Methods of SimulationMethods of Simulation

GROUP MEMBERSGROUP MEMBERS

ROY THOMAS ROY THOMAS SAM SCARIA SAM SCARIA SONU SEBASTIANSONU SEBASTIAN SILPA MATHEWSILPA MATHEW AMMU VIJAYANAMMU VIJAYAN SIJU JOSESIJU JOSE SAJITH P SSAJITH P S SCARIA JOSEPHSCARIA JOSEPH

What is simulation:What is simulation:

The process of designing a The process of designing a mathematical or logical model of a mathematical or logical model of a real-system and then conducting real-system and then conducting computer-based experiments with computer-based experiments with the model to describe, explain, and the model to describe, explain, and predict the behavior of the real predict the behavior of the real system. system.

Monte carlo method & Monte carlo method & system simulation system simulation

methodmethod

What is a Monte Carlo simulation?What is a Monte Carlo simulation?

• Monte carlo method is a substitution for the Monte carlo method is a substitution for the mathematical evaluation of a model.mathematical evaluation of a model.

• Darker and Kac define monte carlo method as Darker and Kac define monte carlo method as combination of probability methods & sampling combination of probability methods & sampling techniques providing solution to complicated techniques providing solution to complicated partial or integral differential equation.partial or integral differential equation.

• In short, monte carlo technique is concerned In short, monte carlo technique is concerned with experiments on random numbers & it with experiments on random numbers & it provides solutions to complicated OR provides solutions to complicated OR problems. problems.

Uses of monte carlo techniqueUses of monte carlo technique Where one is dealing with a problem Where one is dealing with a problem

which has not yet arisen.which has not yet arisen.

Where the mathematical and Where the mathematical and statistical problems are too statistical problems are too complicated and some alternative complicated and some alternative methods are needed.methods are needed.

To estimate parameters to a model.To estimate parameters to a model.

Steps of Monte Carlo methodSteps of Monte Carlo method A Flow diagram is drawn.A Flow diagram is drawn.

Probability distribution for the Probability distribution for the variables of our interest is variables of our interest is determined.determined.

Probability distribution is converted Probability distribution is converted to cumulative distribution function.to cumulative distribution function.

Sequence of random numbers is Sequence of random numbers is selected .selected .

Sequence of values of the variables Sequence of values of the variables of our interest is determined with the of our interest is determined with the sequence of random numbers sequence of random numbers obtained.obtained.

Some standard mathematical Some standard mathematical functions is applied to the sequence functions is applied to the sequence of values obtainedof values obtained

Advantage Advantage

Find solution of complicated Find solution of complicated mathematical expressions.mathematical expressions.

Difficulties of trial and error Difficulties of trial and error experimentation are avoided by experimentation are avoided by these method.these method.

DisadvantagesDisadvantages

These are costly way of getting a These are costly way of getting a solution of any problem.solution of any problem.

These method do not provide optimal These method do not provide optimal answer to the problems. The answers answer to the problems. The answers are good only when the size of the are good only when the size of the sample is sufficiently large.sample is sufficiently large.

ApplicationsApplications

It is applied to a wide diversity of It is applied to a wide diversity of problems such as queuing problems, problems such as queuing problems, inventory problems, risk analysis inventory problems, risk analysis concerning a major capital concerning a major capital investment.investment.

It is very useful in budgeting.It is very useful in budgeting.

System Simulation MethodSystem Simulation Method

Under this method operating Under this method operating environment is produced and environment is produced and systems allows for analysing the systems allows for analysing the response from the environment to response from the environment to alternative management actions.alternative management actions.

The method is complicated and The method is complicated and costly.costly.

Generation of random numbersGeneration of random numbers

Random numbersRandom numbers

It is a number in a sequence of It is a number in a sequence of numbers whose probability of numbers whose probability of occurrence is same as that of any occurrence is same as that of any other number in that sequence.other number in that sequence.

Pseudo-random Numbers:Pseudo-random Numbers:

Random numbers are called pseudo Random numbers are called pseudo random numbers when they are random numbers when they are generated by some deterministic generated by some deterministic process. But they qualify the pre process. But they qualify the pre determined statistical test for determined statistical test for randomness.randomness.

Generating of random numbers:Generating of random numbers:

For solving simulation problems, For solving simulation problems, there is the need of generating a there is the need of generating a sequence of random numbers.sequence of random numbers.

Random numbers may be found by Random numbers may be found by computer ,by random tables, computer ,by random tables, manually etc.manually etc.

Most common method to obtain Most common method to obtain random numbers is to generate them random numbers is to generate them by a computer programme.by a computer programme.

These numbers lie between 0 and These numbers lie between 0 and 1,in conjunction with the cumulative 1,in conjunction with the cumulative probability distribution of a random probability distribution of a random variable including 0 but not 1.variable including 0 but not 1.

Waiting Line simulation modelWaiting Line simulation model

In this type problems the simulation In this type problems the simulation technique can be applied to solve technique can be applied to solve problems of complex nature.problems of complex nature.

The uncertain characteristics of this The uncertain characteristics of this model are the arrival behaviour of model are the arrival behaviour of the customer in the system and the the customer in the system and the service time distribution.service time distribution.

Inventory Simulation ModelInventory Simulation Model