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System Simulation and Modelling
System
• A system is defined as aggregation or assemblage of objects joined in
some regular interaction or interdependence.
• A collection of entities”eg.people or machine” that act together towards
the accomplishment of some logical end.
• Any set of interrelated components acting together to achieve a common
objective.
Examples:
1. Battery
• Consists of anode, cathode, acid and other components.
• These components act together to achieve one objective like preserving
electricity.
2. University
• Consists of professors, students and employees.
• These objects act together to achieve the objective of teaching & learning
process.
System Environment
The region outside the system is called as
the surrounding or environment
Boundary
It is real or imaginary surface
which separates the system from its environment.
Example
Components of system
Outputs and Inputs
• The main aim of a system is to produce
an output which is useful for its user.
• Inputs are the information that enters
into the system for processing.
eg. Human, machine, money, time etc.
Processor(s)
• The processor is the element of a system that
involves the actual transformation of input into output.
• It is the operational component of a system.
• Processors may modify the input either totally or partially,
depending on the output specification.
Control
• The control element guides the system.
• It is the decision–making subsystem that controls the pattern of activities governing input,
processing, and output.
• The behavior of a computer System is controlled by the Operating System and software. In
order to keep system in balance, what and how much input is needed is determined by
Output Specifications.
.
Environment
• The environment is the “supersystem” within which an organization operates.
• It is the source of external elements that strike on the system.
• It determines how a system must function. For example, vendors and competitors of
organization’s environment, may provide constraints that affect the actual performance
of the business.
Boundaries and Interface
• A system should be defined by its boundaries. Boundaries are the limits that identify its
components, processes, and interrelationship when it interfaces with another system.
• The knowledge of the boundaries of a given system is crucial in determining the nature
of its interface with other systems for successful design.
Feedback
• Feedback provides the control in a dynamic
system.
• Positive feedback is routine in nature that
encourages the performance of the system.
No Controller action is required
• Negative feedback is informational in nature that provides the controller with
information for action. Controller action is required.
Modelling and Simulation
.
Modelling Simulation
1.It is the process of representing a model
which includes its construction and
working.
2.This model is similar to a real system,
which helps the analyst predict the effect
of changes to the system.
3.modelling is creating a model which
represents a system including their
properties.
4.It is an act of building a model
1.It is the operation of a model in terms of
time or space, which helps analyze the
performance of an existing or a proposed
system.
2.simulation is the process of using a model
to study the performance of a system.
3. It is an act of using a model
Developing Simulation Models
• Step 1 − Identify the problem with an existing system or set
requirements of a proposed system.
• Step 2 − Design the problem while taking care of the existing
system factors and limitations.
• Step 3 − Collect and start processing the system data, observing its
performance and result.
• Step 4 − Develop the model using network diagrams and verify it
using various verifications techniques.
• Step 5 − Validate the model by comparing its performance under
various conditions with the real system.
• Step 6 − Create a document of the model for future use, which
includes objectives, assumptions, input variables and performance
in detail.
• Step 7 − Select an appropriate experimental design as per
requirement.
• Step 8 − Induce experimental conditions on the model and observe
the result.
Performing Simulation Analysis
• Step 1 − Prepare a problem statement.
• Step 2 − Choose input variables and create entities for the simulation process.
There are two types of variables - decision variables and uncontrollable variables.
Decision variables are controlled by the programmer, whereas uncontrollable
variables are the random variables.
• Step 3 − Create constraints on the decision variables by assigning it to the
simulation process.
• Step 4 − Determine the output variables.
• Step 5 − Collect data from the real-life system to input into the simulation.
• Step 6 − Develop a flowchart showing the progress of the simulation process.
• Step 7 − Choose an appropriate simulation software to run the model.
• Step 8 − Verify the simulation model by comparing its result with the real-time
system.
• Step 9 − Perform an experiment on the model by changing the variable values to
find the best solution.
• Step 10 − Finally, apply these results into the real-time system.
Scope of Simulation in different area
• Healthcare (Clinical) Simulators
• Computer Simulators
• Military Simulations
• Finance Simulations
• Flight Simulators
• Engineering, Technology or Process
Simulation
Modelling & Simulation ─ Advantages
• Following are the advantages of using Modelling and Simulation −
• Easy to understand − Allows to understand how the system really operates
without working on real-time systems.
