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A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of models; the model represents the key characteristics or behaviors of the selected system or process, whereas the simulation represents the evolution of the model over time. Often, computers are used to execute the
simulation A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of models; the model represents the key characteristics or behaviors of the selected system or process, whereas the ...
. Simulation is used in many contexts, such as simulation of technology for performance tuning or optimizing, safety engineering, testing, training, education, and video games. Simulation is also used with
scientific modelling Scientific modelling is a scientific activity, the aim of which is to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate by referencing it to existing and usually commonly accepted ...
of natural systems or human systems to gain insight into their functioning, as in economics. Simulation can be used to show the eventual real effects of alternative conditions and courses of action. Simulation is also used when the real system cannot be engaged, because it may not be accessible, or it may be dangerous or unacceptable to engage, or it is being designed but not yet built, or it may simply not exist. Key issues in modeling and simulation include the acquisition of valid sources of information about the relevant selection of key characteristics and behaviors used to build the model, the use of simplifying approximations and assumptions within the model, and fidelity and validity of the simulation outcomes. Procedures and protocols for model verification and validation are an ongoing field of academic study, refinement, research and development in simulations technology or practice, particularly in the work of computer simulation.


Classification and terminology

Historically, simulations used in different fields developed largely independently, but 20th-century studies of systems theory and cybernetics combined with spreading use of computers across all those fields have led to some unification and a more systematic view of the concept. '' Physical simulation'' refers to simulation in which physical objects are substituted for the real thing (some circles use the term for computer simulations modelling selected laws of physics, but this article does not). These physical objects are often chosen because they are smaller or cheaper than the actual object or system. ''Interactive simulation'' is a special kind of physical simulation, often referred to as a '' human-in-the-loop'' simulation, in which physical simulations include human operators, such as in a flight simulator, sailing simulator, or driving simulator. '' Continuous simulation'' is a simulation based on continuous-time rather than discrete-time steps, using numerical integration of differential equations.McLeod, J. (1968) "Simulation: the Dynamic Modeling of Ideas And Systems with Computers", McGraw-Hill, NYC. '' Discrete-event simulation'' studies systems whose states change their values only at discrete times. For example, a simulation of an epidemic could change the number of infected people at time instants when susceptible individuals get infected or when infected individuals recover. '' Stochastic simulation'' is a simulation where some variable or process is subject to random variations and is projected using
Monte Carlo Monte Carlo (; ; french: Monte-Carlo , or colloquially ''Monte-Carl'' ; lij, Munte Carlu ; ) is officially an administrative area of the Principality of Monaco, specifically the ward of Monte Carlo/Spélugues, where the Monte Carlo Casino i ...
techniques using pseudo-random numbers. Thus replicated runs with the same boundary conditions will each produce different results within a specific confidence band. '' Deterministic simulation'' is a simulation which is not stochastic: thus the variables are regulated by deterministic algorithms. So replicated runs from the same boundary conditions always produce identical results. ''Hybrid simulation'' (or combined simulation) corresponds to a mix between continuous and discrete event simulation and results in integrating numerically the differential equations between two sequential events to reduce the number of discontinuities. A ''stand-alone simulation'' is a simulation running on a single workstation by itself. A is one which uses more than one computer simultaneously, to guarantee access from/to different resources (e.g. multi-users operating different systems, or distributed data sets); a classical example is Distributed Interactive Simulation (DIS). ''Parallel simulation'' speeds up a simulation's execution by concurrently distributing its workload over multiple processors, as in High-Performance Computing. ''Interoperable simulation'' is where multiple models, simulators (often defined as federates) interoperate locally, distributed over a network; a classical example is High-Level Architecture. ''Modeling and simulation as a service'' is where simulation is accessed as a service over the web. ''Modeling, interoperable simulation and serious games'' is where
serious game A serious game or applied game is a game designed for a primary purpose other than pure entertainment. The "serious" adjective is generally prepended to refer to video games used by industries like defense, education, scientific exploration, he ...
approaches (e.g. game engines and engagement methods) are integrated with interoperable simulation. ''Simulation fidelity'' is used to describe the accuracy of a simulation and how closely it imitates the real-life counterpart. Fidelity is broadly classified as one of three categories: low, medium, and high. Specific descriptions of fidelity levels are subject to interpretation, but the following generalizations can be made: * Low – the minimum simulation required for a system to respond to accept inputs and provide outputs * Medium – responds automatically to stimuli, with limited accuracy * High – nearly indistinguishable or as close as possible to the real system A ''synthetic environment'' is a computer simulation that can be included in human-in-the-loop simulations. ''Simulation in failure analysis'' refers to simulation in which we create environment/conditions to identify the cause of equipment failure. This can be the best and fastest method to identify the failure cause.


