UNIT-2 REPRESENTATION AND ANALYSIS OF SYSTEM STRUCUTRE MODELS FOR REPRESENTING SYSTEM RN.KARTHIKA VMP-401
Nov 02, 2014
UNIT-2REPRESENTATION AND ANALYSIS OF SYSTEM STRUCUTRE
MODELS 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 diagrams
The 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.
Experiment
Computation
Theory
Mathematical Modeling Process
MATHEMATICAL MODEL PROCESSING 1. 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-relationships
3.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 solution Choice of the numerical method Choice of the algorithm Software
5.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
Performance ratings Salary
history
Pension Lifeinsurance
Health
Employee
Comparison Job assignment Benefits
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 MODEL
In 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 office◦ He 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 happened◦ Since 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?
Call
Burglary
Alarm
Earthquake
Newscast
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 hold 0.02m3 (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 $0.30 per 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 = w × w × h = w2hAnd we are told that the volume should
be 0.02m3:w2h = 0.02Areas:Area of the 4 Sides = 4 × w × h = 4whArea of Double Tops and
Bases = 4 × w × w = 4w2
Total 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 width and height.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 × (4w×0.02/w2 + 4w2)And now the cost is related directly to width 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 for widths between 0.0 m and 0.55m:
Plot of y= 0.3(0.08/x+4x2)x is width, and y is cost
Just by eye, I see the cost reaches a minimum at about (0.22, 0.17). In other words:
when the width is about 0.22 m (x-value),the minimum cost is about $0.17 per 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+
4×0.222) = $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 assembly Include 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
FAQ’S
2 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 THE 8TH PHI DELHI 04 7 227,229
JANE P.LAUDON DIGITAL FIRM.