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Introduction to Modeling: Concepts and Classifications

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Lecture 1- Overview
What is a model?
Why to use models?
Characteristics of a model
Forms of models
Classification of models (temporal
dimension)
Course scope
3
What is a model?
A model is a simplification of a reality. In this course, a model is
a simplification of a real system
A system is a collection of entities (physic (e.g., people and
machines) or abstract (e.g., administrative units) that act and
interact together toward the accomplishment of some logical
end
Manufacturing systems (production lines, inventory
systems, etc.).
Computer and communication systems (client-server
systems, communication networks, etc.)
Etc.
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2
Lecture 1- Overview
What is a model?
Why to use models?
Characteristics of a model
Forms of models
Classification of models (temporal
dimension)
Course scope
5
Why to use models?
To understand, describe and exchange knowledge about the
structure and the behaviour of the real system
To predict the behaviour of the system under different
conditions (what-if experimentations)
Why does the network performance die when more than 10 people
are at work?
It is very costly, dangerous and often impossible to make
experiments with real systems. Provided that models are adequate
descriptions of reality, experimenting with them can save money,
suffering and even time.
To study new or imaginary systems
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3
Lecture 1- Overview
What is a model?
Why to use models?
Characteristics of a model
Forms of models
Classification of models (temporal
dimension)
Course scope
7
Characteristics of a model
A model is always a simplification of the reality (or the modeled
system)
It only captures certain relevant aspects of the real system, the
other aspects are ignored
This is why we say that « all models are wrong, but some
models are useful » or « not all models are useful »
You shoud interpret « wrong » by « not the reality »
In order to be useful, the model must be validated, that is, we must
prove that it is a good approximation of the real system it
represents
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4
Lecture 1- Overview
What is a model?
Why to use models?
Characteristics of a model
Forms of models
Classification of models (temporal
dimension)
Course scope
9
Forms of models (1/5)
Physical models: a scaled-down physical objects
(scale model of a building, a car, etc.)
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5
Forms of models (2/5)
Mathematical or analytical models: set of
equations or relations among mathematical
variables (set of equations describing the
workflow on a factory floor, etc.)
Example: Q = m C (t1 - t2) - a model of heat emitted
by a body of mass m, when cooling from temperature
t1 to temperature t2.
t2. C is the heat capacity
parameter.
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Forms of models (3/5)
Diagrammatic models
A drawing is also a model, and in some cases it can offer much
more information than the verbal description
A drawing may be better than a thousand words
Charest
N
Bus Station
Ste-Foy
University
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Forms of models (4/5)
Computer simulation models:
A simulation is a computer program that
mimics the behavior of a real-world
system, including its inputs
Suitable for complex dynamic systems
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Forms of models (5/5)
SYSTEM
Experiment with the
Actual System
Experiment with a
Model of the System
There is always the
question of whether it
actually reflects the
system.
•Too costly or disruptive
•Not appropriate for the
design
Physical Model
Mathematical Model
Make assumptions that take
the form of mathematical or
logical relationships
E.g., table top scale
models of material
handling systems
Analytical Solution
Simulation
If the model is simple enough. E.g.,
calculus, algebra, probability theory
Highly complex systems
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Lecture 1- Overview
What is a model?
Why to use models?
Characteristics of a model
Forms of models
Classification of models (temporal
dimension)
Course scope
15
Classification of models (time) (1/4)
We may distinguish different types of models according to several
aspects (characteristics of the real system, of the studied problem,
etc.)
Time is one of the most important aspects of a model, and we should
ask the following questions:
Do we need to see how does the system evolve in time, like in a movie, or
we just need a snapshot of the reality, like on a photo?
If the system is evolving, how does it change from one state to another?
Is it a continuous process or a discrete, instantaneous one?
Is the next state of the system totally defined by its current one, or future
states occur spontaneously with certain probability?
We distinguish:
Static vs. Dynamic Models
Deterministic vs. Stochastic Models
Continuous vs. Discrete Models
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Classification of models (time) (2/4)
1. Static vs. Dynamic Models (does the system
change?)
Static model
Time plays no role; represents a system at a
particular point in time (a snapshot)
Example: a map, a photo, etc.
Dynamic model
Represents a system as it evolves over time
(time changes and so do variables in the
system)
Example: a cartoon, a 3d animation, etc.
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Classification of models (time) (3/4)
2. Deterministic vs. Stochastic Models (can we
exactly predict the change?):
Deterministic model
A dynamic model where the state* of the system at time ti+1 is
entirely defined by its state at time ti.
Example: chemical reactions
Stochastic model
A dynamic model where the state of the system at time ti+1
may take several values, each value with a certain probability
Example: most queueing and inventory systems
* A state is a variable characterizing an attribute in the system (level of stocks
in inventory, number of jobs waiting for process, etc.)
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Classification of models (time) (4/4)
3. Continuous vs. Discrete Models (When does the
system changes?):
Continuous: the state of the system changes
continuously (e.g., chemical processes)
Discrete model: the state of the system changes only at
discrete points in time
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• Continuous-time models evolve their variable values continuously over time
• Discrete-time models may change their variable values only at
discrete points in time
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Lecture 1- Overview
What is a model?
Why to use models?
Characteristics of a model
Forms of models
Classification of models (temporal
dimension)
Course scope
21
Course scope
In this course we are interested in the modeling of
real-world stochastic systems using computer
simulation
Particularly, we focus on “discrete-event” systems
although we shall see other examples
As we shall see, simulating a system properly
requires several disciplines
Hopefully, you will learn many useful “transferable”
skills, even if you do not choose to specialize in
modeling
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Lecture 1- Overview
What is a model?
