This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Stochastic Automata Network of Modeling Parallel Systems
October 1991 (vol. 17 no. 10)
pp. 1093-1108

A methodology for modeling a system composed of parallel activities with synchronization points is proposed. Specifically, an approach based on a modular state-transition representation of a parallel system called the stochastic automata network (SAN) is developed. The state-space explosion is handled by a decomposition technique. The dynamic behavior of the algorithm is analyzed under Markovian assumptions. The transition matrix of the chain is automatically derived using tensor algebra operators, under a format which involves a very limited storage cost.

[1] S. Aggarwal, R. P. Kurshan, and K. Sabnami, "A calculus for protocol specification and validation," inProtocol Specification, Testing and verification, vol. III, H. Rudin and C. H. West, Eds. Amsterdam: Elsevier-North Holland, 1983.
[2] M. Arbib,Algebraic Theory of Machines Languages and Semi-Groups. New York: Academic, 1968.
[3] A. Arnold, "Mec: a system for constructing and analyzing transition systems," inProc. 3rd Workshop on Protocol Verification(Grenoble, France), June 1989.
[4] S. Berson, E. Souza e Silva, and R. Muntz, "A methodology for specification and generation of Markov models," inProc. 1st Int. Conf. Numerical Solution of Markov Chains(Raleigh, NC), Jan. 1990.
[5] B. Charron-Bost, "Mesures de la concurrence et du parallélisme des calculs repartis," Ph.D. thesis, Paris VII Univ., France, Sept. 1989.
[6] G. Chiola, "Greatspn 1.5, " inProc. 5th Int. Conf. Modeling Techniques and Tools for Comput. Performance Evaluation(Torino, Italy), Feb. 1991, pp. 117-132.
[7] M. Davio, "Kronecker products and shuffle algebra,"IEEE Trans. Computers, vol. C-30, Feb. 1981.
[8] D. Geniet and L. Thimonier, "Fast computing of concurrency measure and mutual exclusion," Paris-Sud Univ.. France, Tech. Rep. RR 432, July 1988.
[9] J. Hartmanis and R. E. Stearns,Algebraic Structure Theory of Sequential Machines. Englewood Cliffs, NJ: Prentice-Hall, 1966.
[10] H. Kobayashi, "Discrete time queuing systems," inProbability Theory and Computer Science, G. Louchard and G. Latouche, Eds. New York: Academic, 1983, chap. 4.
[11] L. Lamport, "A fast mutual exclusion algorithm,"ACM Trans. Computer Syst., vol. 5, no. 1, pp. 1- 11, Feb. 1987.
[12] 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.
[13] J. P. Merlet, "Notice d' utilisation JpDraw version 2.3 sur SUN," INRIA, Sophia Antipolis, France, 1990.
[14] M. Molloy, "Performance analysis using stochastic petri nets,"IEEE Trans. Computers, vol. C-31, Sept. 1982.
[15] B. Plateau, "On the stochastic structure of parallelism and synchronization models for distributed algorithms, " inProc. ACM Sigmetrics Conf. Measurement and Modeling of Comput. Syst. (Austin, TX), Aug. 1985.
[16] B. Plateau and K. Atif, "A method for handling complex Markov models of parallel systems," IMAG Instit., Grenoble, France, Tech. Rep. RR 826 I, Sept. 1990.
[17] B. Plateau and J.M. Fourneau, "A methodology for solving Markov models of parallel systems,"J. Parallel and Distributed Comput., vol. 12, 1991.
[18] B. Plateau, J. M. Fourneau, and K. H. Lee, "Peps: a package for solving complex Markov models of parallel systems," inModeling Techniques and Tools for Computer Performance Evaluation(Palma, Spain), R. Puigjaner and D. Potier, Eds., Sept. 1988.
[19] M.A. Marsan, S. Donatelli, and F. Neri, "Gspn models of Markovian multiserver multiqueue systems,"Perform. Eval., vol. 11, no. 4, Nov. 1990.
[20] F. Fogelman Soulie, Y. Robert, and M. Tchuente,Automata Networks in Computer Science, Theory and Applications. Manchester, UK: Manchester Univ. Press, 1987.
[21] K. S. Trivedi,Probability and Statistics with Queuing and Science Applications. Englewood Cliffs, NJ: Prentice-Hall, 1982.
[22] M. K. Vernon and M. A. Holliday, "Performance analysis of multiprocessor cache consistency protocols using generalized timed petri nets," inProc. Performance '86 and ACM Sigmetrics 1986, Raleigh, NC, May 1986, pp. 9-17.

Index Terms:
parallel activities; synchronization points; modular state-transition representation; parallel system; stochastic automata network; SAN; state-space explosion; decomposition technique; Markovian assumptions; transition matrix; tensor algebra operators; storage cost; parallel algorithms; parallel architectures; performance evaluation; stochastic automata
Citation:
B. Plateau, K. Atif, "Stochastic Automata Network of Modeling Parallel Systems," IEEE Transactions on Software Engineering, vol. 17, no. 10, pp. 1093-1108, Oct. 1991, doi:10.1109/32.99196
Usage of this product signifies your acceptance of the Terms of Use.