A small airline has 6 planes. For routine maintenance of the planes the airline operates a maintenance hangar that can work on one plane at a time. Each plane requires maintenance about 3 times a week, Poisson distributed. The maintenance hangar takes on average 1 day to perform a maintenance task on a plane, exponentially distributed. For this queueing system, calculate the following:
Utilization
Average number of planes out of commission
Average days that a plane is out of commission
Probability that a plane gets serviced as soon as it arrives at the maintenance bay (i.e., no waiting).
How many hangars should the airline have to ensure that a plane is out of commission no more than 1 day?