Skip to main content
SpringerLink
Log in

Formal techniques for performance analysis: blending SAN and PEPA

  • Original Article
  • Published:
Formal Aspects of Computing

Abstract

In this paper we consider two performance modelling techniques from the perspectives of model construction, generation of an underlying continuous time Markov process, and the potential for reduction in the Markov process. Such careful comparison of modelling techniques allows us to appreciate the strengths and weaknesses of different approaches, and facilitates cross-fertilization between them. In the present case we take a characteristic of one formalism, functional rates in Stochastic Automata Networks, and introduce it to the other formalism, Performance Evaluation Process Algebra. We investigate the benefits of this cross-fertilization, particularly from the perspectives of Markov process generation and reduction.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ajmone Marsan M, Conte G, Balbo G (1984) A class of generalised stochastic petri nets for the performance evaluation of multiprocessor systems. ACM Trans Comput Syst 2(2):93–122

    Article  Google Scholar 

  2. Benoit A, Brenner L, Fernandes P, Plateau B, Stewart W (2003) The PEPS software tool. In: Proceedings of the 13th international conference on modelling techniques and tools for computer performance evaluation, Illinois, September 2–7 2003, pp 215–234

  3. Benoit A, Brenner L, Fernandes P, Plateau B (2003) Aggregation of stochastic automata networks with replicas. In: Proceedings of the international conference on the numerical solution of markov chains (NSMC’03), Illinois, September 2–7 2003, pp 215–234

  4. Bernardo M, Gorrieri R (1998) A tutorial on EMPA: a theory of concurrent processes with nondeterminism, priorities, probabilities and time. Theor Comput Sci 202:1–54

    Article  MATH  MathSciNet  Google Scholar 

  5. Buchholz P, Kemper P (2002) Efficient computation and representation of large reachability sets of composed automata. Dis Event Dynam Syst: Theor Appl 12:265–286

    Article  MATH  MathSciNet  Google Scholar 

  6. Bortolussi L (2006) Stochastic concurrent constraint programming. In: Proceedings of workshop on quantitative analysis of programming languages (QAPL) Vienna, April 2006

  7. Buchholz P (1994) Compositional analysis of a markovian process algebra. In: Herzog U, Rettelbach M (eds) Proceedings of the 2nd process algebra and performance modelling workshop

  8. Buchholz P (1999) Hierarchical structuring of superposed GSPNs. IEEE Trans Softw Eng 25(2):166–181

    Article  MathSciNet  Google Scholar 

  9. Clark G, Gilmore S, Hillston J, Thomas N (1999) Experiences with the PEPA performance modelling tools. IEE Softw 146(1): 11–19

    Article  Google Scholar 

  10. Ciardo C, Tilgner M (1996) On the use of Kronecker operators for the solution of generalized stochastic Petri nets. Technical Report 96-35, Institute for Computer Applications in Science and Engineering, Hampton, VA, May 1996

  11. Ciardo G, Miner AS (1999) A data structure for the efficient kronecker solution of gspns. In: In P. Buchholz editor, Proc. of the 8th International Workshop on Petri Nets and Performance Models (PNPM’99), Saragoza, Spain, pp 22–31

  12. Dayar T (1998) Iterative methods based on splittings for stochastic automata networks. Eur J Oper Res 110:166–186

    Article  MATH  Google Scholar 

  13. Donatelli S, Hermanns H, Hillston J, Ribaudo M (1995) GSPN and SPA compared in practice: modelling a distributed mail system. In: Baccelli F, Jean-Marie A, Mitrani I (eds) Quantitative methods in parallel systems. Springer, Berlin Heidelberg New York, pp. 38–51

    Google Scholar 

  14. D’Argenio P, Hermanns H, Katoen J-P, Klaren R (2001) MoDeST – a modelling and description language for stochastic timed systems. In: Process algebra and probabilistic methods, performance modeling and verification: Joint international workshop, PAPM-PROBMIV, Aachen, Germany, September 2001. LNCS, vol 2165, pp 87–104. Springer, Berlin Heidelberg New York

