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Louisiana State University
ISDS 3115
Chapter7D
True/False
1)Waitingline models are useful to operations in such diverse settings as service systems, maintenance activities, and shopfloor control
Louisiana State University
ISDS 3115
Chapter7D
True/False
1)Waitingline models are useful to operations in such diverse settings as service systems, maintenance activities, and shopfloor control
Operations Management
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Louisiana State University
ISDS 3115
Chapter7D
True/False
1)Waitingline models are useful to operations in such diverse settings as service systems, maintenance activities, and shopfloor control.
 The two characteristics of the waiting line itself are whether its length is limited or unlimited and the discipline of the people or items in it.
 A waitingline system has three parts: the size of the arrival population, the behavior of arrivals, and the statistical distribution of arrivals.
 A copy center has five machines that serve many customers throughout the day; the waitingline system for copy service has an infinite population while the waitingline system for copier maintenance has a finite population
 In queuing problems, arrival rates are generally described by the normal probability distribution.
 Balk and renege are elements of queue discipline.
 A hospital emergency room always follows a firstin, firstserved queue discipline in the interest of fairness.
 In queuing problems, the term “renege” refers to the fact that some customers leave the queue before service is completed.
 A waitingline system with one waiting line and three sequential processing stages is a multi channel singlephase system.
 If the service time within a queuing system is constant, the service rate can be easily described by a negative exponential distribution.
 The cost of waiting decreases as the service level increases.
 LIFS (lastin, firstserved) is a common queue discipline, most often seen where people, not objects, form the waiting line.
 A bank office with five tellers, each with a separate line of customers, exhibits the characteristics of a multiphase queuing system.
 In the analysis of queuing models, the Poisson distribution often describes arrival rates and service times are often described by the negative exponential distribution.
 The study of waiting lines calculates the cost of providing good service but does not value the cost of customers' waiting time.
 As the average service rate μ grows larger, the slope of the distribution of service time probabilities grows larger and larger, eventually becoming positive.
 Four of the most widely used waiting line models—M/M/1 or A, M/M/S or B, M/D/1 or C, and Limited population or D—all share three characteristics: Poisson arrivals, FIFO discipline, and exponential service times.
 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.
 The greater the margin by which the arrival rate exceeds the service rate, the better the performance of the waiting line.
 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.
 A finite population waiting line model has an average service time T of 100 minutes and an average time between service requirements U of 400 minutes; the service factor X is 0.25.
Multiple Choice
 Study of waitingline models helps operations managers better understand
 service systems such as bank teller stations
 maintenance activities that might repair broken machinery
 shopfloor control activities
 service systems such as amusement park rides
 all of the above
 Which of the following is not a common queuing situation?
 grocery shoppers being served by checkout clerks
 commuters slowing or stopping at toll plazas to pay highway tolls
 machinery waiting to be repaired or maintained
 parcel delivery truck following its computergenerated route
 patients in a health clinic waiting to see one of several doctors
 In queuing problems, which of the following probability distributions is typically used to describe the number of arrivals per unit of time?
 binomial
 normal

 Poisson
 exponential
 lognormal
 In queuing problems, which of the following probability distributions is typically used to describe the time to perform the service?
 binomial
 normal
 Poisson
 negative exponential
 lognormal
 The common measures of a queuing system's performance include
 probability that the service facility will be idle, average queue length, probability that the waiting time will exceed a specified duration
 average time each customer spends in the system, probability that the service system will be idle, average time each customer spends in the queue
 average queue length, maximum time a customer may spend in the queue, the utilization factor for the system
 average time each customer spends in the system, maximum queue length, probability of a specific number of customers in the system
 none of the above
 The shopper who says to himself, “I’ve waited too long in this line. I don’t really need to buy this product today,” and leaves the store is an illustration of which element of arrival behavior?
 random arrival
 renege
 random departure
 balk
 none of the above
 A waiting line, or queuing, system has three parts, which are
 distribution of arrival times, discipline while waiting, and distribution of service times
 arrival rate, service rate, and utilization rate
 arrival discipline, queue discipline, and service sequencing
 arrival or inputs, queue discipline or the waiting line itself, and the service facility
 sequencing policy, penalty for reneging, and expediting of arrivals
 The source population is considered to be either in its size.
 finite or infinite
 fixed or variable
 known or unknown
 random or scheduled
 small or large
 The potential restaurant customer who says to her husband, “The line looks too long; let's eat somewhere else,” is an illustration of which element of queue discipline?
 firstin, firstout
 balk
 renege
 random departure
 none of the above
 An airline ticket counter, with several agents for one line of customers, is an example of a
 single channel, single phase system
 single channel, multiphase system
 multichannel, single phase system
 multichannel, multiphase system
 none of the above
 A concert hall, employing both ticket takers and ushers to seat patrons, behaves typically as a
 multichannel, single phase system
 multichannel, multiphase system
 single channel, single phase system
 single channel, multiphase system
 none of the above
 If the food service for the university operates a cafeteria with a single serving line, that system behaves most like a
 single channel, single phase system
 single channel, multiphase system
 multichannel, single phase system
 multichannel, multiphase system
 none of the above
 The sign at the bank that reads “Wait here for the first available teller” suggests the use of a
waiting line system.

