Computer Simulations

TagsComputer scienceComputingMathematical ModelingModeling and Computer Simulationcomputer experiments



Learning ethics


What is a Computer simulation?

A computer simulation is the running of a mathematical model that performs on a computer.

The mathematical model's intents imitate the real-world processes focusing on an interesting area, one that is called a system, and the computer simulation’s goal is understanding how it behaves. When we’re getting exact information, we’re obtaining the analytical solution, such models don’t fit with computer simulation. However, when you have a complex system finding an analytical solution is hard o impossible, so you need simulations to find numerical solutions, estimate the system behavior and it shed some light on your research questions.

You ought not to simulate its behavior when you can solve it analytically, it is easier to do the experiments directly, the costs are higher than the budget, or you cannot verify the model. You ought to have a complex system.

As maybe you have noted, we have some crucial concepts, in the one hand a system where we definite it as a collection of entities altogether interact to the accomplishment of some aim where its state is the collection of variables at an instant of time that authors classifies them as discrete and continuous. In another hand, the models are mathematical models that estimate complex systems’ behavior normally queue systems, differential equations, or agents with probabilistic behavior.

Why does Computer simulation matter to you?

Simulation is the most used operations research and management science technique.

Advantages and disadvantages of simulation. Areas of application.



Standards, jobs, industry, roles, …



Once upon a time when you have to develop in special languages such as Simula or GGPSS, but today you can develop in whatever programming language you like, indeed a spreadsheet is enough to show results. Of course, developers have developed some libraries or systems based on some theory and include interactive animations that you could do easily. Some of those are

Check out other ones on https://en.wikipedia.org/wiki/List_of_computer_simulation_software

Simulations Framework

Components of a system

Discrete and continuous systems.

Model of a system.

Types of models; Discrete-Event System Simulation

Steps in a simulation study

Case of study


Computer simulation have been started on August 13, 1942, when John V. Neumann and S.Ulam simulates the nuclear weapon behavior in the Manhattan project developing the Monte Carlo method. Nowadays computer simulation serves to understand business, military, and scientific systems.


Worked examples

Part I. Discrete Event Simulation

“Nothing in Nature is random. A thing appears random only through the incompleteness of our knowledge.” Baruch Spinoza. Ethics.

Elements of probability on focus simulation

A stochastic process is a collection of random variables that represent the behavior of a system over time. A nondeterministic process doesn’t equal a stochastic process.

Stochastic process. Stochastic simulation.

Random variables

Random numbers

Middle-square method

Linear congruential generator

Generating Discrete Random Variables

Número pseudoaleatorio.

Una variable pseudoaleatoria es aquella generada por una función determinista.

Inverse transform sampling


Generating Continuous Random variables

Markov chain

Monte Carlo

Statistical Analysis of Simulated data

Statistical Validation techniques




Reference Notes

The discrete event simulation approach


Discrete-Event Simulation

Waiting for lines concepts

Probability distributions

Paradigms are Event worldview, Processing Network Worldview, and Object worldview.

Single-Server Queue System

A queuing system with two servers in Series

A queuing System with two parallel servers

An Inventory system

An Insurance Risk Model

A repair problem

Parallel/Distributed Simulation

List Processing in Simulation

Time-Shared Computer Model

Multiteller Bank with Jockeying

Job-Shop Model

Efficient Event-List Management

Worked examples

Variance-Reduction Techniques

Experimental Design and Optimization

Output data analysis for a single system

Comparing Alternative system configurations

Agent-Based Simulation and System Dynamics

Simulation of Manufacturing systems



Part II. Continuous and nonlinear Event Simulation

An introduction to computer simulation. M.M. Woolfson and G.J. Pert

Computer Aided Simulations

Differential equations




The Monte Carlo method

Particle methods

Continuum physics — the finite-difference method

Continuum physics

Complex models

Validation and testing

Finite-difference methods

Simulation with particles

The Monte Carlo method

The wave equation

The finite-element method

Computational fluid dynamics

Next steps


[1] Daniel P. Maki Maynard Thompson, Mathematical Modeling and Computer Simulation

[2] W. David Kelton, Randall P. Sadowski, Nancy B. Zupick, Simulation with Arena, 6th edition. (McGraw-Hill Professional, 2014). ISBN 978-0-07-337628-8

[3] Altiok, Tayfur and Benjamin Melamed.Simulation Modeling and Analysis with ARENA. Elsevier, Inc., 2007. ISBN 978-0-12-370523-5

[4] Rossetti, Manuel D. Simulation Modeling with Arena. John Wiley & Sons, Inc., 2010. ISBN 978-0-470-09726-7

[5] Sturrock, D.T., Pegden, C.D., Introduction to SIMAN, Simulation Conference, 1990. Proceedings.,

[6] Winter C. Dennis Pegden, Robert E. Shannon, Randall P. Sadowski, Introduction to Simulation Using Siman, McGraw-Hill 1995

[7] Fishman, G. (2013). Discrete-event simulation: modeling, programming, and analysis. Springer Science & Business Media.

