Defining simulation

•A Simulation is the imitation of the operation of a real-world process or system over time. Simulation involves generation of artificial history of a system and drawing inferences from it.

•The behavior of a system as it evolves over time is studied by developing a simulation model.

• This model takes the form of a set of assumptions concerning the operation of the system.

•The model takes a set of expressed assumptions:

Mathematical, logical

Symbolic relationship between the entities

When Simulation Is the Appropriate Tool

•Simulation enables the study of and experimentation with the internal interactions of a complex system, or of a subsystem within a complex system.

•Informational, organizational and environmental changes can be simulated and the effect of those alternations on the model's behavior can be observed.

•The knowledge gained in designing a simulation model can be of great value toward suggesting improvement in the system under investigation.

•By changing simulation inputs and observing the resulting outputs, valuable insight may be obtained into which variables are most important and how variables interact

•Simulation can be used as a device to reinforce analytic solution methodologies.

•Simulation can be used to experiment with new designs or policies prior to implementation, so as to prepare for what may happen.

•Simulation can be used to verify analytic solutions.

•Simulation models designed for training, allow learning without the cost and disruption of on- the-job learning.

•Animation shows a system in simulated operation so that the plan can be visualized.

•The modern system(factory, water fabrication plant, service organization, etc) is so complex that the interactions can be treated only through simulation.

When Simulation Is Not Appropriate

•When the problem can be solved by common sense.

•When the problem can be solved analytically.

•If it is easier to perform direct experiments.

•If cost exceed savings.

•If resource or time are not available.

•If system behavior is too complex.

•If no data is available about the system, not even estimates

Systems and System Environment

•A system is defined as a groups of objects that are joined together in some regular interaction toward the accomplishment of some purpose. An autorobile factory: Machines, components parts and workers operate jointly along assembly line

•A system is often affected by changes occurring outside the system: system environment

•Factory : Arrival orders Effect of supply on demand : relationship between factory output and arrival (activity of system)

•Banks : Arrival of customers

Components of system

•Entity : An entity is an object-of interest in a system.

Ex: In the factory system, departments, orders, parts and products are The entities.

•Attribute An attribute denotes the property of an entity.

Ex: Quantities for each order, type of part, or number of machines in a Department are attributes of factory system.

• Activity Any process causing changes in a system is called as an activity.

Ex: Manufacturing process of the department.

•State of the System The state of a system is defined as the collection of variables necessary to describe a system at any time, relative to the objective of study. In other words, state of the system mean a description of all the entities, attributes and activities as they exist at one point in time.

•Event An event is defined as an instantaneous occurrence that may change the state of the system.

•Endogenous System The term endogenous is used to describe activities and events occurring within a system.

Ex: Drawing cash in a bank.

•Exogenous System The term exogenous is used to describe activities and events in the environment that affect the system.

Ex: Arrival of customers.

•Closed System A system for which there is no exogenous activity and event is said to be a closed.

Ex: Water in an insulated flask.

•Open system A system for which there is exogenous activity and event is said to be a open.

Ex: Bank system.

Example of system and it's components

Discrete system

A discrete system is one in which the state variables change only at a discrete set of points in time. Ex: Bank - the number of customer's changes only when a customer arrives or when the service provided a customer is completed

Continuous system

A continues system is one in which the state variables change continuously over time: Head of water behind the dam.

Model of a system

• A model is defined as a representation of a system for the purpose of studying the system

•The various types models are:

Mathematical or Physical Model

Static Model

Dynamic Model

Deterministic Model

Stochastic Model

Discrete Model

• Mathematical Model

Uses symbolic notation and the mathematical equations to represent a system.

• Static Model

Represents a system at a particular point of time and also known as Monte-Carlo simulation.

• Dynamic Model

Represents systems as they change over time. Ex: Simulation of a bank

• Deterministic Model

Contains no random variables. They have a known set of inputs which will result in a unique set of outputs. Ex: Arrival of patients to the Dentist at the scheduled appointment time.

• Stochastic Model

Has one or more random variable as inputs. Random inputs leads to random outputs. Ex: Simulation of a bank involves random interarrival and service times

• Discrete-Event System Simulation

Modeling of systems in wnich the state variable changes only at a discrete set of points in time.

The simulation models are analyzed by numerical rather than by analytical methods