W10 Stochastic Modeling

Question 1

Simple(r) Models are created using two things….

Answer 1

Assumptions

Simplifications

Question 2

Frequent Mistake when evaluating stochastic models?

Answer 2

only considering the mean!

Question 3

Examples for stochastic elements

Answer 3

• customer arrivals
• type of customers
• serving times
• machine cycle times
• machien breakdowns
• defective parts
• travel times

Question 4

Where do probabilities come from?

Answer 4

past data
expert judgement
nature of situation

->need to be validated

Question 5

Congruental Number Generators

Answer 5

only possible values are fractions of m;
repeating cycle
maximum period before repetition is m

Question 6

Testing random number generators

Answer 6

• range
• correlations
• pairs
• plot
• statistical test (chis-squared)

Question 7

Continuous Distributions and applications

Answer 7

negative exponential- arrivals
lognormal -service times
erlang -service times
weibull - times between breakdowns
normal - finance
uniform -equal probs
triangular - min max mode
empirical if nothing else fits

Question 8

Discrete Distributions

Answer 8

e.g. binomial or Poisson for customer arrival probs

Question 9

Multiple Simulation Runs
why?
what do?

Answer 9

one run purely random

do many, compute statistical measures and CIs

every run is a sample

Question 10

CI example
alpha = 0.05
p = 0.01
conv after 20

Answer 10

with a 95% probability, the mean as observed over 20 runs does not deviate by more than 1% from the population mean.

Question 11

why student distribution?

Answer 11

limited number of random draws from n.d. pop follows Student (t) distr