Simulation and Modelling Reading Notes.pptx

COMP 494: Simulation and Modelling
• Dr.Pheobe N Fedha

• Introduce Modelling, simulation
• Develop appreciation for the need for
simulation
• Applications
• The modelling cycle

Basics of modeling and simulation
• Man has the ability to define what is
likely to happen in the future and to
chose among alternatives.
• To reduce the level of disparity between
outcome and reality, we can use a
decision analysis and support tools to
enable evaluate, compare and
optimise among alternatives.

• Simulation model: is a computer model that
imitates real life situation.
• A simulation model involves generation of
artificial history of a system and drawing
inferences from it.
• This way you are able to see how the outputs
vary as a function of the varying inputs.

When you run a simulation;
• You allow random variables to take on various
values and you keep track of any resulting output
variables of interest.
• Like mathematical models it explicitly incorporates
uncertainty in one or more complex input
variables.
• The model takes the form of assumptions
concerning the operations of a system. i.e.
mathematical, logical, symbolical relationships
between the entities.

• Simulation of a system is the operation of a
model in terms of time or space, which helps
analyze the performance of an existing or a
proposed system.
• Perform experiments to understand the
behavior of system and evaluating new
strategies. By observing
–events, processes, properties and behavior
of system with a computer model.

• In Simulation we can use mathematical
model to determine the response of the
system in different situations in a
Computer system.
• Simulation can be viewed as a numerical
technique for solving complicated
probability models, ordinary differential
equation and partial differential
equation.

• Through experimentation and
observation, scientists develop theories
that are then tested with additional
experimentation.
• Scientists and engineers translate
mathematical expressions into computer
codes that allow imitate the operation of
the system over time.

• The cause and effect relationships
associated with those discoveries are
represented by;
• mathematical expressions to
approximate the behavior of the
system under study.
• Simulation provides insight into the
processes associated with the model.

• Scientific visualization is concerned with data
extraction to determine which data values
are important and which are not.
• Data manipulation convert the data to other
forms or to different units to enhance
display. i.e.
–A two dimension graph
–A three dimension image
• Visual representation helps identify
important features of the model output

A simulation
• A simulation is the imitation of the
operation of facility, or real world
process over time.
–know intricacies
–know measures of performance

Simulation
• According to Shannon : "Simulation is the process
of designing a model of a real system and
conducting experiments with this model for the
purpose of understanding the behavior (with the
limits imposed by a criterion or set of criteria) for
the operation of the system".
• This can assist in the design, creation, and
evaluation of complex systems.

• Designers, program managers, analysts,
and engineers use computer simulation and
modeling to understand and evaluate ‘what
if’ case scenarios.
It is useful when;
• Changes to the actual system are difficult to
implement,
• involve high costs, or are impractical
e.g. weather forecasting, flight simulators
and car crash modeling.

• The model takes a set of assumptions /
approximations concerning the operation of
the system i.e.
–Mathematical relationships
–Logical relationships(Process)
–Symbolic relationships
• If the model structure is simple one can use
mathematical models to answer questions of
interest.

Through system simulation:
• We can Perform experiments to understand
the behavior of a system and evaluate new
strategies.
–Live
–Virtual
–Constructive
This can be done by observing events,
processes, properties and behavior of system
with a computer model.

Formal Definition(s)
• Simulation is a technique for studying
real-world dynamical systems by
imitating their behavior using a
mathematical model of the system
implemented on a digital computer.

• In DIP we can translate mathematical expressions
into computer codes to imitate the operation of
the system over time.
f(x,y)=r(x,y)*i(x.y) = analytical solutions
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IN MATLAB
• Simulink is an interactive environment
for modeling, simulating, and analyzing
dynamic, multidomain systems.
• Simulink lets you build block diagrams,
simulate the system’s behavior,
evaluate its performance, and refine
the design.

• Simulink integrates seamlessly
with MATLAB, providing you with
immediate access to an extensive
range of analysis and design tools.
• These benefits make Simulink the
tool of choice for control system
design, DSP design,
communications system design,
and other simulation applications.

• No universal models exist that can
accurately simulate any business
process.
• Depending on the industry or the
nature of the task, the process may
change over time or contain many
unique unknowns which require
simulation.
• A model is a physical,
mathematical, or otherwise logical
representation of a system, entity,
phenomenon, or process.

The nature of simulation
• Most complex systems require models that
are complex to be valid.
• Uncertainty is ever-present arising from the
model itself, theoretical flaws, design flaws,
and logical errors.
• These must be studied via simulation i.e.
evaluate the model numerically and collect
data to estimate model characteristics.

Example consider:
• If Egerton University would like to expand
its existing affiliated colleges. The question
would be whether;
• To build and see if it works or
• Simulate the current scenario and expand its
operations to help investigate many other
issues along the way quickly and cheaply.

• Modeling is the process of representing a
model its construction and its workability.
• Modeling is creating a model which
represents a physical system including its
properties.
• The model should be similar to a real system,
to help the analyst predict the effect of
changes to the system.

• A computer model: is a simulation of a situation
in the real world or an imagery which has
parameters that the user can alter
• Modeling and simulation: Is a discipline for
developing a level of understanding of the
interaction of the part of a system and the
system as a whole.
• Modeling and simulation (M&S) is the use of a
physical or logical representation of a given
system to generate data and help determine
decisions or make predictions about the
system.

