TCOM 512 Modeling and Simulation

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TCOM 512 Modeling and Simulation

• Fall 2004

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What is Modeling?

• Modeling is a process for studying the behavior
  of complex systems
• abstracting important details of system
• Ignore rest
• Study simpler system to understand behavior of
  complex system.
• How do we know what details we can ignore?
• Knowledge
• Heuristics
• Experience
• Iteration

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How do we choose between alternatives?

• What are the properties we need?
• What are the properties each approach possesses?
• Known
• Need analysis
• Estimate performance
• average case
• worst case
• Under what assumptions?

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Approaches to modeling

• Various Approaches
• Analytic Equations (or other formalisms) that
  result in closed-form solution of system.
• Simulation Program, or physical model, or
  systems of equations, that describe instantaneous
  state of system --- that we can use to emulate
  the behavior of the system
• Emulation combine simulation and a live network
• Prototype a proof of concept implementation
• Operational system The real stuff
• In all approaches, several basic steps
• Develop model
• Verify model
• Evaluate results of model
• Validate model
• Iterate, if necessary

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Developing a model

• What does my system do?
• Understand how to deal with basic issues how do
  I deal with things that proceed in parallel?
• How do I know when I can ignore details?
• Hard rules? No
• Heuristics.
• Often dependent on particular type of analysis

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Back of envelope calculations

• Simplest form of analysis
• Implication get rid of all details so resulting
  computation can fit on a piece of paper as small
  as the back of an envelope
• Another implication you can do this sort of
  analysis in your head

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Sensitivity

• Given model, how sensitive is it to values of
  parameters?
• When can I round numbers?
• How sensitive is it to errors?
• How accurate is my estimate?
• When can I drop more details?
• Do I need to simulate a component in detail, or
  can I summarize it?

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Verification

• Is the model represented correctly? Bugs in the
  equations?
• Are the input parameters accurate? Correct?

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Validation

• Is model/results believable?
• Matches known/measurable behavior?
• Consistent (roughly) with another model?
• Careful that you don't make the same mistake!
• Usually use one or more attempts at
  back-of-the-envelope modeling to validate other
  approaches. Not as useful for validating back of
  the envelope approach, unless more than one model
  is possible.
• Violates laws of probability or reality?

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Simulations

• Must start with a model that abstracts away
  certain details.
• Abstraction differs from analytic model
• Functional/procedural/operational description
• Must frame things in terms of events

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What is simulation?
system boundary
system under study (has deterministic rules
governing its behavior)
exogenous inputs to system (the environment)
real life
observer
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Why Simulation?

• goal study system performance, operation
• real-system not available, is complex/costly or
  dangerous (eg space simulations, flight
  simulations)
• quickly evaluate design alternatives (eg
  different system configurations)
• evaluate complex functions for which closed form
  formulas or numerical techniques not available

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Simulation advantages/drawbacks

• advantages
• save lives, money
• find bugs (in design) in advance
• generality over analytic/numerical techniques
• detail can simulate system details at arbitrary
  level
• drawbacks
• caution does model reflect reality
• large scale systems lots of resources to
  simulate (especially accurately simulate)
• may be slow (computationally expensive 1 min
  real time could be hours of simulated time)
• art determining right level of model complexity
• statistical uncertainty in results

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Programming a simulation

• Whats in a simulation program?
• simulated time internal (to simulation program)
  variable that keeps track of simulated time
• system state variables maintained by
  simulation program define system state
• e.g., may track number (possibly order) of
  packets in queue, current value of retransmission
  timer
• events points in time when system changes state
• each event has associated event time
• e.g., arrival of packet to queue, departure from
  queue
• precisely at these points in time that simulation
  must take action (change state and may cause new
  future events)
• model for time between events (probabilistic)
  caused by external environment

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Discrete Event Simulation

• simulation program maintains and updates list of
  future events event list
• simulator structure

initialize event list
get next (nearest future) event from event list

• Need
• well defined set of events
• for each event simulated system action, updating
  of event list

time event time
process event (change state values, add/delete
future events from event list
update statistics
n
done?
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Simulation example

• processes arrive (avg. interrarrival time 1/ l)
  for execution (avg. execution time 1/m) on
  dual-processor system
• arriving customer joins CPU queue with smallest
  number of waiting processes

m1
l
m2

• state of system size of each queue
• system events
• job arrivals
• service time completions
• define performance measure to be gathered