• Easy to test − Allows to make changes into the system and their effect on the
output without working on real-time systems.
• Easy to upgrade − Allows to determine the system requirements by applying
different configurations.
• Easy to identifying constraints − Allows to perform bottleneck analysis that causes
delay in the work process, information, etc.
• Easy to diagnose problems − Certain systems are so complex that it is not easy to
understand their interaction at a time. However, Modelling & Simulation allows to
understand all the interactions and analyze their effect. Additionally, new policies,
operations, and procedures can be explored without affecting the real system.
Modelling & Simulation ─ Disadvantages
• Following are the disadvantages of using Modelling and Simulation −
• Designing a model is an art which requires domain knowledge, training and
experience.
• Operations are performed on the system using random number, hence difficult to
predict the result.
• Simulation requires manpower and it is a time-consuming process.
• Simulation results are difficult to translate. It requires experts to understand.
• Simulation process is expensive.
Models & Events
• Object is an entity which exists in the real world to study the behavior of a
model.
• Base Model is a hypothetical explanation of object properties and its
behavior, which is valid across the model.
• System.
• Experimental Frame
 It is used to study a system in the real world, such as experimental
conditions, aspects, objectives, etc.
 Basic Experimental Frame consists of two sets of variables.
 The Frame input variable is responsible for matching the inputs applied to
the system or a model. The Frame output variable is responsible for
matching the output values to the system or a model.
• Lumped Model is an exact explanation of a system which follows the
specified conditions of a given Experimental Frame.
• Verification can be done by comparing the consistency of a simulation
program and the lumped model to ensure their performance.
• Validation comparing experiment measurements with the simulation
results within the context of an Experimental Frame. The model is invalid,
if the results mismatch.
Applications of Simulation
System State Variables
• The system state variables are a set of data, required to define the
internal process within the system at a given point of time.
• In a discrete-event model, the system state variables remain constant
over intervals of time and the values change at defined points called event
times.
• In continuous-event model, the system state variables are defined by
differential equation results whose value changes continuously over time.
Following are some of the system state variables −
• Entities & Attributes − An entity represents an object whose value can be
static or dynamic, depending upon the process with other entities.
Attributes are the local values used by the entity.
• Resources − A resource is an entity that provides service to one or more
dynamic entities at a time. The dynamic entity can request one or more
units of a resource; if accepted then the entity can use the resource and
release when completed. If rejected, the entity can join a queue.
• Lists − Lists are used to represent the queues used by the entities and
resources. There are various possibilities of queues such as LIFO, FIFO, etc.
depending upon the process.
• Delay − It is an indefinite duration that is caused by some combination of
system conditions.
System models/Classification of
models
• Discrete models/Discrete-Event Simulation Model − In this model, the
state variable values change only at some discrete points in time where
the events occur. Events will only occur at the defined activity time and
delays.
• Deterministic Models : In these models, input and output variables should
not be random variables and exact functional relationship is used to
describe the models.
• Stochastic Models : In these models, probability functions are used to
describe at least one of the variables or functional relationship.
• Static Models : Representation of a system at a particular time or
representation of a system in which time does not play any role is known
as static simulation model. Monte Carlo Models is an example of static
simulation.
• Dynamic Models : A system which changes over the time is represented
by a dynamic simulation model such as conveyor system in a factory.
Benefits of Simulation
• Discrete vs. Continuous System models −
Discrete system: is affected by the state variable changes at a discrete point
of time. Its behavior is depicted in the following graphical representation.
The bank is an example, since the state variable the number of customer in
the bank changes only when a customer arrives or when the service provided
a customer is completed.
Continuous system:-
is affected by the state variable, which changes continuously as a function
with time. Its behavior is depicted in the following graphical representation.
Types of Simulation
1. Deterministic and Probabilistic Simulation :
• If a process is very complex or consist of multiple stages with
complicated (but known) procedural interactions between them
then deterministic simulation is used.