To measure and estimate performance,
improve operations and prepare for failures

• Drug screening is another example of how
computer modeling can shorten the time for
discovery.
• The drug screening pipeline requires a model of a
target protein or macromolecular structure that is
associated with a specific disease mechanism.
• A list of potential candidate compounds is tested
to see which have the highest affinity to bind to
that protein, potentially inhibiting the medical
problem (COVID 19).

• Another example is when we want to decide
on a travel route that gets us to several
shopping locations faster or with the fewest
traffic headaches.
• To do this, we analyze information from
previous trips to make an informed decision
about where there may be heavy traffic,
construction, or other impediments to our
trip

• A model describes the mathematical
relationship between inputs and outputs.
• A model is a pattern, plan, representation
or description designed to show the main
object, workings of an object ,system or
concept.
• A representation of one or more concepts
that may be realized in the physical world

MODEL
• A miniature(abstract) representation of
something
• A pattern of something to be made
• An example of imitation
• A representation used to visualize something
• A mathematical model is a representation of the
behavior of real objects and phenomena in
mathematical language. Represented in form of;
(Algebraic, differential and integral equations,
algorithms, formulae or theorems).

MODEL:
A simplified representation of a system at some
particular point in time or space intended to
promote understanding of the real system
(Bellinger 2004).
An abstraction of a system, (Dori 2002); aimed at
understanding, communicating, explaining, or
designing aspects of interest of that system.
Every model; is a view of reality; has a purpose
and employs abstraction(ignores the irrelevant),
structure and information hiding.

• Models allow simulating and analyzing the
system. They are never exact
• Modeling depends on your goal
–A single system may have many models
–Always understand the purpose of the model
–Large libraries of standard model templates exist
The main goals of modelling is ;
• Conceptual analysis
• Detailed analysis

A Simulation model allows;
• An entire distribution of results not simply a single
bottom line result.
• Each different set of values for the uncertain
quantities are to be considered a scenario.
• Companies generate multiple scenarios each
leading to a particular output.
• At the end you see a whole list of distribution
outputs not a single best guess. i.e the average
output, worst output and best output.

The simulation model allows;
• Determine how sensitive a system is to
changes in operating conditions.
• It enables managers to answer what if
questions without actually changing or
building a physical system.

• A spreadsheet simulation is similar to
other modelling applications. Where you
start with input variables and relate to
appropriate excel formulas to produce
output variables of interest.
• Simulation uses random numbers to drive
the whole process. These random
numbers are generated with special
functions.

Use Simulation to
• Study internals of a complex system e.g.
biological system
• Optimise an existing design e.g. routing
algorithms, assembly line
• Examine effect of environmental changes e.g.
weather forecasting
• When it is impossible to observe/influence/build
the system

Use Simulation to
• Know if the system is dangerous or destructive e.g.
atom bomb, atomic reactor, missile launching
• Study importance of variables
• Verify analytic solutions (theories)
• Test new designs or policies
• To inspect system internals that might not
otherwise be observable

Use Simulation to
• Get insights into system behavior. By
allowing one to ask what if questions about
how the system change
under different circumstances of model and
its underlying mathematical structure.
• Adjust system parameters in the simulation
model, allow assessment of sensitivity i.e.
scale of impact on the overall system
behavior.

Use Simulation to;
• Verify analysis of a complex system, or as a
teaching tool to provide insight into
analytical techniques
• To instruct, or avoid tying up or damaging an
expensive, actual system (e.g., a flight
simulation vs. use of multimillion dollar
aircraft)

Advantages of Modelling and Simulation
• They are cheaper, safer.
• Faster or slower
• More configurable and controllable
• They are less expensive. E.g. practical simulators are
used to train pilots.
• Direct Experimentation can be disruptive
• Direct Experimentation can be dangerous

Advantages of Modeling 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

Advantages of Simulations
• It is used to verify analytical solutions
• They are easier to control than the real world coun
terparts.
• Animation shows the operations so that a plan
can be visualised.
• Designed for training: Learning without the cost
and disruption i.e. on the job training

• Time scale can be altered as needed i.e. time
compression or expansion
• It allows comparisons of alternative designs or
operating policies
• When mathematical analysis methods are not
available, simulation may be the only investigation
tool
• When mathematical analysis methods are available
but are so complex simulation may provide a solution

• Models help us frame our thinking about ob
jects in the real world.
• Simulated system imitate the operation of
actual system over time .
• Conclusions about actual system
characteristics can be inferred i.e. the actual
system (real system) is compared with
simulation
•

• Artificial history of system can be generated
and observed
• Helps study experimentation with internal
interactions of a complex system or a
subsystem within a complex system.
–Internal (perhaps unobservable) behavior of
system can be studied

• Informational, organizational and
environmental changes can be simulated and
the effect observed
• By varying inputs and observing the
resulting output valuable insights may be
obtained into which variables are most
important and how variables interact.

• The knowledge gained can be of great
value in suggesting areas of
improvement in the system under
investigation
• Used to experiment with new designs or
policies prior to implementation so as to
prepare for what may happen.

• 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.

