System Modeling
A
model is defined as a representation of a system for the purpose of studying
the system. It is necessary to consider only those aspects of the system that
affect the problem under investigation. These aspects are represented in a
model, and by definition it is a simplification of the system.
The
aspect of system that affect the problem under investigation, are represented
in a model of the system. Therefore model is the simplification of the real
system.
There
is no unique model of a system. Different models of the same system will be
produced by different system analysts who are interested in different aspect of
system.
The
task of deriving a model of a system may be divided broadly into two sub tasks:
Establishing model parameter and supplying data.
Establishing
model structure determines system boundary and identifies the entities,
attributes, activities and events of a system.
Supplying
data provides value contained an attribute and define relationships involved in
the activities.
Types
of Model
The
various types of models are listed below.
·
Mathematical and Physical Model
·
Static Model
·
Dynamic Model
·
Deterministic Model
·
Stochastic Model
·
Discrete Model
· Continuous
Model
Physical
model
These models are based on some analogy between mechanical and electrical
system. The system attributes are represented by physical measures such as
voltage. The system activities are represented by physical laws.
Physical models are of two types, static and dynamic. Static physical
model is a scaled down model of a system which does not change with time. 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. Similarly for conducting trials in
water, we make small water tanks, which are replica of sea, and fire small
scaled down shells in them. This tank can be treated as a static physical model
of ocean. Dynamic physical models are ones which change with time or which are
function of time. In wind tunnel, small aircraft models (static models) are
kept and air is blown over them with different velocities and pressure profiles
are measured with the help of transducers embedded in the model. Here wind
velocity changes with time and is an example of dynamic physical model.
Let us take an example of hanging wheel of a stationary truck and analyze
its motion under various forces. Consider a wheel of mass M, suspended
in vertical direction, a force F(t), which varies with time, is
acting on it. Mass is connected with a spring of stiffness K, and a
piston with damping factor D. When force F (t), is
applied, mass M oscillates under the action of these three forces.
This model can be used to study the oscillations in a motor wheel. Figure
1.2 shows such a system. This is a discrete physical static model. Discrete in
a sense, that one can give discrete values F and observe the
oscillations of wheel with some measuring equipment. When force is applied on
it, which is a function of time, this discrete physical static model becomes
dynamic model. Parameters K and D can also be adjusted in order
to get controlled oscillations of the wheel. This type of system is called spring-mass
system or wheel suspension. Load on the beams of a building can be studied by
the combination of spring-mass system.
Mathematical
Model
It uses symbolic notation and mathematical equation to represent system. The
system attributes are represented by variables and the activities are
represented by mathematical function.
Example: f(x) = mx+c is a
mathematical model of a line.
Static Model
Static models can only show the values that the system attributes value
does not change over time.
Example: Scientist has used models in which sphere represents atom, sheet
of metal to connect the sphere to represent atomic bonds. Graphs are used to
model the various system based on network.
A map is also a kind of graph. These models are sometimes said to be
iconic models and are of kind static physical models.
Dynamic Model
Dynamic models follow the changes over time that result from system
activities. The mechanical and electrical systems are the example of dynamic
system. Generally, dynamic models involve the computation of variable value
over time and hence they are represented by differential equations.
Analytical
Models:
In mathematical model, we can differentiate the model on the basis of
solution technique used to solve the model. Analytical technique means using
deductive reasoning of mathematical theory to solve a model. Such models are
known as analytical model.
Numerical models
Numerical models involve applying computational process to solve
equations. For example: we may solve differential equation numerically when the
specific limit of variable is given.
The analytical methods to produce solution may take situation numerical
methods are preferred.
Deterministic
Model
Contain no random variables. They have a known set of inputs which will
result in a unique set of outputs. Ex: Arrival of patients to the Dentist at
the scheduled appointment time.
Stochastic Model
Has one or more random variable as inputs. Random inputs leads to random
outputs. Ex: Simulation of a bank involves random inter-arrival and service
times.
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