ISYE 6644 MIDTERM EXAM
NEWEST EXAM WITH COMPLETE
QUESTIONS AND DETAILED ANSWERS
Which type of simulation focuses on long-term behavior? Examples include: long-
running assembly line in a factory, performance of a transportation network under
various conditions, and an estimate of the unemployment rate 30 years from now
(M1L9). - ✔✔✔ Correct Answer > Steady-state simulations
Which method is used to analyze the simulation output for terminating simulations
(M1L9)? - ✔✔✔ Correct Answer > Independent Replications.
Make indep runs under the same conditions, get the sample mean. Sample means
will approximate iid normal (by CLT), which can use classical stats tests. NOTE:
sample means are used and NOT the original data since raw output is likely not iid,
normal.
What is one method described in class to analyze simulation output for steady state
simulations (M1L9)? - ✔✔✔ Correct Answer > Batch means.
This involves warming up the simulation (initialization bias / not included in
analysis). Make one long run. Break up run into evenly sized batches and calculate
sample mean from each batch. Do classic stats assuming iid normal on the batch
means (relies on CLT).
Name the two numerical methods covered in class to find the zeroes (roots) of a
complicated non-linear function that may not have a closed-form solution. - ✔✔✔
Correct Answer > 1. Bisection method
2. Newton's method
,Be able to apply either one to find the zeroes of a function on a test.
Bisection: linear convergence (slower), but guaranteed to find a zero if continuous
function.
Newton's method: quadratic convergence (faster), but NOT guaranteed to find a
zero.
Some apply a hybrid approach :)
What is simulation (M1L3)? - ✔✔✔ Correct Answer > Imitation of a real-world
process or system over time.
What is a model (M1L3)? - ✔✔✔ Correct Answer > High-level representations of
the operation of a real-word process or system.
, Graphically, what is an indication that your pseudorandom number generator is "no
good" (M1L7). - ✔✔✔ Correct Answer > Example was graphing two "random
variates" in the x-y plane that were generated from uniform distributions
transformed into normal distr (Box Muller Method). If a pattern in the graph
appears, this is "bad." You expect lots of random points clustered around the center
that spread out evenly in all directions from the center. Spiral patterns = no good.
In Queuing models, what does each part of the Kendall notation mean: A/B/C
(general version) applied to a M/M/1 (a specific version)(M1L7)? - ✔✔✔ Correct
Answer > A = Distrib of arrival times
B = Distrib. of service times
C = # of servers in the system
M = arrival times are Poisson process (lambda)
M = exponential service times (mu)
1 = a single server
"M" stands for Markov, but really it means exponential?
Describe what a "random walk" model is and what "motion" it converges to
(M1L7)? - ✔✔✔ Correct Answer > Model where the variable "step" size changes
randomly with each time increment (step size = randomly sampled from a normal
distribution?).
Converges to Brownian Motion: as time steps become smaller and # of steps larger.
Continuous time, stochastic.
NEWEST EXAM WITH COMPLETE
QUESTIONS AND DETAILED ANSWERS
Which type of simulation focuses on long-term behavior? Examples include: long-
running assembly line in a factory, performance of a transportation network under
various conditions, and an estimate of the unemployment rate 30 years from now
(M1L9). - ✔✔✔ Correct Answer > Steady-state simulations
Which method is used to analyze the simulation output for terminating simulations
(M1L9)? - ✔✔✔ Correct Answer > Independent Replications.
Make indep runs under the same conditions, get the sample mean. Sample means
will approximate iid normal (by CLT), which can use classical stats tests. NOTE:
sample means are used and NOT the original data since raw output is likely not iid,
normal.
What is one method described in class to analyze simulation output for steady state
simulations (M1L9)? - ✔✔✔ Correct Answer > Batch means.
This involves warming up the simulation (initialization bias / not included in
analysis). Make one long run. Break up run into evenly sized batches and calculate
sample mean from each batch. Do classic stats assuming iid normal on the batch
means (relies on CLT).
Name the two numerical methods covered in class to find the zeroes (roots) of a
complicated non-linear function that may not have a closed-form solution. - ✔✔✔
Correct Answer > 1. Bisection method
2. Newton's method
,Be able to apply either one to find the zeroes of a function on a test.
Bisection: linear convergence (slower), but guaranteed to find a zero if continuous
function.
Newton's method: quadratic convergence (faster), but NOT guaranteed to find a
zero.
Some apply a hybrid approach :)
What is simulation (M1L3)? - ✔✔✔ Correct Answer > Imitation of a real-world
process or system over time.
What is a model (M1L3)? - ✔✔✔ Correct Answer > High-level representations of
the operation of a real-word process or system.
, Graphically, what is an indication that your pseudorandom number generator is "no
good" (M1L7). - ✔✔✔ Correct Answer > Example was graphing two "random
variates" in the x-y plane that were generated from uniform distributions
transformed into normal distr (Box Muller Method). If a pattern in the graph
appears, this is "bad." You expect lots of random points clustered around the center
that spread out evenly in all directions from the center. Spiral patterns = no good.
In Queuing models, what does each part of the Kendall notation mean: A/B/C
(general version) applied to a M/M/1 (a specific version)(M1L7)? - ✔✔✔ Correct
Answer > A = Distrib of arrival times
B = Distrib. of service times
C = # of servers in the system
M = arrival times are Poisson process (lambda)
M = exponential service times (mu)
1 = a single server
"M" stands for Markov, but really it means exponential?
Describe what a "random walk" model is and what "motion" it converges to
(M1L7)? - ✔✔✔ Correct Answer > Model where the variable "step" size changes
randomly with each time increment (step size = randomly sampled from a normal
distribution?).
Converges to Brownian Motion: as time steps become smaller and # of steps larger.
Continuous time, stochastic.