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Simulation example

• Simulator initialization
• event list
• state variables

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Simulation example

• Simulator actions on arrival event
• if a queue empty place job in service (pick
  one of empty queues), determine its service time
  (a random number drawn from service time
  distribution) add future event onto event list
  for job completion, set number of jobs in queue
  to 1
• if both queues full increment dropped
  packets, ignore arrival
• else find which queue to place job in
  (shortest, with ties broken randomly), increment
  number in queue where queued
• create event for next arrival (generate
  interarrival time) stick event on event list

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Simulation example

• Simulator actions on departure event
• Remove event, update simulation time, update
  performance statistics
• decrement counter of number of jobs in queue
• If (number of jobs in queue gt 0) put next job
  into service schedule a completion event
  (generate service time for job)

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Back of the envelope calculation
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Objectives

• Back of envelope calculation
• Goal is to make rapid estimates
• To eliminate candidate solutions
• Establish feasibility
• Sketch potential paths to a solution
• Most engineers remember key numbers related to
  their field, no one has all the details
• Need to estimate not only the values of numbers
  we need, but which numbers are appropriate, and
  how to perform the calculation
• Need to emphasize that these are rough estimates
• Emphasis here is on order of magnitude
  estimates

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Accuracy of calculations

• Well-known curve of calculations accuracy versus
  mental effort

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Fermi questions

• How many piano tuners are there in Chicago?
• Idea is to think about the process of estimating
  an answer without any specialized knowledge
• Requires estimation of physical quantities to
  arrive at an answer
• Goal is to get an answer to an order of magnitude
  by making reasonable assumptions about the
  situation
• Not relying on definite knowledge for an exact
  answer

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Fermi questions

• Posed with limited information given
• How many water balloons would it take to fill the
  school gymnasium?
• Requires that many more questions be asked
• How big is a water balloon
• What are the approximate dimensions of the gym
• What measurement must be estimated using the
  dimensions of the gym
• Requires communication
• Utilizes estimation
• Emphasizes process rather than the answer

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Fermi question

• How many piano tuners in NYC?
• Approximately how many people in NYC?
• 10,000,000
• Does every individual own a piano?
• No
• Okay families own a piano
• How many families are there in NYC
• Perhaps 2,000,000 families in NYC
• Does every family own a piano?
• No
• Perhaps one out of every five does
• It means that there are about 400,000 pianos in
  NYC

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Fermi question

• How many piano tuners for 400,000 pianos
• Assume on the average every piano gets tuned once
  a year, that there are 400,000 piano tunings
  every year
• How many piano tunings can one piano tuner do?
• Lets assume four pianos a day
• Assume 200 working days per year
• So every tuner can tune about 800 pianos per year
• How many piano tuners are needed in NYC?
• Number of tuners is approximately 400,000/800 or
  500 piano tuners

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General principles

• Einsteins famous advice
• Everything should be made as simple as possible,
  but no simpler
• Ignore factors of 2, pi etc
• Round to the nearest 0,5,10
• Corollary do not make numbers more precise than
  is necessary
• Guess numbers that you do not know
• Try to make your guesses good ones within the
  bounds of common sense
• Adjust geometry to suit you

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General principles

• Use the principle of conservation
• What goes in must come out or stay
• Ensure formulas are dimensionally correct
• Apply a plausibility filter
• Need best case or worst case

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Some examples

• What is the mass in pounds of the number of
  students in this class?
• How many gallons of gasoline are used by cars
  each year in NYC?
• How high would a stack reach if you piled on a
  million dollar bills in a single stack
• How many hairs are on your head

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WLAN networks

• How many data sessions possible?
• How many voice sessions possible?

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WLAN networks

• How many voice conversations are possible in a
  WLAN network?
• How many data conversations are possible in a
  WLAN network?
• How many APs needed to support an enterprise?
• Size of the office
• Types of applications desired
• Coverage area of AP

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802.11 medium access rules
Basic medium access
Fragmentation
Transmission of multiple fragment MSDU using SIFS
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TCP throughput/loss relationship
packets sent per period
W
TCP window size
W/2
period
time (rtt)
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TCP throughput/loss relationship
packets sent per period
W
TCP window size
W/2
period
time (rtt)
B throughput formula can be extended to model
timeouts and slow start (PFTK)
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The end!