Skip to main content
SpringerLink
Log in

Modeling and Analysis of Multi-class Threshold-Based Queues with Hysteresis Using Stochastic Petri Nets

  • Conference paper
  • First Online:
Application and Theory of Petri Nets 2002 (ICATPN 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2360))

Included in the following conference series:

  • 734 Accesses

Abstract

This paper deals with multi-class queueing systems where thresholds are included in order to smooth the variations of throughput and delay by modifying the queue behaviour. Hysteresis is also inserted, so that the control mechanism will not switch too much. One motivation for using multiple classes of customers is its capability to model heterogeneous traffics like data, voice and video. Moreover, threshold queues have many applications in the transport protocols of communication networks. The analysis is done using Stochastic Petri Nets and Fluid Stochastic Petri Nets. This powerful paradigm helps to obtain a very simple representation of the systems and the analysis is transparent using an available Petri net package. Numerous numerical illustrations are given in order to validate the use of threshold queues with hysteresis as well as their representation by SPNs and FSPNs and performances of various scheduling schemes are compared in order to minimize a cost function.

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. K. D. Ansell, P. S. Glazebrook and I. Mitrani. Threshold policies for a single-server queuing network. Probability in the Engineering and Informational Sciences, 15:15–33, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  2. B. D. Choi, S. H. Choi, B. Kim, and D. K. Sung. Analysis of priority queueing system based on thresholds and its application to signaling system no. 7 with congestion control. Computer Networks, 32:149–170, 2000.

    Article  Google Scholar 

  3. H. Choi, V. G. Kulkarni, and K. S. Trivedi. Markov Regenerative Stochastic Petri Nets. Performance Evaluation, 20(1–3):337–357, 1993.

    MathSciNet  Google Scholar 

  4. G. Ciardo, A. Blakemore, P. F. Chimento, J. K. Muppala, and K. S. Trivedi. Automated Generation and Analysis of Markov Reward Models using Stochatic Reward Nets. In Carl Meyer and Robert Plemmons, editors, Linear Algebra, Markov Chains and Queuing Models, volume 48 of IMA Volumes in Mathematics and its Applications, pages 145–191. Springer-Verlag, Heidelberg, 1993.

    Google Scholar 

  5. G. Ciardo, J. K. Muppala, and K. S. Trivedi. SPNP: Stochastic Petri net Package. In Proc. Third International Workshop on Petri Nets and Performance Models, PNPM’89, pages 142–151, 1989.

    Google Scholar 

  6. G. Ciardo, J. K. Muppala, and K. S. Trivedi. Analyzing Concurrent and Fault-tolerant Software Using Stochatic Reward Nets. Journal of Parallel and Distributed Computing, 15:255–269, 1992.

    Article  Google Scholar 

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

    Article  Google Scholar 

  8. M. E. Crovella. Performance Characteristics of the World Wide Web. In G. Haring et al., editor, Performance Evaluation, volume 1769 of Lecture Notes in Computer Science, pages 219–232. Springer-Verlag, 2000.

    Google Scholar 

  9. G. S. Fishman. Monte Carlo: Concepts, Algorithms and Applications. Springer-Verlag, 1997.

    Google Scholar 

  10. P. W. Glynn and D. L. Iglehart. Importance Sampling for Stochastic Simulations. Management Science, 35(11):1367–1392, November 1989.

    Google Scholar 

  11. L. Golubchik and J. C. S. Lui. A fast and accurate iterative solution of a multi-class threshold-based queuing system with hysteresis. In Proc. of the ACM SIGMETRICS Conference, pages 196–206, Santa Clara, June 2000.

    Google Scholar 

  12. A. Goyal, P. Shahabuddin, P. Heidelberger, V. F. Nicola, and P. W. Glynn. A Unified Framework for Simulating Markovian Models of Highly Dependable Systems. IEEE Transactions on Computers, 41(1):36–51, January 1992.

    Google Scholar 

  13. B. R. Haverkort. Performance of Computer Communication Systems. John Wiley and Sons, 1998.

    Google Scholar 

  14. C. Hirel, B. Tuffin, and K. S. Trivedi. SPNP Version 6.0. In B. R. Haverkort, H. C. Bohnenkamp, and C. U. Smith, editors, Computer performance evaluation: Modelling tools and techniques; 11th International Conference; TOOLS 2000, Schaumburg, Il., USA, volume 1786 of Lecture Notes in Computer Science, pages 354–357. Springer Verlag, 2000.

    Google Scholar 

  15. G. Horton, V. Kulkarni, D. Nicol, and K. S. Trivedi. Fluid Stochastic Petri nets: Theory, Application and Solution. European Journal of Operational Research, 105:184–201, 1998.

