Graduate Program in
Business Information Systems
Simulation
Aslı Sencer
Simulation
– Very broad term – methods and
applications to imitate or mimic real
systems, usually via computer
 Applies in many fields and industries
 Very popular and powerful method

BIS 517-Aslı Sencer
Advantages of Simulation





Simulation can tolerate complex systems where
analytical solution is not available.
Allows uncertainty, nonstationarity in modeling
unlike analytical models
Allows working with hazardous systems
Often cheaper to work with the simulated system
Can be quicker to get results when simulated
system is experimented.
BIS 517-Aslı Sencer
The Bad News





Don’t get exact answers, only approximations,
estimates
Requires statistical design and analysis of
simulation experiments
Requires simulation expert and compatibility with
a simulation software
Softwares and required hardware might be costly
Simulation modeling can sometimes be time
consuming.
BIS 517-Aslı Sencer
Different Kinds of Simulation

Static vs. Dynamic
 Does

time have a role in the model?
Continuous-change vs. Discrete-change
 Can
the “state” change continuously or only at
discrete points in time?

Deterministic vs. Stochastic
 Is
everything for sure or is there uncertainty?
BIS 517-Aslı Sencer
Using Computers to Simulate


General-purpose languages (C, C++, Visual
Basic)
Simulation softwares, simulators
 Subroutines
for list processing, bookkeeping, time
advance
 Widely distributed, widely modified

Spreadsheets
 Usually
static models
 Financial scenarios, distribution sampling, etc.
BIS 517-Aslı Sencer
Simulation Languages and
Simulators

Simulation languages
 GPSS,
SIMSCRIPT, SLAM, SIMAN
 Provides flexibility in programming
 Syntax knowledge is required

High-level simulators
 GPSS/H,
Automod, Slamsystem, ARENA, Promodel
 Limited flexibility — model validity?
 Very easy, graphical interface, no syntax required
 Domain-restricted (manufacturing, communications)
BIS 517-Aslı Sencer
When Simulations are Used

The early years (1950s-1960s)




Very expensive, specialized tool to use
Required big computers, special training
Mostly in FORTRAN (or even Assembler)
The formative years (1970s-early 1980s)



Computers got faster, cheaper
Value of simulation more widely recognized
Simulation software improved, but they were still languages to
be learned, typed, batch processed
BIS 517-Aslı Sencer
When Simulations are Used
(cont’d.)

The recent past (late 1980s-1990s)
 Microcomputer
power, developments in softwares
 Wider acceptance across more areas




Traditional manufacturing applications
Services
Health care
“Business processes”
 Still
mostly in large firms
 Often a simulation is part of the “specs”
BIS 517-Aslı Sencer
When Simulations are Used
(cont’d.)

The present
 Proliferating
into smaller firms
 Becoming a standard tool
 Being used earlier in design phase
 Real-time control

The future
 Exploiting
interoperability of operating systems
 Specialized “templates” for industries, firms
 Automated statistical design, analysis
BIS 517-Aslı Sencer
Popularity of Simulation

Consistently ranked as the most useful, popular tool in the
broader area of operations research / management science
 1979: Survey 137 large firms, which methods used?
1. Statistical analysis (93% used it)
2. Simulation (84%)
3. Followed by LP, PERT/CPM, inventory theory, NLP,
 1980: (A)IIE O.R. division members
 First in utility and interest — simulation
 First in familiarity — LP (simulation was second)
 1983, 1989, 1993: Heavy use of simulation consistently
reported
1. Statistical analysis 2. Simulation
BIS 517-Aslı Sencer
Today: Popular Topics
 Real
time simulation
 Web based simulation
 Optimization using simulation
BIS 517-Aslı Sencer
Simulation Process

Develop a conceptual model of the system
 Define
the system, goals, objectives, decision
variables, output measures, input variables and
parameters.

Input data analysis:
 Collect
data from the real system, obtain probability
distributions of the input parameters by statistical
analysis

Build the simulation model:
 Develop
the model in the computer using a HLPL, a
simulation language or a simulation software
BIS 517-Aslı Sencer
Simulation Process (cont’d.)

