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Erschienen in:
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2013 | OriginalPaper | Buchkapitel

3. DEDS Stochastic Behaviour and Modelling

verfasst von : Louis G. Birta, Gilbert Arbez

Erschienen in: Modelling and Simulation

Verlag: Springer London

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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.

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Vorheriges Kapitel The Modelling and Simulation Process
Nächstes Kapitel A Conceptual Modelling Framework for DEDS
Fußnoten
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.
 
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.
 
Literatur
1.
Banks J, Carson JS II, Nelson BL, Nicol DM (2005) Discrete-event system simulation, 4th edn. Pearson Prentice Hall, Upper Saddle River
2.
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
3.
Choi SC, Wette R (1969) Maximum likelihood estimation of the parameters of the gamma distribution and their bias. Technometrics 11:683–690CrossRefMATH
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Couture R, L’Ecuyer P (1998) (eds) Special issue on Random Variate Generation. ACM Trans Model Simul 8(1)
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6.
Harrell C, Ghosh BK, Bowden RO Jr (2004) Simulation using ProModel, 2nd edn. McGraw-Hill, New York
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8.
Kelton DW, Sadowski RP, Sturrock DT (2004) Simulation with Arena, 3rd edn. McGraw-Hill, New York
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Kleijnen Jack PC (1987) Statistical tools for simulation practitioners. Marcel Dekker, Inc, New YorkMATH
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Knuth DE (1998) The Art of computer programming, vol 2: Seminumerical algorithms, 3rd edn. Addison-Wesley, ReadingMATH
11.
L’Ecuyer P (1990) Random numbers for simulation. Commun ACM 33:85–97CrossRef
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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
13.
Law AM, Kelton DW (2000) Simulation modeling and analysis, 3rd edn. McGraw-Hill, New York
14.
Leemis LM, Park SK (2006) Discrete event simulation: a first course. Pearson Prentice Hall, Upper Saddle River
15.
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
16.
Ross SM (1990) A course in simulation. Macmillan Publishing, New YorkMATH
17.
Metadaten
Titel
DEDS Stochastic Behaviour and Modelling
verfasst von
Louis G. Birta
Gilbert Arbez
Copyright-Jahr
2013
Verlag
Springer London
Buch
Modelling and Simulation

Print ISBN: 978-1-4471-2782-6

Electronic ISBN: 978-1-4471-2783-3

Copyright-Jahr: 2013

DOI
https://doi.org/10.1007/978-1-4471-2783-3_3

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