Assignment:
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?
Provide complete and step by step solution for the question and show calculations and use formulas.