# Simulation

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Elements of a system:Basically, a system consists of entities, activities, resources and controls, these elements define who, what, where, when and how about the system processing.Entities:are the items processed through the system, such as products, customers and documents. They can be classified into three types:

* Human or animated (clients, patients, etc.)..

* Inanimate (parts, stationery, etc.)..

* Intangibles (calls, emails, projects, etc.)..Activitiesare tasks that are performed in the system, such as filling, cutting, repair, customer service, etc.. The activities have a duration and generally use resources.Resourcesare the means by which activities are implemented, for example: personnel, equipment, tools, energy, time, money, etc.. Resources may be such as capacity, speed, reliability, cycle time and also are defining who or what performs the activity and where.Controls: Theseare the ones who decide how, when and where actions are performed, as well as determine the action when certain events occur or conditions. At the highest level, we can find controls in the form of policies, plans or schedules, whereas a low level are in the form of procedures or programs.Measures the performance of a system:the system performance is measured by its effectiveness and efficiency in achieving the objectives for which it was designed. In many situations, the targets are set based on cost effectiveness or the utility generated by the system. The data for determining such performance measures are generally:prices, costs, and quantitative characteristics of the system.The system objectives are met when the performance measures achieved the desired levels.Systems approach: Becausethe elements of a system are interdependent, it is not possible to know how the system responds to each element separately studying is why it is required to perform a systems approach as this can be divided into its structure, but such may not hold office. To view a system as a whole is necessary to understand the cause-effect relationships and the decision-response.Model:.Models are abstractions of systems. In order to design new systems and optimize existing models are used as experiment with the system itself can be very costly, the system can be destroyed or at least temporarily withheld in its operation, or it may simply be impossible to experiment with it. Thus a model must be sufficiently valid to make decisions similar to those that would be taken in case of direct experimentation with the system. However, the simulation results, though valid, would not be used in the decision making process if the model is not credible. Put another way, we have two tasks: building a model attached to the real (valid) and to convince "those above" that is (credible).

For simulation, the models are generally used for descriptive study the behavior of systems over time. And based on this research it is possible to determine the conditions under which the system would operate more effectively and efficiently.The simulation models are not designed to find optimal solutions. It is an experimental technique (random events), evaluates various alternatives and make decisions based on the comparison of results.Since simulation models are often used to study complex systems, usually for use numerical analysis methods rather than analytical. Most of the simulation models are probabilistic and are tailored to the client.

With regard to simulation models of interest include:As to time:1) Static: Representation of a system at a particular instant of time.

2) Dynamic: Representation of a system over a period of time.As for the variables:1) Deterministic: If it contains no random variables.

2) Stochastic: If it contains one or more random variables.

They can also be discrete or continuous, and whose characteristics were defined for the systems.Simulation is a tool for operations research that lets us know and analyze the behavior of a real or proposed system to determine courses of action: modify, accept or reject it.Simulation is considered as a process that involves building a descriptive model of a real system, in order to study the behavior of the system over time, with the advantage that you do not need a break (if very expensive) destroy it (if you want to know their maximum resistance) or build (if only one proposed).

The process for the successful development of a simulation model, is to start with a simple model, which can be enriched in an evolutionary manner to meet the requirements of solving a problem. AM Law and MG McComas (Hector Vargas."Simulation: More than just a tool."Vanguardia Magazine, August 1994. CETYS Faculty of Engineering) mention the following elements for a successful simulation project:

* Knowledge of the methodology of the simulation, probabilistic models of operations research, probability theory and statistics.

* Formulation correct the problem.

* Adequate information on the operation of the system.

* Proper modeling system randomness.

* Choose the right software and use it correctly.

* Validate the model and its credibility.

* Use appropriate statistical procedures for interpreting the results of the simulation.

* Use appropriate techniques of project management.

The steps are presented below are a guide for development of a simulation study. It is clear that the time required for each step depends on the system to model, also some simulation projects may require some steps are not included.Simulation Process Steps:1.Planeación strategic TácticaEstablecer experimental conditions for the use of modelo.2. Formulation of the problem and ProblemaDefinición wording of Objective 3. Construction problema4 mathematical ModeloAbstracción. Getting InformaciónIdentificación, specification and data collection 5. ProgramaPreparar Development for procesamiento6 model. VerificaciónAsegurar the proper functioning of the program 7. ValidaciónCorrespondencia between the model and the model for realidad8.ExperimentaciónUso obtaining Result resultados9.Análisis inferences and recommendations based on the Use and Documentation modelo10.Implementación results for decision-making and document the operation and use of the modelApplications and Uses of Simulation

Today there are a variety of applications of the simulation due to the various advantages it offers over other tools. Some of these applications are:

• In the cost reduction.

