Modeling and Performance Analysis of Concurrent Processes in the Algebra $dtsPBC$
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 9 (2009) no. 4, pp. 90-117 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Petri box calculus $PBC$ is a well-known process algebra with Petri net semantics. The author proposed discrete time stochastic extension of finite $PBC$ called $dtsPBC$ and enriched with iteration operator later. In this paper, in the framework of the $dtsPBC$ with iteration, a method of modeling, performance analysis and behaviour preserving reduction of concurrent processes with stochastic time delays is described applied to a shared memory system.
Keywords: stochastic process algebra, stochastic Petri net, Petri box calculus, iteration, discrete time, transition system, operational semantics, dts-box, denotational semantics, stochastic equivalence, modeling, performance analysis, reduction.
@article{VNGU_2009_9_4_a9,
     author = {I. V. Tarasyuk},
     title = {Modeling and {Performance} {Analysis} of {Concurrent} {Processes} in the {Algebra~}$dtsPBC$},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {90--117},
     year = {2009},
     volume = {9},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2009_9_4_a9/}
}
TY  - JOUR
AU  - I. V. Tarasyuk
TI  - Modeling and Performance Analysis of Concurrent Processes in the Algebra $dtsPBC$
JO  - Sibirskij žurnal čistoj i prikladnoj matematiki
PY  - 2009
SP  - 90
EP  - 117
VL  - 9
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VNGU_2009_9_4_a9/
LA  - ru
ID  - VNGU_2009_9_4_a9
ER  - 
%0 Journal Article
%A I. V. Tarasyuk
%T Modeling and Performance Analysis of Concurrent Processes in the Algebra $dtsPBC$
%J Sibirskij žurnal čistoj i prikladnoj matematiki
%D 2009
%P 90-117
%V 9
%N 4
%U http://geodesic.mathdoc.fr/item/VNGU_2009_9_4_a9/
%G ru
%F VNGU_2009_9_4_a9
I. V. Tarasyuk. Modeling and Performance Analysis of Concurrent Processes in the Algebra $dtsPBC$. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 9 (2009) no. 4, pp. 90-117. http://geodesic.mathdoc.fr/item/VNGU_2009_9_4_a9/

[1] Tarasyuk I. V., Ekvivalentnosti dlya povedencheskogo analiza parallelnykh i raspredelennykh vychislitelnykh sistem, Akadem. izd-vo «Geo», Novosibirsk, 2007

[2] Best E., Devillers R., Hall J. G., “The Box Calculus: a New Causal Algebra with Multi-Label Communication”, Lect. Notes Comp. Sci., 609, 1992, 21–69 | DOI | MR

[3] Best E., Devillers R., Koutny M., Petri Net Algebra, EATCS Monographs on Theoretical Computer Sci., Springer Verlag, 2001 | DOI | MR

[4] Bernardo M., Gorrieri R., “A Tutorial on EMPA: a Theory of Concurrent Processes with Nondeterminism, Priorities, Probabilities and Time”, Theoretical Computer Sci., 202, July (1998), 1–54 | DOI | MR | Zbl

[5] Best E., Koutny M., “A Refined View of the Box Algebra”, Lect. Notes Comp. Sci., 935 (1995), 1–20 | DOI | MR

[6] Buchholz P., Tarasyuk I. V., “Net and Algebraic Approaches to Probablistic Modeling”, Joint Novosibirsk Computing Center and Institute of Informatics Systems Bulletin. Series Computer Science (Novosibirsk), 15, 2001, 31–64 | MR | Zbl

[7] Hillston J., A Compositional Approach to Performance Modelling, Cambridge University Press, Great Britain, 1996 | MR

[8] Hermanns H., Rettelbach M., “Syntax, Semantics, Equivalences and Axioms for MTIPP”, Proceedings of $2^\text{nd}$ Workshop on Process Algebras and Performance Modelling, Arbeitsberichte des IMMD, 27, eds. U. Herzog, M. Rettelbach, University of Erlangen, Germany, Regensberg–Erlangen, 1994, 71–88

[9] Marsan M. A., Balbo G., Conte G. et al., Modelling with Generalized Stochastic Petri Nets, Wiley Series in Parallel Computing, John Wiley and Sons, 1995

[10] Molloy M., “Discrete Time Stochastic Petri Nets”, IEEE Transactions on Software Engineering, 11:4 (1985), 417–423 | DOI | MR | Zbl

[11] Macià H. S., Valero V. R., Cazorla D. L. et al., Introducing the Iteration in sPBC, Technical Report DIAB-03-01-37, Department of Computer Science, University of Castilla-La Mancha, Albacete, Spain, September 2003

[12] Macià H. S., Valero V. R., Cazorla D. L. et al., “Introducing the Iteration in sPBC”, Proceedings of the $24^{th}$ International Conference on Formal Techniques for Networked and Distributed Systems–04, FORTE'04 (Madrid, Spain, October 2004), Lect. Notes Comp. Sci., 3235, 292–308 | DOI

[13] Macià H. S., Valero V. R., Cuartero F. G., A Congruence Relation in Finite sPBC, Technical Report DIAB-02-01-31, Department of Computer Science, University of Castilla-La Mancha, Albacete, Spain, October 2002

[14] Macià H. S., Valero V. R., de Frutos D. E., “sPBC: a Markovian Extension of Finite Petri Box Calculus”, Proceedings of $9^\text{th}$ IEEE International Workshop on Petri Nets and Performance Models–01, PNPM'01 (Aachen, Germany, September 2001), IEEE Computer Society Press, 207–216

[15] Macià H. S., Valero V. R., de Frutos D. E. et al., “Extending PBC with Markovian Multiactions”, Proceedings of XXVII Conferencia Latinoamericana de Informática–01, CLEI'01 (Mérida, Venezuela, September 2001), eds. J. A. Montilva, I. Besembel, Universidad de los Andes, 12 | Zbl

[16] Tarasyuk I. V., Discrete Time Stochastic Petri Box Calculus, Berichte aus dem Department für Informatik, 3/05, Carl von Ossietzky Universität, Oldenburg, Germany, November 2005

[17] Tarasyuk I. V., “Iteration in Discrete Time Stochastic Petri Box Calculus”, Bulletin of the Novosibirsk Computing Center. Series Computer Science, 24, NCC Publisher, Novosibirsk, 2006, 129–148

[18] Tarasyuk I. V., “Stochastic Petri Box Calculus with Discrete Time”, Fundamenta Informaticae, 76:1–2 (2007), 189–218 | MR | Zbl