  15. Donatelli S, Hillston J, Ribaudo M (1995) A comparison of performance evaluation process algebra and generalized stochastic Petri nets. In: Proceedings of the 6th Petri Nets and Performance Models Workshop, October 1995, pp 158–168. IEEE Computer Society Press

  16. DiPierro A, Hankin C, Wiklicky H (2004) Continuous-time probabilistic KLAIM. In: Proceedings of SECCO 2004, Electronic Notes in Theoretical Computer Science

  17. Donatelli S, Kemper P (2001) Integrating synchronization with priority into a kronecker representation. Perform Evaluat 44(1–4):73–96

    Article  MATH  Google Scholar 

  18. DeNicola R, Latella D, Massink M (2005) Formal modelling and quantitative analysis of KLAIM-based mobile systems. In: Proceedings of SAC’05

  19. Donatelli S (1994) Superposed generalised stochastic Petri nets: definition and efficient solution. In: Silva M (ed) Proceedings of the 15th international conference on application and theory of Petri nets

  20. Fourneau JM, Kloul L, Valois F (2000) Performance evaluation of a hierarchical cellular network using PEPA. Technical Report RR 2000/2, Laboratoire PRiSM, University of Versailles

  21. Fourneau JM, Kloul L, Valois F (2002) Performance evaluation of a hierarchical cellular network using PEPA. Perform Evaluat 50:83–99

    Article  MATH  Google Scholar 

  22. Fernando P, Plateau B, Atif K (1998) Efficient descriptor–vector multiplications in stochastic automata networks. JACM 3:381–414

    Article  Google Scholar 

  23. Fernando P, Plateau B, Stewart WJ (1996) Numerical iusses for stochastic automata networks. In: Ribaudo M, (ed) Proceedings of the fourth process algebra and performance modelling workshop, pp 215–234. CLUT

  24. Gilmore S, Hillston J, Kloul L, Ribaudo M (2003) PEPA nets: a structured performance modelling formalism. Perform. Evaluat 54(2):79–104

    Article  Google Scholar 

  25. Götz N, Herzog U, Rettelbach M (1993) Multiprocessor and distributed system design: the integration of functional specification and performance analysis using stochastic process algebras. In: Performance’93

  26. Gilmore S, Hillston J, Recalde L (1997) Elementary structural analysis for PEPA. Technical Report ECS-LFCS-97-377, Laboratory for Foundations of Computer Science, Department of Computer Science, The University of Edinburgh

  27. Gilmore S, Hillston J, Ribaudo M (2001) An efficient algorithm for aggregating PEPA models. IEEE Trans Softw Eng 27(5): 449–464

    Article  Google Scholar 

  28. Groote JF, Ponse A (1995) The syntax and semantics of μ CRL. In: Ponse A, Verhoef C, van Vlijmen SFM (eds) Algebra of communicating processes ’94, workshops in computing series. Springer, Berlin Heidelberg New York, pp. 26–62

    Google Scholar 

  29. Hermanns H (1999) Interactive Markov chains. PhD thesis, Erlangen-Nurnberg University

  30. Hillston J (1994) A Compositional Approach to Performance Modelling. Phd. Thesis, University of Edinburgh, 1994

  31. Hillston J (1995) Compositional Markovian modelling using a process algebra. In: Stewart WJ, (ed) Numerical solution of Markov chains. Kluwer

  32. Hillston J (2005) Fluid flow approximation of pepa models. In: Second international conference on the quantitative evaluation of systems, Torino, Italy, September 2005, pp 33–42. IEEE Computer Society Press

  33. Hillston J (2005) Tuning systems: from composition to performance. Comput J. The Needham Lecture

  34. Hillston J, Kloul L (2001) An efficient kronecker representation for pepa models. In: Proceedings of the joint international workshop, PAPM-PROBMIV 2001, LNCS, vol 2165, pp 120–135, Aachen, Germany. Springer, Berlin Heidelberg New York