• It provides a way to study complex, real world systems
that cannot be accurately described by a
mathematical model that can be evaluated
analytically.
• Allows estimation of an existing system under some
projected set of operating conditions.
• Allows comparisons of alternate proposed system
designs to see which one best meets a specified
requirement.
• Allows study a system with a long time frame in
compressed time, or alternatively study detailed
working of a system in expanded time.

Disadvantages:
• Manpower and time-consuming
• Each stochastic simulation provides only
estimates of solution, only solves one
parameter at a time, can take a large amount
of development and/or computer time.
• Don’t use computer simulation if common-
sense or analytical solution is available, or if
resources are insufficient, or if simulation
costs outweigh benefits.

Disadvantages:
• Provides only individual, not general solutions
• Mistakes may be made in the programming or
rules of the simulation or model.
• The cost of a simulation or running several
different simulations model can be high.
• Simulation results are difficult to translate. It
requires experts to understand and Time to make
sense of the results.

Disadvantages:
• 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.

58
Pitfalls/risks to the successful completion of a
simulation study
 Failure to have a well-defined set of objectives at
the beginning of the simulation study
 Inappropriate level of model detail
 Failure to communicate with management
throughout the course of the simulation study
 Misunderstanding of simulation by management
 Treating a simulation study as if it were primarily
an exercise in computer programming

59
Pitfalls/risks to the successful completion of
a simulation study
 Using the wrong performance measure
 Failure to collect good system data
 Inappropriate simulation software
 Failure to have people with a knowledge of simulation
methodology and statistics on the modeling team
 Ignorant use of simulation software products whose
complex statement may not be well documented and may
not implement the desired modeling logic

Don’t use simulation is
• If t is easy to perform direct experiments
• If system behavior is too complex
• If no data is available about the system not
even estimates.

APPLICATION AREAS
• Designing and analyzing manufacturing systems
• Evaluating military weapons systems or their logistics
requirements
• Determining hardware requirements or protocols for
communications networks
• Determining hardware and software requirements for a
computer system
• Designing and transportation systems such as airports,
freeways, ports, and subways
• Evaluating designs for service organizations such as call
centers, fast-food restaurants, hospitals, and post offices
• Reengineering of business processes
• Determining ordering policies for an inventory system
• Analyzing financial or economic systems
61

Application Areas
• Military applications,
• training & support,
• designing semiconductors,
• telecommunications,
• civil engineering designs & presentations,
• E-business models.

• A model, is a simplification of a real
system for the purpose of studying
• It must contain sufficient details to
permit valid conclusions to be drawn
about the real system.
• It is a process of representing a system
with a specific tool to study its behavior.

• A model is a pattern, plan,
representation or description
designed to show the main object,
workings of an object ,system or
concept. Models give us something
to;
 Think about
Communicate about

MODEL
• A model is a miniature (abstract)
representation of something OR
• A representation of an object, a system or an
idea in some form other than that of the
entity itself.

• Object is an entity which exists in the real world
that enable us study the behavior of a model.
Or flow units that is translated with time.
• Conceptual/Base Model is a hypothetical
explanation of object properties and its behavior,
which is valid across the model. It is highly abstract
where we hide complexities at an initial stage.
• It shows key concepts of an explanation theory
and the hypothesized relationship between
them.

Conceptual modeling
Is the process of developing an abstract model or
graphic representation using real world concepts or
ideas.
Various assumptions are made on how the system
functions, they illustrate the dominant processes on
a system and how they are linked.
The processes may include known change in the
system or may encompass the consequence of
change in the factors themselves.

Conceptual models
• Conceptual models help stakeholders better
understand a situation and are used as a
starting point in participatory or
collaborative modeling.
• Stakeholder groups establish a common
language that encourages innovative
planning, evaluation, and collaborative
decision-making.

• Scientists need to decide whether to build
the model that contains as much detail as
possible. (Closest to the real system and so the
most accurate).
• The problem is
–We have limited knowledge of the real
system and limited time,
–The real system rarely exists at the time of
modeling (it is a proposed world) and a
decision needs to be made given the time
frame.

• To develop a simplified model, we
need to determine the level of
abstraction at which to work.
•Develop the hypothesis
•Identify concepts to study
•Interpret research results

CONCEPTUAL DATA MODEL?
It is a pictorial representation of
entities and its relationships
• Only entities are visible
• Easily understood
• Highly abstract
• There is abstract relationship
• No software is required to define the
conceptual data model.

The hardest part is in building the
appropriate conceptual model and
assembling data

A conceptual data model
A conceptual data model identifies the highest
level of relationships between different
entities.
Features;
• Important entities and relationships
• No attribute is specified
• No primary keys

• Data model: It is a pictorial
representation of tables it represents
the relationship between tables and it is
easily understood.

Conceptual Dictionary Def
• Conceptual of, relating to, concerned
with, concepts, abstract.
• It concerns with the definitions or
relations of concepts rather than facts.
• Concept is an idea of what something is
or how it works; a mental image.

Developing Conceptual Model
• It consist of the following
components:
–system entities,
–input variables
–Functional relationships.
–Performance measures,

• Conceptual modeling: (Robinson 2008a)‘…
Is a non-software specific description of the
computer simulation model (that will be, or
has been developed), describing the
objectives, inputs, outputs, content,
assumptions and simplifications of the
model.’
• It consists of concepts used to help
people know, understand, or simulate a
subject the model represents.

