Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
all notes of simulation and modeling compiled in one
Typology: Lecture notes
1 / 212
This page cannot be seen from the preview
Don't miss anything!
1
Week 1
February 19 – 23, 2011 Dr. Hedi Haddad
CS 433 – Modeling and Simulation
2
3
4
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.
7
8
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
9
10
13
14
Experiment with the Actual System
Experiment with a Model of the System
Physical Model
Analytical Solution Simulation
There is always the question of whether it actually reflects the system.
Mathematical Model E.g., table top scale models of material handling systems
Make assumptions that take the form of mathematical or logical relationships
If the model is simple enough. E.g., calculus, algebra, probability theory Highly complex systems
15
16
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
Classification of models (time) (1/4)
19
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
Classification of models (time) (4/4)
20
21
22
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
25
Problem Analysis
Data Collection
Computational Model Development
Model Verification
Model Validation
Data Collection
Computational Model Development
Data Collection
Model Verification
Computational Model Development
Data Collection
Model Validation
Model Verification
Model Implementation
Conceptual Modeling and Specification
Real Data Collection system
Useful (valide) Model for a specific purpose
An iterative process
26
A Waiting Line System is characterized by:
customers
27
28
31
Problem Analysis Conceptual M & S Data Collection Implementation Verification Validation
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
32
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.
Problem Analysis Conceptual M & S Data Collection Implementation Verification Validation
33
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
Problem Analysis Conceptual M & S Data Collection Implementation Verification Validation
34
Problem Analysis Conceptual M & S Data Collection Implementation Verification Validation
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.
37
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?
Problem Analysis Conceptual M & S Data Collection Implementation Verification Validation
38
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
Problem Analysis Conceptual M & S Data Collection Implementation Verification Validation
39
