Question 1

As the average service rate μ grows larger,the slope of the distribution of service time probabilities grows larger and larger,eventually becoming positive.

Accepted Answer

A) True 
 B)False

Question 2

A dental clinic at which only one dentist works is open only two days a week.During those two days,the traffic arrivals follow a Poisson distribution with patients arriving at the rate of three per hour.The doctor serves patients at the rate of one every 15 minutes.
a.What is the probability that the clinic is empty (except for the dentist)?
b.What is the probability that there are one or more patients in the system?
c.What is the probability that there are four patients in the system?
d.What is the probability that there are four or more patients in the system?

Accepted Answer

(a)Po = 1 - 3/4 = 0.25; (b)The probabili

Question 3

Students arrive randomly at the help desk of the computer lab.There is only one service agent,and the time required for inquiry varies from student to student.Arrival rates have been found to follow the Poisson distribution,and the service times follow the negative exponential distribution.The average arrival rate is 12 students per hour,and the average service rate is 20 students per hour.What is the average service time for this problem?

Accepted Answer

A) 1 minute 
B) 2 minutes 
C) 3 minutes 
D) 5 minutes 
E) 20 minutes 
A) 1 minute 
B) 2 minutes 
C) 3 minutes 
D) 5 minutes 
E) 20 minutes

Question 4

A waiting-line system that meets the assumptions of M/M/1 has = 1,= 4.Calculate Po.Build a table showing the probability of more than 0,1,2,3,4,5,6,and 7 units in the system.Round to six decimal places in your work

Accepted Answer

The answer of A waiting-line system that meets the assumptions...

Question 5

A queuing model which follows the M/M/1 assumptions has λ = 2 and μ = 3.The average number in the system is

Accepted Answer

A) 2/3. 
B) 1. 
C) 1.5. 
D) 2. 
E) 6. 
A) 2/3. 
B) 1. 
C) 1.5. 
D) 2. 
E) 6.

Question 6

A crew of mechanics at the Highway Department garage repair vehicles which break down at an average of λ = 5 vehicles per day (approximately Poisson in nature).The mechanic crew can service an average of μ= 10 vehicles per day with a repair time distribution that approximates an exponential distribution.
a.What is the probability that the system is empty?
b.What is the probability that there is precisely one vehicle in the system?
c.What is the probability that there is more than one vehicle in the system?
d.What is the probability of 5 or more vehicles in the system?

Accepted Answer

(a)P0 = 1 - 5/10 = 0.50; (b)Pn

Question 7

In a repetitive focus factory,the number of phases found in the system might refer to

Accepted Answer

A) the number of successive operations that have to be performed on a part. 
B) the number of machines doing the same necessary operations. 
C) the number of parts waiting to be processed. 
D) the number of workers waiting to perform their task. 
E) the number of units with defects requiring rework. 
A) the number of successive operations that have to be performed on a part. 
B) the number of machines doing the same necessary operations. 
C) the number of parts waiting to be processed. 
D) the number of workers waiting to perform their task. 
E) the number of units with defects requiring rework.

Question 8

There is only one bay and one type of service at an automatic car wash.Provide the most likely characteristics of this system.
a.name of model
b.number of channels
c.number of phases
d.arrival rate distribution
e.service time distribution
f.population size
g.queue discipline

Accepted Answer

Constant service (M/

Question 9

Customers take a number as they join the waiting line of the customer service counter at a discount store.There are two customer service agents.Provide the most likely characteristics of this system.
a.name of model
b.number of channels
c.number of phases
d.arrival rate distribution
e.service time distribution
f.population size
g.queue discipline

Accepted Answer

Multi-channel system

Question 10

In the M/M/1 waiting line model with an arrival rate of 2 per hour and a service rate of 6 per hour,the utilization factor for the system is approximately 0.333.

Accepted Answer

A) True 
 B)False

Question 11

In queuing problems,which of the following probability distributions is typically used to describe the number of arrivals per unit of time?

Accepted Answer

A) binomial 
B) normal 
C) Poisson 
D) exponential 
E) lognormal 
A) binomial 
B) normal 
C) Poisson 
D) exponential 
E) lognormal

Question 12

What costs are present in waiting line analysis? How do these costs vary with the level of service?