• A probabilistic simulation follows a certain probability distribution
because one or more independent variables
2. Time Dependent and Time Independent Simulation :
• In time independent simulation it is not necessary to know the
exact time of happening the event. For example, in an inventory
control situation, one may know that the demand of the inventory
is five units per day, but it is not necessary to know that the in
which time the items was demanded.
• In time dependent simulation it is required to know the exact time
when the event is likely to occur. For example, in a queuing
situation the precise time of arrival should be known.
3.Visual Interactive Simulation :
Computer graphic displays are used by the visual
interactive simulation to present the consequences of
change in the value of input variation in the model.
4.Business Games :
Several participants are involved in a business game
simulation model and they are required to play a role in a
game that simulates a realistic competitive situation.
5. Corporate and Financial Simulations : Corporate
planning, especially the financial aspects uses the
corporate and financial simulation. The models
incorporate production, finance, marketing, and possibly
other functions, into one model which can be
deterministic or probabilistic when risk analysis is desired.
Types of Systems
1.Physical or Abstract Systems
• Physical systems are tangible entities. We can touch and feel them.
• Physical System may be static or dynamic in nature. For example, desks
and chairs are the physical parts of computer center which are static. A
programmed computer is a dynamic system in which programs, data, and
applications can change according to the user's needs.
• Abstract systems are non-physical entities or conceptual that may be
formulas, representation or model of a real system.
2. Deterministic and Probabilistic System
• Deterministic system operates in a predictable manner and the
interaction between system components is known with certainty. For
example, two molecules of hydrogen and one molecule of oxygen makes
water.
• Also known as Discrete system.
• Probabilistic System (continuous)
shows uncertain behavior. The exact output is not known. For eg. Weather
forecasting, mail delivery.
3.Open or Closed Systems
• An open system must interact with its environment. It receives inputs from and delivers
outputs to the outside of the system. For example, an information system which must adapt
to the changing environmental conditions, watch, scooter engine.
• A closed system does not interact with its environment. It is isolated from environmental
influences. A completely closed system is rare in reality.Like Pressure cooker,Bulbs,
lamp,electrolyte battery etc.
4. Adaptive and Non Adaptive System
• Adaptive System responds to the change in the environment in a way to improve
their performance and to survive. For example, human beings, animals.
• Non Adaptive System is the system which does not respond to the environment.
For example, machines.
5 .Permanent or Temporary System
• Permanent System persists for long time. For example, business policies.
• Temporary System is made for specified time and after that they are demolished.
6. Social, Human-Machine, Machine System
• Social System is made up of people. For example, social clubs, societies.
• In Human-Machine System, both human and machines are involved to perform a
particular task. For example, Computer programming.
• Machine System is where human interference is neglected. All the tasks are
performed by the machine. For example, an autonomous robot.
7.Man–Made Information Systems
• It is an interconnected set of information resources to manage data for particular
organization, under Direct Management Control (DMC).
• This system includes hardware, software, communication, data, and application for
producing information according to the need of an organization.
Man-made information systems are divided into three types −
• Formal Information System − It is based on the flow of information in the form of
memos, instructions, etc., from top level to lower levels of management.
• Informal Information System − This is employee based system which solves the day to
day work related problems.
• Computer Based System − This system is directly dependent on the computer for
managing business applications. For example, automatic library system, railway
reservation system, banking system, etc.
Types of activity
Endogenous:
Activities are occurring within the system only.
Exogenous:
Activities are occurring within the environment.
Deterministic and stochastic model/ simulation/ variables
An activity whose outcome is known before performing. Eg. Gun Shot form a
gun
An activity whose outcome is not known before performing.
Characterizing a system
Linear System
A system is said to be linear if it obeys the principle of homogeneity and principle of superposition.
• Principle of Homogeneity
The principle of homogeneity says that a system which generates an output y(t) for an input x(t) must
produce an output ay(t) for an input ax(t).
x(t) y(t)
ax(t) ay(t)
• Superposition Principle/ Additive
According to the principle of superposition, a system which gives an output 𝑦1(𝑡) for an input 𝑥1(𝑡) and
an output 𝑦2(𝑡) for an input 𝑥2(𝑡) must produce an output [𝑦1(𝑡) + 𝑦2(𝑡)] for an input [𝑥1(𝑡) + 𝑥2(𝑡)].
if 𝑥1(𝑡) 𝑦1(𝑡)
𝑥2(𝑡) 𝑦2(𝑡)]
Then [𝑥1(𝑡) + 𝑥2(𝑡)] [𝑦1(𝑡) + 𝑦2(𝑡)]
Eg: Wave propagation such as sound and electromagnetic waves.