A conceptual model, when implemented properly will ,
• Enhance an individual's understanding of the
representative system
• Facilitate efficient communication of system
details between stakeholders
• Provide a point of reference for system designers
to extract system specifications
• Document the system for future reference and
provide a means for collaboration

To model answer these questions;
–What content will the conceptual
model represent?
–How will the conceptual model be
presented?
–Who will be using or participating
in the conceptual model?

• How will the conceptual model describe
the system?
• What is the focus of observation?
• Will the conceptual model be efficient or
effective in describing the system?

Logical Dictionary def;
Logical;
• Of or according to the rules of logic or
formal argument; characterized by or
capable of clear, sound reasoning.
• Synonyms: natural, reasonable, sensible,

Logical data model
• A model of some user domain complete
and understandable in the detail needed
to represent that domain, built
according to and consistent with some
formal modelling scheme with a well
defined scope.
• i.e. It must be understandable: defined,
documented and communicated.

Logical model
• It describes the data in much more detail form
compared to conceptual data model without
any dependency on how it will be in the
physical data model.
• The Components include;
–Primary and foreign key
–Relationships between entities
–Entity attributes
–Tables

Characteristics of Logical Model
• User friendly attribute names
• More detailed than conceptual model
• More effort is required than the conceptual
model
• Database-agnostic (capacity of software to
function with any vendor's database
management system (DBMS)).
• One can use data modelling tools e.g, ERWin,
Powerdesigner.

Logical Model
• Like the conceptual model the logical model
defines what to store but not how to store.
• It is platform-independent representation
of the entities and their relationships.
• It is adapted to the type of data storage that
is used (relational database) e.g. MySQL,
Oracle etc.

Logical model
• It does not handle physical storage like
views or indexes.
• This stage of data modeling provides
organizations with insight pertaining to the
limitations of their current technologies.

Physical model ( Tables, columns, data Types etc)
Physical model should have sufficient
details to implement.
It is a stored representation of logical
model.
It deals with how data is encoded and
stored.

Physical model ( Tables, columns, data Types etc)
It is implemented in some data system
dealing with storage, processing
performance, volumetric (time and
space), partitioning and distribution.

Physical Model
• Specifies everything related to how the data
is defined in the logical model and stored
• It is enterprise wide and more detailed.
• It is adapted to specific DBMS to be used
• Objects such as Index, Indices, constraints,
triggers, security, keys, indexes, views are
dealt with

• They are used to define the implementation of
logical data models employing a particular
database management system (DBMS).
• They are built with the current or expected (as
is/to be) - technological capabilities.
• Database developers and analysts work with
physical data models to enact the ideas and
processes refined by conceptual and logical
models.

DEFINITIONS
• A system is a collection of entities that
act and interact together under some
definite conditions, that exist in the real
world. OR
• System: any set of interrelated
components acting together to achieve a
common objective.

System Components
System
Entity
Attribute
State
Activity
Event
98
Object of interest in
the system
Property of an
entity
Collection of variables
necessary to describe the
system at a particular time,
An action that takes place
over a period of specified
length and changes the state
of the system
An instantaneous
occurrence that may
change the state of
the system

System Components Example
Queuing
System
Packet
Entity
Length,
Destination
Attribute
Nof Packets
State
FIFO
Activity
Packet
Arrival
Event
99

• A University system consists of professors,
students and employees these objects act
together to achieve the objective of teaching
& learning process.
• A system consists of input elements that
cause changes in the systems variables.
–The inputs are the experimental factors
that are altered in order to try and achieve
the modeling objectives.

• Output Response Systems (process) define
the relationship between the inputs and
output
–The outputs are the statistics that inform us as
to whether the modeling objectives were
achieved.
–Example: The time required to clear all
students from the University system after four
years and if not, why it is not being achieved.
• Knowing the objectives, inputs and outputs
of the model informs the content of the
model.

• In a health setup; the model must be
able to receive the inputs (e.g. it must
model the consultation rooms) and it
must provide the outputs (e.g. it must
model the flow of patients until all have
exited the system).
• The model content can be thought of in
terms of the model scope (what to
model) and the level of detail (how to

• The state of a system is a collection of
variables and their values needed to describe
the system at any particular time.
• State variables define the state of the system
e,g length of the queue.
• A variable is a mathematical quantity that
defines one key aspect of a system. A
variable may be: Endogenous, Exogenous.
• An endogenous variable (dependent) these are
influenced by one or more independent
variables. 105

• Endogenous(dependent variables): If the value
changes it is because there are changes to its
relationships with other variables in the same
model.
• The amount of crop yields is dependent on many
other variables, such as the weather, soil fertility,
water availability, pests, and diseases.
• Supply and demand factors depend on change in
income, changes in consumer preference, growth
in the economy, availability of alternative goods
and services.

• An exogenous variable is a variable that
depends on external factors outside of
the model, so it is not impacted by
variables within the model.
• E.G. rainfall is exogenous to the process
of farming and crop output.
• Assumptions are made either when
there are uncertainties or beliefs about
the real world being modeled.

