Problem $4$

At a toll booth, vehicles arrive with a mean arrival rate of four vehicles per minute, and they are processed with a mean rate of five vehicles per minute. Determine the average length of the queue, the average time spent in the toll booth, and the average waiting time ifthe vehicles arrive according to a Poisson process and

a$)$ they are processed at a uniform deterministic rate.

b$)$ they are processed at an exponential rate.