Consider a single-server first-come, first-served queueing system where the maximum number of customers in the system is 4 (including the customer in service). Arrivals are Poisson with rate λ = 10 / hour. Service times are exponential with a mean of 5 minutes.

(a) Compute the fraction of customers that are denied service because the system is full.

(b) Compute the average wait in queue of customers who enter service.

(c) Now consider the following exception: When there are 4 customers in the system, the server works 50% faster, but otherwise works at the service rate stated above. Recompute the fraction of customers that are denied service because the system is full.