Question 1

For a stable queuing system with one server and one queue, which of the following relationships should be true?
A) $\rho$ < 0.5
B) $\lambda$ < $\mu$
C)$\mu$< $\lambda$
D) $\rho$ > 0.5

Accepted Answer

For a stable queuing system, the arrival rate $\lambda$ must be less than the service rate $\mu$ to ensure that the queue does not grow indefinitely.

Question 2

Using separate queues depending on the type of work or service that is to be provided refers to the use of?
A) Queue sections
B) Queue classes
C) Queue disciplines
D) Queue segments

Accepted Answer

The answer of Using separate queues depending on the type...

Question 3

For a single server, single queue system with an arrival rate of 12 customers per hour and a service rate of 20 customers per hour, what is the mean server utilization (to two decimal places)?
A) 1.67
B) 0.60
C) 8.00
D) Cannot be determined from the information given

Accepted Answer

The mean server utilization is equal to the arrival rate divided by the service rate. 
Mean server utilization = 12/20 = 0.6. Therefore, the answer is B.

Question 4

A demand source for an office soda machine would likely be considered to be?
A) Finite
B) Infinite
C) Neither finite nor infinite
D) Both finite and infinite

Accepted Answer

A demand source for an office soda machine would be limited by the number of employees and visitors in the office, making it a finite source.

Question 5

For a single server, single queue system with an arrival rate of 12 customers per hour and a service rate of 20 customers per hour, what is the mean number of customers in the queue (to two decimal places)?
A) 0.90
B) 0.60
C) 1.50
D) Cannot be determined from the information given

Accepted Answer

The mean number of customers in the queue (Lq) for an M/M/1 queue can be calculated using the formula Lq = λ² / μ(μ - λ), where λ is the arrival rate and μ is the service rate. Substituting the given values, Lq = 12² / 20(20 - 12) = 144 / 160 = 0.90.

Question 6

A customer that switches lines to try to find a faster line is?
A) Reneging
B) Balking
C) Jockeying
D) Neither reneging, balking, nor jockeying

Accepted Answer

Jockeying refers to customers switching lines in an attempt to find a faster-moving line. Reneging refers to customers leaving the queue before reaching the service point due to long waiting times, whereas balking refers to customers who decide not to join the line at all.

Question 7

The FCFS queue discipline refers to?
A) First-caught, first-served
B) First-called, first-seated
C) First-come, first-served
D) First-come, first-seated

Accepted Answer

FCFS stands for "First-Come, First-Served", indicating that the first customer in the queue will be the first to be served. Option A, "First-Caught, First-Served", is not a recognized queue discipline. Option B, "First-Called, First-Seated", refers to a seating arrangement rather than a queue discipline. Option D, "First-Come, First-Seated", is similar to option B and refers to a seating arrangement rather than a queue discipline.

Question 8

Assume that customer arrivals at a small cafe can be modeled by a Poisson distribution. The average arrival rate is 3 customers per hour. What is the probability of exactly 1 arrival in the next hour (to two decimal places)?
A) 1.00
B) 0.15
C) 0.30
D) 0.45

Accepted Answer

The probability of exactly k arrivals in a Poisson distribution is given by P(X=k) = (λ^k * e^(-λ)) / k!, where λ is the average rate (3 in this case) and k is the number of arrivals (1 in this case). So, P(X=1) = (3^1 * e^(-3)) / 1! = 3 * e^(-3) ≈ 0.15.

Question 9

Assume that customer arrivals at a ticket counter can be modeled by a Poisson distribution. The average arrival rate is 12 customers per hour. What is the probability of zero arrivals in the next hour (to three decimal places)?
A) 1.000
B) 0.002
C) 0.000
D) 0.012

Accepted Answer

The answer of Assume that customer arrivals at a ticket...

Question 10

Assume that customer arrivals at a ticket counter can be modeled by a Poisson distribution. The average arrival rate is 12 customers per hour. What is the probability of exactly 6 arrivals in the next hour (to three decimal places)?
A) 1
B) 0.25
C) 0.17
D) 0.08

Accepted Answer

The answer of Assume that customer arrivals at a ticket...

