Simulation and Modelling MIS 7102
Introduction to Simulation & Modelling
Week 1
By Agnes Rwashana Semwanga
[email protected]
Friday 6.00p.m.- 9.00p.m.
Faculty of Technology Room 143
Introduction : Simulation and Modeling Wk1
Slide 1
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Core for
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MIS - Computer Information Systems (CIS) option
Elective for
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MIS – Management Information System (MIS) option
MIS – Information System management (ISM)
MIS – Internet and Database System (IDS)
MSC Computer Science
Introduction : Simulation and Modeling Wk1
Slide 2
Course schedule
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Week 1 : Introduction to Simulation & Modelling
Week 2 : Introduction to System Dynamics
Week 3 : Systems thinking and Causal Loop Diagramming
Week 4 : System Archetypes + Assignment for Class Presentation
Week 5 : Assignment / Test 1
Week 6 : Causal Loop Diagrams with Vensim
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Discrete Event Simulation by Guest Lecturer : Mr. John Ngubiri (next 3 weeks 1 hr [8-9])
Week 7 : Graphical Integration
Week 8 : Feedback Structures
Week 9-11 : Class Presentations - Assignment 3
Week 12 : Assignment / Test 2
Week 13 : Model Testing & Validation
Week 14 : Stock and Flow with STELLA software - Practice
Week 15 : Preparation for Exams
Introduction : Simulation and Modeling Wk1
Slide 3
References
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Senge Peter (2003). The Fifth Discipline.
Steward Robinson (2004). Simulation. The Practice of Model
Development and Use. John Wiley and Sons Ltd.
Goodman Michael R. (1989) Study Notes in System Dynamics
Pid, M., (1992) Computer Simulation in Management Science, 3Ed John
Wiley, Chichester
Introduction : Simulation and Modeling Wk1
Slide 4
Simulation Is …
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Simulation – Definition : An imitation of a system. Imitation
implies mimicking or copying something else.
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
Static simulation – imitates a system at a point in time
Dynamic simulation – imitates a system as it progresses
through time e.g movement of trains
Computer based dynamic simulation – an imitation (on a
computer) of a system as it progresses through time.
Introduction : Simulation and Modeling Wk1
Slide 5
Illustration(Descriptive – Performance Analysis)
Simulation
vs.
Real World
Introduction : Simulation and Modeling Wk1
Slide 6
Typical Uses of Simulation
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Estimating a set of productivity measures in production systems,
inventory systems, manufacturing processes, materials handling and
logistics operations.
Designing and planning the capacity of computer systems and
communication networks so as to minimize response times.
Conducting war games to train military personnel or to evaluate the
efficacy of proposed military operations
Evaluating and improving maritime port operations, such as container
ports or bulk-material marine terminals (coal, oil or minerals), so as to
find ways of reducing vessel port times.
Improving health care operations, financial and banking operations,
transportation systems and airports, among many others.
Introduction : Simulation and Modeling Wk1
Slide 7
Use of Simulation Modelling
Simulation is one of the most powerful management
science/operation research tools applied to solve real problems.
•The modelling itself leads to greater insight into the Corporate
investments appraisal.
•Involves the construction of a model of the problem domain
which involves learning through experiments and then permits
testing alternative scenarios using “what if ..?” analysis.
Simulation in Business Modelling
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The essence of Modelling is that a manager makes decisions
in advance of the real product, services or process being
created.
Simulation is one of the most fundamental approach to
decision making.
A tool to gain insights and explore possibilities through the
formalised (situation) involved in using simulation models.
Simulation explores the consequences of decision making
rather than directly advising on the decision itself - it is a
predictive rather than an optimising technique.
Currently there are many tools both simulation language and
packages that could be used for exploring the impacts of
different decisions.
Systems
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System – a collection of parts organized for some purpose
(Coyle, 1996).
Checkland (1981) identifies 4 main classes of systems :
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Natural system – origins lie in the origins of the universe eg. Atom
Designed physical systems – physical systems that are a result of
human design e.g house, car
Designed abstract systems – abstract systems that are a result of
human design e.g. mathematics and literature
Human activity systems – systems of human activity that are
consciously or unconsciously ordered. e.g. Family, city , political
system.
Introduction : Simulation and Modeling Wk1
Slide 10
Why simulate ? – The Nature of operations
Systems
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Variability - many operation systems are subject to variability.
Some are predictable e.g. changing number of operators in a
call centre during the day to meet the changing call volumes
and others are unpredictable e.g arrival rate of patients at
hospital emergency.
Interconnectedness – components of the system do not work
in isolation but affect one another. It is difficult to predict the
effect of the interconnections. e.g customers who have to pass
through various interconnected stages
Complexity – many operations systems are complex,
interconnections and combinations between the components of
the system.
Introduction : Simulation and Modeling Wk1
Slide 11
The Advantages of Simulation
Some of the reasons why simulation is preferable to direct experimentation :
• Cost – Experimentation with real system is likely to be costly.
 It is expensive to interrupt day to day operations to try out new ideas
 If alterations cause operation’s performance to worsen- loss of customer
satisfaction
• Time – Time consuming to experiment with the real system and this may
take many weeks and months before a true reflection is obtained.
• Control of experimental conditions – It is useful to control the conditions
under which the experiment is being done. e.g. it is not easy to control the
arrival of patients at a hospital
• The real system does not exist. The real system may not exist.
• Flexibility to model things as they are (even if messy and complicated)
Introduction : Simulation and Modeling Wk1
Slide 12
Disadvantages of Simulation
Some of the problems associated with using simulation
• Expensive – simulation software is not necessarily cheap and
cost of model development and use may be considerable.
• Time consuming – simulation is a time consuming approach
• Data hungry – most simulations require significant amount of
data
• Requires expertise – requires skills in conceptual modelling,
validation and statistics.
Introduction : Simulation and Modeling Wk1
Slide 13
Applications for which Simulation might be used
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Manufacturing systems
Public systems, health care, military, natural resources
Transportation systems
Construction systems
Restaurant and entertainment systems
Business process reengineering / management
Food processing
Computer system performance
Introduction : Simulation and Modeling Wk1
Slide 14
Models
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Model – set of assumptions/approximations about how the
system works
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Study the model instead of the real system … usually much easier,
faster, cheaper, safer
Can try wide-ranging ideas with the model
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Make your mistakes on the computer where they don’t count, rather than for
real where they do count
Often, just building the model is instructive – regardless of results
Model validity (any kind of model … not just simulation)
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Care in building to mimic reality faithfully
Level of detail
Get same conclusions from the model as you would from system
More in Chapter 12
Introduction : Simulation and Modeling Wk1
Slide 15
Types of Models
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Physical (iconic) models
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Mock-ups of fast-food restaurants
Hospital scheduling
Operating room scheduling
Flight simulators
Logical (mathematical) models
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Approximations and assumptions about a system’s operation
Often represented via computer program in appropriate software
Exercise the program to try things, get results, learn about model
behavior
Introduction : Simulation and Modeling Wk1
Slide 16
Model Classification
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Physical (prototypes)
Analytical (mathematical)
Computer
(Monte Carlo Simulation)
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Descriptive (performance
analysis)
• Prescriptive (optimization)
Introduction : Simulation and Modeling Wk1
Slide 17
Physical
(Prototypes)
Introduction : Simulation and Modeling Wk1
Slide 18
Analytical
(Mathematical)