Electrical circuits composed of resistors, capacitors
Electronic corcuit such as amplifiersand filters
Non-Linear System
A system is said to be a non-linear system if it does not obey the principle of homogeneity and principle
of superposition.
Static and dynamic systems
• It is a system in which output at any instant of time depends on input sample at the same time.
• Example:
• 1) y(n) = 9x(n)
• In this example 9 is constant which multiplies input x(n). But output at nth instant that means y(n)
depends on the input at the same (nth) time instant x(n). So this is static system.
• Why static systems are memory less systems?
Answer:
• Observe the input output relations of static system. Output does not depend on delayed [x(n-k)] or
advanced [x(n+k)] input signals. It only depends on present input (nth) input signal. If output
depends upon delayed input signals then such signals should be stored in memory to calculate the
output at nth instant.
Static systems
• It is a system in which output at any instant of time depends on input sample at the same time as
well as at other times.
• Here other time means, other than the present time instant. It may be past time or future time.
Note that if x(n) represents input signal at present instant then,
1) x(n-k); that means delayed input signal is called as past signal.
2) x(n+k); that means advanced input signal is called as future signal.
Thus in dynamic systems, output depends on present input as well as past or future inputs.
Examples:
1) y(n) = x(n) + 6x(n-2)
Here output at nth instant depends on input at nth instant, x(n) as well as (n-2)th instant x(n-2) is
previous sample. So the system is dynamic.
Question: Why dynamic systems are memory systems?
Real life examples
In engineering static systems do not move, change states, or do not
move /; change states quickly. Examples of static systems include
furniture, dishes, buildings, bridges, etc.
Dynamic systems by their very nature are change states or moving all
the time or must change states be useful. These type of systems
include: vehicles, entertainment equipment (radios, televisions, tape
recorders, etc.), computers and printers, etc.
Time-Invariant System
If the input and output characteristics of a system do not change with
time, the system is called the time-invariant system.
Time-Variant System
A system whose input and output characteristics change with the time
is known as time-variant system.

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System Simulation and Modelling with types and Event Scheduling

  • 2. System • A system is defined as aggregation or assemblage of objects joined in some regular interaction or interdependence. • A collection of entities”eg.people or machine” that act together towards the accomplishment of some logical end. • Any set of interrelated components acting together to achieve a common objective. Examples: 1. Battery • Consists of anode, cathode, acid and other components. • These components act together to achieve one objective like preserving electricity. 2. University • Consists of professors, students and employees. • These objects act together to achieve the objective of teaching & learning process.
  • 3. System Environment The region outside the system is called as the surrounding or environment Boundary It is real or imaginary surface which separates the system from its environment. Example
  • 4. Components of system Outputs and Inputs • The main aim of a system is to produce an output which is useful for its user. • Inputs are the information that enters into the system for processing. eg. Human, machine, money, time etc. Processor(s) • The processor is the element of a system that involves the actual transformation of input into output. • It is the operational component of a system. • Processors may modify the input either totally or partially, depending on the output specification. Control • The control element guides the system. • It is the decision–making subsystem that controls the pattern of activities governing input, processing, and output. • The behavior of a computer System is controlled by the Operating System and software. In order to keep system in balance, what and how much input is needed is determined by Output Specifications. .
  • 5. Environment • The environment is the “supersystem” within which an organization operates. • It is the source of external elements that strike on the system. • It determines how a system must function. For example, vendors and competitors of organization’s environment, may provide constraints that affect the actual performance of the business. Boundaries and Interface • A system should be defined by its boundaries. Boundaries are the limits that identify its components, processes, and interrelationship when it interfaces with another system. • The knowledge of the boundaries of a given system is crucial in determining the nature of its interface with other systems for successful design. Feedback • Feedback provides the control in a dynamic system. • Positive feedback is routine in nature that encourages the performance of the system. No Controller action is required • Negative feedback is informational in nature that provides the controller with information for action. Controller action is required.
