Abstract
Time Parallel Simulation (TPS) is the construction of the time-slices of a sample-path on a set of parallel processors (see [11] chap. 6 and references therein). TPS has a potential to massive parallelism as the number of logical processes is only limited by the number of time intervals which is a direct consequence of the time granularity and the simulation length. Stochastic Automata Networks (SAN in the following) and some stochastic process algebra (like PEPA) allow the construction of extremely large Markov chains which are difficult to analyze due to their size. Here, we show how we can use TPS to solve efficiently some models based on SAN or PEPA. The approach uses some graph theoretical properties which can be checked easily on a SAN or a PEPA model. The quantitative results are obtained by a TPS based on linear recurrence equations of the daters with associative operators.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Baccelli, F., Cohen, G., Olsder, G.J., Quadrat, J.-P.: Synchronization and Linearity: An Algebra for Discrete Event Systems. Willey, New York (1992)
Baccelli, F., Gaujal, B., Furmento, N.: Parallel and Distributed Simulation of Free Choice Petri Nets. In: Parallel and Distributed Simulation, Lake Placid, USA (1995)
Ben-Othman, J., Mokdad, L., Cheikh, M.O., Sene, M.: Performance analysis of composite web services using stochastic automata networks over ip network. In: Proceedings of the 14th IEEE Symposium on Computers and Communications (ISCC 2009), Sousse, Tunisia, pp. 92–97. IEEE (2009)
Dao Thi, T.H., Fourneau, J.M.: Stochastic automata networks with master/slave synchronization: Product form and tensor. In: Al-Begain, K., Fiems, D., Horváth, G. (eds.) ASMTA 2009. LNCS, vol. 5513, pp. 279–293. Springer, Heidelberg (2009)
Fernandes, P., Plateau, B., Stewart, W.J.: Efficient descriptor-vector multiplications in Stochastic Automata Networks. J. ACM 45(3), 381–414 (1998)
Fourneau, J.-M., Kadi, I., Pekergin, N.: Improving time parallel simulation for monotone systems. In: Turner, S.J., Roberts, D., Cai, W., El-Saddik, A.B. (eds.) 13th IEEE/ACM International Symposium on Distributed Simulation and Real Time Applications, pp. 231–234. IEEE Computer Society Press, Singapore (2009)
Fourneau, J.-M., Pekergin, N.: An algorithmic approach to stochastic bounds. In: Calzarossa, M.C., Tucci, S. (eds.) Performance 2002. LNCS, vol. 2459, pp. 64–88. Springer, Heidelberg (2002)
Fourneau, J.-M., Plateau, B., Stewart, W.: An algebraic condition for product form in Stochastic Automata Networks without synchronizations. Performance Evaluation 85, 854–868 (2008)
Fourneau, J.-M., Quessette, F.: Monotonicity and efficient computation of bounds with time parallel simulation. In: Thomas, N. (ed.) EPEW 2011. LNCS, vol. 6977, pp. 57–71. Springer, Heidelberg (2011)
Fujimoto, R.M., Cooper, C.A., Nikolaidis, I.: Parallel simulation of statistical multiplexers. J. of Discrete Event Dynamic Systems 5, 115–140 (1994)
Fujimoto, R.M.: Parallel and Distributed Simulation Systems. Wiley Series on Parallel and Distributed Computing (2000)
Greenberg, A.G., Lubachevsky, B.D., Mitrani, I.: Algorithms for unboundedly parallel simulations. ACM Trans. Comput. Syst. 9(3), 201–221 (1991)
Gusak, O., Dayar, T., Fourneau, J.-M.: Lumpable continuous-time stochastic automata networks. European Journal of Operational Research 148(2), 436–451 (2003)
Hillston, J.: A compositional approach to Performance Modeling. PhD thesis. University of Edinburgh (1994)
Kiesling, T.: Using approximation with time-parallel simulation. Simulation 81, 255–266 (2005)
Kijima, M.: Markov Processes for Stochastic Modeling. Chapman & Hall, London (1997)
Lin, Y., Lazowska, E.: A time-division algorithm for parallel simulation. ACM Transactions on Modeling and Computer Simulation 1(1), 73–83 (1991)
Muller, A., Stoyan, D.: Comparison Methods for Stochastic Models and Risks. Wiley, New York (2002)
Nicol, D.M., Greenberg, A.G., Lubachevsky, B.D.: Massively parallel algorithms for trace-driven cache simulations. IEEE Trans. Parallel Distrib. Syst. 5(8), 849–859 (1994)
Plateau, B.: On the stochastic structure of parallelism and synchronization models for distributed algorithms. In: Proc. of the SIGMETRICS Conference, Texas, pp. 147–154 (1985)
Plateau, B., Fourneau, J.M., Lee, K.H.: PEPS: A package for solving complex Markov models of parallel systems. In: Proceedings of the 4th Int. Conf. on Modeling Techniques and Tools for Computer Performance Evaluation, Majorca, Spain, pp. 341–360 (1988)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Dao Thi, T.H., Fourneau, JM., Quessette, F. (2014). Time-Parallel Simulation for Stochastic Automata Networks and Stochastic Process Algebra. In: Sericola, B., Telek, M., Horváth, G. (eds) Analytical and Stochastic Modeling Techniques and Applications. ASMTA 2014. Lecture Notes in Computer Science, vol 8499. Springer, Cham. https://doi.org/10.1007/978-3-319-08219-6_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-08219-6_10
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08218-9
Online ISBN: 978-3-319-08219-6
eBook Packages: Computer ScienceComputer Science (R0)