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To Q or Not To Q: Is Simulation the Question?
CMG 2011Session 325 – Paper Number 1115 – Tuesday, Dec 6, 2011
Dr. Tim R. Norton
SimSolTrainingSM Training division of Simalytic Solutions, LLC
719-635-5825
email: [email protected]
http://www.simalytic.com
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 2
Agenda
What is Modeling? Brief look at Modeling Concepts Modeling Fundamentals
Practical Application of Modeling Real-world considerations
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 3
What is Modeling? A Model:
A schematic description of a system, theory, or phenomenon that accounts for its known or inferred properties and may be used for further study of its characteristics.
The American Heritage Dictionary, 3rd Edition, 1992
Modeling: To make or use a model.
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 4
What is Modeling? Modeling
A formula A picture An object A technique A useful representation
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 5
Classes of Modeling Physical
An object somewhat like the system Aerodynamics
Mathematical A formula representing system attributes
Ballistics
Process A representation of system interactions
Artificial environments Virtual physical models
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 6
Modeling Fundamentals What are the parts to Modeling?
Events or processes Queuing Distributions Modeling Techniques
Analytic Formulae Simulation – DES and Continuous Markov Chains Petri Nets Others
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 7
Modeling Fundamentals What are Events or Processes?
Events Something discrete – counted – beginning & end
Transactions, customers, cars, etc.
Processes Something that happens over time – measured
Bouncing ball, cloud formation, business workflow, etc.
Independent Model uses one or the other
Inter-Related Events trigger processes – processes trigger events
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 8
Modeling Fundamentals Queuing
Behavior where events or processes are waiting External – to get into the system Internal – at service points within the system
Major consideration in many models Slows down the system
Increases response time Reduces through-put
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 9
Modeling Fundamentals Service Centers and Queues
T = Total time at the Service Center W = Time waiting for service S = Time getting service
QueueArrivals Departures
ServiceCenter
W S
T
Queue Queue
Arrivals
Departures
ServiceCenter
ServiceCenter
Simple Service Center with Queue System of Simple Service Centers
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 10
Modeling Fundamentals Open Class
Workload Intensity – Arrival rate Unbounded customers
Closed Class Workload Intensity – Customer population Bounded customers
QueueArrivals Departures
ServiceCenter
Queue
ServiceCenter
Queue
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 11
Modeling Fundamentals Distribution Functions are patterns
Need to match model drivers Complex or simple Is close good enough?
Why Distributions Matter How to know the unknown future?
Uncertainty Variability Randomness
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 12
Modeling Fundamentals Modeling Techniques
Analytic Formulae Simulation
DES Continuous
Markov Chains Petri Nets Others
S
ST
1
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 13
Modeling Fundamentals Markov Chains
Foundation of most modeling Finite state-space Probabilities for state transitions
0 1 2 3 k
0 1 2 3 k-1 k
0 1 2 3 k k+1
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 14
Modeling Fundamentals Petri Nets
Places, transitions, arcs and tokens Tokens move from place to pace Transitions
control movement Rules to move
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 15
Modeling Fundamentals Analytic Formula
Queuing Theory Queuing Networks
Example Calculate how long it takes a customer to get their
fast food T is the average total time per customer S is the time at the counter (lambda) is the number of customers that come into
the restaurant per minute
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 16
Modeling Fundamentals Morning vs. Lunch?
Is another register needed? Does single server scenario exceed expectation?
Time to serve a customer, S, is the same 3 minutes for both cases
Customer arrivals, (lambda), changes Morning: 0.1 per minute (1 every 10 minutes) Lunch: 0.3 per minute (~1 every 3 minutes)
Calculate T for each case: Morning: T = 4.286 minutes Lunch: T = 30 minutes
S
ST
1
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 17
Modeling Fundamentals Why so long?
Customers show up slower that it takes to get their order.
The formulae assumes a non-uniform distribution Distributions are the key
Most activities involving people are Poisson arrivals The system is just as busy in either case
Simulation chart
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 18
Modeling Fundamentals What is “Poisson Arrivals”?
The inter-arrival times are non-uniform random numbers from an exponential distribution.
