Abstract
This chapter is devoted to the modelling and simulation process within the domain of discrete-event dynamic systems (DEDS). This chapter provides a foundation for these discussions by exploring a variety of key topics. To a large extent the discussion is dominated by considerations relating to the inherently stochastic nature of the DEDS domain. Within this context we introduce the notion of a discrete-time variable which is central to our characterization of both the input and output of a conceptual model. Related concepts such as random number generation, random variate generation, random variate procedures and deterministic value procedures are also introduced. The need to recognize an important distinction between two general categories of modelling and simulation studies is emphasized. This relates to the nature of the observation interval that is associated with the study and two associated notions are pointed out, namely, bounded horizon studies and steady-state studies. Data modelling is likewise an important facet of model development in the DEDS domain, and important aspects of this topic are discussed.
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
Notes
- 1.
This is an example of the statistical notion of an arrival process.
- 2.
Some care is nevertheless required in clarifying which of two possible values is to be taken at the discrete points in time where change occurs. Our convention will be that x(t) = x k for t k ≤ t < t k+1 for k = 0, 1, 2….
- 3.
The intent here is to circumvent any possible misinterpretation with respect to guidelines (a) and (b).
- 4.
The collection of all values of this output variable D(t) resulting from an experiment, namely, {d 1 , d 2 , … d N } (where N is the total number of messages passing through the network over the course of the observation interval), is an observation of a stochastic process.
- 5.
The notable exception here is the case where a graphical presentation of the data is desired.
- 6.
The notable exception here is the case where a graphical presentation of the data is desired.
- 7.
These two types of study are often referred to as ‘terminating simulations’ and ‘nonterminating simulations’, respectively.
- 8.
Generated using the Microsoft® Office Excel 2003 Application.
- 9.
Source: http://ottawa.weatherstats.ca
- 10.
The test is shown for the continuous distribution. For discrete distributions, each value in the distribution corresponds to a class interval and p i  = P(X = x i ). Class intervals are combined when necessary to meet minimum-expected-interval-frequency requirement (E i is less than 5).
- 11.
It is also possible to derive the CDF directly from the collected data.
- 12.
The Empirical Class is provided as part of the cern.colt Java package provided by CERN (European Organization for Nuclear Research). See Chap. 5 for more details on using this package.
- 13.
mod is the modulo operator; p mod q yields the remainder when p is divided by q where both p and q are positive integers.
References
Banks J, Carson JS II, Nelson BL, Nicol DM (2005) Discrete-event system simulation, 4th edn. Pearson Prentice Hall, Upper Saddle River
Biller B, Nelson BL (2002) Answers to the top ten input modeling questions. In: Proceedings of the 2002 winter simulation conference, published by ACM. San Diego, California
Choi SC, Wette R (1969) Maximum likelihood estimation of the parameters of the gamma distribution and their bias. Technometrics 11:683–690
Couture R, L’Ecuyer P (1998) (eds) Special issue on Random Variate Generation. ACM Trans Model Simul 8(1)
Coveyou RR (1960) Serial correlation in the generation of pseudo-random numbers. J ACM 7:72–74
Harrell C, Ghosh BK, Bowden RO Jr (2004) Simulation using ProModel, 2nd edn. McGraw-Hill, New York
Hull TE, Dobell AR (1962) Random number generators. SIAM Rev 4:230–254
Kelton DW, Sadowski RP, Sturrock DT (2004) Simulation with Arena, 3rd edn. McGraw-Hill, New York
Kleijnen Jack PC (1987) Statistical tools for simulation practitioners. Marcel Dekker, Inc, New York
Knuth DE (1998) The Art of computer programming, vol 2: Seminumerical algorithms, 3rd edn. Addison-Wesley, Reading
L’Ecuyer P (1990) Random numbers for simulation. Commun ACM 33:85–97
Law Averill M, McComas MG (1997) Expertfit: total support for simulation input modeling. In: Proceedings of the 1997 winter simulation conference, published by ACM. Atlanta, GA, pp 668–673
Law AM, Kelton DW (2000) Simulation modeling and analysis, 3rd edn. McGraw-Hill, New York
Leemis LM, Park SK (2006) Discrete event simulation: a first course. Pearson Prentice Hall, Upper Saddle River
Lehmer DH (1949, 1951) Mathematical methods in large scale computing units. In: Proceedings of the second symposium on large-scale digital calculating machinery, 1949 and Ann Comput Lab 1951 (26):141–146. Harvard University Press, Cambridge, MA
Ross SM (1990) A course in simulation. Macmillan Publishing, New York
Rotenberg A (1960) A new pseudo-random number generator. J ACM 7:75–77
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag London
About this chapter
Cite this chapter
Birta, L.G., Arbez, G. (2013). DEDS Stochastic Behaviour and Modelling. In: Modelling and Simulation. Simulation Foundations, Methods and Applications. Springer, London. https://doi.org/10.1007/978-1-4471-2783-3_3
Download citation
DOI: https://doi.org/10.1007/978-1-4471-2783-3_3
Published:
Publisher Name: Springer, London
Print ISBN: 978-1-4471-2782-6
Online ISBN: 978-1-4471-2783-3
eBook Packages: Computer ScienceComputer Science (R0)