The Taj Service Station has five mechanics each of whom can service a scooter in 2 hours on an average. The scooters are registered at a single counter and then sent for servicing to different mechanics.

Scooters arrive at the service station at an average rate of 2 scooters per hour.

Assuming that the scooter arrivals are Poisson distributed and the servicing times are distributed exponentially, determine,

(a) utilisation factor,

(b) the probability that the system shall be idle,

(c) the probability that there shall be 3 scooters in the service centre,

(d) the probability that there shall be eight scooters in the centre,

(e) the expected number of scooters waiting in the queue,

(f) the expected number of scooters in the service centre,

(g) the average waiting time in the queue, and

(h) the average time spent by a scooter in waiting and getting serviced.