Modelling Concepts
• Creating, testing, and applying
mathematical models require an
iterative process.
• It starts with an initial set of
simplifying assumptions , testing,
alteration, and application of the
model

109
To create a model;
• make assumptions / approximations,
both logical and mathematical, about
how the real system works
• Distill from the mass of details about the
real system, those aspects that are
essential in studying the system
• Use mathematical methods to answer
questions of interest

112
Steps in a Simulation Project
8. Experimental Design
9. Model runs and analysis
10. More runs
No
Yes
3. Model conceptualization 4. Data Collection
5. Model Translation
6. Verified
7. Validated
Yes
No
No No
Yes
Phase 3
Experimentation
1. Problem formulation
2. Set objectives and overall project plan
Phase 1
Problem Definition
Phase 2
Model Building
11. Documentation, reporting
and
implementation
Phase 4
Implementation

Steps to develop a simulation model.
Problem formulation: Clearly state the problem.
• Step 1: Examine the problem. Understand
the problem and choose its classification
accordingly, such as deterministic or
stochastic.
–Identify the problem with an existing
system or set of requirements of a
proposed system.
• Prepare a problem statement.

Step 2: Setting of objectives and overall
project plan:
• Analyze the problem and define the
objectives of the model.
–This include a review of the literature to
uncover previous research on the topic,
experimental or field-measured data
showing various states of the system and
the measured outcomes, mathematical
representations of the system derived from
theories, and previous modeling efforts

• Several questions must be addressed while
considering the model objectives:
• What are the outcomes that we expect the
model to predict?
• Are we interested in every possible outcome
or is there a subset of conditions that would
satisfy our model objectives? E.g average,
sum etc.

• What level of accuracy is required for
the predicted outcomes?
– This will impact the nature of
simplifying assumptions,
–input data, and
–computing algorithms that are
required to build the model.

Step 3: Model conceptualization i.e. establish
a reasonable model.
• Design the conceptual model while taking care of
the existing system factors and limitations.
• Choose input variables and create entities
for the simulation process.
–Consider decision variables and uncontrollable
variables.
• Decision variables are controlled by the
programmer, these are variables that change
or affect the solution
• Uncontrollable variables are the random
variables.

• Step 4: Collect data:
– Collect data as per the system behavior
and future requirements.
– Analyze the system features, its
assumptions and necessary actions to be
taken to make the model successful.
– Determine the variable names, functions,
its units, relationships, and their
applications as used in the model.

Data collection
• Collect the data necessary to run the simulation
(such as arrival rate, arrival process, service
discipline, service rate etc.).
• Collect and start processing the system data,
observing its performance and result.
– Create constraints on the decision variables by
assigning it to the simulation process.
• Provide recommendations after completing the
conceptual process related to the model. It
includes investment, resources, algorithms,
techniques, etc.

Step 5: Model translation convert the
model into a programming language.
• Develop the model using network
diagrams and verify it using various
verifications techniques.
.

Verification
• The process of determining whether a
simulation computer program works as
intended and that data accurately represent
the developer’s conceptual description and
specifications.
• Compare the model’s implementation with
the developer's conceptual description and
specifications. (debugging).
• Determine the output variables

Verification
• Answers the question is the system built
right?
• Has the model and simulation been built
so that they fully satisfy the developer’s
intent (as indicated in specifications)?
• Verification (efficiency)
–Is the model correctly built /
programmed?
–Is it doing what it is intended to do?

VERIFICATION
• It includes inspection by QA engineers to
confirm that product or service meets the
specified specifications.
• Also known as qualification and must pass
before validation.
• Is done through inspection against drawings,
document reviews, visual checks through
actual site visits and alternative calculations

VALIDATION
Validate the model by comparing its
performance under various conditions
with the real system.

Step 6: Validation
• Collect data from the real-life system to input
into the simulation
• Answer the question are we building the
right system/product.
• This include dynamic testing or simulations
of product or service to confirm that they
meet product applications or purpose.

Validation;
• Confirms product or service performance in
actual working or usage conditions.
• Is done through human based testing or
computer based simulations by testing or
simulation teams.
• Is initiated only after product or service
passes verification

Validation - an Iterative Calibration
Process

Validation
• Validation is the process of comparing
two results i.e. compare the
representation of a conceptual model to
the real system.
• The process of determining whether the
conceptual model is an accurate
representation of the actual system
from the perspective of the intended
uses of the model.

Validation
• Did I build the right thing? Will the
model or simulation be able to
adequately support its intended use?

132
–Is the right model built?
–Does the model adequately
describe the reality you want to
model?
–Does the involved decision makers
trust the model?
Validation (effectiveness)

KEY DIFFERENCE
• Verification process includes checking of
documents, design, code and program whereas
Validation process includes testing of the actual
product.
• Verification does not involve code execution while
Validation involves code execution.
• Verification checks whether the software confirms
a specification whereas Validation checks whether
the software meets the requirements and
expectations.

KEY DIFFERENCE
• Verification finds the bugs early in the
development cycle whereas Validation finds the
bugs that verification can not catch.
• In software testing, Verification process targets
on software architecture, design, database, etc.
while Validation process targets the actual
software product.
• Validation ensures that the simulation model
replicates the real system's behavior, while
verification ensures that the model is implemented
correctly. Both are crucial to building confidence in
the simulation results and supporting decision-
making."

