Problem $4$: $(25)$

Given: Airplanes arrive at a single landing strip at an average rate of $10$ planes per hour. On average, a

plane requires four minutes to land and taxi to its terminal. Assume that the plane arrival pattern can be

described by the Poisson distribution and that service time is exponentially distributed.

Find: Calculate the following performance characteristics of the queuing system considering steady state

condition.

$($a$)$ the percent of the time that the runway will be idle,

$($b$)$ the probability that at any given time, there will be three planes in the queuing system,

$($c$)$ the average number of planes in the queuing system,

$($d$)$ the average queue length, and

$($e$)$ the average time each plane spends in the queuing system.