This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Stochastic Well-Formed Colored Nets and Symmetric Modeling Applications
November 1993 (vol. 42 no. 11)
pp. 1343-1360

The class of stochastic well-formed colored nets (SWN's) was defined as a syntactic restriction of stochastic high-level nets. The interest of the introduction of restrictions in the model definition is the possibility of exploiting the symbolic reachability graph (SRG) to reduce the complexity of Markovian performance evaluation with respect to classical Petri net techniques. It turns out that SWN's allow the representation of any color function in a structured form, so that any unconstrained high-level net can be transformed into a well-formed net. Moreover, most constructs useful for the modeling of distributed computer systems and architectures directly match the "well-formed" restriction, without any need of transformation. A nontrivial example of the usefulness of the technique in the performance modeling and evaluation of multiprocessor architectures is included.

[1] M. K. Molloy, "Performance analysis using stochastic Petri nets,"IEEE Trans. Comput., vol. C-31, pp. 913-917, Sept. 1982.
[2] M. Ajmone Marsan, G. Balbo, G. Conte, and F. Gregoretti, "Modeling bus contention and memory interference in a multiprocessor system,"IEEE Trans. Comput., vol. C-32, pp. 60-72, Jan. 1983.
[3] M. Ajmone Marsan, G. Balbo, and G. Conte, "A class of generalized stochastic Petri nets for the performance evaluation of multiprocessor systems,"ACM Trans. Comput. Syst., vol. 2, pp. 93-122, May 1984.
[4] M. Ajmone Marsan, G. Balbao, and G. Conte,Performance Modeling of Multiprocessor Systems. Cambridge, MA: MIT Press, 1986.
[5] M. Ajmone Marsan and G. Chiola, "Construction of generalized stochastic Petri net models of bus oriented multiprocessor systems by stepwise refinements," inProc. 2nd Int. Conf. Modeling Techniques and Tools for Performance Analysis, France, June 1985.
[6] M. Ajmone Marsan, G. Balbo, G. Chiola, and G. Conte, "Modeling the software architecture of a prototype parallel machine," inProc. 1987 SIGMETRICS Conf., Alberta, Canada, May 1987.
[7] C. Lin and D. C. Marinescu, "Stochastic high-level Petri nets and applications,"IEEE Trans. Comput., vol. 37, pp. 815-825, July 1988.
[8] S. Haddad, "Une categorie regulier de reseau de Petri de haut niveau: Definition, proprietes et reductions," Ph.D. dissertation, Lab. MASI, Universite P. et M. Curie (Paris 6), Paris, France, Oct. 1987. These de Doctorat, RR87/197 (in French).
[9] K. Jenson, "Coloured Petri nets and the invariant method,"Theoretical Comp. Sci., vol. 14, pp. 317-336, 1981.
[10] C. Dutheillet and S. Haddad, "Regular stochastic Petri nets," inProc. 10th Int. Conf. on Application and Theory of Petri Nets(Bonn, Germany), June 1989.
[11] C. Dutheillet and S. Haddad, "Aggregation of states in colored stochastic Petri nets: application to a multiprocessor architecture," inProc. 3rd Int. Workshop on Petri Nets and Performance Models(Kyoto, Japan), Dec. 1989, pp. 40-49.
[12] P. Huber, A. M. Jensen, L. O. Jepsen, and K. Jensen, "Towards reachability trees for high-level Petri nets,"Lecture Notes Comput. Sci., vol. 188, pp. 215-233, 1985.
[13] A. Zeine, "Coloured stochastic Petri nets," inProc. Int. Workshop Timed Petri Nets, Torino, Italy, July 1985, pp. 262-271.
[14] J. A. Carrasco, "Automated construction of compound Markov chains from generalized stochastic high-level Petri nets," inProc. 3rd Int. Workshop Petri Nets and Performance Models, Kyoto, Japan, Dec. 1989, pp. 93-102.
[15] G. Chiola, C. Dutheillet, G. Franceschinis, and S. Haddad, "On wellformed coloured nets and their symbolic reachability graph," inProc. 11th Int. Conf. Application and Theory of Petri Nets, Paris, France, June 1990; reprinted inHigh-Level Petri Nets, Theory and Application, K. Jensen and G. Rozenberg, Eds. New York: Springer-Verlag, 1991.
[16] C. Dutheillet, "Symétries dans los réseaux colorés. Définition, analyse et applicationàl'évaluation de performances," Ph.D. dissertation, Lab. MASI, UniversitéP. et M. Curie (Paris 6), France, Jan. 1991 (in French).
[17] T. Murata, "Petri nets: Properties, analysis, and applications,"Proc. IEEE, vol. 77, no. 4, pp. 541-580, Apr. 1989.
[18] K. Jensen and G. Rozenberg, Eds.High-Level Petri Nets; Theory and Application. New York: Springer-Verlag, 1991.
[19] G. Chiola, M. Ajmone Marsan, G. Balbo, and G. Conte, "Generalized stochastic Petri nets: A definition at the net level and its implications,"IEEE Trans. Software Eng., vol. 19, pp. 89-102, Feb. 1993.
[20] G. Chiola, C. Dutheillet, G. Franceschinis, and S. Haddad, "Stochastic well-formed coloured nets and multiprocessor modeling applications," inHigh-Level Petri Nets; Theory and Application, K. Jensen and G. Rozenberg, Eds. New York: Springer Verlag, 1991.
[21] G. Chiola, R. Gaeta, and M. Ribaudo, "Designing an efficient tool for stochastic well-formed coloured Petri nets," inProc. 6th Int. Conf. Modeling Techniques and Tools for Computer Performance Evaluation, Edinburg, UK, Sept. 1992, pp. 391-395.
[22] G. Chiola, "Great SPN1.5 software architecture," inProc. 5th Int. Conf. Modeling Techniques and Tools for Computer Performance Evaluation, Torino, Italy, Feb. 1991.
[23] M. Ajmone Marsan, G. Balbo, and G. Conte, "Comparative performance analysis of single bus multiprocessor architectures,"IEEE Trans. Comput., vol. C-31, Dec. 1982.
[24] S. Haddad, "Generalization of reduction theory to coloured nets," inProc. 9th Europ. Workshop Application and Theory of Petri Nets, Venezia, Italy, June 1988.
[25] G. Chiola, S. Donatelli, and G. Franceschinis, "GSPN versus SPN: What is the actual role of immediate transitions?" inProc. 4th Int. Workshop Petri Nets and Performance Models, Melbourne, Australia, Dec. 1991, pp. 20-31.
[26] G. Balbo, G. Chiola, S. C. Bruell, and P. Chen, "An example of modeling and evaluation of a concurrent program using coloured stochastic Petri nets: Lamport's fast mutual exclusion algorithm,"IEEE Trans. Parallel Distrib. Syst., vol. 3, pp. 221-240, Mar. 1992.

Index Terms:
stochastic well-formed colored nets; SWN; stochastic high-level nets; syntactic restriction; model definition; symbolic reachability graph; complexity; Markovian performance evaluation; Petri net; performance modeling; computational complexity; memory contention; lumpability condition; computational complexity; multiprocessing systems; performance evaluation; Petri nets.
Citation:
G. Chiola, C. Dutheillet, G. Franceschinis, S. Haddad, "Stochastic Well-Formed Colored Nets and Symmetric Modeling Applications," IEEE Transactions on Computers, vol. 42, no. 11, pp. 1343-1360, Nov. 1993, doi:10.1109/12.247838
Usage of this product signifies your acceptance of the Terms of Use.