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 probability that a machine will have to wait for service with two operators?
A).654
B).090
C).346
D).910
E).016

Question

Quizplus · Accepted Answer

The system can be modeled as an M/M/c queue with λ = 1/44 per minute and μ = 1/6 per minute. With 10 machines and 2 operators, the traffic intensity ρ = (10/44) / (2/6) = 0.6818. Using the Erlang B formula for the probability of delay in an M/M/c queue, the probability that a machine will have to wait for service is approximately 0.346.

A Bank of 10 Machines Requires Regular Periodic Service