Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-12T20:29:35.691Z Has data issue: false hasContentIssue false
  • English
  • Français

WARM-UP PERIODS IN SIMULATION CAN BE DETRIMENTAL

Published online by Cambridge University Press:  27 May 2008

Winfried K. Grassmann
Winfried K. Grassmann
Affiliation:
Department of Computer ScienceUniversity of SaskatchewanSaskatoon, SK S7N 5C9, Canada E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The question of how long to run a discrete event simulation before data collection starts is an important issue when estimating steady-state performance measures such as average queue lengths. By using experiments based on numerical (nonsimulation) methods published elsewhere, we shed light on this question. Our experiments indicate that no initialization phase should be used when starting in state with a reasonable high equilibrium probability. Delaying data collection is only justified if the starting state is highly unlikely, and data collection should start as soon as a system enters a state with reasonably high probability.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 22 , Issue 3 , July 2008 , pp. 415 - 429
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Banks, J., Carson, J.S., Nelson, B.L. & Nicol, D.M. (2005). Discrete event simulation Englewood Cliffs, NJ: Prentice Hall.Google Scholar
2Ciardo, G. (2007). SMART, a stochastic model checking analyser for reliability and timing. Available from http://www.cs.urs.edu/~ciardo/SMART (accessed June 11, 2007).Google Scholar
3Conway, R.W. (1963). Some practical problems in simulation. Management Science 10: 47–61.Google Scholar
4Grassmann, W.K. (1982). 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, Piscataway, NJ: Institute of Electrical and Electronics Engineers, pp. 377–384.Google Scholar
5Grassmann, W.K. (1987). Means and variances of time averages in Markovian environments. European Journal of Operations Research 31: 132–139.Google Scholar
6Grassmann, W.K. (1987). The asymptotic variance of a time average in a birth-death process. In Albin, S.L. & Harris, C.M., (eds.) Statistical and computational issues in probability modeling, Part 2 Annals of Operations Research, Vol. 8. Basel: Balzers AG, pp. 165–174.Google Scholar
7Grassmann, W.K. (1991). Finding transient solutions in Markovian event systems through randomization. In Stewart, W.J., (ed.) Numerical solutions of Markov chains New York: Marcel Dekker.Google Scholar
8Grassmann, W.K. (1993) Means and variances in Markov reward systems. In Meyer, C.D. & Plemmons, R.J., (eds.) Linear algebra, Markov chains and queueing models The IMA Volumes in Mathematics and Its Applications, Vol. 8, New York: Springer-Verlag, pp. 193–204.Google Scholar
9Grassmann, W.K. & Luo, J. (2005). Simulating Markov-reward processes with rare events. ACM Transactions on Modelling and Computer Simulation 15(2): 138–154.CrossRefGoogle Scholar
10Hazen, G.B. & Pritsker, A.A.B. (1980). Formulas for the variance of the sample mean in finite state Markov processes. Journal of Statistical Computation and Simulation 20: 25–40.Google Scholar
11Hordiijk, A., Iglehart, D.L. & Schassberger, R. (1976). Discrete methods for simulating continuous time Markov chains. Advances in Applied Probability 13: 772–788.CrossRefGoogle Scholar
12Kelton, W.D. & Law, A.M. (1983). A new approach for dealing with the startup problem in discrete event simulation. Naval Research Logistics Quarterly 30: 641–658.CrossRefGoogle Scholar
13Kelton, W.D. & Law, A.M. (1985). The transient behavior of the M/M/c queue, with implication for steady-state simulation. Operations Research 33: 378–396.Google Scholar
14Law, A.M. & Kelton, W.D. (2000). Simulation modelling and analysis Third Edition. New York: McGraw Hill.Google Scholar
15Lock, S.W.K. (1988). Some experimental designs for determining run-lenghts in simulation. Master's thesis, Art University of Saskatchewan, Saskatoon, Canada.Google Scholar
16Madansky, A. (1976). Optimal conditions for a simulation problem. Operations Research 24: 572–577.Google Scholar
17Oni, O.A. (2003). Initial bias in the simulation of Markovian event systems. Master's thesis, University of Saskatchewan, Saskatoon, Canada.Google Scholar
18Reynolds, J.F. (1972). Some theorems on the covariance structure of Markov chains. Journal of Applied Probability 9: 214–218.Google Scholar
19Reynolds, J.F. (1975). The covariance structure of queues and related processes—A survey of recent work. Advances in Applied Probability 7: 383–415.Google Scholar
20Sanders, W.H. (2007). Möbius, model-based environment for validation of system reliability, availability, security and performance. Available from http://www.mobius.uiuc.edu/papers.html (accessed June 11, 2007).Google Scholar
21Sethi, S. (2007). Factors affecting the variance, the bias and the MSE of time averages in Markovian event systems. Master's thesis, University of Saskatchewan, Saskatoon, Canada.Google Scholar
22van Moorsel, A.P.A., Kant, L.A. & Sanders, W.H. (1996). Computation of the asymptotic bias and variance for simulation of Markov reward models. In Znati, T.F. & Wilsey, P.A. (eds.), Proceedings of the 29th simulation symposium, Piscataway, NJ: IEEE.Google Scholar
23Whitt, W. (1989). Planning queueing simulation. Management Science 35(11): 1341–1366.CrossRefGoogle Scholar
24Whitt, W. (1991). The efficiency of one long run versus independent replications in steady-state simulation. Management Science 37(6): 645–666.Google Scholar
25Whitt, W. (1992). Asymptotic formulas for Markov processes with applications to simulation. Operations Research 40(2): 279–291.Google Scholar
26Wilson, J.R. & Prisker, A.A.B. (1978). A survey of research on the simulation startup problem. Simulation 31: 55–58.CrossRefGoogle Scholar
27Wilson, J.R. & Prisker, A.A.B. (1978). Evaluation of startup policies in simulation experiments. Simulation 31: 79–88.Google Scholar
28Zeigler, B.P. (1976). Theory of modelling and simulation New York: Wiley–Interscience.Google Scholar