Sampling of Variables in Discrete-Event Simulation using the Example of Inventory Evolutions in Job-Shop-Systems Based on Deterministic and Non-Deterministic Data

Time series analysis often requires data that represents the evolution of an observed variable in equidistant time steps. In order to collect this data sampling is applied. While continuous signals may be sampled, analyzed and reconstructed applying Shannon-s sampling theorem, time-discrete signals have to be dealt with differently. In this article we consider the discrete-event simulation (DES) of job-shop-systems and study the effects of different sampling rates on data quality regarding completeness and accuracy of reconstructed inventory evolutions. At this we discuss deterministic as well as non-deterministic behavior of system variables. Error curves are deployed to illustrate and discuss the sampling rate-s impact and to derive recommendations for its wellfounded choice.

Authors:

• Bernd Scholz-Reiter
• Christian Toonen
• Jan Topi Tervo
• Dennis Lappe

Keywords:

• discrete-event simulation
• job-shop-system
• sampling rate.

References:

[1] Banks, J. (ed.): Handbook of Simulation, Wiley and Sons, New York,
1998.
[2] Banks, J.; Carson, J.; Nelson, B.L.; Nicol, D.: Discrete-Event System
Simulation, Prentice Hall, 2009.
[3] Zeigler, B.P.; Praehofer, H.; Kim, T.G.: Theory of Modeling and
Simulation, Academic Press, 2000.
[4] Law, A.M.: Simulation Modeling and Analysis, McGraw-Hill
Professional, 2007.
[5] Lohr, S.L.: Sampling: Design and Analysis, Duxbury Press, 1. edition
1999.
[6] Unser, M.: Sampling - 50 Years After Shannon. Proceedings of the
IEEE, Vol. 80, No. 4, April 2000.
[7] Gold, B.: Speech and Audio Signal Processing, John Wiley & Sons,
1999.
[8] Shannon, C. E.: Communication in the Presence of Noise. In:
Proceedings IRE. Vol. 37 (1949) 1, pp. 10-21.
[9] Marks II, R.J.: Introduction to Shannon Sampling and Interpolation
Theory, Springer Verlag, New York, 1991.
[10] Stankovic, R.S.; Astola, J.T.; Karpovsky, M.G.: Some historic Remarks
in Sampling Theorem, 2008.
[11] Li, H.; Muskulus, M.: Analysis and Modeling of Job Arrivals in a
Production Grid. In: ACM SIGMETRICS Performance Evaluation
Review, 34 (2007) 4, pp. 59-70.
[12] Radons, G.; Neugebauer, R.: Nonlinear Dynamics of Production
Systems, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2004.
[13] Kantz, H.; Schreiber, T.: Nonlinear Time Series Analysis. Cambridge
University Press, Cambridge, 2004
[14] Scholz-Reiter, B.; Kleiner, M.; Nathansen, K.; Proske, G.: Chaos
Control in Production Systems. In: Proceedings of the 15th IMACS
World Congress on Scientific Computation, Modelling and Applied
Mathematics, Vol. 5. Wissenschaft & Technik Verlag, Berlin, 1997, pp.
701-706.
[15] Scholz-Reiter, B.; Freitag, M.; Schmieder, A.: A dynamical approach for
modelling and control of production systems. In: Boccaletti, S. et al.
(ed.) Proc. 6th Experimental Chaos Conference, AIP Conference
Proceedings 622 (1), 2002, pp. 199-210.
[16] Scholz-Reiter, B.; Toonen, C.; Tervo, J.T.: Investigation of the Influence
of Capacities and Layout on a Job-Shop-System's Dynamics.
Proceedings of the 2nd LDIC - International Conference on Dynamics in
Logistics 2009. In Print.
[17] Katzorke, I.; Pikovski, A.: Chaos and Complexity in a Simple Model of
Production Dynamics. In: Discrete Dynamics in Nature and Society,
Vol. 5 2000, pp. 179-187.
[18] Scholz-Reiter, B.; Toonen, C.; Tervo, J.T.; Lappe, D.: Einfluss der
Abtastrate auf Ergebnisse der ereignisdiskreten Simulation. In: ZWF -
Zeitschrift f├╝r wirtschaftlichen Fabrikbetrieb 105 (2010) 3, pp. 211-215.
[19] Scholz-Reiter, B.; Toonen, C.; Tervo, J.T.; Lappe, D.: Einfluss der
Abtastrate auf die Fehlerentstehung in der Auswertung ereignisdiskret
simulierter Werkstattfertigungen. In: Industrie Management 26 (2010) 6.
In Print.
[20] Bronstein, I.N.; Semendyayev, K.A.; Musiol, G., Muehlig, H.:
Handbook of Mathematics. Springer Verlag, Berlin, 5. ed. 2007.