Abstract
We present a new version of the time-parallel simulation with fix-up computations for monotone systems. We use the concept of monotony of a model related to the initial state of the simulation to derive upper and lower bounds of the sample-paths. For a finite state space with some structural constraints, we prove that the algorithm provides bounds at the first step. These bounds are improved at every fix-up computation steps leading to a natural trade-off between accuracy of the simulation results and efficiency of the parallel computations. We also show that many queueing networks models satisfy these constraints and show the links with the monotone version of the Coupling From The Past technique.
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References
Andradottir, S., Hosseini-Nasab, M.: Parallel simulation of transfer lines by time segmentation. European Journal of Operational Research 159(2), 449–469 (2004)
Bušić, A., Gaujal, B., Perronnin, F.: Perfect Sampling of Networks with Finite and Infinite Capacity Queues. In: Al-Begain, K., Fiems, D., Vincent, J.-M. (eds.) ASMTA 2012. LNCS, vol. 7314, pp. 136–149. Springer, Heidelberg (2012)
Bušić, A., Gaujal, B., Vincent, J.-M.: Perfect simulation and non-monotone markovian systems. In: Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools, ValueTools 2008, pp. 27:1–27:10. ICST (Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering), Brussels (2008)
Dopper, J., Gaujal, B., Vincent, J.-M.: Bounds for the coupling time in queueing networks perfect simulation. In: Numerical Solutions for Markov Chain (NSMC 2006), Celebration of the 100th anniversary of Markov, Charleston, pp. 117–136 (2006)
El Rabih, D., Pekergin, N.: Statistical Model Checking Using Perfect Simulation. In: Liu, Z., Ravn, A.P. (eds.) ATVA 2009. LNCS, vol. 5799, pp. 120–134. Springer, Heidelberg (2009)
Fourneau, J.-M., Kadi, I.: Time parallel simulation of monotone systems. In: Poster Session, IFIP Performance Conference, Namur, Belgique (2010)
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. (eds.) 13th IEEE/ACM International Symposium on Distributed Simulation and Real Time Applications, Singapore, pp. 231–234. IEEE Computer Society (2009)
Fourneau, J.-M., Kadi, I., Pekergin, N., Vienne, J., Vincent, J.-M.: Perfect simulation and monotone stochastic bounds. In: Glynn, P.W. (ed.) Proceedings of the 2nd International Conference on Performance Evaluation Methodolgies and Tools, VALUETOOLS 2007, Nantes, France. Icst (2007)
Fourneau, J.-M., Kadi, I., Quessette, F.: Time parallel simulation and hv-monotonicity. In: Gelenbe, E., Lent, R., Sakellari, G. (eds.) Proceedings of the 26th Internation Symposium on Computer and Information Sciences. Springer Lectures Notes in Electrical Engineering, pp. 201–207 (2011)
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., Quessette, F.: Monotone Queuing Networks and Time Parallel Simulation. In: Al-Begain, K., Balsamo, S., Fiems, D., Marin, A. (eds.) ASMTA 2011. LNCS, vol. 6751, pp. 204–218. Springer, Heidelberg (2011)
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.: Parallel and Distributed Simulation Systems. Wiley Series on Parallel and Distributed Computing (2000)
Glasserman, P., Yao, D.D.: Monotone Structure in Discrete-Event Systems. Series in Probability and Mathematical Statistics. Wiley Inter-Science, New York (1994)
Greenberg, A.G., Lubachevsky, B.D., Mitrani, I.: Algorithms for unboundedly parallel simulations. ACM Trans. Comput. Syst. 9(3), 201–221 (1991)
Kiesling, T.: Using approximation with time-parallel simulation. Simulation 81, 255–266 (2005)
Lin, Y., Lazowska, E.: A time-division algorithm for parallel simulation. ACM Transactions on Modeling and Computer Simulation 1(1), 73–83 (1991)
Nicol, D., Greenberg, A., Lubachevsky, B.: Massively parallel algorithms for trace-driven cache simulations. IEEE Trans. Parallel Distrib. Syst. 5(8), 849–859 (1994)
Propp, J., Wilson, D.: Exact sampling with coupled Markov chains and applications to statistical mechanics. Random Structures and Algorithms 9(1&2), 223–252 (1996)
Vincent, J.-M., Vienne, J.: Perfect simulation of index based routing queueing networks. SIGMETRICS Performance Evaluation Review 34(2), 24–25 (2006)
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Fourneau, J.M., Quessette, F. (2013). Tradeoff between Accuracy and Efficiency in the Time-Parallel Simulation of Monotone Systems. In: Tribastone, M., Gilmore, S. (eds) Computer Performance Engineering. EPEW UKPEW 2012 2012. Lecture Notes in Computer Science, vol 7587. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36781-6_6
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DOI: https://doi.org/10.1007/978-3-642-36781-6_6
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