Source: https://rossetti.github.io/RossettiArenaBook/modeling-a-simple-discrete-event-dynamic-system.html This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

**What’s new?**

In a 10 June 2021 posting on IISE Connect, Professor Manuel Rossetti of the University of Arkansas announced the availability of the third edition of his textbook Simulation Modeling and Arena as an open text. Previous editions were published in book form by Wiley, and Professor Rossetti decided to make this edition available for free, saying:

With technology constantly changing, I thought that it would be useful to get this book on-line so that I can more readily keep it up to date. It is my hope to provide updated versions when there are significant changes made within Arena.

**What does it mean?**

Humans are makers, including makers of tools. An important tool for humans and especially for humans who are engineers is a model, that is, a representation, sometimes conceptual or physical but often mathematical, of a real-world system.

Mathematical models can be analyzed using mathematics; that is, we can use mathematics to elicit results concerning the behavior of the model. For example, the differential equation that describes a pendulum swinging in small angles can be solved to give a mathematical description of the pendulum’s motion over time, but the differential equation is an approximation and does not hold if the pendulum swings in a large arc. Also, the more accurate differential equation that describes large swings cannot be solved to give an equation of motion over time, but rather must be solved using numerical methods, again giving an approximate solution.

The real-world systems of our organizations are complicated, so the models of them must be complicated. Also, unlike a pendulum whose motion can be predicted with certainty, we are inherently uncertain about what will happen in the future with many real-world systems. Professor Rossetti starts his book by describing the behavior of an emergency room in a hospital. Randomness abounds in such a system, so any model must use the mathematics of uncertainty. Probability is the field that enables us, indeed requires us, to talk precisely about our uncertainty.

Having good data makes your model a more accurate representation of the real-world system. But even without data, methods can elicit the knowledge of experts and express them in a way that can be used in a simulation.

Professor Rossetti uses the simulation computer program Arena throughout his book. The graphical user interface of Arena supports a drag-and-drop approach to select model components from menus. If you want to get a feel for what kinds of systems can be modeled, what the necessary steps are, how Arena is programmed, and what the resulting model looks like, section 4.5 of the book has an extended example. Depending on your background, you may not understand all of what is shown there, but you will get a feel for simulation models and Arena. The book has other examples that will help you understand simulation more.

The book is not about the simulation of all systems. “This book primarily examines stochastic, dynamic, discrete systems.” “Stochastic” means that the system has randomness, “dynamic” means that it changes over time, and “discrete” means that changes in the system occur at specific times (for example, when a patient arrives at the emergency department) not continuously (for example, when water flows out of a reservoir). Many of our organizations have systems that can be modeled in such a way.

**What does it mean for you?**

As Professor Rossetti points out: “A simulation model can be used to predict future behavior through running what-if scenarios.” *You can perform experiments in the simulation*, experiments that you can’t perform on the real-world system. What if the number of people arriving at the emergency room spikes due to a pandemic? What if we added two more nurses at certain times of the day? You can ask – and answer – questions like these and determine the likely effects on important performance measures, such as the waiting time for patients, the number of patients in the hospital, and the health outcomes of the patients. The simulation operates, of course, much more rapidly than the real-world system so you can simulate years of operation in seconds. Thus, you can ask a lot of questions and a get a feel for how the simulation performs in many different scenarios. Section 8.1.1 shows the results of several what-if simulations of the model from section 4.5.

A key point to remember, however, is one of my favorite phrases, “it’s only a model.” A model gives you numerical predictions of the future, but because of the randomness in the real-world system and because a model does not represent all aspects of the real-world system, most people use simulations of models to gain insight rather than exact predictions. For example, what changes to the model have the biggest impact on performance measures?

If you haven’t considered using simulation in your organization, Professor Rossetti’s book is a place to start. I think you will get a good idea from the many examples in the book about whether this approach is worth trying for your organization.

**Where can you learn more?**

The major point of this post is that you can learn more in Professor Rossetti’s book – and it is free. His book has advice on how to continue your education in simulation.

A library of videos about Arena is available here, including videos showing the animation of Arena models, a very powerful feature for understanding a model.

This work is licensed under a Creative Commons Attribution 4.0 International License.