25 May Question 71) A post office has a single line for customers waiting fo
Question
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
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