FA 2 - CS0019 || CANVAS

Which statement correctly describes an event?

It is always one outcome only

It must have probability one

It is the probability measure itself

It is a subset of the sample space

It is a subset of the sample space

Why is output data analysis necessary in a stochastic simulation?

Simulation results must be processed into useful performance information

One output value always equals the true performance

It prevents random-number generation

It converts DES into a continuous model

Simulation results must be processed into useful performance information

Which situation most strongly supports using a normal distribution?

Variability around an average caused by many small effects

Only minimum, mode, and maximum are known

Equally likely values over a finite interval

Time until the next memoryless arrival only

Variability around an average caused by many small effects

A customer joins a line but leaves before service. This behavior is:

Jockeying

Balking

Reneging

FIFO

Reneging

Which input-modeling approach stores observed sample values and reuses them directly?

Analytic queueing

Direct use of sample data

Fixed-increment advance

Theoretical distribution

Direct use of sample data

When no satisfactory theoretical distribution fits the observations, the module recommends considering:

Removal of all input data

A continuous system instead

An empirical distribution

A deterministic constant only

An empirical distribution

Which distribution is commonly used to model interarrival times in DES?

Normal only

Uniform on all real numbers

Triangular only

Exponential

Exponential

A customer priority carried through the system is best represented as a(n):

Attribute

Clock

Resource

Report generator

Attribute

A bank has three tellers who can each serve one customer. What is the resource capacity?

Unlimited

2

1

3

3

Which role of statistics is most directly needed before a stochastic DES run can begin?

Guaranteeing that one run gives the true mean

Eliminating variability from input data

Replacing every event with a continuous equation

Representing randomness and generating random-variate streams

Representing randomness and generating random-variate streams

A major limitation of direct sample-data use is that:

Rare legal values absent from the sample cannot be generated

It automatically smooths sample irregularities

It creates an unlimited stream efficiently

It always generates illegal values

Rare legal values absent from the sample cannot be generated

Which three components define a probability space?

Domain, codomain, range

Mean, variance, standard deviation

Entity, resource, queue

Sample space, sigma algebra, probability measure

Sample space, sigma algebra, probability measure

In a linear congruential generator, what is Z0?

The cycle length

The modulus

The seed

The probability density

The seed

Let A={1,2,3} and B={3,4}. What is A intersection B?

{1,2}

{3}

{1,2,3,4}

{}

{3}

A customer switches from one line to another to reduce waiting. This is:

Jockeying

Balking

Faffing

Reneging

Jockeying

Which DES component maintains an ordered list of scheduled event times?

Universal set

Probability density

Next-event list

Attribute memory

Next-event list

For a random variable X, what does F(x) represent?

The sample-space size

The derivative of X

P(X is greater than x)

P(X is less than or equal to x)

P(X is less than or equal to x)

An LCG whose period p equals its modulus m is called a:

Density generator

Full-cycle generator

Empirical generator

Fixed-increment generator

Full-cycle generator

Which queue discipline serves the earliest arrival first?

SIRO

FCFS

LIFO

STP

FCFS

Which condition is required of a valid probability measure?

Disjoint probabilities are multiplied

P(S)=0

P(S)=1

P(E) may be negative

P(S)=1

Let A={1,2,3} and B={3,4}. What is A union B?

{1,2,3,4}

{3}

{1,2,3,3,4}

{1,2,4}

{1,2,3,4}

A server completes the previous customer at time 10, and the next customer begins service at time 13. What is the server idle time?

3 minutes

0 minutes

23 minutes

10 minutes

3 minutes

A sample space has four outcomes. How many events are in its full sigma algebra?

4

8

32

16

16

Which description best defines discrete-event simulation?

State variables change continuously at every instant

The system has no randomness or time

Only physical prototypes are permitted

State variables change instantaneously at separated event times

State variables change instantaneously at separated event times

A process time can take any value from 4 to 10 minutes with all values equally likely. Which distribution is most appropriate?

Triangular(4,10,10)

Uniform(4,10)

Normal(4,10)

Exponential(4)

Uniform(4,10)

A server is busy for 42 minutes during a 60-minute run. What is its utilization?

30%

60%

70%

42%

70%

Which property must a probability density function satisfy?

It can be negative if the mean is positive

Its total area is zero

It must be constant everywhere

Its total area over all real values is one

Its total area over all real values is one

Which subprogram advances the clock to the next scheduled event?

Initialization subprogram

Library subprogram

Report generator

Timing subprogram

Timing subprogram

In the module, a simulation random number is sampled from:

EXPONENTIAL(1)

UNIFORM(0,1)

NORMAL(0,1)

TRIANGULAR(0,0.5,1)

UNIFORM(0,1)

A rule maps each experimental outcome to a real number. In probability, this rule defines a:

Simulation clock

Sigma algebra

Queue discipline

Random variable

Random variable

Why are LCG constants and the seed selected carefully?

To force all values to equal the mean

To produce a long cycle before repetition

To make every output truly nonnumeric

To eliminate the modulus

To produce a long cycle before repetition

Two disjoint events have probabilities 0.35 and 0.25. What is the probability of their union?

0.35

0.875

0.60

0.10

0.60

Interarrival times, service times, schedules, failure rates, and travel times belong primarily to:

Clock initialization only

Data modeling

Structural modeling

Queue discipline only

Data modeling

What are the two basic steps in generating a random variate?

Generate a random number, then transform it

Choose an event, then delete it

Create a queue, then add a server

Estimate a mean, then set variance to zero

Generate a random number, then transform it

Only the minimum, most likely, and maximum repair times are known. Which distribution is the best initial model?

Triangular

Normal

Exponential

Uniform

Triangular

In a checkout DES, which occurrence is an event?

The color of the simulation interface

A customer arriving at the queue

The passage of time with no state change

The permanent definition of the model

A customer arriving at the queue

Which combination characterizes DES in the module?

Static, stochastic, continuous

Stochastic, dynamic, discrete

Static, deterministic, continuous

Deterministic, static, discrete

Stochastic, dynamic, discrete

Which is an advantage of a fitted theoretical distribution?

It can only produce observed values

It guarantees a perfect fit

It smooths irregularities from limited sample data

It eliminates fitting effort

It smooths irregularities from limited sample data

Which modeling component defines entities, locations, resources, and processes?

Structural modeling

Output modeling

Data modeling

Report generation

Structural modeling

A customer sees a long line and decides not to enter it. This behavior is:

Reneging

Faffing

Jockeying

Balking

Balking

Which tool is specifically mentioned for estimating the mean performance from simulation output?

Set difference

Confidence interval

Fixed time slice

Inverse function only

Confidence interval

With universal set U={1,2,3,4,5} and A={1,3,5}, what is the complement of A?

{2,4}

{1,2,3,4,5}

{1,3,5}

{}

{2,4}

A customer arrives at time 6, begins service at 9, and service lasts 4 minutes. How long does the customer spend in the system?

3 minutes

4 minutes

13 minutes

7 minutes

7 minutes

In a single-server queue, a customer arrives at time 6 and the previous service ends at time 9. When does service begin?

6

15

7

9

9

When a resource is occupied, the list an entity joins is the:

Accumulator

Queue

Codomain

Sample space

Queue

What is a limitation of an empirical distribution based on a finite sample?

It cannot reproduce any observed value

It requires differential equations

It always produces negative times

It may not generate rare outliers missing from the sample

It may not generate rare outliers missing from the sample

Why is next-event time advance generally more efficient than fixed-increment advance?

It forces events to interval boundaries

It skips periods with no events

It prevents state updates

It examines every small idle interval

It skips periods with no events