 single phase
 multiphase
 single channel
 multichannel
 multiple line
 A small hair styling salon has several operators. While customers do not have appointments, each is waiting to be served by a specific operator. This scenario provides an example of a
 multiplechannel, multiphase, limited queue length
 singlechannel, multiphase, limited queue length
 multichannel, limited queue length
 multiple singlechannel systems, limited queue length
 none of the above
 A large discount store and supermarket has a hair styling salon on its premises. The salon has several operators. Salon customers can shop in other parts of the store until their name is called for salon service, at which time the customer will be served by the next available stylist. This scenario provides an example of a
 multiplechannel, multiphase, unlimited queue length
 singlechannel, multiphase, limited queue length
 multichannel, unlimited queue length
 multiple singlechannel systems, limited queue length
 none of the above
 A university has only one technician in the repair station to care for the computers in the student
labs. This system is most likely

 a single channel, limited queue system
 a single channel, limited population system
 a multichannel, limited queue system
 a multichannel, limited population system
 none of the above
 “Women and children first!” declares the captain of a sinking ship. His directive employs which of the following queue disciplines in disembarking passengers?
 priority
 random
 FIFO or FIFS
 LIFO or LIFS
 none of the above
 A university has several technicians in the repair station to care for the computers in the student labs. This system is most likely
 single channel, limited queue system
 single channel, limited population system
 multichannel, limited queue system
 multichannel, limited population system
 none of the above
 A system in which the customer receives service from only one station and then exits the system is
 a singlephase system
 a single channel system
 a multiplechannel system
 a multiplephase system
 none of the above
 In a repetitive focus factory, the number of phases found in the system might refer to
 the number of successive operations that have to be performed on a part
 the number of machines doing the same necessary operations
 the number of parts waiting to be processed
 all of the above depending on the layout
 none of the above
 Which of the following is a measure of queue performance?
 utilization factor
 average queue length
 probability of a specific number of customers in the system
 average waiting time in the line
 all of the above
 Which of the following is most likely to be served in a lastin, firstserved (LIFS) queue discipline?
 customers checking out at a grocery store
 the inbasket on a manager's desk
 patients entering a hospital emergency room
 patrons waiting to be seated in a casualdining restaurant
 all of the above
 In a repetitive focus factory, the number of channels available for the processing of a certain part would likely refer to
 the number of successive operations that have to be performed on that part
 the number of machines doing the same necessary operations
 the number of parts waiting to be processed
 all of the above depending on the layout
 none of the above
 A waiting line meeting the assumptions of M/M/1 has average time between arrivals of 20 minutes and services items in an average of 10 minutes each; the utilization factor is approximately
a. 0.25
b. 0.33
c. 0.50
d. 0.67
e. 3.00
 A waiting line model meeting the assumptions of M/M/1 has an arrival rate of 2 per hour and a service rate of 6 per hour; the utilization factor for the system is approximately
a. 0.25
b. 0.33
c. 0.50
d. 0.67
e. 3.00
 As the average service rate μ increases, the shape of the negative exponential distribution of service times
 grows steadily steeper without limit
 has an ever steeper slope that eventually turns positive
 becomes less gently curved as it moves ever closer to the graph origin
 takes on a more uniform slope over a wide range of service times
 changes in appearance from convex to concave
 Which one of the following is not a characteristic of a Model A or M/M/1 system?
 exponential service time pattern
 single number of channels
 single number of phases
 Poisson arrival rate pattern
 limited population size
 Which one of the following is not a characteristic of a Model B or M/M/S system?
 unlimited population size
 single channel
 single queue
 single phase
 Poisson arrival rate pattern
 Which one of the following is not a characteristic of a Model C or M/D/1 system?
 single channel
 single phase

