A bank of 10 machines requires regular periodic service. Machine running time and service time are both exponential. Machines run for an average of 44 minutes between service requirements, and service time averages six minutes per machine. What is the average number of machines down when there is one operator?
A)1.49
B)3.35
C)4.40
D)6.65
E)8.51

Question

Quizplus · Accepted Answer

The average number of machines down can be calculated using the formula L = λ / (μ - λ), where λ is the arrival rate (1/44 per minute) and μ is the service rate (1/6 per minute). With one operator, the system is an M/M/1 queue. Solving gives L = (10 * 1/44) / (1/6 - 1/44) = 3.35.

A Bank of 10 Machines Requires Regular Periodic Service