Output Data Analysis:
 Run
the simulation several times and apply statistical
analysis of the ouput data to estimate the
performance measures

Verification and Validation of the Model:
 Verification:
Ensuring that the model is free from
logical errors. It does what it is intended to do.
 Validation: Ensuring that the model is a valid
representation of the whole system. Model outputs
are compared with the real system outputs.
BIS 517-Aslı Sencer
Simulation Process (cont’d.)

Analyze alternative strategies on the validated
simulation model. Use features like
 Animation
 Optimization
 Experimental

Design
Sensitivity analysis:
 How
sensitive is the performance measure to the
changes in the input parameters? Is the model
robust?
BIS 517-Aslı Sencer
Static Simulation:
Monte-Carlo Simulation





Static Simulation with no time dimension.
Experiments are made by a simulation model to estimate
the probability distribution of an outcome variable, that
depends on several input variables.
Used the evaluate the expected impact of policy
changes and risk involved in decision making.
Ex: What is the probability that 3-year profit will be less
than a required amount?
Ex: If the daily order quantity is 100 in a newsboy
problem, what is his expected daily cost? (actually we
learned how to answer this question analytically)
BIS 517-Aslı Sencer
Ex1: Simulation for Dave’s Candies

Dave’s Candies is a small family owned business that
offers gourmet chocolates and ice cream fountain
service. For special occasions such as Valentine’s day,
the store must place orders for special packaging
several weeks in advance from their supplier. One
product, Valentine’s day chocolate massacre, is bought
for $7,50 a box and sells for $12.00. Any boxes that are
not sold by February 14 are discounted by 50% and can
always be sold easily. Historically Dave’s candies has
sold between 40-90 boxes each year with no apparent
trend. Dave’s dilemma is deciding how many boxes to
order for the Valentine’s day customers.
BIS 517-Aslı Sencer
Ex1: Dave's Candies Simulation
If the order quantity, Q is 70, what is the expected profit?
Selling price=$12
Cost=$7.50
Discount price=$6
 If D<Q
Profit=selling price*D - cost*Q + discount price*(Q-D)
 D>Q
Profit=selling price*Q-cost*Q
BIS 517-Aslı Sencer
Probability Distribution for Demand
Year
Demand
Demand Distribution
Demand
Probability
(xi, i=1,...,6) P(Demand=xi)
2009
90
2008
80
40
1/6
2007
50
50
1/6
2006
60
60
1/6
2005
40
70
1/6
2004
70
80
1/6
2003
90
90
1/6
.
.
.
.
BIS 517-Aslı Sencer
Generating Demands Using
Random Numbers



During simulation we need to generate
demands so that the long run
frequencies are identical to the
probability distribution found.
Random numbers are used for this
purpose. Each random number is used
to generate a demand.
Excel generates random numbers
between 0-1. These numbers are
uniformly distributed between 0-1.
Random
numbers
0.12878
0.43483
0.87643
0.65711
0.03742
0.46839
0.04212
0.89900
BIS 517-Aslı Sencer
Generating random demands:
Inverse transformation technique
P(demand<=xi)
P(demand=xi)
1.
2.
Generate U~UNIFORM(0,1)
Let U=P(Demand<=D) then D=P-1(U)
U1
1
5/6
4/6
3/6
U2
2/6
1/6
1/6
(xi)
(xi)
40
50
60
70
80
90
40
50
D2=50
BIS 517-Aslı Sencer
60
70
80
D1=80
90
Generating Demands
Demand
(xi)
Probability
P(Demand=xi)
Cumulative
Probability
P(Demand<=xi)
40
1/6
1/6
[0-1/6]
50
1/6
2/6
(1/6-2/6]
60
1/6
3/6
(2/6-3/6]
70
1/6
4/6
(3/6-4/6]
80
1/6
5/6
(4/6-5/6]
90
1/6
1
(5/6-1]
BIS 517-Aslı Sencer
Random numbers
Ex1: Simulation in Excel for
Dave’s Candies
Use the following excel functions to generate a random
demand with a given distribution function.
RAND():
Generates a random number which is
uniformly distributed between 0-1.
VLOOKUP(value, table range, column #): looks up a
value in a table to detremine a random demand.
IF(condition, value if true, value if false): Used to
calculate the total profit according to the random
demand.
BIS 517-Aslı Sencer
BIS 517-Aslı Sencer
Dynamic Simulation:
Queueing System
Arrivals
Departures
Service
is identified by:
•Arrival rate, interarrival time distribution
•Service rate, service time distribution
•# servers
•# queues
•Queue capacities
•Queue disciplines, FIFO, LIFO, etc.
BIS 517-Aslı Sencer
M/M/1 Queueing System
Arrivals
Departures
Service
M: interarrival time is exponentially distributed
M: service time is exponentially distributed
1: There is a single server
BIS 517-Aslı Sencer
Ex3: Model Specifics