Accepted Answer

The costs are the cost of providing serv

Question 13

Which of the following represents an unlimited queue?

Accepted Answer

A) drive-through lane at a fast-food restaurant 
B) small barbershop with only 5 chairs for waiting customers 
C) toll booth serving automobiles on an interstate 
D) faculty office with limited seating during office hours 
E) restaurant with no outside seating and limited capacity due to fire department restrictions 
A) drive-through lane at a fast-food restaurant 
B) small barbershop with only 5 chairs for waiting customers 
C) toll booth serving automobiles on an interstate 
D) faculty office with limited seating during office hours 
E) restaurant with no outside seating and limited capacity due to fire department restrictions

Question 14

A system in which the customer receives service from only one station and then exits the system is

Accepted Answer

A) a single-phase system. 
B) a single channel system. 
C) a multiple-channel system. 
D) a multiple-phase system. 
E) unlimited channel system. 
A) a single-phase system. 
B) a single channel system. 
C) a multiple-channel system. 
D) a multiple-phase system. 
E) unlimited channel system.

Question 15

Suppose that customer arrivals are governed by a Poisson distribution.If the average arrival rate is 60 customers each hour,how many times will 60 customers arrive during a one hour period for each time that only 40 customers arrive.

Accepted Answer

P(60)= e^-60∗60^60/

Question 16

What are the assumptions underlying the M/M/1 waiting line model? Which of these also hold for the M/D/1 model?

Accepted Answer

The assumptions underlying the standard

Question 17

Of the three types of queue discipline,only ________ is assumed by the four primary waiting line models.

Accepted Answer

FIFO or FI

Question 18

In queuing problems,which of the following probability distributions is typically used to describe the time to perform the service?

Accepted Answer

A) binomial 
B) normal 
C) Poisson 
D) negative exponential 
E) lognormal 
A) binomial 
B) normal 
C) Poisson 
D) negative exponential 
E) lognormal

Question 19

In the basic queuing model (M/M/1),arrival rates are distributed by

Accepted Answer

A) continuous probability distributions. 
B) normal probability distributions. 
C) negative exponential probability distributions. 
D) Poisson distributions. 
E) lognormal distributions. 
A) continuous probability distributions. 
B) normal probability distributions. 
C) negative exponential probability distributions. 
D) Poisson distributions. 
E) lognormal distributions.

Question 20

A waiting-line system has three parts: the size of the arrival population,the behaviour of arrivals,and the statistical distribution of arrivals.

Accepted Answer

A) True 
 B)False

Exam 24: Waiting-Line Models

As the average service rate μ grows larger,the slope of the distribution of service time probabilities grows larger and larger,eventually becoming positive.

A waiting-line system that meets the assumptions of M/M/1 has = 1,= 4.Calculate Po.Build a table showing the probability of more than 0,1,2,3,4,5,6,and 7 units in the system.Round to six decimal places in your work

A queuing model which follows the M/M/1 assumptions has λ = 2 and μ = 3.The average number in the system is

In a repetitive focus factory,the number of phases found in the system might refer to

There is only one bay and one type of service at an automatic car wash.Provide the most likely characteristics of this system. a.name of model b.number of channels c.number of phases d.arrival rate distribution e.service time distribution f.population size g.queue discipline

In the M/M/1 waiting line model with an arrival rate of 2 per hour and a service rate of 6 per hour,the utilization factor for the system is approximately 0.333.

In queuing problems,which of the following probability distributions is typically used to describe the number of arrivals per unit of time?

What costs are present in waiting line analysis? How do these costs vary with the level of service?

Which of the following represents an unlimited queue?

A system in which the customer receives service from only one station and then exits the system is

Suppose that customer arrivals are governed by a Poisson distribution.If the average arrival rate is 60 customers each hour,how many times will 60 customers arrive during a one hour period for each time that only 40 customers arrive.

What are the assumptions underlying the M/M/1 waiting line model? Which of these also hold for the M/D/1 model?

Of the three types of queue discipline,only ________ is assumed by the four primary waiting line models.

In queuing problems,which of the following probability distributions is typically used to describe the time to perform the service?

In the basic queuing model (M/M/1),arrival rates are distributed by

A waiting-line system has three parts: the size of the arrival population,the behaviour of arrivals,and the statistical distribution of arrivals.

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