[8] Gordon, G. (1969). System simulation. Ed. PrenticeHall.

[9] Kelton, W. D., & Law, A. M. (2000). Simulation modeling and analysis. Boston: McGraw Hill.

[10] Michael Pidd. Computer Simulation in Management Science

[11] Young, Joseph and Findley, Michael. 2014. "Computational Modeling to Study Conflicts and Terrorism." Routledge Handbook of Research Methods in Military Studies edited by Soeters, Joseph; Shields, Patricia and Rietjens, Sebastiaan. pp. 249–260. New York: Routledge,

[12] R. Frigg and S. Hartmann, Models in Science. Entry in the Stanford Encyclopedia of Philosophy.

[13] E. Winsberg Simulation in Science. Entry in the Stanford Encyclopedia of Philosophy.

[14] S. Hartmann, The World as a Process: Simulations in the Natural and Social Sciences, in: R. Hegselmann et al. (eds.), Modelling and Simulation in the Social Sciences from the Philosophy of Science Point of View, Theory and Decision Library. Dordrecht: Kluwer 1996, 77–100.

[15] E. Winsberg, Science in the Age of Computer Simulation. Chicago: University of Chicago Press, 2010.

[16] P. Humphreys, Extending Ourselves: Computational Science, Empiricism, and Scientific Method. Oxford: Oxford University Press, 2004.

[17] James J. Nutaro (2011). Building Software for Simulation: Theory and Algorithms, with Applications in C++. John Wiley & Sons. ISBN 978-1-118-09945-2.

[18] Desa, W. L. H. M., Kamaruddin, S., & Nawawi, M. K. M. (2012).

[19] Tutorial: Web-Based Simulation with OESjs. (2023, January 31). Retrieved from https://sim4edu.com/reading/introtutorial

[20] Nature in Code Biology in Javascript - Learning programming while discovering the rules that govern life by Marcel Salathe

Modeling of Aircraft Composite Parts Using Simulation. Advanced Material Research, 591–593, 557–560.

"Simulation Modeling and Analysis" by Law. Other fine choices include "Discrete-Event System Simulation" by Banks, Carson, & Nelson, "Principles of Discrete-Event Simulation" by Fishman, "Discrete-Event Simulation: A First Course" by Leemis & Park, or "Graphical Simulation Modeling and Analysis Using SIGMA for Windows" by Schruben

Discrete Event Simulation Engineering. (2023, January 31). Retrieved from https://sim4edu.com/reading/des-engineering

Winter Simulation Conference Archive , pick any year, and check out the articles in either the introductory or advanced tutorials. I'd particularly recommend Schriber's Inside Discrete-Event Simulation Software: How It Works and Why It Matters series, and Fundamentals of Simulation Modeling by Sanchez.

"Discrete-Event System Simulation" by Banks, Carson, Nelson & Nicol and "Simulation Modeling and Analysis" by Law & Kelton to be most helpful) 'Simulation' by Ross is another very useful resource.

Simulation modeling and analysis by Averill M. Law


BANKS J., J. S. Carson and B. L. Nelson 1996. Discrete-Event System Simulation,

second edition. Prentice-Hall, Englewood Cliffs, NJ.

GORDON G. 1996. System Simulation, second edition. Prentice-Hall, Englewood Cliffs,


LAW A. and W. D. Kelton 1991. Simulation Modeling and Analysis, second edition.

McGraw-Hill, New York, NY.

SCHRUBEN L. W. 1983. Simulation modeling with event graphs. Communications of

the ACM, 26:957-963


"* Simulations | AP CSP | Khan Academy." 2 Mar. 2023, www.khanacademy.org/computing/ap-computer-science-principles/x2d2f703b37b450a3:simulations.

Collaboration., Dylan Nelson for the Tng. "IllustrisTNG - Main." 2 Mar. 2023, www.tng-project.org.