Initially (time 0) empty and idle
Base time units: minutes
Input data (assume given for now …), in
minutes:
Part Number
1
2
3
4
5
6
7
8
9
10
11
.
.

Arrival Time
0.00
1.73
3.08
3.79
4.41
18.69
19.39
34.91
38.06
39.82
40.82
.
.
Interarrival Time
1.73
1.35
0.71
0.62
14.28
0.70
15.52
3.15
1.76
1.00
.
.
.
Service Time
2.90
1.76
3.39
4.52
4.46
4.36
2.07
3.36
2.37
5.38
.
.
.
Stop when 20 minutes of (simulated) time have
passed
BIS 517-Aslı Sencer
Queuing Simulation

Random variables:



Events:



Arrival of a customer to the system
Departure from the system.
State variables:



Time between arrivals
Service time represented by probability distributions.
# customers in the queue
Worker status {busy, idle}
Output measures:



Average waiting time in the queue
% utilization of the server
Average time spent in the system
BIS 517-Aslı Sencer
Output Performance Measures


Total production of parts over the run (P)
Average waiting time of parts in queue:
N
N = no. of parts completing queue wait
 WQi WQi = waiting time in queue of ith part
i 1
Know: WQ1 = 0 (why?)
N
N > 1 (why?)

Maximum waiting time of parts in queue:
max WQi
i 1,...,N
BIS 517-Aslı Sencer
Output Performance Measures (cont’d.)

Time-average number of parts in queue:
20
0 Q(t ) dt


Q(t) = number of parts in queue at time t
20
Q(t )
max
Maximum number of parts in queue: 0t 20
Average and maximum total time in system of
parts:
P
TSi
i 1
P
TSi = time in system of part i
,
max TSi
i 1,...,P
BIS 517-Aslı Sencer
Output Performance Measures (cont’d.)

Utilization of the machine (proportion of
time busy)
20
0 B(t ) dt
20

1 if the machine is busy at time t
, B(t )  
0 if the machine is idle at time t
Many others possible (information
overload?)
BIS 517-Aslı Sencer
Simulation by Hand
Manually track state variables, statistical
accumulators
 Use “given” interarrival, service times
 Keep track of event calendar
 “Lurch” clock from one event to the next
 Will omit times in system, “max”
computations here (see text for complete
details)