Single Stage Queuing Model
 


W 
 n  P( N  n )
  1   
1
 
L  W 
Wq  W 

 
Introduction : Simulation and Modeling Wk1
1



    
2
Lq  Wq 
    
Slide 19
Computer
(Monte Carlo Simulation)
Monte Carlo simulation is a spreadsheet simulation, which
randomly generates values for uncertain variables over
and over to simulate a model.
Introduction : Simulation and Modeling Wk1
Slide 20
Prescriptive
(Optimization)
Introduction : Simulation and Modeling Wk1
Slide 21
Studying Logical Models
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If model is simple enough, use traditional mathematical
analysis … get exact results, lots of insight into model
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But complex systems can seldom be validly represented by a
simple analytic model
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Queueing theory
Differential equations
Linear programming
Danger of over-simplifying assumptions … model validity?
Often, a complex system requires a complex model, and
analytical methods don’t apply … what to do?
Introduction : Simulation and Modeling Wk1
Slide 22
Computer Simulation
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Broadly interpreted, computer simulation refers to methods for
studying a wide variety of models of systems
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Numerically evaluate on a computer
Use software to imitate the system’s operations and characteristics,
often over time
Can be used to study simple models but should not use it if an
analytical solution is available
Real power of simulation is in studying complex models
Simulation can tolerate complex models since we don’t even
aspire to an analytical solution
Introduction : Simulation and Modeling Wk1
Slide 23
Different Kinds of Simulation
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Static vs. Dynamic
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Continuous-change vs. Discrete-change
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Can the “state” change continuously or only at discrete points in
time?
Deterministic vs. Stochastic
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Does time have a role in the model?
Is everything for sure or is there uncertainty?
Most operational models:
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Dynamic, Discrete-change, Stochastic
Introduction : Simulation and Modeling Wk1
Slide 24
Using Computers to Simulate
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General-purpose languages (FORTRAN)
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Support packages
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Tedious, low-level, error-prone
But, almost complete flexibility
Subroutines for list processing, bookkeeping, time advance
Widely distributed, widely modified
Spreadsheets
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Usually static models
Financial scenarios, distribution sampling, SQC
Introduction : Simulation and Modeling Wk1
Slide 25
Using Computers to Simulate (cont’d.)
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Simulation languages
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GPSS, SIMSCRIPT, SLAM, SIMAN
Popular, still in use
Learning curve for features, effective use, syntax
High-level simulators
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Very easy, graphical interface
Domain-restricted (manufacturing, communications)
Limited flexibility — model validity?
Introduction : Simulation and Modeling Wk1
Slide 26
The System:
A Simple Processing System
Machine
(Server)
Arriving
Blank Parts
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6
5
Queue (FIFO)
Departing
Finished Parts
4
Part in Service
General intent:
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7
Estimate expected production
Waiting time in queue, queue length, proportion of time
machine is busy
Time units
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Can use different units in different places … must declare
Be careful to check the units when specifying inputs
Declare base time units for internal calculations, outputs
Be reasonable (interpretation, roundoff error)
Introduction : Simulation and Modeling Wk1
Slide 27
Model Specifics
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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
Introduction : Simulation and Modeling Wk1
Slide 28
Goals of the Study:
Output Performance Measures
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Total production of parts over the run (P)
Average waiting time of parts in queue:
N
 WQi
i 1
N
•
N = no. of parts completing queue wait
WQi = waiting time in queue of ith part
Know: WQ1 = 0 (why?)
N > 1 (why?)
Maximum waiting time of parts in queue:
max WQi
i 1,...,N
Introduction : Simulation and Modeling Wk1
Slide 29
Goals of the Study:
Output Performance Measures (cont’d.)
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Time-average number of parts in queue:
20
0 Q (t ) dt
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Q(t) = number of parts in queue
at time t
20
max Q (t )
Maximum number of parts in queue:
0t 20
Average and maximum total time in system of parts (a.k.a. cycle
time):
P
TSi
i 1
P
,
max TSi
TSi = time in system of part i
i 1,...,P
Introduction : Simulation and Modeling Wk1
Slide 30
Goals of the Study:
Output Performance Measures (cont’d.)
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Utilization of the machine (proportion of time busy)
20
0 B(t ) dt
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1 if the machine is busy at time t
, B(t )  
20
0 if the machine is idle at time t
Many others possible (information overload?)
Introduction : Simulation and Modeling Wk1