  • 6. Modelling and Simulation . Modelling Simulation 1.It is the process of representing a model which includes its construction and working. 2.This model is similar to a real system, which helps the analyst predict the effect of changes to the system. 3.modelling is creating a model which represents a system including their properties. 4.It is an act of building a model 1.It is the operation of a model in terms of time or space, which helps analyze the performance of an existing or a proposed system. 2.simulation is the process of using a model to study the performance of a system. 3. It is an act of using a model
  • 7. Developing Simulation Models • Step 1 − Identify the problem with an existing system or set requirements of a proposed system. • Step 2 − Design the problem while taking care of the existing system factors and limitations. • Step 3 − Collect and start processing the system data, observing its performance and result. • Step 4 − Develop the model using network diagrams and verify it using various verifications techniques. • Step 5 − Validate the model by comparing its performance under various conditions with the real system. • Step 6 − Create a document of the model for future use, which includes objectives, assumptions, input variables and performance in detail. • Step 7 − Select an appropriate experimental design as per requirement. • Step 8 − Induce experimental conditions on the model and observe the result.
  • 8. Performing Simulation Analysis • Step 1 − Prepare a problem statement. • Step 2 − Choose input variables and create entities for the simulation process. There are two types of variables - decision variables and uncontrollable variables. Decision variables are controlled by the programmer, whereas uncontrollable variables are the random variables. • Step 3 − Create constraints on the decision variables by assigning it to the simulation process. • Step 4 − Determine the output variables. • Step 5 − Collect data from the real-life system to input into the simulation. • Step 6 − Develop a flowchart showing the progress of the simulation process. • Step 7 − Choose an appropriate simulation software to run the model. • Step 8 − Verify the simulation model by comparing its result with the real-time system. • Step 9 − Perform an experiment on the model by changing the variable values to find the best solution. • Step 10 − Finally, apply these results into the real-time system.
  • 9. Scope of Simulation in different area • Healthcare (Clinical) Simulators • Computer Simulators • Military Simulations • Finance Simulations • Flight Simulators • Engineering, Technology or Process Simulation
  • 10. Modelling & Simulation ─ Advantages • Following are the advantages of using Modelling and Simulation − • Easy to understand − Allows to understand how the system really operates without working on real-time systems. • Easy to test − Allows to make changes into the system and their effect on the output without working on real-time systems. • Easy to upgrade − Allows to determine the system requirements by applying different configurations. • Easy to identifying constraints − Allows to perform bottleneck analysis that causes delay in the work process, information, etc. • Easy to diagnose problems − Certain systems are so complex that it is not easy to understand their interaction at a time. However, Modelling & Simulation allows to understand all the interactions and analyze their effect. Additionally, new policies, operations, and procedures can be explored without affecting the real system. Modelling & Simulation ─ Disadvantages • Following are the disadvantages of using Modelling and Simulation − • Designing a model is an art which requires domain knowledge, training and experience. • Operations are performed on the system using random number, hence difficult to predict the result. • Simulation requires manpower and it is a time-consuming process. • Simulation results are difficult to translate. It requires experts to understand. • Simulation process is expensive.
  • 11. Models & Events • Object is an entity which exists in the real world to study the behavior of a model. • Base Model is a hypothetical explanation of object properties and its behavior, which is valid across the model. • System. • Experimental Frame  It is used to study a system in the real world, such as experimental conditions, aspects, objectives, etc.  Basic Experimental Frame consists of two sets of variables.  The Frame input variable is responsible for matching the inputs applied to the system or a model. The Frame output variable is responsible for matching the output values to the system or a model. • Lumped Model is an exact explanation of a system which follows the specified conditions of a given Experimental Frame. • Verification can be done by comparing the consistency of a simulation program and the lumped model to ensure their performance. • Validation comparing experiment measurements with the simulation results within the context of an Experimental Frame. The model is invalid, if the results mismatch.