Arrival # Interarrival time1 0.62 1.63 2.84 0.05 1.16 2.37 8.68 3.39 6.6
10 0.611 4.112 4.913 2.314 1.0Generated using EasyFitXL
15 3.216 11.417 3.118 1.019 0.720 0.321 3.922 3.023 0.124 8.025 2.126 1.327 4.628 7.729 0.430 3.1
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 19
Modeling Fundamentals Other Distributions
Useful for specific situations Normal – testing Erlang – telephony Pareto (heavy-tail) – network traffic Many, many others
Normal Pareto Triangular
Exponential
Erlang
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 20
Modeling Fundamentals Queuing Theory Formulae
Built-in assumptions about the arrival and service distributions
Kendall notation: A/B/C/K/N/D – often shortened to A/B/C
A = Arrival distribution B = Service distribution C = Number of servers K = Number of places in the system (capacity); defaults to N = Source population size; defaults to D = Queuing discipline; defaults to FIFO
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 21
Modeling Fundamentals Common Distributions for A & B
M – Markovian (Poisson/Exponential) D – Degenerate (deterministic or fixed) Ek – Erlang (k = the shape parameter) G – General Some others
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 22
Modeling Fundamentals M/M/1 Model
Poisson arrivals Exponential service time One server Infinite capacity in the system Infinite number of potential customers FIFO priority
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 23
Modeling Fundamentals Simulation
DES – Discrete Event Simulation Models that evolve over time where system state
variables change instantaneously at separate (countable) points in time.
Continuous Models that evolve over time where the values of
system state variables can be calculated for any arbitrary point in time.
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 24
Modeling Fundamentals
DES Example Calculate how long it takes customers to get
their fast food at lunch S is the time at the counter
3 minutes Customer arrivals
Exponential inter-arrival time distribution (shown in table from earlier example)
Arrival # Interarrival time1 0.62 1.63 2.84 0.05 1.16 2.37 8.68 3.39 6.6
10 0.611 4.112 4.913 2.314 1.0
15 3.216 11.417 3.118 1.019 0.720 0.321 3.922 3.023 0.124 8.025 2.126 1.327 4.628 7.729 0.430 3.1
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 25
Modeling Fundamentals DES Example
Step through each arrival
Increment clockfor each event
Additional system state counters
Customers Waiting Waiting time etc.
Analytic chart
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 26
Modeling Fundamentals Continuous Example
Uses formulaeto calculate positionfor each plot point
Gravity: acceleration down
Elasticity: acceleration up
Energy is absorbed etc.
Use SlideShow mode to see active graph.
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 27
Modeling Fundamentals
Business Modeling Continuous Simulation Models Business elements
Process Flowsand Levels
Business Modeling Tools
Powersim, Vensim, STELLA and ithink
Call_Backlog
Transactions_per_Call
Computer_Time
Number_of_Operators
Transaction_Setup_Time
Calls_Completed
Transaction_Response_Time
New_Calls
Calls_per_Operator
Other_Time
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 28
Practical Application
Real-world considerations Modeling Often Not Well Received
Large effort for unwanted results? Modeling takes too long? Doesn’t provide anything useful? Looking for the ‘right’ modeling tool?
Modeling Problem Business problem Not technical problem
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 29
Practical Application
Common sense axioms Modeling technique Target system Business problem
Practical techniques
“The right answer and it’s provable.” vs.
“A reasonable answer and it’s useful.”
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 30
“The Problem”
How to identify the Desired Result and differentiate it from the Requested Result? Identify the Recipient Understand their Goals
“I know that your believe that you understand what you think I said, BUT I am not sure your realize that what your heard is not what I meant!” Anonymous (on a postcard), © 1982 H. a L. Inc.
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 31
Know Your Goals
Benefit of Understanding Goals “If you don't care where you’re going, then any
road will do.” Example of Goal Impacting Solution
Taking a Trip
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 32
The Trip
Planning a Trip to New York City What are the goals? Who are the players? What are the constraints?
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 33
The Trip - Why
What is the Reason for the Trip? Business Pleasure Family emergency Have to leave town
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 34
The Trip - Who
Who Else is Taking the Trip? Person alone Boss Co-worker Couple Family Group
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 35
The Trip - How
How many modes of transport are there to get from Washington DC to New York City Car, train, bus, plane, boat, bike, walk, others... Which one to pick depends on the objectives of
the trip: Get there fast, see the sites, relax and enjoy, get there
cheap, safety first, visit someone on the way, hidden agenda.
Each “Why” maps to one or more “How”
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 36
The Trip - Summary
What makes a Good Plan? Hard to judge without fully understanding the goals Approach:
Who & Why Then How
Is the Desired Result different from the Requested Result? Hidden agenda?
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 37
Modeling Objectives
Objective Find the successful middle ground
Cost Performance
Performance Assessed against business objectives and goals
Projected business volume and functionality Model to predict the likely performance Meet business goals at future volumes
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 38
Problem Identification
Identify Key Players and Objectives Focus on the right problem
Approach: Establish a Process
Informal for own use Formal for project results Standardized for certification
Standardize the Deliverables Quantifies time and effort required
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 39
Where to Focus
Where to Focus the Modeling Effort? Find the Answer
vs. Justify the Solution
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 40
Required Solution
What is the Required Solution? Scope
The extent it applies to one or more domains Granularity
The level of detail to be included Scale
The relative time scale to use Measurement
The technique to determine success
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 41
Solution Scope
Technical Identify the best technology to solve the problem
CPU X runs workload 20% faster than CPU Y
Political Support the solution implemented for “business”
reasons Will CPU Y will provide the workload acceptable
resources for the rest of the year?