Slide 31
Pieces of a Simulation Model
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Entities
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“Players” that move around, change status, affect and are affected by
other entities
Dynamic objects — get created, move around, leave (maybe)
Usually represent “real” things
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Can have “fake” entities for modeling “tricks”
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Our model: entities are the parts
Breakdown demon, break angel
Usually have multiple realizations floating around
Can have different types of entities concurrently
Usually, identifying the types of entities is the first thing to do in building
a model
Introduction : Simulation and Modeling Wk1
Slide 32
Pieces of a Simulation Model (cont’d.)
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Attributes
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Characteristic of all entities: describe, differentiate
All entities have same attribute “slots” but different values for different
entities, for example:
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Time of arrival
Due date
Priority
Color
Attribute value tied to a specific entity
Like “local” (to entities) variables
Some automatic in Arena, some you define
Introduction : Simulation and Modeling Wk1
Slide 33
Pieces of a Simulation Model (cont’d.)
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(Global) Variables
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Reflects a characteristic of the whole model, not of specific entities
Used for many different kinds of things
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Travel time between all station pairs
Number of parts in system
Simulation clock (built-in Arena variable)
Name, value of which there’s only one copy for the whole model
Not tied to entities
Entities can access, change variables
Writing on the wall
Some built-in by Arena, you can define others
Introduction : Simulation and Modeling Wk1
Slide 34
Pieces of a Simulation Model (cont’d.)
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Resources
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What entities compete for
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Entity seizes a resource, uses it, releases it
Think of a resource being assigned to an entity, rather than an entity
“belonging to” a resource
“A” resource can have several units of capacity
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–
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People
Equipment
Space
Seats at a table in a restaurant
Identical ticketing agents at an airline counter
Number of units of resource can be changed during the simulation
Introduction : Simulation and Modeling Wk1
Slide 35
Pieces of a Simulation Model (cont’d.)
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Queues
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Place for entities to wait when they can’t move on (maybe since the
resource they want to seize is not available)
Have names, often tied to a corresponding resource
Can have a finite capacity to model limited space — have to model what
to do if an entity shows up to a queue that’s already full
Usually watch the length of a queue, waiting time in it
Introduction : Simulation and Modeling Wk1
Slide 36
Pieces of a Simulation Model (cont’d.)
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Statistical accumulators
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Variables that “watch” what’s happening
Depend on output performance measures desired
“Passive” in model — don’t participate, just watch
Many are automatic in Arena, but some you may have to set up and
maintain during the simulation
At end of simulation, used to compute final output performance
measures
Introduction : Simulation and Modeling Wk1
Slide 37
Pieces of a Simulation Model (cont’d.)
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Statistical accumulators for the simple processing system
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Number of parts produced so far
Total of the waiting times spent in queue so far
No. of parts that have gone through the queue
Max time in queue we’ve seen so far
Total of times spent in system
Max time in system we’ve seen so far
Area so far under queue-length curve Q(t)
Max of Q(t) so far
Area so far under server-busy curve B(t)
Introduction : Simulation and Modeling Wk1
Slide 38
Simulation Dynamics:
The Event-Scheduling “World View”
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Identify characteristic events
Decide on logic for each type of event to
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Effect state changes for each event type
Observe statistics
Update times of future events (maybe of this type, other types)
Keep a simulation clock, future event calendar
Jump from one event to the next, process, observe statistics,
update event calendar
Must specify an appropriate stopping rule
Usually done with general-purpose programming language (C,
FORTRAN, etc.)
Introduction : Simulation and Modeling Wk1
Slide 39
Events for the
Simple Processing System
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Arrival of a new part to the system
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Update time-persistent statistical accumulators (from last event to now)
–
–
–
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“Mark” arriving part with current time (use later)
If machine is idle:
–
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Start processing (schedule departure), Make machine busy, Tally waiting time in
queue (0)
Else (machine is busy):
–

