half-maked-modelling-notes

model.txt

What is a model ?
        A model is a representation of a system ,idea or a object, made of the composition of concepts which are used to help people know, understand or simulate a subject the model represents.

What is Simulation?
        Simulation is the process of designing a model of a real system in the motive of conducting expriments with it to either understading the behaviour of it or evaluating various strategies for the operation of system.

When to use Simulation?
        1. When system is very complex .
        2. When it is too risky to go straight with the project.
        3. To study any problem that cause uncertainty.
        4. When it is not advisable to experiment with nature or reality.
        5. When real system is very costly.

When not to use Simulation?
        1. When problem can be solved by common sense.
        2. When problem can be solved analytically.
        3. If it is too costly to perfom.
        4. If system behaviour is too complex.

What is System and System environment
        System is a group of objects which are connected together in some fashion to accomplish a purpose. E.g Automobile company :-> workers, machines operates jointly to make automobiles.
        System Enviorment is anything that surronds the system. Which can influence the system state.

Components of System
        1. Entity , a object of interest in system is known as entity of system.
        2. Attribute, property of an entity.
        3. Activity, a time period of specific length.
        4. State, collecttion of all system variables that depicts the system behaviour , status of system like busy ,waiting etc.
        5. Event, an instantaneous change that can might change the state of system is called Event.
        6. Endogeneous And Exogeneous

Types of System
        1. Discrete :-> where state variables changes only at a discrete set of points in time.E.g Bank system.
        2. Continous :-> where state variables changes continously over time. Eg. Amount of liquid in tank,

Modelling
        Art of designing the models is known as modelling.

Types of Modelling
        1. Mathematical Model , it is precise model, concise model

Classification of Models
        1 i.  Deterministic model, it always depicts same output on same starting point. it contains no random variations.
          ii. Stochastic Or Probablistic model, statistical in nature

        2 i.  Linear Model, If all operator in a mathematical model exhibit linearity , then model is linear.
          ii. Non-Linear Model, else model is not linear.

        3 Static Vs Dynamic, in dynamic model state of models changes with time. while not in static model.

Example of Model
        suppose we want to describe the long term growth of population
                                1996    19m
                                1998    20m
                                2000    25m
                                2002    36m
        let r$R be the net reproduction rate per individual
        n(t) is the size of population at time t>=0
                r(t)=lim 1/n(t)*((n(t+t1)-n(t))/t1) lim t1->0

        Or popular model in computer science is the model of machine better knowns as dfa

Stochastic variable
        a radnom variable whose output is a possible outcome of a event.

Discrete and Continous Probability distributions
        A continuous distribution describes the probabilities of the possible values of a continuous random variable.
        A discrete distribution describes the probability of occurrence of each value of a discrete random variable.

Distribution Functions
        1.  binomial
               nCr * p^r * q^(n-r)

        2.  Poisson, if we know the rate of event occuruence and event are occurring independently of time, since last event we can use poisson distribution to tell probability of given no of event, When to apply poisson distribution. a) occurence of one event doesn't effect other event b) rate at which event occurs remains constant c) two event can't occur exactly at same time.
               e^(-lemda)*(((lemda)^k)/k!)
        3.  Normal or Gaussian,