  • 13. System State Variables • The system state variables are a set of data, required to define the internal process within the system at a given point of time. • In a discrete-event model, the system state variables remain constant over intervals of time and the values change at defined points called event times. • In continuous-event model, the system state variables are defined by differential equation results whose value changes continuously over time. Following are some of the system state variables − • Entities & Attributes − An entity represents an object whose value can be static or dynamic, depending upon the process with other entities. Attributes are the local values used by the entity. • Resources − A resource is an entity that provides service to one or more dynamic entities at a time. The dynamic entity can request one or more units of a resource; if accepted then the entity can use the resource and release when completed. If rejected, the entity can join a queue. • Lists − Lists are used to represent the queues used by the entities and resources. There are various possibilities of queues such as LIFO, FIFO, etc. depending upon the process. • Delay − It is an indefinite duration that is caused by some combination of system conditions.
  • 14. System models/Classification of models • Discrete models/Discrete-Event Simulation Model − In this model, the state variable values change only at some discrete points in time where the events occur. Events will only occur at the defined activity time and delays. • Deterministic Models : In these models, input and output variables should not be random variables and exact functional relationship is used to describe the models. • Stochastic Models : In these models, probability functions are used to describe at least one of the variables or functional relationship. • Static Models : Representation of a system at a particular time or representation of a system in which time does not play any role is known as static simulation model. Monte Carlo Models is an example of static simulation. • Dynamic Models : A system which changes over the time is represented by a dynamic simulation model such as conveyor system in a factory. Benefits of Simulation
  • 15. • Discrete vs. Continuous System models − Discrete system: is affected by the state variable changes at a discrete point of time. Its behavior is depicted in the following graphical representation. The bank is an example, since the state variable the number of customer in the bank changes only when a customer arrives or when the service provided a customer is completed. Continuous system:- is affected by the state variable, which changes continuously as a function with time. Its behavior is depicted in the following graphical representation.
  • 16. Types of Simulation 1. Deterministic and Probabilistic Simulation : • If a process is very complex or consist of multiple stages with complicated (but known) procedural interactions between them then deterministic simulation is used. • A probabilistic simulation follows a certain probability distribution because one or more independent variables 2. Time Dependent and Time Independent Simulation : • In time independent simulation it is not necessary to know the exact time of happening the event. For example, in an inventory control situation, one may know that the demand of the inventory is five units per day, but it is not necessary to know that the in which time the items was demanded. • In time dependent simulation it is required to know the exact time when the event is likely to occur. For example, in a queuing situation the precise time of arrival should be known.
  • 17. 3.Visual Interactive Simulation : Computer graphic displays are used by the visual interactive simulation to present the consequences of change in the value of input variation in the model. 4.Business Games : Several participants are involved in a business game simulation model and they are required to play a role in a game that simulates a realistic competitive situation. 5. Corporate and Financial Simulations : Corporate planning, especially the financial aspects uses the corporate and financial simulation. The models incorporate production, finance, marketing, and possibly other functions, into one model which can be deterministic or probabilistic when risk analysis is desired.
  • 18. Types of Systems 1.Physical or Abstract Systems • Physical systems are tangible entities. We can touch and feel them. • Physical System may be static or dynamic in nature. For example, desks and chairs are the physical parts of computer center which are static. A programmed computer is a dynamic system in which programs, data, and applications can change according to the user's needs. • Abstract systems are non-physical entities or conceptual that may be formulas, representation or model of a real system.
  • 19. 2. Deterministic and Probabilistic System • Deterministic system operates in a predictable manner and the interaction between system components is known with certainty. For example, two molecules of hydrogen and one molecule of oxygen makes water. • Also known as Discrete system. • Probabilistic System (continuous) shows uncertain behavior. The exact output is not known. For eg. Weather forecasting, mail delivery.
  • 20. 3.Open or Closed Systems • An open system must interact with its environment. It receives inputs from and delivers outputs to the outside of the system. For example, an information system which must adapt to the changing environmental conditions, watch, scooter engine. • A closed system does not interact with its environment. It is isolated from environmental influences. A completely closed system is rare in reality.Like Pressure cooker,Bulbs, lamp,electrolyte battery etc.
