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.
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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
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
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
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
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
Bortolussi L (2006) Stochastic concurrent constraint programming. In: Proceedings of workshop on quantitative analysis of programming languages (QAPL) Vienna, April 2006
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
Buchholz P (1999) Hierarchical structuring of superposed GSPNs. IEEE Trans Softw Eng 25(2):166–181
Clark G, Gilmore S, Hillston J, Thomas N (1999) Experiences with the PEPA performance modelling tools. IEE Softw 146(1): 11–19
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
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
Dayar T (1998) Iterative methods based on splittings for stochastic automata networks. Eur J Oper Res 110:166–186
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
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
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
DiPierro A, Hankin C, Wiklicky H (2004) Continuous-time probabilistic KLAIM. In: Proceedings of SECCO 2004, Electronic Notes in Theoretical Computer Science
Donatelli S, Kemper P (2001) Integrating synchronization with priority into a kronecker representation. Perform Evaluat 44(1–4):73–96
DeNicola R, Latella D, Massink M (2005) Formal modelling and quantitative analysis of KLAIM-based mobile systems. In: Proceedings of SAC’05
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
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
Fourneau JM, Kloul L, Valois F (2002) Performance evaluation of a hierarchical cellular network using PEPA. Perform Evaluat 50:83–99
Fernando P, Plateau B, Atif K (1998) Efficient descriptor–vector multiplications in stochastic automata networks. JACM 3:381–414
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
Gilmore S, Hillston J, Kloul L, Ribaudo M (2003) PEPA nets: a structured performance modelling formalism. Perform. Evaluat 54(2):79–104
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
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
Gilmore S, Hillston J, Ribaudo M (2001) An efficient algorithm for aggregating PEPA models. IEEE Trans Softw Eng 27(5): 449–464
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
Hermanns H (1999) Interactive Markov chains. PhD thesis, Erlangen-Nurnberg University
Hillston J (1994) A Compositional Approach to Performance Modelling. Phd. Thesis, University of Edinburgh, 1994
Hillston J (1995) Compositional Markovian modelling using a process algebra. In: Stewart WJ, (ed) Numerical solution of Markov chains. Kluwer
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
Hillston J (2005) Tuning systems: from composition to performance. Comput J. The Needham Lecture
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
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
Henderson W, Pearce CEM, Taylor PG, van Dijk NM (1990) Closed queueing networks with batch services. Que Sys 6:59–70
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
Henderson W, Taylor PG (1990) Product form in networks of queues with batch arrivals and batch services. Que Syst 6:71–88
Hillston J, Thomas N (1999) Product form for a class of PEPA models. Perform Evaluat 35:171–192
ISO/IEC JTCI/SC33. ISO/IEC FCD 15437—Enhancements to LOTOS, May 1998
Jacobson S, Lazowska E (1982) Analysing queueing networks with simultaneous resource possession. Commun ACM, 25(2):142–151
Kemper P (1996) Numerical Analysis of Superposed GSPNs. IEEE Trans Softw Eng 22(9):615–628
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
Molloy MK (1982) Performance analysis using stochastic petri nets. IEEE Trans Comput 31(9):913–917
Plateau B, Fourneau JM (1991) A methodology for solving markov models of parallel systems. J Parallel Distrib Comput
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
Plateau B (1984) De l’Evolution du Parallélisme et de la Synchronisation. PhD Thesis, Université de Paris-Sud, Orsay
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
Priami C (1995) Stochastic π-calculus. Comput J 38(6). Special Issue: Proceedings of the 3rd process algebra and performance modelling workshop
Ribaudo M (1995) On the relationship between stochastic petri nets and stochastic process algebras. PhD Thesis, Dipartimento di Informatica, Università di Torino, May 1995
Stewart WJ, Atif K, Plateau B (1995) The numerical solution of stochastic automata networks. Euro J Oper Res 86:503–525
Sanders WH, Meyer JF (1991) Reduced base model construction methods for stochastic activity networks. IEEE J Select Areas Commun 9(1):25–36
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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
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DOI: https://doi.org/10.1007/s00165-006-0011-6