[Queuing Theory - Operations Research]

Visitors' parking space is limited only to four spaces. Cars making use of this space arrive according to a Poisson distribution at a rate of 10 cars per hour. Parking time is exponential with mean 40 minutes. Visitors who cannot find an empty space immediately on arrival may temporarily wait outside the compound until a parked car leaves. That temporary space can hold only four cars. All other cars that cannot park or find a temporary waiting space must go elsewhere. Determine the following:

(a) the probability of having cars in the system

(b) the effective arrival rate of cars

(c) the average number of occupied parking space.