modeling and simulation (an...
TRANSCRIPT
1
Modeling and Simulation
(An Introduction)
The Nature of Simulation
2
Conceptions
Application areas
Impediments
Conceptions
3
Simulation course is about techniques for using computers to
imitate or simulate the operations of various kinds of real world
facilities or processes.
A simulation is the imitation of the operation of a real-world
process or system over time. Steps include
Generating an artificial history of a system
Observing the behavior of that artificial history
Drawing inferences concerning the operating characteristics of
the real system
Conceptions
4
Use the operation of a bank as an example:
Counting how many people come to the bank; how many tellers,
how long each customer is in service; etc.
Establishing a model and its corresponding computer program.
Executing the program, varying parameters (number of tellers,
service time, arrival intervals) and observing the behavior of the
system.
Drawing conclusions: increasing number of tellers; reducing
service time; changing queuing strategies; etc.
Conceptions
5
The behavior of a system as it evolves over time is studied by
developing a simulation model.
A model is a set of entities and the relationship among them. For the
bank example: entities would include customers, tellers, and
queues. Relations would include customers entering a queue; tellers
serving the customer; customers leaving the bank.
Once developed, a model has to be validated. There are many
different ways to validate a model: observation (measurement);
analytical model comparison (analysis).
Application areas
6
Designing and analyzing manufacturing systems
evaluating military weapons systems or their logistics requirements
determining hardware requirements or protocols for
communication networks
Determining hardware and software requirements for a computer
system
Designing and operating transportation systems such as airports,
freeways, ports and subways
Application areas
7
Evaluating designs for service organizations such as call centers, fast-
food restaurants, hospitals, and post offices.
Reengineering of business processes
Determining ordering polices for an inventory system
Analyzing financial or economic systems.
Impediments
8
Models used to study large-scale systems tend to be very
complex, and writing computer programs to execute them can
be an arduous task indeed. (excellent software products)
Large amount of computer time is sometimes required. (cheaper
and faster computer)
An unfortunate impression that simulation is just an exercise in
computer programming, albeit a complicated one. (attitude,
simulation methodology)
Systems, Models & Simulation
9
System is defined to be a collection of entities, e.g., people or
machines, which act and interact together toward the
accomplishment of some logical end.
System depends on the objectives of a particular study.
State of a system: collection of variables necessary to describe a
system at a particular time, relative to the objectives of a study. (the
number of busy tellers, the number of customers in the bank, the time of
arrival of each customer in the bank)
Types of systems:
Discrete and continuous.
Continue...
10
discrete system: the state variables change instantaneously at separated points in time.
(a bank, e.g., the number of customers in the bank)
continuous system: the state variables change continuously with respect to time. (an
airplane moving through the air, e.g., position and velocity )
• Many systems are partly discrete, partly continuous
Study on a system: try to gain some insight into the relationships
among various components, or to predict performance under some
new conditions being considered.
Ways to study a system:
Example
12
One study on a bank to determine the number of tellers needed to
provide adequate service for customers who want just to cash a
check or make a savings deposite, the system can be defined to be
that portion of the bank consisting of the tellers and the customers
waiting in line or being served.
If the loan officer and the safety deposite boxes are to be included,
the definition of the system must be expanded in an obvious way.
Systems, Models & Simulation
13
• Classification of simulation models
– Static vs. dynamic
– Deterministic vs. stochastic
– Continuous vs. discrete
• Most operational models are dynamic, stochastic, and
discrete – will be called discrete-event simulation models
Types of Simulation
Model Classifications
15
deterministic (input and output variables are fixed);
stochastic (at least one of the input or output variables is
probabilistic);
static (time is not taken into account);
dynamic (time-varying interactions among variables are
taken into account).
System Terminology:
16
State: A variable characterizing an attribute in the system such as level of stock
in inventory or number of jobs waiting for processing
Event: An occurrence at a point in time which may change the state of the
system, such as arrival of a customer or start of work on a job.
System Terminology:
17
Entity: An object that passes through the system, such as cars in an intersection
or orders in a factory. Often an event (e.g., arrival) is associated with an
entity (e.g., customer).
Queue: A queue is not only a physical queue of people, it can also be a task list, a
buffer of finished goods waiting for transportation or any place where
entities are waiting for something to happen for any reason.
System Terminology:
18
Creating: Creating is causing an arrival of a new entity to the system at some point
in time.
Scheduling:
Scheduling is the act of assigning a new future event to an existing entity.
System Terminology:
19
Random Variable: is a quantity that is uncertain, such as interarrival time between two
incoming flights or number of defective parts in a shipment.
Random Variate:
is an artificially generated random variable.
System Terminology:
20
Distribution: is the mathematical law which governs the probabilistic features of a
random variable.
Example:
21
Building a simulation gas station with a single pump served
by a single service man assume that the arrival of cars as well as their service times are random
Solution (1):
22
At first identify the:
states
events
entities
queue
random realizations
distributions
Solution (1):
23
after identification of the different system requirements, you will come up with the different values:
states:
o Number of cars waiting for service, number of cars served at any moment
events:
o Number of cars, start of service, end of service
entities:
o cars
Solution (1):
24
queue
o The queue of cars in front of the pump, waiting for
services
random realizations:
o inter-arrival times, service times
distributions:
o assume exponential distribution for both inter-arrival
time and service time
Solution (2): Arrival Routine
25
Solution (2): Departure Routine
26