Abstract
In this paper, we show that when estimating equilibrium expectations by Monte-Carlo simulation, it is often better to use multiple runs. Specifically, instead of a single run of length T, one should use n runs, each of length \(T/n\). In particular, it is argued that if there is a good state to start the simulation in, multiple runs may be advantageous. To illustrate this, we use numerical examples. These examples are obtained by using deterministic methods, that is, methods based on probability calculus which avoid any random numbers. The paper builds on results of earlier papers that show that when good starting states are chosen, warm-up periods are not only useless, they are outright detrimental.
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References
Alexopoulos, C., Goldman, D.: To batch or not to batch? ACM Trans. Model. Comput. Simul. 14(4), 76–214 (2004)
Asmussen, S., Glynn, P.W.: Stochastic Simulation: Algorithms and Analysis, volume 57 of Stochastic Modelling and Applied Probability. Springer, New York (2007)
Franklin, W.W., White, K.P.: Stationarity tests and MSER-5: exploring the intuition behind mean-squared-error-reduction in detecting and correcting initialization bias. In: Mason, S.J., Hill, R.R., Mönch, L., Rose, O., Jefferson, T., Fowler, J.W. (eds.) Proceedings of the 2008 Winter Simulation Conference, pp. 541–546. The Institute of Electrical and Electronics Engineers, Inc. (2008)
Grassmann, W.K.: Optimal estimation of the expected number in an M/D/∞/ system. Oper. Res. 29(6), 1208–1211 (1981)
Grassmann, W.K.: Initial bias and estimation error in discrete event simulation. In: Highland, H.G., Chao, Y.W., Madrigal, O. (eds.) Proceedings of the 1982 Winter Simulation Conference. pp, pp. 377–384. The Institute of Electrical and Electronics Engineers Inc, Piscataway, NY (1982)
Grassmann, W.K.: Means and variances of time averages in Markovian environments. Eur. J. Oper. Res. 31, 132–139 (1987)
Grassmann, W.K.: Warm-up periods in simulation can be detrimental. Probab. Eng. Inf. Sci. 22, 415–429 (2008)
Grassmann, W.K.: Rethinking the initialization bias problem in steady-state discrete event simulation. In: Jain, S., Creasey, R.R., Himmelspach, J., White, K.P., Fu, M. (eds.) Proceedings of the 2011 Winter Simulation Conference. pp, pp. 593–599. The Institute of Electrical and Electronics Engineers Inc, Piscataway, NY (2011)
Grassmann, W.K.: Factors affecting warm-up periods in discrete event simulation. Simulation 90(1), 11–23 (2014)
Kelton, W.D.: Random initialization methods in simulation. IIE Trans. 21(4), 355–367 (1989)
Madansky, A.: Optimal conditions for a simulation problem. Oper. Res. 24, 572–577 (1976)
McNickle, D., Ewing, G.C., Pawlikowski, K.: Transient deletion and the quality of sequential steady-state simulation. In: Proceedings of the 21st European Conference on Modelling and Simulation, Prague, Czech Republic (2007)
Meisner, D., Wu, J., Wenisch, T.F.: Bighouse: a simulation infrastructure for data center systems. http://www.ece.umich.edu/cse/awards/pdfs/ispass12.pdf (2015). Accessed 31 Oct 2015
Mokashi, A.C., Tejada, J.J., Yousefi, F., Wilson, J.R., Tafazzoli, A., Steiger, N.M.: Performance comarison of MSER-5 and N-Sart on the simulation start-up problem. In: Jahansson, B., Jain, S., Montoya-Torres, J., Hugan, J., Yücesan, E. (eds.) Proceeding of 2010 Simulation Conference, pp. 971–982. IEEE, Piscataway, NJ (2010)
Newell, G.F.: Applications of Queueing Theory, second edn. Chapman and Hall, London (1982)
Pasupathy, R., Schmeiser, B.: The initial transient in steady state point estimation: context, a biography, the MSE criterium, and the MSER statistic. In: Johansson, B., Jain, S., Montaya-Torres, J., Hugan, J., Yücesan, E. (eds.) Proceedings of the 2010 Winter Simulation Conference. pp, pp. 184–197. The Institute of Electrical and Electronics Engineers Inc, Piscataway, NY (2010)
Pawlikowski, K.: Steady-state simulation of queueing processes: a survey of problems and solutions. ACM Comput. Surv. 22(2), 123–170 (1990)
Tocher, K.D.: The Art of Simulation. English University Press, London (1963)
Whitt, W.: The efficiency of one long run versus independent replications in steady-state simulation. Manage. Sci. 37(6), 645–666 (1991)
Wilson, J.R., Prisker, A.A.B.: Evaluation of startup policies in simulation experiments. Simulation 31, 79–88 (1978)
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This research was supported by NSERC of Canad, Discovery Grant 8112.
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Grassmann, W. (2016). Multiple Runs in the Simulation of Stochastic Systems Can Improve the Estimates of Equilibrium Expectations. In: Obaidat, M., Kacprzyk, J., Ören, T., Filipe, J. (eds) Simulation and Modeling Methodologies, Technologies and Applications. Advances in Intelligent Systems and Computing, vol 442. Springer, Cham. https://doi.org/10.1007/978-3-319-31295-8_3
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DOI: https://doi.org/10.1007/978-3-319-31295-8_3
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