BIS 517-Aslı Sencer
Simulation by Hand: Setup
System
Clock
Number of
completed waiting
times in queue
Total of
waiting times in queue
B(t)
Q(t)
Arrival times of
custs. in queue
Area under
Q(t)
Event calendar
Area under
B(t)
4
Q(t) graph
3
2
1
0
B(t) graph
0
5
10
15
20
0
5
10
15
20
2
1
0
Interarrival times
Time (Minutes)
1.73, 1.35, 0.71, 0.62, 14.28, 0.70, 15.52, 3.15, 1.76, 1.00, ...
Service times
2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...
BIS 517-Aslı Sencer
Simulation by Hand: t = 0.00, Initialize
System
Number of
completed waiting
times in queue
0
Clock
B(t)
Q(t)
0.00
0
0
Arrival times of
Event calendar
custs. in queue
[1, 0.00,
Arr]
<empty> [–, 20.00,
End]
Total of
waiting times in queue
Area under
Q(t)
Area under
B(t)
0.00
0.00
0.00
4
Q(t) graph
3
2
1
0
B(t) graph
0
5
10
15
20
0
5
10
15
20
2
1
0
Interarrival times
Time (Minutes)
1.73, 1.35, 0.71, 0.62, 14.28, 0.70, 15.52, 3.15, 1.76, 1.00, ...
Service times
2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...
BIS 517-Aslı Sencer
Simulation by Hand: t = 0.00, Arrival of Part 1
System
1
Number of
completed waiting
times in queue
1
Clock
B(t)
Q(t)
Total of
waiting times in queue
Arrival times of
Event calendar
custs. in queue
[2, 1.73,
Arr]
<empty> [1, 2.90,
Dep]
[–, 20.00,
End]
Area under
Area under
Q(t)
B(t)
0.00
1
0
0.00
0.00
0.00
4
Q(t) graph
3
2
1
0
B(t) graph
0
5
10
15
20
0
5
10
15
20
2
1
0
Interarrival times
Time (Minutes)
1.73, 1.35, 0.71, 0.62, 14.28, 0.70, 15.52, 3.15, 1.76, 1.00, ...
Service times
2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...
BIS 517-Aslı Sencer
Simulation by Hand: t = 1.73, Arrival of Part 2
System
2
1
Number of
completed waiting
times in queue
1
Clock
B(t)
Q(t)
Total of
waiting times in queue
Arrival times of
Event calendar
custs. in queue
[1, 2.90,
Dep]
(1.73) [3, 3.08,
Arr]
[–, 20.00,
End]
Area under
Area under
Q(t)
B(t)
1.73
1
1
0.00
0.00
1.73
4
Q(t) graph
3
2
1
0
B(t) graph
0
5
10
15
20
0
5
10
15
20
2
1
0
Interarrival times
Time (Minutes)
1.73, 1.35, 0.71, 0.62, 14.28, 0.70, 15.52, 3.15, 1.76, 1.00, ...
Service times
2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...
BIS 517-Aslı Sencer
Simulation by Hand: t = 2.90, Departure of Part 1
System
2
Number of
completed waiting
times in queue
2
Clock
B(t)
Q(t)
Total of
waiting times in queue
Arrival times of
Event calendar
custs. in queue
[3, 3.08,
Arr]
<empty> [2, 4.66,
Dep]
[–, 20.00,
End]
Area under
Area under
Q(t)
B(t)
2.90
1
0
1.17
1.17
2.90
4
Q(t) graph
3
2
1
0
B(t) graph
0
5
10
15
20
0
5
10
15
20
2
1
0
Interarrival times
Time (Minutes)
1.73, 1.35, 0.71, 0.62, 14.28, 0.70, 15.52, 3.15, 1.76, 1.00, ...
Service times
2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...
BIS 517-Aslı Sencer
Simulation by Hand: t = 3.08, Arrival of Part 3
System
3
2
Number of
completed waiting
times in queue
2
Clock
B(t)
Q(t)
Total of
waiting times in queue
Arrival times of
Event calendar
custs. in queue
[4, 3.79,
Arr]
(3.08) [2, 4.66,
Dep]
[–, 20.00,
End]
Area under
Area under
Q(t)
B(t)
3.08
1
1
1.17
1.17
3.08
4
Q(t) graph
3
2
1
0
B(t) graph
0
5
10
15
20
0
5
10
15
20
2
1
0
Interarrival times
Time (Minutes)
1.73, 1.35, 0.71, 0.62, 14.28, 0.70, 15.52, 3.15, 1.76, 1.00, ...
Service times
2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...
BIS 517-Aslı Sencer
Simulation by Hand: t = 3.79, Arrival of Part 4
System
4
3
2
Number of
completed waiting
times in queue
2
Clock
B(t)
Q(t)
Total of
waiting times in queue
Arrival times of
Event calendar
custs. in queue
[5, 4.41,
Arr]
(3.79, 3.08) [2, 4.66,
Dep]
[–, 20.00,
End]
Area under
Area under
Q(t)
B(t)
3.79
1
2
1.17
1.88
3.79
4
Q(t) graph
3
2
1
0
B(t) graph
0
5
10
15
20
0
5
10
15
20
2
1
0
Interarrival times
Time (Minutes)
1.73, 1.35, 0.71, 0.62, 14.28, 0.70, 15.52, 3.15, 1.76, 1.00, ...
Service times
2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...
BIS 517-Aslı Sencer
Simulation by Hand: t = 4.41, Arrival of Part 5
System
5
4
3
2
Number of
completed waiting
times in queue
2
Clock
B(t)
Q(t)
Total of
waiting times in queue
Arrival times of
Event calendar
custs. in queue
[2, 4.66,
Dep]
(4.41, 3.79, 3.08) [6, 18.69,
Arr]
[–, 20.00,
End]
Area under
Area under
Q(t)
B(t)
4.41
1
3
1.17
3.12
4.41
4
Q(t) graph
3
2
1
0
B(t) graph
0
5
10
15
20
0
5
10
15
20
2
1
0