KEY DIFFERENCE
• Verification is done by the QA team
while Validation is done by the
involvement of testing team with QA
team.
• Verification process comes before
validation whereas Validation process
comes after verification.

Can a product pass verification and fail in
validation
• When product application or usage condition
are not factored out while finalising product
or service requirements.
• Wrong assumptions about real working
conditions while finalising product or service
requirements.

To ensure the reliability of simulation
To ensure the reliability of simulation results,
implement thorough validation by comparing model
outputs with real-world data.
conduct verification to ensure the correct
implementation of the model.
Cross-verification with multiple sources of data and
expert opinions further enhances the reliability of
the simulation results.

Step 7: Experimental design:
• Select an appropriate experimental design as
per requirement.
–Choose an appropriate simulation software
to run the model.
•Determine how many runs? For how long?
•What kind of input variations?
•Production runs and analysis: Actual running
the simulation, collect and analyze the output.
•Repetition: Repeat the experiments if necessary.

Step 8: Document and report:
Create a document of the model for
future use, which include objectives,
assumptions, input variables and
performance in detail.
–Develop a flowchart showing the
progress of the simulation process.
–Document and report the results.

Summary steps in a Simulation Study
Problem formulation: Clearly state the
problem.
Setting of objectives and overall project plan:
How we should approach the problem.
Model conceptualization: Establish a
reasonable model.
Data collection: Collect the data necessary to run
the simulation (such as arrival rate, arrival
process, service discipline, service rate etc.).
Model translation: Convert the model into a
programming language.

Steps in a Simulation Study
Verification: Verify the model by
checking if the program works properly.
Use common sense.
Validation: Check if the system
accurately represent the real system.
Experimental design: How many runs?
For how long? What kind of input
variations?

Steps in a Simulation Study
Production runs and analysis: Actual
running the simulation, collect and
analyze the output.
Repetition: Repeat the experiments if
necessary.
Document and report: Document and
report the results.

144
• General Principles
– The system is broken down into suitable
components or entities
– The entities are modeled separately and are
then connected to a model describing the
overall system
• The basic principles apply to all types of
simulation models
– Static or Dynamic
– Deterministic or Stochastic
– Discrete or continuous
Building a Simulation Model

• One may go through several
iterations before the model provides
sufficiently accurate results.
• This can be validated against
available experimental or field data
to provide a quantitative assessment
of model accuracy.

• Judgment of whether a model is
giving reasonable results is
sometimes as much an art as a
science.
• Confidence in that judgment is a
function of the experience of the
modeler and the breadth and depth of
the previous research about the system
under study.

Techniques for Validation
• White box testing methods, classes,
details of implementation. This includes
unit and integration testing.
• White box testing deals with the internal
structure/design/ implementation of the
item being tested and details are
known to the tester.
• Implementation and impact of the code
are tested.

Black box testing:
• Internal structure/design/implementation
of the item being tested is not known to
the tester.
• Only the external design and structure are
tested. Test based on input output (not
concerned with internal details)
–while designing the model discuss with the
system experts
– The model must interact with the client
throughout the process.
– The output must be supervised by system
experts.

DEFINITIONS
• A system is a simplified representation
of reality.
• A system: Is any set of interrelated
components acting together to achieve a
common objective.
• It is a series of selected, chosen elements with
specified boundaries and has pre-determined time
characteristics .

• A system is often affected by changes
occurring outside the system: system
environment.
–Factory : Arrival orders
Effect of supply on demand.
Relationship between factory output
and arrival (activity of system).
– Banks : arrival of customers

The coffee shop
• It has customers who place orders and staff
who process them.
• At times it may have few customers, or the
place is very busy given that it is nearby the
University, and has free wi-fi, which the
students use .

Components of a System
• Entities represents an object of interest in the
system whose value can be static or dynamic.
• Attributes are the local values(property) used by
the entity. Attributes are used to control the
behavior of the object.
• It can be considered as a tag that is attached
to an entity e.g. arrival time, a rework priority, a
due date, color, state of an employee.i.e. whether
busy or available or a type of donut (chocolate,
vanilla or jam).

• Lists: Lists are used to represent queues used
by the entities and resources such as LIFO,
FIFO, etc. depending upon the process.
• Activity: A time period of specified length
• State: The collection of variables necessary
to describe the system at any given time
relative to the objective of the study. E.g.
number of customers queuing and number
of busy employees

• Resources: A resource is an entity that provides
service to one or more dynamic entities at a time.
• Entities compete for resources such as personnel,
machines, equipment, etc.
• The dynamic entity can request/seize for one or
more units of a resource; if accepted then the
entity will use the resource and release when
completed. If rejected, the entity can join a queue.

• Event: A momentary occurrence that may
change the state of the system.
• Event: instant of time where the state of the
system changes. In the donut shop problem
suppose that there are two customers being
served.
• An event occurs once a customer has finished
being served: Which implies the number of busy
employees decreases by one and there is one less
customer queuing.

Operations of the objects
• Activity: a time period of specified length which is
known when it begins (although its length may be
random).
• The time an employee takes to serve a customer is
an example of an activity: this may be specified in
terms of a random distribution.
• Clock: Variable representing simulated time.

