71) A post office has a single line for customers waiting for the next available postal clerk. There are two postal clerks who work at the same rate. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. The average arrival rate is three per minute and the average service rate is two per minute for each of the two clerks. What is the average length of the line? A) 3.429 B) 1.929 C) 1.143 D) 0.643 E) None of the above

71) A post office has a single line for
customers waiting for the next available postal clerk. There are two postal
clerks who work at the same rate. The
arrival rate of customers follows a Poisson distribution, while the service
time follows an exponential distribution. The average arrival rate is three per
minute and the average service rate is two per minute for each of the two
clerks. What is the average length of
the line?
A) 3.429
B) 1.929
C) 1.143
D) 0.643
E) None of the above
72) A post office has a single line for
customers waiting for the next available postal clerk. There are two postal
clerks who work at the same rate. The
arrival rate of customers follows a Poisson distribution, while the service
time follows an exponential distribution. The average arrival rate is three per
minute and the average service rate is two per minute for each of the two
clerks. How long does the average person
spend waiting for a clerk?
A) 3.429 minutes
B) 1.929 minutes
C) 1.143 minutes
D) 0.643 minute
E) None of the above
73) A post office has a single line for
customers waiting for the next available postal clerk. There are two postal
clerks who work at the same rate. The
arrival rate of customers follows a Poisson distribution, while the service
time follows an exponential distribution. The average arrival rate is three per
minute and the average service rate is two per minute for each of the two
clerks. What proportion of time are both
clerks idle?
A) 0.643
B) 0.250
C) 0.750
D) 0.143
E) None of the above

Table 13-1

M/M/2

Mean Arrival Rate:

9 occurrences per minute

Mean Service Rate:

8 occurrences per minute

Number of Servers:

2

Queue Statistics:

Mean Number of Units in the System:

1.646

Mean Number of Units in the Queue:

0.521

Mean Time in the System:

0.183 minutes

Mean Time in the Queue:

0.058 minutes

Service Facility Utilization Factor:

0.563

Probability in No Units in System:

0.280

74) According to the information provided
in Table 13-1, on average, how many units are in the
line?
A) 1.646
B) 0.563
C) 0.280
D) 1.125
E) 0.521

75) According to the information provided
in Table 13-1, what proportion of time is at least one
server busy?
A) 0.563
B) 0.437
C) 0.720
D) 0.280
E) None of the above

76) Using the information provided in
Table 13-1 and counting each person being served and
the people in line, on average, how many people would be in this system?
A) 0.521
B) 1.646
C) 1.125
D) 0.183
E) None of the above
Answer:
B
77) According to the information provided
in Table 13-1, what is the average time spent by a person
in this system?
A) 0.058 minute
B) 1.646 minutes
C) 0.521 minute
D) 0.183 minute
E) None of the above

78) According to the information provided
in Table 13-1, what percentage of the total available
service time is being used?
A) 72.0%
B) 28.0%
C) 56.3%
D) It could be any of the above, depending
on other factors.
E) None of the above

79) Cars arrive at a local JLUBE franchise
at the rate of 1 every 12 minutes.
Service times are exponentially distributed with an average of 15
minutes. Jack Burns, the JLUBE owner,
has decided to open a second work bay, i.e., make the shop into a two-channel system. Under this
new scheme, the average customer will wait in an ________ line
A) M/M/1
B) M/M/2
C) M/D/2
D) M/D/1
E) M/G/2
80) Cars arrive at a local JLUBE franchise
at the rate of 1 every 12 minutes.
Service times are exactly 15 minutes.
Jack Burns, the JLUBE owner, has decided to open a second work bay,
i.e., make the shop into a two-channel system. Under this new scheme, the average customer
will wait in an ________ line
A) M/M/1
B) M/M/2
C) M/D/2
D) M/D/1
E) M/G/2

81) Cars arrive at a local JLUBE franchise
at the rate of 1 every 12 minutes.
Service times are exponentially distributed with an average of 15
minutes. Jack Burns, the JLUBE owner,
has decided to open a second work bay, i.e., make the shop into a two-channel system. Under this
new scheme, the average customer will wait in line
A) approximately 9.6 minutes.
B) approximately 2.5 minutes.
C) approximately 24.6 minutes.
D) approximately 2.1 minutes.
E) None of the above

82) Cars arrive at a local JLUBE franchise
at the rate of 1 every 12 minutes.
Service times are exponentially distributed with an average of 15
minutes. Jack Burns, the JLUBE owner,
has decided to open a second work bay, i.e., make the shop into a two-channel system. Under this
new scheme, the total time an average customer spends in the system will be
A)
37 minutes.
B)
2.1 minutes.
C)
9.6 minutes.
D)
33.3 minutes.
E)
24.6 minutes.
Table 13-2

M/M/2

Mean Arrival Rate:

5 occurrences per minute

Mean Service Rate:

3 occurrences per minute

Number of Servers:

2

Queue Statistics:

Mean Number of Units in the System:

5.455

Mean Number of Units in the Queue:

3.788

Mean Time in the System:

1.091 minutes

Mean Time in the Queue:

0.758 minutes

Service Facility Utilization Factor:

0.833

Probability in No Units in System:

0.091

83) According to the information provided
in Table 13-2, which presents a queuing problem solution,
on average, how many units are in the line?
A) 5.455
B) 3.788
C) 1.091
D) 0.758
E) 0.833