  • 21. 4. Adaptive and Non Adaptive System • Adaptive System responds to the change in the environment in a way to improve their performance and to survive. For example, human beings, animals. • Non Adaptive System is the system which does not respond to the environment. For example, machines. 5 .Permanent or Temporary System • Permanent System persists for long time. For example, business policies. • Temporary System is made for specified time and after that they are demolished. 6. Social, Human-Machine, Machine System • Social System is made up of people. For example, social clubs, societies. • In Human-Machine System, both human and machines are involved to perform a particular task. For example, Computer programming. • Machine System is where human interference is neglected. All the tasks are performed by the machine. For example, an autonomous robot. 7.Man–Made Information Systems • It is an interconnected set of information resources to manage data for particular organization, under Direct Management Control (DMC). • This system includes hardware, software, communication, data, and application for producing information according to the need of an organization.
  • 22. Man-made information systems are divided into three types − • Formal Information System − It is based on the flow of information in the form of memos, instructions, etc., from top level to lower levels of management. • Informal Information System − This is employee based system which solves the day to day work related problems. • Computer Based System − This system is directly dependent on the computer for managing business applications. For example, automatic library system, railway reservation system, banking system, etc.
  • 23. Types of activity Endogenous: Activities are occurring within the system only. Exogenous: Activities are occurring within the environment. Deterministic and stochastic model/ simulation/ variables An activity whose outcome is known before performing. Eg. Gun Shot form a gun An activity whose outcome is not known before performing.
  • 24. Characterizing a system Linear System A system is said to be linear if it obeys the principle of homogeneity and principle of superposition. • Principle of Homogeneity The principle of homogeneity says that a system which generates an output y(t) for an input x(t) must produce an output ay(t) for an input ax(t). x(t) y(t) ax(t) ay(t) • Superposition Principle/ Additive According to the principle of superposition, a system which gives an output 𝑦1(𝑡) for an input 𝑥1(𝑡) and an output 𝑦2(𝑡) for an input 𝑥2(𝑡) must produce an output [𝑦1(𝑡) + 𝑦2(𝑡)] for an input [𝑥1(𝑡) + 𝑥2(𝑡)]. if 𝑥1(𝑡) 𝑦1(𝑡) 𝑥2(𝑡) 𝑦2(𝑡)] Then [𝑥1(𝑡) + 𝑥2(𝑡)] [𝑦1(𝑡) + 𝑦2(𝑡)] Eg: Wave propagation such as sound and electromagnetic waves. Electrical circuits composed of resistors, capacitors Electronic corcuit such as amplifiersand filters Non-Linear System A system is said to be a non-linear system if it does not obey the principle of homogeneity and principle of superposition.
  • 25. Static and dynamic systems • It is a system in which output at any instant of time depends on input sample at the same time. • Example: • 1) y(n) = 9x(n) • In this example 9 is constant which multiplies input x(n). But output at nth instant that means y(n) depends on the input at the same (nth) time instant x(n). So this is static system. • Why static systems are memory less systems? Answer: • Observe the input output relations of static system. Output does not depend on delayed [x(n-k)] or advanced [x(n+k)] input signals. It only depends on present input (nth) input signal. If output depends upon delayed input signals then such signals should be stored in memory to calculate the output at nth instant. Static systems • It is a system in which output at any instant of time depends on input sample at the same time as well as at other times. • Here other time means, other than the present time instant. It may be past time or future time. Note that if x(n) represents input signal at present instant then, 1) x(n-k); that means delayed input signal is called as past signal. 2) x(n+k); that means advanced input signal is called as future signal. Thus in dynamic systems, output depends on present input as well as past or future inputs. Examples: 1) y(n) = x(n) + 6x(n-2) Here output at nth instant depends on input at nth instant, x(n) as well as (n-2)th instant x(n-2) is previous sample. So the system is dynamic.
  • 26. Question: Why dynamic systems are memory systems? Real life examples In engineering static systems do not move, change states, or do not move /; change states quickly. Examples of static systems include furniture, dishes, buildings, bridges, etc. Dynamic systems by their very nature are change states or moving all the time or must change states be useful. These type of systems include: vehicles, entertainment equipment (radios, televisions, tape recorders, etc.), computers and printers, etc. Time-Invariant System If the input and output characteristics of a system do not change with time, the system is called the time-invariant system. Time-Variant System A system whose input and output characteristics change with the time is known as time-variant system.