Simulation is a technique used to model complex systems and estimate statistical measures by representing the system and modeling individual elements' behavior randomly over time. Systems can be discrete, changing at separate points, or continuous, changing continuously. Simulation involves defining the problem, conceptually modeling the system, collecting data, coding the model, validating it, experimenting and analyzing results. It allows studying systems that would be impossible, too expensive, or impractical to study directly.

1. Lecture 5
Simulation

2.  Simulation is a very general
technique for estimating
statistical measures of complex
systems.
 A system is modeled as if the
random variables were known.

3. Definition
 The approach taken is to model
the behaviour of individual
elements within the system,
often using random sampling to
generate realistic variability.

4. Systems, Models, and
Simulation(cont’d.)
 Types of systems
 Discrete
 State variables change instantaneously at separated
points in time
 Bank model: State changes occur only when a customer
arrives or departs
 Continuous
 State variables change continuously as a function of
time
 Airplane flight: State variables like position, velocity
change continuously
 Many systems are partly discrete, partly continuous

5. Studying a System

6. Systems
 Manufacturing facility
 Bank or other
personal-service
operation
 Transportation/logistic
s/distribution
operation
 Hospital facilities
(emergency room,
operating room,
admissions)
 Computer network
 Freeway system
 Business process
(insurance office)
 Chemical plant
 Fast-food restaurant
 Supermarket
 Theme park
 Emergency-response
system

7. kinds of systems
1. continuous systems - state varies
continuously in time, chemical
applications
2. discrete systems - observed only at some
fixed regular time points. An example of a
discrete system is an inventory model in
which we inspect the stock only once a
week.
3. discrete-event systems - the system is
completely determined by a sequence of
random event times t1, t2, . . ., and by
the changes in the state of the system
which take place at these moments.

8. Simulation Process
 The simulation process consists
of problem definition,
conceptual modelling, data
collection, model coding,
model verification and
validation, experimentation
and analysis of results, and
solution implementation.

9. Application Areas
 logistics and supply chain,
 service
 operations management,
 business process improvement,
 health and social care
 information system,
 environment and many more.

10. What is Simulation?
 A Simulation of a system is the operation
of a model, which is a representation of
that system.
 The model is amenable to manipulation
which would be impossible, too
expensive, or too impractical to perform
on the system which it portrays.
 The operation of the model can be
studied, and, from this, properties
concerning the behavior of the actual
system can be inferred.

11. Different Kinds of Simulation
Static vs. Dynamic
Continuous-change vs.
Discrete-change
Deterministic vs.
Stochastic

12. Computer Simulation
 refers to methods for studying
a wide variety of models of
systems
Numerically evaluate on a
computer
Use software to imitate the
system’s operations and
characteristics, often over time

13. Using Computers to Simulate
 General-purpose languages
(FORTRAN)
 Support packages
 Spreadsheets
 Usually static models
 Financial scenarios, distribution
sampling, SQC
 Simulation languages
 GPSS, SIMSCRIPT, SLAM, SIMAN

14. Evolution
 Uses of simulation have evolved
with hardware, software
 The early years (1950s-1960s)
 Very expensive, specialized tool to use
 Required big computers, special
training
 Mostly in FORTRAN (or even Assembler)
 Processing cost as high as $1000/hour
for a sub-286 level machine

15. When Simulations are Used
(cont’d.)
 The formative years (1970s-early
1980s)
 Computers got faster, cheaper
 Often used to clean up “disasters” in
auto, aerospace industries
 The recent past (late 1980s-1990s)
 Wider acceptance across more areas
(Traditional manufacturing
applications, Services, Health care,
“Business processes”)

16. EXAMPLES OF SYSTEMS AND COMPONENTS
System Entities Attributes Activities Events State
Variables
Banking Customers Checking
account
balance
Making
deposits
Arrival;
Departure
# of busy
tellers; # of
customers
waiting
Note: State Variables may change continuously (continuous sys.)
over time or they may change only at a discrete set of points
(discrete sys.) in time.

17. Advantages of Simulation
Flexibility to model things
as they are (even if messy
and complicated)
Allows uncertainty, non-
stationarity in modeling
User friendly computer
applications

18. Monte Carlo simulation
 Monte Carlo simulation is a
computerized mathematical
technique that allows people to
account for risk in quantitative
analysis and decision making.
 furnishes the decision-maker with a
range of possible outcomes and the
probabilities they will occur for any
choice of action.. It shows the
extreme possibilities