```Lecture 2
Model Classification and
Steps in a Simulation Study
Definition of Simulation



Simulation is the imitation of an operation of a realworld process or system over time.
Simulation is a method of understanding,
representing and solving complex interdependent
system.
Simulation is the process of designing a model of a
real system and conducting experiments with this
model for the purpose either of understanding the
behavior of the system or of evaluating various
strategies (with the limits imposed by a criterion or a
set of criteria) for the operation of the system.
2
Definition of Simulation
(cont’)


Simulation in general is to pretend that one deals with
a real thing while really working with an imitation.
A flight simulator on a PC is computer model of some
aspects of the flight: it shows on the screen the
controls and what the “pilot” (the youngster who
operates it) is supposed to see from the “cockpit” (his
armchair).
3
When to use Model



To fly a simulator is safer and cheaper than the real
airplane.
For precisely this reason, models are used in
industry, commerce and military: it is very costly,
dangerous and often impossible to make experiments
with real systems.
Provided that models are adequate descriptions of
reality (they are valid), experimenting with them can
save money, suffering and even time.
4
When to use
Simulations



Systems which change with time such as a gas
station where cars come and go (called dynamic
systems) and involve randomness (nobody can
guess at exactly which time and next cars should
arrive at the station) are good candidates for
simulation.
Modeling complex dynamic systems theoretically
need too many simplifications and the emerging
models may not be therefore valid.
Simulation does not require that many simplifying
assumptions, making it the only tool even in absence
of randomness.
5
How to simulate?




Suppose we are interested in a gas station. We may
describe the behaviour of this system graphically by
plotting the number of cars in the station; the state of
the system.
Every time a car arrives the graph increases by one
unit while a departing car causes the graph to drop
one unit.
This graph (called sample path), could be obtained
from observation of a real station, but could also be
artificially constructed.
Such artificial construction and the analysis of the
resulting sample path consists of the simulation.
6
Types of Models



Models can be classified as being mathematical or
physical.
A mathematical model uses symbolic notation and
mathematical equations to represent a system.
A simulation model is particular type of mathematical
model of a system.
7
Type of Simulation




Simulation models may be further classified as being:
Static model or Dynamic model
Deterministic model or Stochastic model
Discrete model or Continuous model
8
Static vs Dynamic


Static models and dynamic models are classification
by the dependency on time
A static simulation model, sometimes called a Monte
Carlo simulation, represents a system at a particular
point in time.


For example, Mark Six, inventory level
Dynamic simulation models represent systems in
which state of the variables change over time. The
simulation of a bank from 9:00am to 4:00pm is an
example of a dynamic simulation.

For example, service time, waiting time.
9
Deterministic vs
Stochastic


Classification by the nature of the variables
Simulation models that contain no random variables
are classified as deterministic.



For example, deterministic arrivals would occur at a dentist’s
office if all arrived at the scheduled appointment time.
A stochastic simulation model has one or more
random variables as input.
Random inputs lead to random outputs.

For example, random arrival, random product demand, random
incoming calls.
10
Deterministic vs
Stochastic (cont’)

Since the outputs are random, they can be
considered only as estimates of the true
characteristics of a model.

For example, the simulation of a bank would usually involve
random interarrival times and random service times.
11
Discrete vs Continuous




Discrete and continuous models are defined in an
analogous manner, classification by system nature.
A discrete model is one in which the state variable(s)
change only at a discrete set of points in time.
The bank is an example of a discrete system, since
the state variable, the number of customers in the
bank, changes only when a customer arrives or when
the service provided a customer is complete.
Other examples, busy/idle counter, occupied/free
machine.
12
Discrete vs Continuous
(cont’)





A continuous model is one in which the state
variable(s) change continuously over time.
An example is the head of water behind a dam.
During and for some time after a rain storm, water
flows into the lake behind the dam.
Water is drawn from the dam for flood control and to
make electricity.
Evaporation also decreases the water level.
But, continuous system can be approximated by a
discrete-event system, depending on the expected
preciseness and the objective of the study.
13
Applications
- Service Applications



Staffing
A bank manager might determine that three tellers on
duty results in a tolerable wait for service during most
of the day, but that her customers’ “time in queue” is
too long during the busy lunch hour and in the late
afternoon.
She could then assess the impacts of adding
additional part-time help during the peak hours.
14
Applications
- Service Applications
(cont’)



Procedure Improvement
Many organizations have learned that internal
consumers are customers.