Operations of the objects
• Delay: duration of time of unspecified length, which is
not known until it ends.
• Delay: It is an indefinite duration of time that is
caused by some combination of system conditions
• This is not specified by the modeller ahead of time but
is determined by the conditions of the system. Very
often this is one of the desired output of a simulation.
• For instance, a delay is the waiting time of a customer
in the queue of our donut shop.

SYSTEM COMPONENTS
System
Entity
Attribute
State
Activity
Event
160
Object of interest in
the system
Property of an
entity
Collection of variables
necessary to describe the
system at a particular time,
An action that takes place
over a period of specified
length and changes the state
of the system
An instantaneous
occurrence that may
change the state of
the system

A QUEUE
• A queue holds an entity that needs to seize a
resource in a temporary waiting area but the
resource is currently tied up with another
entity.
• E,g. LIFO, FIFO, lowest attribute value,
highest attribute value etc.

A simple simulation model
• Assume you wish to open a donut shop and
are unsure about how many employees to
hire to sell donuts to costumers.
• To understand this behavior/operations we
go for simulation. We assume the following;
• Customers that arrive at our shop at a particular
rate;
• employees (of a number to be given as input)
that take a specific time to serve costumers.

THE DONUT SHOP PROBLEM
• The queue in the shop is possibly infinite:
whenever a customer arrives she will stay in the
queue independent of how many customers are
already queuing and she will wait until she is
served.
• Customers are served on a first-come, first-
served basis.
• There are two employees; On average they take
the same time to serve a customer; whenever an
employee is free, a customer is allocated to that
employee; If both employees are free, either of
the two starts serving a customer.

• A system defines group of objects that are
joined together in some regular interaction
or interdependence toward
accomplishment of some purpose.
• A system environment. These are changes
occurring outside the system.
• Exogenous system: Is used to describe
activities and events in the environment
that affect the system. E.g. Arrival of
customers

• Endogenous system: Describes
activities and events occurring
within a system. E.g. withdrawing
money
• In an open system: There is
exogenous activity e.g. a bank
system.

166
Closed system: There is no exogenous activity
and event. It has no external input.
–Ex: if same jobs leave and re-enter the
queue then it is closed, while if new jobs
enter system then its an open system
cpu
open
cpu
closed

SIMULATION MODELLING TOOL
To choose the appropriate simulation modeling tool
consider
• The complexity of the system,
• The specific features needed,
• Scalability requirements,
• Familiarity with the tool.
• Choose a tool that aligns with the project's goals and
allows for effective model development and analysis.

Classification of Models
• Static Simulation(Monte Carlo Model):
Represents a system at a particular
point in time not affected with time. E.g.
a model of a building.
• Static model assumes an absence
of change in data of the system
over time.
• Class diagram may be used to

Classification of Models
• Dynamic models represent systems as
they evolve over time. The simulation of
a banking system during its working
hours (9am to 4pm) is an example of a
dynamic model.
• The state of the system at any time
period is dependent, on the state of the
system at the previous time period.

171
Stable and unstable
–Model output settles down  stable
–Model output always changes  unstable
Output
Time
(Unstable)
Output
Time
(Stable)

Discrete Systems:
• The system state variables remain
constant over intervals of time and the
values change at defined points called
event times. E.g. Arrival of customers in
banks customers will arrive and be served
at the defined activity time and delays.

Discrete simulation model
• At time zero there is an event: a customer
arrives; at time nine another customer
arrives; at time ten another customer
arrives; at time twelve a customer is served;
and so on. These are examples of events.

HEALTH CENTER PROBLEM
• To simulate the workings of a little health
center. Patients arrive at the health center
and are first visited by a nurse.
• Once they are visited by the nurse they have
an actual consultation with a doctor.
• Once they are finished with the doctor, they
meet the administrative staff to schedule a
follow-up appointment.

• We make the following assumptions:
• That queues are infinite and that patients do
not leave the health center until they are
served by the administrative staff;
• At all steps patients are visited using a first-
come, first-served basis
• The health center has one nurse, two
doctors and one administrative staff. The
two doctors take on average the same time
to visit a patient.

• We make the following assumptions:
• System state:
• QN(t): number of patients queuing to see the nurse;
• QD(t): number of patients queing to see a doctor;
• QA(t): number of patients queuing to see the staff;
• NN(t): number of nurses available to visit patients;
• ND(t): number of doctors available to visit patients;
• NA(t) :number of administrative staff available to
visit patients.

SYSTEM COMPONENTS
• Resources: patients, nurses, doctors and
administrative staff;
• Events: Arrival of a patient, completion of nurse’s
visit, completion of doctor’s visit, completion of
administrative staff’s visit.
• Activities: Time between the arrival of a patient and
the next, visit’s times of nurses, doctors and admin
staff.
• Delay: Customers’ waiting time for nurses, doctors
and administrative staff.
• Sinks: Are how entities leave the model.

• In a bank, the number of customers change
when a customer arrives and when the
service provided to the customer is
completed.
• Others are; grocery stores and manufacturing
applications.
• If countable  discrete Ex: jobs in CPU queue

Deterministic models
• Contain no random variables
• A model is deterministic if its behavior is
entirely predictable.
• Given a set of inputs, the model will
result in a unique set of outputs.