 Poisson arrival rate pattern
 exponential service time pattern
 unlimited population size
 In the basic queuing model (M/M/1), service times are described by
 continuous probability distributions
 negative exponential probability distributions
 Poisson probability distributions
 normal probability distributions
 lognormal distributions
 In the basic queuing model (M/M/1), arrival rates are distributed by
 continuous probability distributions
 normal probability distributions
 negative exponential probability distributions
 Poisson distributions
 lognormal distributions
 A singlephase waitingline system meets the assumptions of constant service time or M/D/1. Units arrive at this system every 10 minutes on average. Service takes a constant 4 minutes. The average length of the queue Lq is
a. 0.4
b. 0.133
c. 4.167
d. 4.583
e. 6
 Which of the following is not an assumption of the M/M/1 model?
 The first customers to arrive are the first customers served.
 Each arrival comes independently of the arrival immediately before and after that arrival.
 The population from which the arrivals come is very large or infinite in size.
 Customers do not renege.
 Service times occur according to a normal curve.
 A singlephase waitingline system meets the assumptions of constant service time or M/D/1. Units arrive at this system every 12 minutes on average. Service takes a constant 8 minutes. The average length of the queue Lq is approximately
a. 0.67
b. 2.5
c. 4.5
d. 5.0
e. 7.5
 A singlephase waitingline system meets the assumptions of constant service time or M/D/1. Units arrive at this system every 12 minutes on average. Service takes a constant 8 minutes. The average number in the system Ls is approximately
a. 2.25
b. 2.5
c. 3.0
d. 1.33
e. 5.0
 A queuing model which follows the M/M/1 assumptions has λ = 2 and μ = 3. The average number in the system is
a. 2/3
b. 1
c. 1.5
d. 2
e. 6
 A queuing model which follows the M/M/1 assumptions has λ = 3 and μ = 2. The average number in the system is
 3
 3
c. 0.667
d. 150 percent
e. growing without limit, since λ is larger than μ.
 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?

 1 minute
 2 minutes
 3 minutes
 5 minutes
 20 minutes
 A queuing model which follows the M/M/1 assumptions has λ = 10 and μ = 12. The average number in the system is
a. 0.83
b. 2
c. 2.5
d. 5
e. 6
 A queuing model which follows the M/M/1 assumptions has λ = 2 and μ = 8. The average number in the system Ls is and the utilization of the system is .
 3; 100 percent
 0.33; 25 percent
 4; 33 percent
 6; 25 percent
 4; 25 percent
 Four of the most widely used waiting line models—M/M/1 or A, M/M/S or B, M/D/1 or C, and Limited population or D—all share three characteristics, which are
 normal arrivals, FIFO discipline, and normal service times
 Poisson arrivals, FIFO discipline, and a singleservice phase
 Poisson arrivals, FIFO discipline, and exponential service times
 Poisson arrivals, no queue discipline, and exponential service times
 none of these
 A queuing model which follows the M/M/1 assumptions has λ = 2 and μ = 3. The average waiting time in the system is
a. 2/3
b. 1
c. 1.5
d. 2
e. 6
 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 utilization factor?
a. 20%
b. 30%
c. 40%
d. 50%
e. 60%
 A finite population waiting line model has an average service time T of 100 minutes and an average time between service requirements U of 400 minutes; the service factor X is
a. 0.20
b. 0.25
 4
 5
 300 minutes
 A finite population waiting line model has an average service time T of 200 minutes and an average time between service requirements U of 300 minutes; the service factor X is
a. 0.20
b. 0.40
c. 0.60
d. 0.67
e. 2.5
 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. A student has just entered the system. How long is she expected to stay in the system?

 0.125 minute
 0.9 minute
 1.5 minutes
 7.5 minutes
 0.075 hour
 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. How many students, on the average, will be waiting in line at any one time?

 0.9 students
 1.5 students
 3 students
 4 students
 36 students
 A waitingline system that meets the assumptions of M/M/S has λ = 5, μ = 4, and M = 2. For these values, Po is approximately 0.23077 and Ls is approximately 2.05128. The average time a unit spends waiting in this system
 is approximately 0.1603
 is approximately 0.2083
 is approximately 0.4103
 is approximately 0.8013
 cannot be calculated because λ is larger than μ
 A waitingline system that meets the assumptions of M/M/1 has λ = 1, μ = 4. For this system, Po is
and utilization is . a. 0.75; 0.25
b. 0.80; .20
c. 3; 4
d. 3; 4
e. none of these
 A waitingline system that meets the assumptions of M/M/S has λ = 5, μ = 4, and M = 2. For these values, Po is approximately 0.23077 and Ls is approximately 2.05128. The average number of units waiting in the queue
 is approximately 0.1603
 is approximately 0.4103
 is approximately 0.8013
 is approximately 1.0417
 cannot be calculated because λ is larger than μ
 A waitingline system that meets the assumptions of M/M/1 has λ = 1, μ = 4. For this system, the probability of more than two units in the system is approximately
 zero
b. 0.015625
c. 0.0625
d. 0.25
e. 0.9375
 A waitingline system that meets the assumptions of M/M/1 has λ = 1, μ = 4. For this system, the probability of fewer than two units in the system is approximately
a. 0.0625
b. 0.25
c. 0.75
d. 0.9375
e. certain