In an effort to improve the responsiveness of their
administrative and support functions many of these
companies are using simulation to model revised
procedures designed to streamline processing of
paperwork, telephone calls and other daily
transactions.
15
Simulation




New policies, operating procedures, decision rules,
information flows, organizational procedures, and so
on can be explored without disrupting ongoing
operations of the real system.
New
hardware
designs,
physical
layouts,
transportation systems, and so on, can be tested
without committing resources for their acquisition.
Hypotheses about how or why certain phenomena
occur can be tested for feasibility.
Time can be compressed or expanded allowing for a
speedup or slowdown of the phenomena under
investigation.
16
Simulation (cont’)





Insight can be obtained about the interaction of
variables.
Insight can be obtained about the importance of
variables to the performance of the system.
Bottleneck analysis can be performed indicating
where work-in-process, information, materials, and so
on are being excessively delayed.
A simulation study can help in understanding how the
system operates rather than how individuals think the
system operates.
17
Simulation




Model building requires special training.
Simulation results may be difficult to interpret.
Simulation modeling and analysis can be time
consuming and expensive. Skimping on resources
for modeling and analysis may result in a simulation
model or analysis that is not sufficient for the task.
Simulation is used in some cases when an analytical
solution is possible, or even preferable. This might
be particularly true in the simulation of some waiting
lines where closed-form queueing models are
available.
18
Defense of Simulation



Vendors of simulation software have been actively
developing packages that contain all or part of
models that need only input data for their operation.
Many simulation software vendors have developed
output analysis capabilities within their packages for
performing very thorough analysis.
Simulation can be performed faster today than
yesterday, and even faster tomorrow.
This is
attributable to the advances in hardware that permit
rapid running of scenarios.
19
Defense of Simulation
(cont’)

Closed-form models are not able to analyze most of
the complex systems that are encountered in
practice.
20
Steps in a
Simulation Study
Problem formulation
Experimental design
Setting of objectives and overall project plan
Production runs and analysis
Model Conceptualization
Data Collection
More runs?
Model translation
No
Documentation
and reporting
Verified?
Yes
No
Validated?
Yes
No
Implementation
21
Steps in a
Simulation Study
(cont’)

Problem formulation


If the statement is provided by the policy makers, or those that
have the problem, the analyst must ensure that the problem being
described is clearly understood. If a problem statement is being
developed by the analyst, it is important that the policy makers
understand and agree with the formulation.
Setting of objectives and overall project plan

The objectives indicate the questions to be answered by simulation.
The overall project plan should include a statement of the
alternative systems to be considered, and a method for evaluating
the effectiveness of these alternatives.
22
Steps in a
Simulation Study
(cont’)

Model conceptualization


Data collection


This is another important and difficult subject. The basic steps are
to consider all the related factors first, then evaluate each one
(keep or ignore) and reach the final model.
The more data you have  the more complete information you
have  the more precise model you can build  the better
solution you would get.
Model translation

Program the model into a computer language. Simulation
languages are powerful and flexible. In most cases, some
computer software packages are involved. The model development
time is greatly reduce. Furthermore, software packages have
added features that enhance their flexibility.
23
Steps in a
Simulation Study
(cont’)

Verified?


Verification pertains to the computer program prepared for the
simulation model. Is the computer program performing properly?
If the input parameters and logical structure or the model are
correctly represented in the computer, verification has been
complete.
Validated?

Validation is the determination that a model is an accurate
representation of the real system. Validation is usually achieved
through the calibration of the model, an iterative process of
comparing the model to actual system behaviour and using the
discrepancies between the two, and the insights gained, to improve
the model.
24
Steps in a
Simulation Study
(cont’)

Experimental design


Production runs and analysis


The alternatives that are to be simulated must be determined. For
each system design that is simulated, decisions need to be made
concerning the length of the initialization period, the length of
simulation runs, and the number of replications to be made of each
run.
Production runs, and their subsequent analysis, are used to
estimate measures of performance for the system designs that are
being simulated.
More runs?

The analyst determines of additional runs are needed and what
design those additional experiments should follow.
25
Steps in a
Simulation Study
(cont’)

Documentation and reporting


Program documentation:
 If the program is going to be used again by the same or
different analysts, it may be necessary to understand
how the program operates.
 The model users can change parameters at will in an
effort to determine the relationships between input
parameters and output measures of performance, or to
determine the input parameters that “optimize” some
output measure of performance.
Progress report:
 It provides the important written history of a simulation
project.
26
Steps in a
Simulation Study
(cont’)

Implementation

The success of the implementation phase depends on how well the
previous eleven steps have been performed.
27
```