    Article  MATH  Google Scholar 

  16. O. C. Ibe and J. Keilson. Multi-server threshold queues with hysteresis. Performance Evaluation, 21:185–213, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  17. R. L. Larsen and A. K. Agrawala. Control of a Heterogeneous Two-Server Exponential Queueing System. IEEE Transactions on Software Engineering, SE-9(4):522–526, 1983.

    Article  Google Scholar 

  18. L-M. Le Ny and B. Tuffin. A simple analysis of heterogeneous multi-server threshold queues with hysteresis. Technical Report 1333, IRISA, 2000.

    Google Scholar 

  19. J. Y. Lee and Y. H. Kim. Performance analysis of a hybrid priority control scheme for input and output queueing ATM switches. In Proceedings of IEEE INFOCOM 98, pages 1470–1477, March 1998.

    Google Scholar 

  20. S. Q. Li. Overload Control in a Finite Message Storage Buffer. IEEE Transactions on Communications, 37(12), December 1989.

    Google Scholar 

  21. W. Lin and P. R. Kumar. Optimal Control of a Queueing System with Two Heterogeneous Servers. IEEE Transactions on Automatic Control, AC-29(8):696–703, 1984.

    Article  MathSciNet  Google Scholar 

  22. J. C. S. Lui and L. Golubchik. Stochastic complement analysis of multi-server threshold queues with hysteresis. Performance Evaluation, 35:185–213, 1999.

    Article  Google Scholar 

  23. J. A. Morrison. Two-server queue with one server idle below a threshold. Queueing Systems: Theory and Applications, 7:325–336, 1990.

    Article  MathSciNet  MATH  Google Scholar 

  24. V. F. Nicola, M. K. Nakayama, P. Heidelberger, and A. Goyal. Fast Simulation of Highly Dependable Systems with General Failure and Repair Processes. IEEE Transactions on Computers, 42(12):1440–1452, December 1993.

    Google Scholar 

  25. D. Sahu, S. Towsley and J. Kurose. A Quantitative Study of Differentiated Services for the Internet. Journal of Communications and Networks, 2:127–137, 2000.

    Google Scholar 

  26. W. J. Stewart. Introduction to the Numerical Solution of Markov Chains. Princeton University Press, 1994.

    Google Scholar 

  27. K. S. Trivedi and V. G. Kulkarni. FSPNs: Fluid Stochastic Petri Nets. In 14th International Conference on Applications and Theory of Petri Nets, pages 24–31, 1993.

    Google Scholar 

  28. B. Tuffin and L-M. Le Ny. Modeling and analysis of threshold queues with hysteresis using stochastic Petri nets: the monoclass case. In Proceedings of Petri Nets and Performance Models, pages 175–184. IEEE CS Press, 2001.

    Google Scholar 

  29. B. Tuffin and K. S. Trivedi. Implementation of importance splitting techniques in stochastic Petri net package. In B. R. Haverkort, H. C. Bohnenkamp, and C. U. Smith, editors, Computer performance evaluation: Modelling tools and techniques; 11th International Conference; TOOLS 2000, Schaumburg, Il., USA, volume 1786 of Lecture Notes in Computer Science, pages 216–229. Springer Verlag, 2000.

    Chapter  Google Scholar 

  30. W. B. van den Hout. The Power-Series Algorithm: A Numerical Approach to Markov Processes. Tilburg University, 1996.

    Google Scholar 

  31. K. Wolter. Performance and Dependability Modelling with Second Order Fluid Stochastic Petri Nets. PhD thesis, Technische Universitat Berlin, 1999.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IRISA-Université de Rennes 1, Campus universitaire de Beaulieu, 35042, Rennes cedex, France

    Louis-Marie Le Ny

  2. IRISA-INRIA, Campus universitaire de Beaulieu, 35042, Rennes cedex, France

    Bruno Tuffin

Authors
  1. Louis-Marie Le Ny
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bruno Tuffin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Division of Informatics, University of Edinburgh, James Clerk Maxwell Building, The King’s Buildings Mayfield Road, Edinburgh, EH9 3JZ, UK

    Javier Esparza

  2. Department of Computer Science, University of Adelaide, North Terrace, Adelaide, SA, 5005, Australia

    Charles Lakos

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Le Ny, LM., Tuffin, B. (2002). Modeling and Analysis of Multi-class Threshold-Based Queues with Hysteresis Using Stochastic Petri Nets. In: Esparza, J., Lakos, C. (eds) Application and Theory of Petri Nets 2002. ICATPN 2002. Lecture Notes in Computer Science, vol 2360. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48068-4_16

Download citation

  • DOI: https://doi.org/10.1007/3-540-48068-4_16

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43787-1

  • Online ISBN: 978-3-540-48068-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation