Virginia's Ron McPherson Electronics Corporation retains a service crew to repair machine breakdowns that occur on average λ = 3 per 8-hour workday (approximately Poisson in nature). The crew can service an average of µ = 8 machines per workday, with a repair time distribution that resembles the negative exponential distribution.
a) What is the utilization rate of this service system?
b) What is the average downtime for a broken machine?
c) How many machines are waiting to be serviced at any given time?
d) What is the probability that more than 1 machine is in the system? The probability that more than 2 are broken and waiting to be repaired or being serviced? More than 3? More than 4?