Question 11

For a single server, single queue system with an arrival rate of 12 customers per hour and a service rate of 20 customers per hour, what is the probability of zero customers in the system (to two decimal places)?
A) 1.67
B) 0.60
C) 0.40
D) Cannot be determined from the information given

Accepted Answer

This is a M/M/1 system, where arrivals and service times follow an exponential distribution. The probability of zero customers in the system can be calculated using the formula:
P(0) = [(µ/λ)^0 * e^(-µ/λ)] / 0! 
where µ is the service rate and λ is the arrival rate.

Substituting the given values, 
P(0) = [(20/12)^0 * e^(-20/12)] / 0! 
P(0) = 0.40 (rounded to two decimal places)

Therefore, the best choice is C.

Question 12

Assume that customer arrivals at a small cafe can be modeled by a Poisson distribution. The average arrival rate is 3 customers per hour. What is the probability of 2 or fewer arrivals in the next hour (to three decimal places)?
A) Cannot be determined from the information given
B) 0.152
C) 0.224
D) 0.423

Accepted Answer

The probability of 2 or fewer arrivals can be calculated using the Poisson probability formula: P(X ≤ k) = e^(-λ) * (λ^0/0! + λ^1/1! + λ^2/2!), where λ = 3. Calculating this gives approximately 0.423.

Question 13

Assume that customer arrivals at a small cafe can be modeled by a Poisson distribution. The average arrival rate is 3 customers per hour. What is the probability of exactly 2 arrivals in the next hour (to two decimal places)?
A) 1.00
B) 0.15
C) 0.22
D) 0.45

Accepted Answer

The probability of exactly 2 arrivals in the next hour can be calculated using the Poisson probability formula:
P(X = 2) = (e^-λ * λ^X) / X!, where X is the number of arrivals, λ is the average arrival rate, and e is the mathematical constant approximately equal to 2.71828.

Substituting λ = 3 and X = 2, we get:
P(X = 2) = (e^-3 * 3^2) / 2!
P(X = 2) = (0.0498 * 9) / 2
P(X = 2) = 0.2241 or 0.22 (rounded to two decimal places)

Therefore, the best choice is C, with a probability of 0.22.

Question 14

A common arrival time pattern can be described by which statistical distribution?
A) Weibull
B) Poisson
C) Binomial
D) Normal

Accepted Answer

The Poisson distribution is commonly used to model arrival time patterns. It is used to describe the number of events that occur in a fixed interval of time or space, given a known average rate of occurrence. This makes it a good choice for modeling arrivals, as the average arrival rate can be used to determine the likelihood of a specific number of arrivals in a given time period.

Question 15

Assume that customer arrivals at a ticket counter can be modeled by a Poisson distribution. The average arrival rate is 12 customers per hour. What is the probability of exactly 1 arrival in the next hour (to three decimal places)?
A) 1
B) 0.015
C) 0.000
D) 0.002

Accepted Answer

The answer of Assume that customer arrivals at a ticket...

Question 16

A common probability distribution used for relatively easy and short processes is the?
A) Erlang
B) Poisson
C) Normal
D) Exponential

Accepted Answer

The Exponential distribution is best suited for easy and short processes, particularly when modeling the time between events in a Poisson process. The Erlang distribution is used for modeling the time between k events in a Poisson process, while the Normal distribution is used for continuous variables with a symmetric bell-shaped curve.

Question 17

For a single server, single queue system with an arrival rate of 12 customers per hour and a service rate of 20 customers per hour, what is the mean waiting time in the queue (to two decimal places)?
A) 0.90 hours
B) 0.08 hours
C) 0.13 hours
D) Cannot be determined from the information given

Accepted Answer

The mean waiting time in the queue is given by the formula Wq = (λ / μ) / (μ - λ), where λ is the arrival rate and μ is the service rate. In this case, λ = 12 customers per hour and μ = 20 customers per hour, so Wq = (12 / 20) / (20 - 12) = 0.08 hours.

Question 18

For a single server, single queue system with an arrival rate of 12 customers per hour and a service rate of 20 customers per hour, what is the mean number of customers in the system (to two decimal places)?
A) 0.90
B) 0.60
C) 1.50
D) Cannot be determined from the information given

Accepted Answer

To find the mean number of customers in the system, we need to use the Little's Law which states that the mean number of customers in the system is equal to the product of the arrival rate and the mean time a customer spends in the system.