Interarrival times
Time (Minutes)
1.73, 1.35, 0.71, 0.62, 14.28, 0.70, 15.52, 3.15, 1.76, 1.00, ...
Service times
2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...
BIS 517-Aslı Sencer
Simulation by Hand: t = 4.66, Departure of Part 2
System
5
4
3
Number of
completed waiting
times in queue
3
Clock
B(t)
Q(t)
Total of
waiting times in queue
Arrival times of
Event calendar
custs. in queue
[3, 8.05,
Dep]
(4.41, 3.79) [6, 18.69,
Arr]
[–, 20.00,
End]
Area under
Area under
Q(t)
B(t)
4.66
1
2
2.75
3.87
4.66
4
Q(t) graph
3
2
1
0
B(t) graph
0
5
10
15
20
0
5
10
15
20
2
1
0
Interarrival times
Time (Minutes)
1.73, 1.35, 0.71, 0.62, 14.28, 0.70, 15.52, 3.15, 1.76, 1.00, ...
Service times
2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...
BIS 517-Aslı Sencer
Simulation by Hand: t = 8.05, Departure of Part 3
System
5
4
Number of
completed waiting
times in queue
4
Clock
B(t)
Q(t)
Total of
waiting times in queue
Arrival times of
Event calendar
custs. in queue
[4, 12.57,
Dep]
(4.41) [6, 18.69,
Arr]
[–, 20.00,
End]
Area under
Area under
Q(t)
B(t)
8.05
1
1
7.01
10.65
8.05
4
Q(t) graph
3
2
1
0
B(t) graph
0
5
10
15
20
0
5
10
15
20
2
1
0
Interarrival times
Time (Minutes)
1.73, 1.35, 0.71, 0.62, 14.28, 0.70, 15.52, 3.15, 1.76, 1.00, ...
Service times
2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...
BIS 517-Aslı Sencer
Simulation by Hand: t = 12.57, Departure of Part 4
System
5
Number of
completed waiting
times in queue
5
Clock
B(t)
Q(t)
12.57
1
0
Arrival times of
custs. in queue
Total of
waiting times in queue
Area under
Q(t)
15.17
15.17
Event calendar
[5, 17.03,
Dep]
() [6, 18.69,
Arr]
[–, 20.00,
End]
Area under
B(t)
12.57
4
Q(t) graph
3
2
1
0
B(t) graph
0
5
10
15
20
0
5
10
15
20
2
1
0
Interarrival times
Time (Minutes)
1.73, 1.35, 0.71, 0.62, 14.28, 0.70, 15.52, 3.15, 1.76, 1.00, ...
Service times
2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...
BIS 517-Aslı Sencer
Simulation by Hand: t = 17.03, Departure of Part 5
System
Number of
completed waiting
times in queue
5
Clock
B(t)
Q(t)
17.03
0
0
Arrival times of
custs. in queue
()
Event calendar
[6, 18.69,
Arr]
[–, 20.00,
End]
Total of
waiting times in queue
Area under
Q(t)
Area under
B(t)
15.17
15.17
17.03
4
Q(t) graph
3
2
1
0
B(t) graph
0
5
10
15
20
0
5
10
15
20
2
1
0
Interarrival times
Time (Minutes)
1.73, 1.35, 0.71, 0.62, 14.28, 0.70, 15.52, 3.15, 1.76, 1.00, ...
Service times
2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...
BIS 517-Aslı Sencer
Simulation by Hand: t = 18.69, Arrival of Part 6
System
6
Number of
completed waiting
times in queue
6
Clock
B(t)
Q(t)
18.69
1
0
Arrival times of
custs. in queue
()
Total of
waiting times in queue
Area under
Q(t)
Event calendar
[7, 19.39,
Arr]
[–, 20.00,
End]
[6, 23.05,
Dep]
Area under
B(t)
15.17
15.17
17.03
4
Q(t) graph
3
2
1
0
B(t) graph
0
5
10
15
20
0
5
10
15
20
2
1
0
Interarrival times
Time (Minutes)
1.73, 1.35, 0.71, 0.62, 14.28, 0.70, 15.52, 3.15, 1.76, 1.00, ...
Service times
2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...
BIS 517-Aslı Sencer
Simulation by Hand: t = 19.39, Arrival of Part 7
System
7
6
Number of
completed waiting
times in queue
6
Clock
B(t)
Q(t)
Total of
waiting times in queue
Arrival times of
Event calendar
custs. in queue
[–, 20.00,
End]
(19.39) [6, 23.05,
Dep]
[8, 34.91,
Arr]
Area under
Area under
Q(t)
B(t)
19.39
1
1
15.17
15.17
17.73
4
Q(t) graph
3
2
1
0
B(t) graph
0
5
10
15
20
0
5
10
15
20
2
1
0
Interarrival times
Time (Minutes)
1.73, 1.35, 0.71, 0.62, 14.28, 0.70, 15.52, 3.15, 1.76, 1.00, ...
Service times
2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...
BIS 517-Aslı Sencer
Simulation by Hand: t = 20.00, The End
System
7
6
Number of
completed waiting
times in queue
6
Clock
B(t)
Q(t)
20.00
1
1
Arrival times of
Event calendar
custs. in queue
[6, 23.05,
Dep]
(19.39) [8, 34.91,
Arr]
Total of
waiting times in queue
Area under
Q(t)
Area under
B(t)
15.17
15.78
18.34
4
Q(t) graph
3
2
1
0
B(t) graph
0
5
10
15
20
0
5
10
15
20
2
1
0
Interarrival times
Time (Minutes)
1.73, 1.35, 0.71, 0.62, 14.28, 0.70, 15.52, 3.15, 1.76, 1.00, ...
Service times
2.90, 1.76, 3.39, 4.52, 4.46, 4.36, 2.07, 3.36, 2.37, 5.38, ...
BIS 517-Aslı Sencer
Ex3:Complete Record of the Hand Simulation
BIS 517-Aslı Sencer
Ex3: Simulation by Hand:
Finishing Up