Area under Q(t)
Max of Q(t)
Area under B(t)
Put part at end of queue, increase queue-length variable
Schedule the next arrival event
Introduction : Simulation and Modeling Wk1
Slide 40
Events for the
Simple Processing System (cont’d.)
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Departure (when a service is completed)
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Increment number-produced stat accumulator
Compute & tally time in system (now - time of arrival)
Update time-persistent statistics (as in arrival event)
If queue is non-empty:
–

Take first part out of queue, compute & tally its waiting time in queue, begin service
(schedule departure event)
Else (queue is empty):
–
Make the machine idle (Note: there will be no departure event scheduled on the
future events calendar, which is as desired)
Introduction : Simulation and Modeling Wk1
Slide 41
Events for the
Simple Processing System (cont’d.)
•
The End
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Update time-persistent statistics (to end of the simulation)
Compute final output performance measures using current (= final)
values of statistical accumulators
After each event, the event calendar’s top record is removed to
see what time it is, what to do
Also must initialize everything
Introduction : Simulation and Modeling Wk1
Slide 42
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, ...
Introduction : Simulation and Modeling Wk1
Slide 43
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, ...
Introduction : Simulation and Modeling Wk1
Slide 44
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, ...
Introduction : Simulation and Modeling Wk1
Slide 45
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, ...
Introduction : Simulation and Modeling Wk1
Slide 46
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, ...
Introduction : Simulation and Modeling Wk1
Slide 47
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, ...
Introduction : Simulation and Modeling Wk1
Slide 48
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, ...
Introduction : Simulation and Modeling Wk1
Slide 49
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, ...
Introduction : Simulation and Modeling Wk1
Slide 50
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, ...
Introduction : Simulation and Modeling Wk1
Slide 51
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, ...
Introduction : Simulation and Modeling Wk1
Slide 52
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, ...
Introduction : Simulation and Modeling Wk1
Slide 53
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, ...
Introduction : Simulation and Modeling Wk1
Slide 54
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, ...
Introduction : Simulation and Modeling Wk1
Slide 55
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, ...
Introduction : Simulation and Modeling Wk1
Slide 56
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, ...
Introduction : Simulation and Modeling Wk1
Slide 57
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 value
20
•
Utilization of drill press:
Area under B(t ) curve 18.34

 0.92 (dimension less)
Final clock value
20
Introduction : Simulation and Modeling Wk1
Slide 58
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
Introduction : Simulation and Modeling Wk1
Slide 59
Overview of a Simulation Study
•
•
•
•
•
•
•
•
•
Understand the system
Be clear about the goals
Formulate the model representation
Translate into modeling software
Verify “program”
Validate model
Design experiments
Make runs
Analyze, get insight, document results
Introduction : Simulation and Modeling Wk1
Slide 60
Review Questions
•
Explain the following concepts, giving examples of the different
types of each :



•
•
•
Simulation
Models
Systems
Explain the advantages and disadvantages using simulation
Using a bank system or supermarket, identify the elements of
variability, interconnectedness and complexity
Using examples of systems on Slide 10, clearly outline what
aspects make simulation appropriate for at least 3 situations
Introduction : Simulation and Modeling Wk1
Slide 61