Question 1

A waiting line meeting the M/M/1 assumptions has an arrival rate of 10 per hour and a service rate of 12 per hour.What is the probability that the waiting line is empty?

Accepted Answer

Po = 1 - λ/μ = 1 - 10/12 = 2/12 or 0.1667.

Question 2

The study of waiting lines calculates the cost of providing good service but does not value the cost of customers' waiting time.

Accepted Answer

A) True 
 B)False  False

Question 3

At the order fulfillment center of a major mail-order firm,customer orders,already packaged for shipment,arrive at the sorting machine to be sorted for loading onto the appropriate truck for the parcel's address.The arrival rate at the sorting machine is at the rate of 140 per hour following a Poisson distribution.The machine sorts at the constant rate of 150 per hour.
a.What is the utilization rate of the system?
b.What is the average number of packages waiting to be sorted?
c.What is the average number of packages in the sorting system?
d.How long must the average package wait until it gets sorted?

Accepted Answer

(a)The utilization rate is = 140/150 = 0.9333 or 93.33 percent; (b)Lq = [(140)(140)] / [(2)(150)(10)] = 6.53;
(c)Ls = 6.53 + 140/150 = 7.46; (d)Wq = 140/ [(2)(150)(10)] = 0.0467 hours,or 2.8 minutes

Question 4

The ________ probability distribution is a continuous probability distribution often used to describe the service time in a queuing system.

Accepted Answer

negative e

Question 5

The source population is considered to be either ________ in its size.

Accepted Answer

A) finite or infinite 
B) fixed or variable 
C) known or unknown 
D) random or scheduled 
E) small or large 
A) finite or infinite 
B) fixed or variable 
C) known or unknown 
D) random or scheduled 
E) small or large

Question 6

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 7

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.On average,how long does it take to service each student?

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 8

A crew of mechanics at the Highway Department Garage repair vehicles that break down at an average of λ = 8 vehicles per day (approximately Poisson in nature).The mechanic crew can service an average of μ= 11 vehicles per day with a repair time distribution that approximates an exponential distribution.The crew cost is approximately $300 per day.The cost associated with lost productivity from the breakdown is estimated at $150 per vehicle per day (or any fraction thereof).What is the expected cost of this system?

Accepted Answer

The number of vehicles out of

Question 9

A crew of mechanics at the Highway Department Garage repair vehicles that 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 > 1 = (5/

Question 10

A bank office with five tellers,each with a separate line of customers,exhibits the characteristics of a multiphase queuing system.

Accepted Answer

A) True 
 B)False

Question 11

A queuing model that follows the M/M/1 assumptions has λ = 3 and μ = 2.What is the average number of units in the system?

Accepted Answer

A) -3 
B) 3 
C) 0.667 
D) 150 percent 
E) Growing without limit,since λ is larger than μ. 
A) -3 
B) 3 
C) 0.667 
D) 150 percent 
E) Growing without limit,since λ is larger than μ.

Question 12

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

Accepted Answer

A) True 
 B)False

Question 13

An M/M/1 model and an M/D/1 model each have an arrival rate of 1 per minute and a service rate of 3 per minute;the average queue length of the M/M/1 will be twice that of the M/D/1.

Accepted Answer

A) True 
 B)False

Question 14

Little's Law is not applicable in which of the following situations?

Accepted Answer

A) the opening of a toy store on Black Friday morning 
B) a 24-hour supermarket 
C) a gas station with 24-hour self-service pumps 
D) B and C 
E) It is applicable to A,B,and C. 
A) the opening of a toy store on Black Friday morning 
B) a 24-hour supermarket 
C) a gas station with 24-hour self-service pumps 
D) B and C 
E) It is applicable to A,B,and C.

Question 15

Which of the following is NOT a measure of a queue's performance?

Accepted Answer

A) average time spent in the queue 
B) average queue length 
C) probability that the service facility will be idle 
D) utilization factor for the system 
E) All of the above are performance measures. 
A) average time spent in the queue 
B) average queue length 
C) probability that the service facility will be idle 
D) utilization factor for the system 
E) All of the above are performance measures.

Question 16

A hospital emergency room always follows a FIFO queue discipline in the interest of fairness.

Accepted Answer

A) True 
 B)False

Question 17

You have seen that,in an M/D/1 problem,the average queue length is exactly one-half the average queue length of an otherwise identical M/M/1 problem.Are all other performance statistics one-half as large also? Explain.

Accepted Answer

Only the average queue length

Question 18

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 and staff)?
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 19

Study of waiting-line models helps operations managers better understand:

Accepted Answer

A) service systems such as bank teller stations. 
B) maintenance activities that might repair broken machinery. 
C) shop-floor control activities. 
D) service systems such as amusement park rides. 
E) all of the above 
A) service systems such as bank teller stations. 
B) maintenance activities that might repair broken machinery. 
C) shop-floor control activities. 
D) service systems such as amusement park rides. 
E) all of the above

Question 20

Provide an example of a limited or finite population for a queue.

Accepted Answer

Answers will vary,but the text

Exam 25: Queuing Models

A waiting line meeting the M/M/1 assumptions has an arrival rate of 10 per hour and a service rate of 12 per hour.What is the probability that the waiting line is empty?

The study of waiting lines calculates the cost of providing good service but does not value the cost of customers' waiting time.

The ________ probability distribution is a continuous probability distribution often used to describe the service time in a queuing system.

The source population is considered to be either ________ in its size.

Which of the following represents an unlimited queue?

A bank office with five tellers,each with a separate line of customers,exhibits the characteristics of a multiphase queuing system.

A queuing model that follows the M/M/1 assumptions has λ = 3 and μ = 2.What is the average number of units in the system?

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

An M/M/1 model and an M/D/1 model each have an arrival rate of 1 per minute and a service rate of 3 per minute;the average queue length of the M/M/1 will be twice that of the M/D/1.

Little's Law is not applicable in which of the following situations?

Which of the following is NOT a measure of a queue's performance?

A hospital emergency room always follows a FIFO queue discipline in the interest of fairness.

You have seen that,in an M/D/1 problem,the average queue length is exactly one-half the average queue length of an otherwise identical M/M/1 problem.Are all other performance statistics one-half as large also? Explain.

Study of waiting-line models helps operations managers better understand:

Provide an example of a limited or finite population for a queue.

Operations and Productivity

The Global Environment and Operations Strategy

Managing Projects

Forecasting Demand

Product Design

Quality Management and International Standards

Process Design

Location Decisions

Layout Decisions

Job Design and Work Measurement

Supply Chain Management

Managing Inventory

Aggregate Scheduling

Material Requirements Planning Mrpand Erp

Scheduling for the Short-Term

Jit,lean Operations,and the Toyota Production System

Maintenance and Reliability Decisions

Sustainability

Statistical Process Control

Capacity Planning

Supply Chain Modeling

Decision Modeling

Linear Programming Models

Transportation Modeling

Learning Curves

Modeling with Simulation

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