Why to use models?
Characteristics of a model
Forms of models
Classification of models (temporal
dimension)
Course scope
23
Lecture 2- Objectives
Introduce the general steps of the
modeling process
Some steps will be detailed / added next
classes
Understand the importance of objectives in
the modeling process
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Modeling process
Problem Analysis
Conceptual Modeling and
Specification
Real
system
Data Collection
Useful
(valide)
Model
Computational
Model
Model
Implementation
Development
for a
specific
purpose
Model Verification
Model Validation
An iterative process
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Waiting Line systems
Service system
Arrivals
Queue
customers
Service
facility
Served
units
A Waiting Line System is characterized by:
-Queue (Buffer): with a finite or infinite size
- Server: with a given processing speed
- Events: Arrivals or Departures with given rates
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Ships example
Ships at
sea
Ship unloading system
Empty
ships
Waiting ship line
Dock
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Bank example
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Work example: airport runway
Control Tower
Aircrafts
Runway
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Problem Analysis
Conceptual M & S
Data Collection
Implementation
Verification
Validation
Problem analysis
• Clearly indentify the problem and the purposes of the model
• Some important questions:
What are the objectives the model will be used for?
Define an achievable goal
“To model the system” is not a goal
“To model the system in order to measure the performance /
…” is a goal
What are the relevant measurements to evaluate goals
achievement?
How can we evaluate that the objectives are achieved?
What are the characteristics of the system?
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Problem Analysis
Conceptual M & S
Data Collection
Implementation
Verification
Validation
Problem analysis (cont.)
Airport example:
Objective: Evaluate the performance of the landing airport
system.
Important performance measures:
Average waiting time: the time an aircraft must wait when arriving at
the airport and before it is allowed to land.
Average service time: the time an aircraft takes to be parked
Only one runway, can not be used by two aircrafts at the same
time
Ground parking capacity: 30 aircrafts
Aircrafts are served first-in-first-out. In emergency situations, the
rule change
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Problem Analysis
Conceptual M & S
Data Collection
Implementation
Verification
Validation
Conceptual modeling and
specification
Establish a clear conceptual model of the system and
specify its behaviour
What should be included to the model? What can be ignored?
What abstractions should be used?
What is the level of detail?
What are important variables and parameters of the system?
What are important inputs / outputs?
How the entities of the system should interact?
Etc.
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Problem Analysis
Conceptual M & S
Data Collection
Implementation
Verification
Validation
Conceptual modeling and
specification (cont.)
Customers: aircrafts that use the system resources
Server: the runway, a resource that can be used by only
one customer at a given time
Queue: the buffer (control tower) holding aircrafts waiting
to land
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Problem Analysis
Conceptual M & S
Data Collection
Implementation
Verification
Validation
Conceptual modeling and
specification (cont.)
Airport example:
Abstractions: aircrafts (customers), runway (server), control tower (manages
the queue), aircrafts arrival and parking (events)
Aircrafts should be modeled individually, they can not be in groups.
Travellers should not be modeled!
Important variables: arrival times, waiting times, parking times, number of
waiting aircrafts, number of parked aircrafts, etc.
Inputs:
Number of arriving aircrafts and their arrival times
Average time of landing
Etc.
Outputs:
Average waiting and service times
Etc.
An aircraft can not land before having the Ok from the control tower
If the runway is busy, the control tower should ask arriving aircrafts to wait
flying
Etc.
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Problem Analysis
Conceptual M & S
Data Collection
Implementation
Verification
Validation
Data collection
Estimate the inputs of the model
In stochastic systems we often use distributions of
random variables
Based on statistics and historical data
Airport example:
What is the arrival process?
Schedule of aircraft arrivals, e.g., log from specific dates
Often, probability distribution defines time between
successive aircrafts arrivals
How much service time (from arrival time to parking time) is
needed for each aircraft?
May use probability distribution to specify aircrafts service
time
Etc.
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Problem Analysis
Conceptual M & S
Data Collection
Implementation
Verification
Validation
Model Implementation
Use an analytical model or a simulation
model?
Analytical: using queuing theory for example (set of equations)
Simulation: using a computer program to execute the model
(mathematical simulations, etc.)
Use a general-purpose programming
language (C++, Visual Basic, etc.) or a
special-purpose simulation language or
environment (like Arena, etc.) ?
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Problem Analysis
Conceptual M & S
Data Collection
Implementation
Verification
Validation
Model Verification
Concerned with the correctness of the transformation
from the abstract representation (the conceptual model)
to the implemented model
Does the implemented model respects the conceptual
specifications?
Often conducted by inspection of the code, i.e., by
comparing the code to the conceptual specifications
If there is a difference, we should change either the
conceptual specifications or the code
Did I build the model right?
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Problem Analysis
Conceptual M & S
Data Collection
Implementation
Verification
Validation
Model Validation
While verification concerns whether or not the program is
working as the specifications expect, validation
considers whether or not the implemented model is a
“good” model of the real system.
A model that can be relied upon to reflect the behavior of
the real system can be considered ‘valid’.
Did I build the right model?
We can not validate a model at 100%, we can only
validate portions of a model
Remember: a model is a simplification of a real system, it
can never behave at 100% like a real system
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Simulation Modeling Process
For simulation models, we will see / detail other
steps in the modeling process, such as
Simulation experiments, Output analysis and
others
We will talk more and more about the modeling
process next courses
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