Computer simulation

A computer simulation (or "sim") is an attempt to model a real-life or hypothetical situation on a computer so that it can be studied to see how the system works. By changing variables in the simulation, predictions may be made about the behaviour of the system. It is a tool to virtually investigate the behaviour of the system under study. Computer simulation has become a useful part of modeling many natural systems in
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which rel ...
, chemistry and
biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditar ...
, and human systems in economics and
social science Social science is one of the branches of science, devoted to the study of societies and the relationships among individuals within those societies. The term was formerly used to refer to the field of sociology, the original "science of soc ...
(e.g.,
computational sociology Computational sociology is a branch of sociology that uses computationally intensive methods to analyze and model social phenomena. Using computer simulations, artificial intelligence, complex statistical methods, and analytic approaches like s ...
) as well as in engineering to gain insight into the operation of those systems. A good example of the usefulness of using computers to simulate can be found in the field of network traffic simulation. In such simulations, the model behaviour will change each simulation according to the set of initial parameters assumed for the environment. Traditionally, the formal modeling of systems has been via a
mathematical model A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, ...
, which attempts to find analytical solutions enabling the prediction of the behaviour of the system from a set of parameters and initial conditions. Computer simulation is often used as an adjunct to, or substitution for, modeling systems for which simple closed form analytic solutions are not possible. There are many different types of computer simulation, the common feature they all share is the attempt to generate a sample of representative scenarios for a model in which a complete enumeration of all possible states would be prohibitive or impossible. Several software packages exist for running computer-based simulation modeling (e.g.
Monte Carlo Monte Carlo (; ; french: Monte-Carlo , or colloquially ''Monte-Carl'' ; lij, Munte Carlu ; ) is officially an administrative area of the Principality of Monaco, specifically the ward of Monte Carlo/Spélugues, where the Monte Carlo Casino i ...
simulation,
stochastic Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselve ...
modeling, multimethod modeling) that makes all the modeling almost effortless. Modern usage of the term "computer simulation" may encompass virtually any computer-based representation.


Computer science

In
computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (includin ...
, simulation has some specialized meanings:
Alan Turing Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist. Turing was highly influential in the development of theoretical c ...
used the term ''simulation'' to refer to what happens when a universal machine executes a state transition table (in modern terminology, a computer runs a program) that describes the state transitions, inputs and outputs of a subject discrete-state machine. The computer simulates the subject machine. Accordingly, in
theoretical computer science Theoretical computer science (TCS) is a subset of general computer science and mathematics that focuses on mathematical aspects of computer science such as the theory of computation, lambda calculus, and type theory. It is difficult to circumsc ...
the term ''
simulation A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of models; the model represents the key characteristics or behaviors of the selected system or process, whereas the ...
'' is a relation between state transition systems, useful in the study of operational semantics. Less theoretically, an interesting application of computer simulation is to simulate computers using computers. In
computer architecture In computer engineering, computer architecture is a description of the structure of a computer system made from component parts. It can sometimes be a high-level description that ignores details of the implementation. At a more detailed level, the ...
, a type of simulator, typically called an '' emulator'', is often used to execute a program that has to run on some inconvenient type of computer (for example, a newly designed computer that has not yet been built or an obsolete computer that is no longer available), or in a tightly controlled testing environment (see Computer architecture simulator and
Platform virtualization Hardware virtualization is the virtualization of computers as complete hardware platforms, certain logical abstractions of their componentry, or only the functionality required to run various operating systems. Virtualization hides the physic ...
). For example, simulators have been used to debug a
microprogram In processor design, microcode (μcode) is a technique that interposes a layer of computer organization between the central processing unit (CPU) hardware and the programmer-visible instruction set architecture of a computer. Microcode is a laye ...
or sometimes commercial application programs, be