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 42
Solution Granularity
High-level Generalized projections of growth
Projected growth requires system hardware increase of 30% next year
Detailed Specific requirements
Sys A needs an additional CPU and Sys B needs 32MB
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 43
Solution Scale
Resource Usage Average consumption over time
Average CPU usage remains below 80%
Bottleneck Identification Transient conditions that impact response time
The “Waiting for CPU” queue goes over 50 every day between 2 PM and 3 PM
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 44
Solution Measurement
Service Level Objectives Objective measurement against business needs
Workload X response time is staying below the goal of 95% in 0.8 seconds
“User Happiness” Subjective measurement
“I just got a call from an unhappy VP in Finance!”
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 45
Solution Focus
Balance Requirements vs. Solutions Requested Result vs. Desired Result Perceptions vs. Reality
Approach: Identify applicable techniques Apply the correct tools How to present the results
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 46
Identify Requirements
Audience: Requester or messenger or both Multiple agendas
Output: Report White paper Presentation
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 47
Spiral Process
Plan How to meet the objectives with least effort
Develop Generate some results
Evaluate How well does output meet the objectives
Present Get feedback to revise plan
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 48
Spiral Model Development
The Spiral Modeling Methodology was derived from the Spiral Software Development Methodology first discussed by Barry W. Boehm in “A Spiral Model of Software Development and Enhancement”, IEEE Computer, May 1988.
Plan
Develop Evaluate
Present
TrendVerify
SWAG
Model ValidateCalibrate
ObjectivesVerify
Validate
Model
Confirm
Informal Formal
Results
Objectives
Feedback:Re-evaluate
and ReviseWhat
How
Tool Assessment
Revised Requirements
Initial Requirements
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 49
Spiral Approach Benefits Objective
Focus on Requester Reduce
Time Effort
Responsiveness Perceived Improvement Adjust to changes
Requirements or objectives
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 50
Increasing Complexity
Start Simple and Work Up Guess
Almost no data but a reasonable conjecture Experience
Little data and a familiar situation Trends
Historical data and statistical analysis Models
Lots of data and a predictive technique
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 51
SWAG
“Scientific Wildly Analyzed Guess” What Effects the End Result:
What’s of interest? (CPU, Disk, etc.) Assume it’s zero Does the response time change significantly? Only worry about things that make a difference
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 52
SWAG Examples
Where is the Major Delay? Only B worth doing a
CPU upgrade Faster Disk helps A
and maybe C High Wait in C may
be application problem Server resources
won’t help D
0 1 2
D
C
B
A
CPU I/O Wait
I/O Network
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 53
Trend Analysis
Patterns in Historical Data Assumes future is an extension of past The more historical data the better
Works Well: Mature and stable environments Accommodates seasonal and regular anomalies
Fails: Sudden growth or erratic environments
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 54
LFFT
“Linear Function Fit Tool” Devised by Ray Wicks (IBM)
Simple Trend Analysis Tool Plot the data Pick up an LFFT (a pencil works well) Lay it on the plot Find the last section of data it fits Extend that section
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 55
LFFT Examples
Four Workloads Uniform growth Trend fits all
months well Good “feel” about
predicting next quarter
0
20
40
60
80
100
120
140
160
Ja
n
Fe
b
Ma
r
Ap
r
Ma
y
Ju
n
Ju
y
Au
g
Sep
ABCD
Trend
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 56
LFFT Examples
Same Four Workloads Workload D jumps
by 40 in April Really two different
the same rate Anomaly not growth Next quarter prediction
better with trend of last group
020406080
100120140160180200220
Ja
n
Fe
b
Ma
r
Ap
r
Ma
y
Ju
n
Ju
l
Au
g
Sep
ABCD
Real Trend
Overall Trend
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 57
Simple Models
What is the Minimum Model? Before You Use a Tool
Collect data at several workload rates Find relationships:
Response time per transaction? Resource usage per transaction? Workload to overall system resource usage? Any others that apply to application?
Project it out and talk to the Requester Understand what type of tool is needed
© 2011 Simalytic Solutions, LLC To Q or Not To Q: Is Simulation the Question? 58
Conclusion
Many Modeling Techniques Analytic Simulation
DES or Continuous Specialized
Petri Nets, Markov Chains, Business Process, etc.
Business Problem Understand the requirements Focus on the requestor’s goals
To Q or Not To Q: Is not the Question,
but ratherWhat’s the best way to a useful
answer?
Presentation will be available at: http://www.simalytic.com/Papers.html