Average waiting time in queue:
Total of times in queue 15.17

 2.53 minutes per part
No. of times in queue
6

Time-average number in queue:
Area under Q(t ) curve 15.78

 0.79 part
Final clock valu e
20

Utilization of drill press:
Area under B(t ) curve 18.34

 0.92 (dimension less)
Final clock valu e
20
BIS 517-Aslı Sencer
Randomness in Simulation


The above was just one “replication” — a sample of size
one (not worth much)
Made a total of five replications:
Note
substantial
variability
across
replications

Confidence intervals for expected values:

In general,
 For expected total production,
X  tn 1,1 / 2s / n
BIS 517-Aslı Sencer
3.80  (2.776)(1.64 / 5)
3.80  2.04
Comparing Alternatives



Usually, simulation is used for more than just a
single model “configuration”
Often want to compare alternatives, select or search
for the best (via some criterion)
Simple processing system: What would happen if
the arrival rate were to double?
 Cut
interarrival times in half
 Rerun the model for double-time arrivals
 Make five replications
BIS 517-Aslı Sencer
Results: Original vs.
Double-Time Arrivals








BIS 517-Aslı Sencer
Original – circles
Double-time – triangles
Replication 1 – filled in
Replications 2-5 – hollow
Note variability
Danger of making
decisions based on one
(first) replication
Hard to see if there are
really differences
Need: Statistical analysis
of simulation output data