  35. Hillston J, Kloul L (2006) A function-equivalent components based simplification technique for pepa models. In: Horváth A, Telek M (eds) Formal methods and stochastic models for performance evaluation, Third European performance engineering workshop (EPEW) Budapest, Hungary, June 21–22 2006. LNCS, vol 4054, pp 16–30. Springer, Berlin Heidelberg New York

  36. Henderson W, Pearce CEM, Taylor PG, van Dijk NM (1990) Closed queueing networks with batch services. Que Sys 6:59–70

    Article  MATH  Google Scholar 

  37. Hillston J, Recalde L, Ribaudo M, Silva M (2001) A comparison of the expressiveness of SPA and bounded SPN models. In: Haverkort B, German R (eds) Proceedings of the 9th international workshop on Petri nets and performance models, Aachen, Germany, September 2001. IEEE Computer Science Press

  38. Henderson W, Taylor PG (1990) Product form in networks of queues with batch arrivals and batch services. Que Syst 6:71–88

    Article  MATH  MathSciNet  Google Scholar 

  39. Hillston J, Thomas N (1999) Product form for a class of PEPA models. Perform Evaluat 35:171–192

    Article  MATH  Google Scholar 

  40. ISO/IEC JTCI/SC33. ISO/IEC FCD 15437—Enhancements to LOTOS, May 1998

  41. Jacobson S, Lazowska E (1982) Analysing queueing networks with simultaneous resource possession. Commun ACM, 25(2):142–151

    Article  Google Scholar 

  42. Kemper P (1996) Numerical Analysis of Superposed GSPNs. IEEE Trans Softw Eng 22(9):615–628

    Article  Google Scholar 

  43. Kwiatkowska M, Norman G, Parker D (2002) PRISM: Probabilistic symbolic model checker. In: Proceedings of 12th international conference on modelling tools and techniques for computer and communication system performance evaluation, London, UK, April 2002. LNCS, vol 2324, pp 200–204. Springer, Berlin Heidelberg New York

  44. Molloy MK (1982) Performance analysis using stochastic petri nets. IEEE Trans Comput 31(9):913–917

    Google Scholar 

  45. Plateau B, Fourneau JM (1991) A methodology for solving markov models of parallel systems. J Parallel Distrib Comput

  46. Plateau B, Fourneau JM, Lee KH (1988) PEPS: a package for solving complex Markov models of parallel systems. In: Proceedings of the 4th international conference on modelling techniques and tools for computer performance evaluation

  47. Plateau B (1984) De l’Evolution du Parallélisme et de la Synchronisation. PhD Thesis, Université de Paris-Sud, Orsay

  48. Plateau B (1985) On the stochastic structure of parallelism and synchronisation models for distributed algorithms. In: Proceedings of the ACM sigmetrics conference on measurement and modelling of computer systems

  49. Priami C (1995) Stochastic π-calculus. Comput J 38(6). Special Issue: Proceedings of the 3rd process algebra and performance modelling workshop

  50. Ribaudo M (1995) On the relationship between stochastic petri nets and stochastic process algebras. PhD Thesis, Dipartimento di Informatica, Università di Torino, May 1995

  51. Stewart WJ, Atif K, Plateau B (1995) The numerical solution of stochastic automata networks. Euro J Oper Res 86:503–525

    Article  MATH  Google Scholar 

  52. Sanders WH, Meyer JF (1991) Reduced base model construction methods for stochastic activity networks. IEEE J Select Areas Commun 9(1):25–36

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory for Foundations of Computer Science, School of Informatics, University of Edinburgh, Edinburgh, EH9 3JZ, UK

    Jane Hillston

  2. PRiSM, Université de Versailles, 45, Avenue des Etats-Unis, 78035, Versailles Cedex, France

    Leïla Kloul

Authors
  1. Jane Hillston
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Leïla Kloul
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Leïla Kloul.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hillston, J., Kloul, L. Formal techniques for performance analysis: blending SAN and PEPA. Form Asp Comp 19, 3–33 (2007). https://doi.org/10.1007/s00165-006-0011-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00165-006-0011-6

Keywords

Search

Navigation