Chapter 12 Waiting Lines and Queuing Theory Models

71) A queuing system with a normally distributed arrival pattern, exponential service times, and three servers would be described as

A) G/G/3.

B) M/M/3.

C) G/M/3.

D) M/G/3.

E) N/E/3.

72) The initial state of a queuing system (for example, when a restaurant first opens), is referred to as the ________ state.

A) steady

B) primary

C) introductory

D) transient

E) start-up

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. What type of queuing model applies here?

A) M/M/1

B) M/M/2

C) M/D/2

D) M/D/1

E) M/G/1

74) 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 normal distribution. What type of queuing model applies here?

A) M/M/1

B) M/M/2

C) M/D/2

D) M/D/1

E) M/G/2

75) 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

76) 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

77) 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 12-1

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

78) According to the information provided in Table 12-1, on average, how many units are in the line?

A) 1.646

B) 0.563

C) 0.280

D) 1.125

E) 0.521

79) According to the information provided in Table 12-1, 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

80) Using the information provided in Table 12-1 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