Csci 418/618 Simulation Models Dr. Ken Nygard, IACC 262B

Models Modeling is the devising of a simplified representation of a complex system. The resultant model is designed to capture aspects of the real system that are relevant in terms of gaining knowledge and insight into the behavior of the real system.

Types of Models Physical – mock-ups and prototypes. Examples include small-scale models of airplanes, ships, equipment, buildings Analytical – equations, inequalities and other mathematical relations among variables. Example techniques include mathematical regression (curve fitting), linear programming, and systems of differential equations. Such models are intended to be mathematically solved in closed form.

Types of Models (continued) Simulation – a computer-based representation of a system upon which experiments can be performed in lieu of experiments on the real system. Such models are descriptive in the sense that they provide a representation that is a substitute for the real system, yet retains characteristics of importance.

What Sort of Insight can be Gained from a Simulation Model? Enhanced understanding of the inner workings of a real system. Evaluation of performance measures for a real system under various conditions and configurations. Such insight is useful in supporting decisions for how to run and configure a real system. In many cases, such evaluation within the real system would be costly, impossible, or dangerous. Evaluation of designs of systems not yet actually built, to help decide which design to use in practice.

Discrete or Continuous Simulation Models Variables of the model – discrete takes on specified available values, continuous takes on any real value Modeling of time – in discrete models variable change at specified points, in continuous models variables change at specified rates Discrete or Continuous Probabilistic or deterministic Static or dynamic

Deterministic or Probabilistic Deterministic models have no random variables – no uncertainty in the values taken by the variables in the model. Probabilistic models have random variables – their values are determined by a probability density function. Common examples of this occur in queueing systems, to model variation in the amount of time elapsing between arrivals, and in the amount of time required to perform a service.

Static or Dynamic Static models place no importance on the role of time. For example, a simulation of 1000 flips of a fair coin would be static. Dynamic models explicitly model the passage of time, and include performance measures that involve time. For example, a queueing system would likely involve an estimator of the average time spent in a waiting line.

Open loop and Closed loop Open loop systems have no provision for output values being directed back into the model and used in subsequent computation. Also referred to as zero feedback models. Closed loop systems have outputs directed back into the model. Also referred to as feedback models. For example, a simulation of an aircraft autopilot might compute the difference between an actual and a desired heading and direct that information back into the model logic to use in issuing a correction to the control systems that determine the course.

Eight Steps in Model Building 1.Problem analysis. Identifying parameters, performance measures (metrics), variables, relationships among parameters and variables, and rules of system operation. 2.Data gathering and estimating. Using data to estimate parameters, statistical distributions driving the system, and descriptors relevant to measuring system performance.

Eight Steps in Model Building 3.Implementation. Selecting of a programming language, writing code. 4.Verification. Establishing that the implemented model actually works computationally as intended. 5.Validation. Establishing that the model properly represents the real system.

Eight Steps in Model Building 6.Designing and conducting the simulation experiments. Selecting the scenarios, running and replicating the experiments with various inputs, capturing output data. 7.Output analysis. Using statistical methods to analyze and estimate model performance. 8.Interpreting and reporting. Determining what has been learned from developing and running the model, and presenting that information in a form that is understandable and useful to the people interested in benefiting from the model.