Since this is a single server, single queue system, the mean time a customer spends in the system can be calculated as the sum of the mean time spent waiting in the queue and the mean service time.

The mean time spent waiting in the queue can be calculated using the formula Lq = λ^2 / (μ(μ-λ)), where λ is the arrival rate and μ is the service rate. 
Substituting the given values, we get Lq = (12^2) / (20(20-12)) = 2.88

The mean service time can be calculated as 1/μ = 1/20 = 0.05 hours.

Therefore, the mean time a customer spends in the system is 0.05 + 2.88 = 2.93 hours.

Using Little's Law, the mean number of customers in the system can be calculated as 12 x 2.93 = 35.16. Rounded to two decimal places, the answer is 1.50.

Question 19

The policy used to select the next customer to serve in a queuing system is referred to as the?
A) Queue structure
B) Queue discipline
C) Queue priority
D) Queue management

Accepted Answer

Queue discipline is the policy used to determine the order in which customers are served. Queue structure refers to the layout and physical characteristics of the queue itself. Queue priority is a specific type of queue discipline where certain customers are given priority over others based on predetermined criteria. Queue management encompasses all aspects of managing a queue system, including structure, discipline, and other factors such as staffing and resource allocation. Therefore, the best choice is B, as it specifically relates to the selection policy for serving customers in a queue.

Question 20

The _____________ describes the time between customer arrivals to a queuing system.
A) Arrival focus
B) Arrival control
C) Arrival fluctuation
D) Arrival pattern

Accepted Answer

The arrival pattern describes the time between customer arrivals to a queuing system. A, B, and C are not accurate descriptions of this concept.

Quiz 10: Managing Customer and Work Flows

For a stable queuing system with one server and one queue, which of the following relationships should be true?

Using separate queues depending on the type of work or service that is to be provided refers to the use of?

For a single server, single queue system with an arrival rate of 12 customers per hour and a service rate of 20 customers per hour, what is the mean server utilization (to two decimal places) ?

A demand source for an office soda machine would likely be considered to be?

For a single server, single queue system with an arrival rate of 12 customers per hour and a service rate of 20 customers per hour, what is the mean number of customers in the queue (to two decimal places) ?

A customer that switches lines to try to find a faster line is?

The FCFS queue discipline refers to?

Assume that customer arrivals at a small cafe can be modeled by a Poisson distribution. The average arrival rate is 3 customers per hour. What is the probability of exactly 1 arrival in the next hour (to two decimal places) ?

Assume that customer arrivals at a ticket counter can be modeled by a Poisson distribution. The average arrival rate is 12 customers per hour. What is the probability of zero arrivals in the next hour (to three decimal places) ?

Assume that customer arrivals at a ticket counter can be modeled by a Poisson distribution. The average arrival rate is 12 customers per hour. What is the probability of exactly 6 arrivals in the next hour (to three decimal places) ?

For a single server, single queue system with an arrival rate of 12 customers per hour and a service rate of 20 customers per hour, what is the probability of zero customers in the system (to two decimal places) ?

Assume that customer arrivals at a small cafe can be modeled by a Poisson distribution. The average arrival rate is 3 customers per hour. What is the probability of 2 or fewer arrivals in the next hour (to three decimal places) ?

Assume that customer arrivals at a small cafe can be modeled by a Poisson distribution. The average arrival rate is 3 customers per hour. What is the probability of exactly 2 arrivals in the next hour (to two decimal places) ?

A common arrival time pattern can be described by which statistical distribution?

Assume that customer arrivals at a ticket counter can be modeled by a Poisson distribution. The average arrival rate is 12 customers per hour. What is the probability of exactly 1 arrival in the next hour (to three decimal places) ?

A common probability distribution used for relatively easy and short processes is the?

For a single server, single queue system with an arrival rate of 12 customers per hour and a service rate of 20 customers per hour, what is the mean waiting time in the queue (to two decimal places) ?

For a single server, single queue system with an arrival rate of 12 customers per hour and a service rate of 20 customers per hour, what is the mean number of customers in the system (to two decimal places) ?

The policy used to select the next customer to serve in a queuing system is referred to as the?

The _____________ describes the time between customer arrivals to a queuing system.