• In a system:

• In developing the method of analysis, as with existing methods for solving problems is invested considerable time to develop the analytical method.

• In the computer programming.

• In the modeling of a system.

• In the experimental trial and error.

• In industry:

• In staff training.

• In aviation:

• In the pilot training.

• In finance: Can be used to calculate budgets, analyzing investment alternatives, cash flow.

• In mercadotencia: The analyst must make decisions to place the promotion of a product in different media: newspapers, radio, television, etc..

• In Human Resources: Benefits of job mobility, the type of person for a particular job, different hierarchical structures and relationships inside a company.

Also, the simulation has been used in systems such as biological, economic, health, business, production, transportation, social, urban, etc..

Over time the use of simulation as a business tool has increased, some of the factors that have increased usage are:

- Ongoing development of languages and computer simulators.

- Flexibility through simulation modeling.

Simulation is a versatile tool that has been used in various ways, including:

* System Design

* Systems Administration

* Training and training

* Communication

* Public relations

This has made the most widely used simulation technique in Scientific Management / Operations Research and the tools of industrial engineering excellence.When is it appropriate to use simulation?Paul Fishwick ("Simulation Model Design and Execution: Building Digital Worlds."Prentice-Hall. America, 1995) suggests that the simulation is recommended when:

(1) The model representing the system under study is very complex and has many variables and interacting components.

(2) The relations between variables are nonlinear.

(3) The model contains random variables.

(4) We require a lively overview of the results obtained by the model.

Although the simulation is by far the best tool to study and observe the conduct or operation of a system is necessary to make some warnings regarding its use:

? Sometimes projects are time-consuming simulation.

? Usually simulation models require lots of data.

? The results can be misinterpreted.

? Some technical and human factors be ignored.

? The validation of simulation models is often difficult.Random Number Generation:Simulation models are often used to analyze a decision under uncertainty, ie a problem in which the behavior of one or more factors can be represented by a probability distribution. This type of simulation is sometimes called Monte Carlo method.Monte Carlo Simulation:Monte Carlo Method historically was viewed as a technique to solve models using random or pseudo-random numbers. Random numbers are basically independent random variables uniformly distributed in a range from 0 to 1. Actually, what we can achieve with an electronic computer is to generate a sequence of pseudorandom numbers (seemingly random, with each digit 0 through 9 occur with almost equal probability).

The term "Monte Carlo" was introduced by Von Neumann and Ulam during World War II as a code for a secret mission at Los Alamos. Monte Carlo is a city in Monaco, famous for its gambling houses, hence the name occurred to them. At that time, the method was applied to the problems related to the atomic bomb, whose experimental tests were made precisely in Los Alamos, New Mexico.

The Monte Carlo method is used not only for stochastic but deterministic problems. This method is currently the most powerful technique commonly used to analyze complex problems.

It is important to note some differences between the Monte Carlo method and stochastic simulation:

• In the Monte Carlo method the time is not as critical as in the stochastic simulation.

• In the Monte Carlo method the observations are independent. In contrast, stochastic simulation observations are serially correlated, as experienced in relation to time.

• In the Monte Carlo method the results can be expressed simply in terms of input stochastic variations. In contrast, stochastic simulation response is usually very complicated and can be expressed only by the program.Random Number Generation:To generate random numbers, at first using manual methods as tossing a coin, a roulette wheel, among others. These physical methods were cumbersome for general use, moreover, the sequences generated by them could not be reproduced. With the advent of computers it was easier to get random numbers. John von Neumann suggested the method "mid-square" (the mean square) using the arithmetic of a computer. His idea was to take the square of the previous random number and make the digits located in the middle. For example, if we have the number 3456, so we square and we get 11,943,936, and now our new number is 9439, and so on. These numbers are not truly random, we just seem to be, and are called pseudo-or quasi-random. Hopefully not meet with zeros because then we'd be in trouble.

The efficiency of a method for generating random numbers can be measured depending on the occurrence of numbers, if they are uniformly distributed, statistically independent and reproducible. Moreover, a method is good if the generator is fast and takes up little memory space. The following example illustrates the application of Monte Carlo Method.