84) According to the information provided
in Table 13-2, which presents a queuing problem solution,
what proportion of time is at least one server busy?
A) 0.833
B) 0.758
C) 0.091
D) 0.909
E) None of the above
85) According to the information provided
in Table 13-2, which presents a queuing problem solution,
there are two servers in this system.
Counting each person being served and the people in line, on average,
how many people would be in this system?
A) 5.455
B) 3.788
C) 9.243
D) 10.900
E) None of the above

Table 13-3

M/M/3

Mean Arrival Rate:

4 occurrences per minute

Mean Service Rate:

2 occurrences per minute

Number of Servers:

3

Queue Statistics:

Mean Number of Units in the System:

2.889

Mean Number of Units in the Queue:

0.889

Mean Time in the System:

0.722 minutes

Mean Time in the Queue:

0.222 minutes

Service Facility Utilization Factor:

0.667

Probability in No Units in System:

0.111

86) According to the information provided
in Table 13-3, which presents a queuing problem solution,
what proportion of time is the system totally empty?
A) 0.111
B) 0.333
C) 0.889
D) 0.667
E) None of the above
87) According to the information provided
in Table 13-3, which presents a queuing problem solution,
on average, how long does each customer spend waiting in line?
A) 0.333 minute
B) 0.889 minute
C) 0.222 minute
D) 0.722 minute
E) 0.111 minute

88) According to the information provided
in Table 13-3, which presents a queuing problem solution
what is the utilization rate of the service facility?
A) 0.111
B) 0.889
C) 0.222
D) 0.722
E) 0.667

89) Little’s Flow Equations are
transferable to a production environment.
Which of the following would be a proper interpretation of Little’s Flow
Equations?
A) Flow Rate= Inventory× Flow Time
B) Flow Time= Inventory× Flow Rate
C) Inventory= Flow Rate× Flow Time
D) Time to Take an Order= Flow Rate× Flow Time
E) Flow Rate= Time to Take an Order× Flow Time
90) If everything else remains constant,
including the mean arrival rate and service rate, except that the service time
becomes constant instead of exponential,
A) the average queue length will be
halved.
B) the average waiting time will be
doubled.
C) the average queue length will be
doubled.
D) There is not enough information to know
what will happen to the queue length and waiting time.
E) None of the above
91) At an automatic car wash, cars arrive
randomly at a rate of 7 cars every 30 minutes.
The car wash takes exactly 4 minutes (this is constant). On average, what would be the length of the
line?
A) 8.171
B) 7.467
C) 6.53
D) 0.467
E) None of the above

92) At an automatic car wash, cars arrive
randomly at a rate of 7 every 30 minutes.
The car wash takes exactly 4 minutes (this is constant). On average, how long would each car spend at
the car wash?
A) 28 minutes
B) 32 minutes
C) 17 minutes
D) 24 minutes
E) None of the above

93) At an automatic car wash, cars arrive
randomly at a rate of 7 every 30 minutes.
The car wash takes exactly 4 minutes (this is constant). On average, how long would each driver have
to wait before receiving service?
A) 28 minutes
B) 32 minutes
C) 17 minutes
D) 24 minutes
E) None of the above
94) At an automatic car wash, cars arrive
randomly at a rate of 7 every 30 minutes.
The car wash takes exactly 4 minutes (this is constant). On average, how many customers would be at
the car wash (waiting in line or being serviced)?
A) 8.17
B) 7.46
C) 6.53
D) 0.46
E) None of the above
95) A(n) ________ state is the normal
operating condition of the queuing system.
A) primary
B) transient
C) NOC
D) balanced
E) steady
96) At a local fast food joint, cars
arrive randomly at a rate of 12 every 30 minutes. The fast food joint takes exactly 2 minutes
(this is constant). The average total
time in the system is
A) 5.4 minutes.
B) 6.0 minutes.
C) 8.0 minutes.
D) 2.5 minutes.
E) None of the above
Table 13-4

M/D/1

Mean Arrival Rate:

3 occurrences per minute

Constant Service Rate:

4 occurrences per minute

Queue Statistics:

Mean Number of Units in the System:

1.875

Mean Number of Units in the Queue:

1.125

Mean Time in the System:

0.625 minutes

Mean Time in the Queue:

0.375 minutes

Service Facility Utilization Factor:

0.750

Probability in No Units in System:

0.250

97) According to the information provided
in Table 13-4, which presents a queuing problem solution
for a queuing problem with a constant service rate, on average, how much time
is spent waiting in line?
A) 1.875 minutes
B) 1.125 minutes
C) 0.625 minute
D) 0.375 minute
E) None of the above
98) According to the information provided
in Table 13-4, which presents a queuing problem solution
for a queuing problem with a constant service rate, on average, how many
customers are in the system?
A) 1.875
B) 1.125
C) 0.625
D) 0.375
E) None of the above

99) According to the information provided
in Table 13-4, which presents a queuing problem solution
for a queuing problem with a constant service rate, on average, how many
customers arrive per time period?
A) 3
B) 4
C) 1.875
D) 1.125
E) None of the above

100) According to Table 13-4, which presents a queuing problem with a constant service rate, on
average, how many minutes does a customer spend in the service facility?
A) 0.375 minutes
B) 4 minutes
C) 0.625 minutes
D) 0.25 minutes
E) None of the above