and Performance Models, Zaragoza, Spain, Sep. 1999, IEEE Computer Society Press, Los Alamitos (1999)

    Google Scholar 

  20. Gribaudo, M., Sereno, M., Bobbio, A., Horvath, A.: Fluid Stochastic Petri Nets augmented with Flush-out arcs: Modelling and Analysis. Discrete Event Dynamic Systems 11(1-2) (2001)

    Google Scholar 

  21. Horton, G., Kulkarni, V.G., Nicol, D.M., Trivedi, K.S.: Fluid stochastic Petri Nets: Theory, Application, and Solution Techniques. European Journal of Operations Research 105(1), 184–201 (1998)

    Article  MATH  Google Scholar 

  22. Karandikar, R.L., Kulkarni, V.G.: Second-order fluid flow models: reflected brownian motion in a random environment. Operations Research 43, 77–88 (1995)

    Article  MATH  Google Scholar 

  23. Kulkarni, V.G.: Fluid models for single buffer systems. In: Dshalalow, J.H. (ed.) Models and Applications in Science and Engineering. Frontiers in Queueing, pp. 321–338. CRC Press, Boca Raton (1997)

    Google Scholar 

  24. Kulkarni, V.G., Nicola, V.F., Trivedi, K.: Effects of checkpointing and queueing on program performance. Stochastic models 4(6), 615–648 (1990)

    Article  MathSciNet  Google Scholar 

  25. Lewis, P.A.W., Shedler, G.S.: Simulation of nonhomogeneous Poisson processes by thinning. Naval Research Logistic Quarterly 26, 403–414 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  26. Allam, M.: Sur l’analyse quantitative des reseaux de Petri hybrides Une approche basee sur les automates hybrides. Laboratoire d’Automatique de Grenoble (1998)

    Google Scholar 

  27. Manini, D., Gribaudo, M.: Modelling search, availability, and parallel download in p2p file sharing applications with fluid model. In: Proceedings of the 14th International Conference on Advanced Computing and Communication, ADCOM (2006)

    Google Scholar 

  28. Mitra, D.: Stochastic Theory of a Fluid Model of Producers and Consumers. Adv. Appl. Prob. 20, 646–676 (1988)

    Article  MATH  Google Scholar 

  29. Nicola, V.F., Martini, R., Chimento, P.F.: The completion time of a job in a failure environment and partial loss of work. In: 2nd Int. Conf. on Mathematical Methods in Reliability (MMR’2000), Bordeaux, France, July 2000, pp. 813–816 (2000)

    Google Scholar 

  30. Pouwelse, J.A., Garbacki, P., Epema, D.H.G., Sips, H.J.: A measurement study of the bittorrent peer-to-peer file-sharing system. In: Proc. 19th IEEE Annual Computer Communications Workshop (2004)

    Google Scholar 

  31. Qureshi, M.A., Sanders, W.H.: Reward model solution methods with impulse and rate rewards: An algorithm and numerical results. Performance Evaluation, 413–436 (1994)

    Google Scholar 

  32. Reibman, A., Smith, R., Trivedi, K.S.: Markov and Markov reward model transient analysis: an overview of numerical approaches. European Journal of Operational Research 40, 257–267 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  33. Ren, Q., Kobayashi, H.: Transient solutions for the buffer behavior in statistical multiplexing. Perform. Eval. 23(1), 65–87 (1995)

    Article  MATH  Google Scholar 

  34. Sericola, B.: Transient analysis of stochastic fluid models. Perform. Eval. 32(4), 245–263 (1998)

    Article  Google Scholar 

  35. Sericola, B.: A finite buffer fluid queue driven by a markovian queue. Queueing Syst. Theory Appl. 38(2), 213–220 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  36. Sericola, B., Tuffin, B.: A fluid queue driven by a markovian queue. Queueing Syst. Theory Appl. 31(3-4), 253–264 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  37. Trivedi, K., Kulkarni, V.: FSPNs: Fluid Stochastic Petri nets. In: Ajmone Marsan, M. (ed.) ICATPN 1993. LNCS, vol. 691, Springer, Heidelberg (1993)

    Google Scholar 

  38. Wolter, K.: Second order fluid stochastic petri nets: an extension of gspns for approximate and continuous modelling. In: Proc. of World Congress on System Simulation, Singapore, Sep. 1997, pp. 328–332 (1997)

    Google Scholar 

  39. Wolter, K.: Jump Transitions in Second Order FSPNs. In: Proc. of MASCOTS’99, Washington, DC (Oct. 1999)

    Google Scholar 

  40. Wolter, K., Horton, G., German, R.: Non-Markovian Fluid Stochastic Petri Nets. Technical report, Tecnical University of Berlin, Berlin, Germany, Report 1996-13 (1996)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dip. di Informatica, Università di Torino,  

    Marco Gribaudo

  2. Dept. of Telecom., Technical University of Budapest,  

    Miklós Telek

Authors
  1. Marco Gribaudo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Miklós Telek
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Marco Bernardo Jane Hillston

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer Berlin Heidelberg

About this chapter

Cite this chapter

Gribaudo, M., Telek, M. (2007). Fluid Models in Performance Analysis. In: Bernardo, M., Hillston, J. (eds) Formal Methods for Performance Evaluation. SFM 2007. Lecture Notes in Computer Science, vol 4486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72522-0_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-72522-0_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72482-7

  • Online ISBN: 978-3-540-72522-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation