This document provides an overview of system modeling concepts. It defines what a system is and basic system components like entities, attributes, and activities. It discusses different types of systems like open vs closed systems, stochastic vs deterministic activities, and continuous vs discrete systems. It also covers various types of models like physical, mathematical, static, and dynamic models. Specific examples are provided to illustrate concepts like static and dynamic physical and mathematical models. Principles of modeling like block-building, relevance, accuracy, and aggregation are also covered.
1. Chapter One:
SYSTEM MODELS
Prepared By:
Towfiqur Rahman
Jessore university of Science and Technology
BAngladesh
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2. The Concepts of a System
A system is an aggregation of objects where objects has regular
interaction and interdependence to perform a certain task.
Example:
FABRICATIO
N DEPT
PURCHASIN
G DEPT
ASSEMBL
Y DEPT
SHIPPIN
G DEPT
PRODUCTION
CONTROL DEPT
COUSTOMER
ORDER
RAW
MATERIALS
FINISHING GOOD
Fig: A factory System 2
3. BASIC COMPONENTS
Entity: An object “component” in the system
Attribute: A property of an entity
Activity: A process that cause changes in the system
System State: Description of system “entities, attributes, and
activities” at any point in time.
Example: If system is a class in a school, then students are entities,
books are their attributes and to study is their activity.
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4. System Environment
The changes that occurring outside the system and affecting the
system called system environment.
Two term are used in system environment.
i. Endogenous: activities occurring within the system.
ii. Exogenous: activities in the environment that affect system. If a
system has no exogenous activities that called closed system and if
has exogenous activities that called open system.
Example: In the factory system the factors controlling the arrival
of orders may be considered to be outside the influence of the
factory. So it is the part of the environment.
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5. Stochastic & Deterministic Activities
When the outcome of an activity can be described completely in terms
of its input, the activity is said to be deterministic . Where the effects of
the activity vary randomly over various possible outcomes , the activity
is said to be stochastic.
Example : Among the 52 cards, if we pick exactly the card containing
the number 3,then it is said to be deterministic . Otherwise, if we pick
any card by not looking to the cards, then we can get any card and that
is said to be stochastic.
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6. Continuous and Discrete Systems
Continuous System: In the system in which change are
predominantly smooth are called continuous system.
Example: In the factory machining proceeds are continuous
system.
Discrete System: In the system in which change are
predominantly discontinuous are called discrete system.
Example: In the factory the start and finish of a job are discrete
changes.
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7. System Modeling
System modeling: System modeling as the body of information
about a system gathered for the purpose of studying the system.
The task the model of a system may be divided into two subtasks.
i. Establishing the model structure: determines the system
boundary, identifies the entities, attributes and activates the system.
ii. Supplying the data: provide the values the attributes and
define the relationships involved in the activates.
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8. Types of Models
MODELS
PHYSICAL MATHEMATICAL
STATIC DYNAMIC STATIC DYNAMIC
NUMERICAL ANALYTICAL NUMERICAL
SYSTEM SIMULATION
Fig : Types of model
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9. Discussion of Model
Physical models: In a physical model the system attributes are represented by such
measurements as a voltage .
Physical model are based on some analogy between such system as mechanical or electrical
Example: The rate at which the shaft of a direct current motor turns depends upon the
voltage applied to the motor.
Mathematical models: In the mathematical models use symbolic notation and
mathematical equation to represent a system. Attributes are represented by variables and
the activates are represented by mathematical function.
Static models: show the value of attributes take when system in balance.
Dynamic models: follow the changes over the time that result from the system activates.
Analytical models: To finding the model that can solved and best fits the system being
studied.
Example: linear differential equation.
Numerical methods: involve applying computational procedures to solve equations.
Example: the solution derived from complicated integral which need a power series.
System simulation: considered to be a numerical computation technique used with
dynamic mathematical models.
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10. Static Physical Models
Static physical models: Static physical model is a scaled down
model of a system which does not change with time.
Example: An architect before constructing a building, makes a
scaled down model of the building, which reflects all it rooms, outer
design and other important features. This is an example of static
physical model.
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11. Dynamic Physical Models
Dynamic physical models :Dynamic physical models are ones
which change with time or which are function of time.
Example: In wind tunnel, small aircraft models are kept and air is
blown over them with different velocities. Here wind velocity changes
with time and is an example of dynamic physical model.
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12. Static mathematical model:
A static model gives the relationships between the system attributes
when the system is in equilibrium.
Example: Here we give a case of static mathematical model from
industry. Generally there should be a balance between the supply and
demand of any product in the market. Supply increases if the price is
higher. But on the other hand demand decreases with the increase of
price. Aim is to find the optimum price with which demand can match
the supply. If we denote price by P, supply by S and demand by Q, and
assuming the price equation to be linear we have
Q = a – bP
S = c + dP
S = Q
In the above equations, a, b, c, d are parameters computed based on
previous market data. Let us take values of a = 600, b = 3000, c = –100
and d =2000. Value of c is taken negative, since supply cannot be
possible if price of the item is zero. In this case no doubt equilibrium
market price will be
P=a-c/ b+d =0.14,s=180
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13. Static mathematical model:
The relationship between demand denoted by Q, and price, denoted by P, are
represented here by the straight line marked “Demand” in fig:1.6 and
supply, denoted by S, is plotted against price & the relationship is the
straight line marked “supply”. Supply equals price where the two line cross.
Fig 1.5:Market model fig 1.6:Non-linear
market model.
More usually, the demand and supply are depicted by curves
with slopes downward and upward respectively (Fig. 1.6). It may not be
possible to express the relationships by equations that can be solved easily.
Some numerical or graphical methods are used to solve such relations.
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14. Dynamic mathematical model:
Dynamic mathematical model allow the change of system attributes to be
derived as a function time.
Fig: graph shows displacement vs. time
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15. Principles Used in Modeling
a) Block-building: The system should be organized in a series of blocks
to simplify of the interactions within the system.
Example: Here each department has been treated as a separate block
with input output begin the work passed from department to department.
FABRICATIO
N DEPT
PURCHASIN
G DEPT
ASSEMBL
Y DEPT
SHIPPIN
G DEPT
PRODUCTION
CONTROL DEPT
Fig: A factory System
RAW MATERIALS
FINISHING GOOD
COUSTOMER
ORDER
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16. b) Relevance: The model should only include those aspects of the system that
are relevant to the study objectives. while irrelevant information may do not
any harm, it should be excluded because it increase the complexity and need
doing more work to do solve.
Example: If the factory system aim to compare the effects of different operating
rules on efficiency, it should not to do consider the hiring employees.
c)Accuracy: The accuracy of the information for the model should be considered.
In the aircraft system the accuracy which the movement of the aircraft
depends on the representation of the airframe. If the airframe regard as a
rigid body then it necessary to recognize the flexibility of the airframe. An
engineer responsible for estimating the fuel consumption satisfied with the
simple representation. Another engineer responsible for considering the
comfort the passenger, vibrations and will want the description of airframe.
d)Aggregation: Aggregation to be considered is the extent to which the number
of individual entities can be grouped together into larger entities.
Example: The production manager will want to consider the shops of the
departments as individual entities.
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