UNIT-2REPRESENTATION AND ANALYSIS OF SYSTEM STRUCUTREMODELS FOR REPRESENTING SYSTEM

RN.KARTHIKAVMP-401

OVERVIEWMATHEMATICAL MODELGRAPHICAL MODELHIERARCHICAL OR NETWORK MODEL

OBJECTIVEThey provide a natural framework for the design of new system.Specialized techniques that have been developed in one field can be transferred between research communities and exploited more widely

INTRODUCTIONThe different models are organized into a organisation chart or a tree like diagramsThe models are the flexible way of representing objects and their relationships.They provide a natural tool for dealing with problems.

Mathematical Modeling?Mathematical modeling seeks to gain an understanding of science through the use of mathematical models on HP computers

Mathematical modeling involves teamwork

Mathematical ModelingComplements, but does not replace, theory and experimentation in scientific research.

Mathematical Modeling Process

MATHEMATICAL MODEL PROCESSING1. Identify Real-World Problem:Understand current activity and predict future behavior. 2. Working Model : describe important aspects of Real World Problem; deter mine those factors that can be neglected. State simplifying assumptions. Determine governing principles, physical laws.Identify model variables and inter-relationships3.Mathematical Model: In general, the success of a mathematical model depends on how easy it is to use and how accurately it predicts.

4.Computational Model: Change Mathematical Model into a form suit able for computational solution.Existence of unique solutionChoice of the numerical methodChoice of the algorithmSoftware5.Results/Conclusions: : Run Computational Model to obtain Results; draw Conclusions.Verify your computer program; use check cases; explore ranges of validity. Graphs, charts, and other visualization tools are useful in summarizing results and drawing conclusions.

GRAPHICAL MODELGraphical models are a marriage between probability theory and graph theory.Two problems that occur throughout applied mathematics and engineering -- uncertainty and complexity.In particular they are playing an increasingly important role in the design and analysis .

GRAPHICAL MODELThe idea of a graphical model is the notion of modularity .Mixture models, factor analysis, hidden Markov models, Kalman filters and Ising models these are the examples of graphical model.The graphical model framework provides a way to view all of these systems as instances

ADVANTAGE OF THE VIEW:

In particular, specialized techniques that have been developed in one field can be transferred between research communities and exploited more widely. Moreover, the graphical model formalism provides a natural framework for the design of new systems.--- Michael Jordan, 1998

HIERARCHICAL MODEL

HIERARCHICAL MODELWe can still find older systems that are based on a hierarchical or network data model.A hierarchical database model is a data model in which the data is organized into a tree-like structure.

Within a record each data elements are organised in to a pieces of records called segments.To user each record looks like an organisation chart with one top level segment called the root.

EXAMPLE FOR HIERARCHICAL MODEL

EXAMPLE FOR HIERARCHICAL MODELIn a database an entity type is the equivalent of a table. Each individual record is represented as a row, and each attribute as a column. Entity types are related to each other using 1:N mappings, also known as one-to-many relationships. This model is recognized as the first database model created by IBM in the 1960s.Currently the most widely used hierarchical databases are IMS developed by IBM and Windows Registry by Microsoft.

NETWORK MODELThe network model's original inventor was Charles Bachman, and it was developed into a standard specification published in 1969 by the CODASYL Consortium.The network model is a database model conceived as a flexible way of representing objects and their relationships.

Its distinguishing feature is that the schema, viewed as a graph .Object types are nodes and relationship types are arcs.

CASE STUDY

Mr. Rajini is in his officeHe receives a call from his neighbor that the alarm of his house went off.He thinks that somebody broke into his house.Afterwards he hears an announcement from radio that a small earthquake just happenedSince the alarm has been going off during an earthquake.He concludes it is more likely that earthquake causes the alarm.

Earthquake or burglary?

Earthquake or burglary?

BY THIS EXAMPLE CAN U PPL GUESS WHAT MODEL THIS REPRESENTS ?

A Bigger Example: Most Economical Size

Let us have a go at building and using a mathematical model to solve a real world problem.Your company is going to make its own boxes!It has been decided the box should hold0.02m3(0.02 cubic meters which is equal to 20 liters) of nuts and bolts.The box should have a square base, and double thickness top and bottom.Cardboard costs$0.30per square meter.It is up to you to decide the most economical size.

Step One: Draw a sketch!

It helps to sketch out what you are trying to solve! The base is square, so we will just use "w" for both lengths.The box has 4 sides, and double tops and bottoms.The box shape could be cut out like this (but would probably be more complicated):

Step Two: Make Formulas.

Ignoring thickness for this model:Volume=wwh =w2hAnd we are told that the volume should be 0.02m3:w2h = 0.02Areas:Area of the 4 Sides=4wh =4whArea of Double Tops and Bases=4ww =4w2Total cardboard needed:Area of Cardboard =4wh +4w2

Step Three: Make a Single Formula For Cost

We want a single formula for cost:Cost = $0.30 Area of Cardboard=$0.30 (4wh +4w2)And that is the cost when we know widthandheight.That could be hard to work with ... a function with two variables.But we can make it simpler! Because width and height are already related by the volume:Volume=w2h = 0.02... which can be rearranged to ...h = 0.02/w2... and that can be put into the cost formula ...Cost=$0.30 (4w0.02/w2+4w2)And now the cost is related directly towidth only.With a little simplification we get:Cost=$0.30 (0.08/w+4w2)

Step Four: Plot it and find minimum cost

What to plot? Well, the formula only makes sense for widths greater than zero, and I also found that for widths above 0.5 the cost just gets bigger and bigger.So here is a plot of that cost formula forwidths between 0.0 m and 0.55m:

Plot of y=0.3(0.08/x+4x2) xis width, andyis costJust by eye, I see the cost reaches a minimum at about(0.22, 0.17). In other words:when the width is about0.22 m(x-value),the minimum cost is about$0.17per box (y-value).In fact, looking at the graph, the width could be anywhere between 0.20 and 0.24 without affecting the minimum cost very much.

Step Five: Recommendations

Using this mathematical model you can now recommend:Width = 0.22 mHeight = 0.02/w2= 0.02/0.222= 0.413 mCost =$0.30 (0.08/w+ 4w2) = $0.30 (0.08/0.22+ 40.222) = $0.167Or about 16.7 cents per boxBut any width between 0.20 m and 0.24 m would be fine.You might also like to suggest improvements to this model:Include cost of glue/staples and assemblyInclude wastage when cutting box shape from cardboard.Is this box a good shape for packing, handling and storing?Any other ideas you may have!

HEY FRIENDZ CAN U IDENTIFY WHAT MODEL IS THIS

FAQS2 mark1.Differentiate between mathematical model and graphical model for represnting systems?(June-2012)16 mark (June-2012)1.Enumerate on the following hierarchical modelsi)tree diagramii)organization chart

SUMMARYGraphical model is a combination of probability theory and graph theory.Two problems faced in this model are uncertinity and complexity.Graphical model provides a natural frame work for the design of new system.A hierarchical database model is a data model in which the data is organized into a tree-like structure.Network model is a flexible way of representing objets and relationship

GLOSSARYHierarchical:Older logical db model that organizes data in a tree like structure.Network:Older logical db model that is useful for depicating many-to-many relationship.Legacy system:System that has been in existance for a long time,used to avoid high cost of replacing or redesign.

REFERENCE S.NO AUTHOR NAME BOOK NAME EDITION PUBLISHER PLACE YEAR CHAPTER PAGE 1. KENNETH C.LAUDON MANAGING THE8TH PHIDELHI 04 7 227,229 JANE P.LAUDON DIGITAL FIRM.