Date post: | 30-Dec-2015 |
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Models vs. Simulations
• Model▫The actual program▫The abstraction of the real world▫Captures the elements of the system and the
behavior of the elements being modeled
• Simulation▫Running the model to simulate the passage of time▫Exploring the behavior of the modeled system over
time.▫ In studying complex systems, sometime
unexpected patterns emerge that weren’t explicitly programmed into the model.
Simulations on Your Computer•Why?
Once the model is developed▫Can run many trials▫Can run many parameters
Can develop models for situations where experimentation is difficult
▫Too dangerous▫Too expensive▫Too time intensive
Deterministic vs. Stochastic•Two types of simulation models:
▫Deterministic simulation models: Provide single outputs for each set of inputs No Randomness involved
▫Stochastic simulation models Can produce somewhat different outputs for each
set of inputs Randomness IS involved Agent-based models of Complex Adaptive Systems
have Randomness -> they are stochastic Look at the probability distribution of possible
outcomes.
How to run a Simulation
•Simple parameter sweeping (one dimension)
▫Hold all other variables constant▫Set min, max, and increment for one
variable. ▫Sweep one variable (from min to max
value)
•Repetition – Because the models are stochastic
▫Repetitions at each setting▫Take the average?
•What output do you want?
Ant Foraging Model•Food piles•Ants wander around looking for food•Ant finds a piece of food
▫Carries the food back to the nest▫Drops a chemical as it moves – trail
Chemical evaporation Chemical diffusion
•Other ants find the chemical trail, ▫Follow the chemical to food▫Carries the food back to the nest▫Reinforce chemical trail
•Repeated until there is no more food in that pile.
Ant Foraging Experiment/Simulation
•Three Parameters
▫Number of ants (0-200)
▫Diffusion rate (0-99) How quickly the chemical diffuses How wide the trail is
▫Evaporation rate (0-99) How fast the chemical evaporates How long the trail lasts
Ant Foraging Experiment/Simulation
•NEED TO KNOW WHAT OUTPUT DATA you are collecting….
Is it food left after # ticks?Is it ticks before all food is found?
Parameter Sweeping
•Picking Sample Points (where and how many)
▫Make sense no ants does not make sense
▫Must represent the variable or parameter being explored
Extremes are not enough▫2 points = line…. assumption
Must use points in the middle▫More points if behavior is complicated
Ant Simulation – Parameter Sweeping
•Parameter Sweeping▫Ants (3 sample points)
50, 100, 200▫Diffusion rate (4 sample points)
0, 33, 66, 99▫Evaporation rate (4 sample points)
0, 33, 66, 99
•Total Number of sampling points▫3 x 4 x 4▫48 sample points
Repetitions
•Stochastic model
•Must run repetitions at each sample point
•How many repetitions?▫How random is the process?▫Up to the experimenter – YOU!
Ant Simulation - Repetitions
•I get to decide▫Run the model to see how random ▫5 repetitions
•How many experiments?
(number of sample points) x (number of repetitions)
( 48 ) x ( 5) = 240
•Can Limit Experiments ▫Fix the number of ants to 100
(number of sample points) x (number of repetitions)
( 4 x 4 ) x ( 5) = 80
What Output?•Simulation Output depends on the model
▫Number of ticks▫Number of agents▫Number of patches of color
•Epidemic model▫Ticks until everyone infected▫Number of agents infected after number of
ticks•Ants Model
▫Amount of food left after # ticks▫Ticks before all food is found▫Ticks before all found gathered
Stopping Forever Button
•Forever GO button can go forever•Want an accurate measurement•Automatically Stop the Forever GO button
▫Conditional Stop at the TOP of GO procedure
to go if condition? [ stop ] ...end
Table of Results
Average Number of Ticks Until Food is Gathered
Evaporation Rate
0 33 66 99
Diffusion Rate
0 1565 1558 1442 1516
33 1329 2507 1988 1320
66 1561 2892 2066 1428
99 1521 3467 2157 1440
Graph of Results
0 33 66 990
500
1000
1500
2000
2500
3000
3500
4000
EFFECT OF DIFFUSION RATE
0336699
DIFFUSION RATE
AV
ER
AG
E T
ICK
S
Graph of Results
0 33 66 990
500
1000
1500
2000
2500
3000
3500
4000
EFFECT OF EVAPORATION RATE
0336699
EVAPORATION RATE
AV
ER
AG
E T
ICK
S
Computer Simulation Write-up:•Must include enough replication
▫Description of problem of interest and abstraction
▫Description of Model Assumptions/Simplifications Variables/Parameters
▫Description of Simulation Parameter Sweeping Repetitions
▫Description of Results Verbal Description Tables/Graphs
▫Discussion of Results/Conclusions
Summary• Model – The program that captures the elements of the
system being modeled and the behavior of those elements
• Simulation - Running the model to explore the behavior of the modeled system over time.
• Deterministic simulation models: Provide single outputs for each set of inputs because No Randomness involved
• Stochastic simulation models: produce different outputs for each set of inputs because Randomness IS involved
Agent-based models of Complex Adaptive Systems have Randomness -> they are stochastic
Look at the probability distribution of possible outcomes.
• How to perform a Stochastic Simulation Parameter Sweeping Repetition
• When you write up simulation results must include enough detail for simulation to be repeated and explained