• In a deterministic simulation, all events and
relationships among the variables are governed
by a combination of known, but possibly
complicated, rules.
• It is a mathematical model in which
outcomes are precisely determined through
known relationships among states and
events without room for random variation

Deterministic Models
• It deals with systematic and
definitive outcomes as opposed to
random results and they don’t make
allowance for error.
• This relationship allows one to make
predictions and see how one
variable affects the other.

• In a deterministic model we would
for instance assume that;
• A new customer arrives every 5
minutes and an employee takes 2
minutes to serve a customer.

188
Deterministic and probabilistic models
–If output is predicted with certainty 
deterministic
–If output different for different repetitions 
probabilistic/stochastic
Output
Input
Output
Input
(Deterministic) (Probabilistic)

Stochastic vs deterministic simulations
• A model is deterministic if its
behavior is entirely predictable.
Given a set of inputs, the model will
result in a unique set of outputs.
• A model is stochastic if it has random
variables as inputs, and
consequently also its outputs are
random.

Stochastic/probability simulation
• A probability model is a mathematical
representation of a random phenomenon.
• It is defined within the sample space by the
sample space events and probabilities.
• Also referred to as statistical analysis tools
that estimate on the basis of historical data,
the probability of an event occurring again.

• Simulation involves the use of a probability
model to artificially recreate a random
phenomenon using a computer.
• Given a probability model, we can simulate
outcomes, occurrences of events, and values
of random variables, according to the
specifications of the probability measure.
• Interest rate in bank/insurance companies
Computation
–Gives more than one output results

Probabilistic model
• Unlike the deterministic models the
probabilistic model include some element of
randomness.
• This model is likely to produce different
results with the same initial conditions.
• There is always an element of chance or
uncertainty involved which imply that there
are possible alternate solutions.

• Stochastic simulation has one or more
random variables as inputs. Random
inputs lead to random outputs.
• An example is the spread of a disease
say COVID 19 that is passed by human
contact.
• A susceptible person may make contact
with an infected person but will not
necessarily become infected.

• The probability of being infected is
related to the virility of the disease, the
state of health of the susceptible person,
and the nature of the contact.
• ‘‘random variables’’ are included in the
model to represent the influence of
factors that are unpredictable,
unknown, or beyond the scope of the
model.

• In a stochastic model we would assume
that the arrival times and the serving
time follows some random variables:
• Given a probability model, we
can simulate outcomes, occurrences of
events, and values of random variables,
according to the specifications of the
probability

Continuous system
–The state variables change continuously as
a function of time and the behavior of the
system is typically described by differential
equations.
– results whose value changes
continuously over time.
– If uncountably infinite  continuous
•Ex: time spent by students on hardware

• Variables of interest change
continuously over time. i.e. Y=dy/dt.
• Suppose a simulation for a car journey is
to be created where interest is on the
speed of the car throughout the
journey.

Symmetric vs skewed
• A probability distribution can either be symmetric
or skewed to the left or right.
• you choose between symmetric or skewed based
on realism.

Bounded vs unbounded
• A probability distribution is bounded if there is A
and B such that the possible value can be less that
A or greater than B.
• The value of
–A is the minimum possible value
–B is the maximum possible value.
–It is possible for a distribution to be bound in
one direction.
• The distribution is unbounded if there are no such
bounds.

• The basic idea behind simulation models is to
predict how a real system would react to a set of
variables.
• Implementing a simulation model will help you
understand the consequences of certain decisions
as well as how they might impact your business
whether adversely or beneficially.
• Selecting a model depends on the nature of
business, its specific requirements, and your
desired outcomes.

What is queuing process?
• A queuing process is a model of waiting lines,
constructed so that queue length and waiting
times can be predicted.
• The symbolic representation of a queuing
process makes it easy to simulate its
behavior, estimate its parameters from data,
and compute state probabilities at finite and
infinite time horizons.

What is Queuing Theory?
• Mathematical analysis of queues and waiting
times in stochastic systems.
– Is used extensively to analyze production and
service processes exhibiting random variability in
market demand (arrival times) and service times.
• Queues arise when the short term demand for
service exceeds the capacity
– Most often caused by random variation in service
times and the times between customer arrivals.
– If long term demand for service is greater than
capacity the queue will explode!

Why is queuing theory important.
• Queuing theory is the study of congestion
and waiting in line.
• The theory can help with creating an efficient
and cost-effective workflow, allowing the
user to improve traffic flow.
• Queuing theory can address staffing,
scheduling, and customer service shortfalls.

Why is Queuing Analysis Important?
• Capacity problems are very common in
industry and one of the main drivers of
process redesign
–Need to balance the cost of increased
capacity against the gains of increased
productivity and service
• Queuing and waiting time analysis is
particularly important in service systems
–Large costs of waiting and of lost sales due
to waiting

A basic queuing system consists of;
• Arrival process (how customers arrive at
the queue, how many customers are present
in total).
• The queue itself;
• The service process for attending to those
customers;
• Departures from the system.

Simulation of a Queuing System
• A queue is the combination of all entities in
the system being served and those waiting
for their turn.
• A queuing system: Is described by its calling
population, the nature of the arrivals, the service
mechanism, the system capacity, and the queuing
discipline.

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