Consider a sequential-service system consisting of two servers, A and B. Arriving customers will enter this system only if server A is free. If a customer does enter, then he is immediately served by server A. When his service by A is completed, he then goes to B if B is free, or if B is busy, he leaves the system. Upon completion of service at server B, the customer departs. Assume that the (Poisson) arrival rate is two customers an hour, and that A and B serve at respective (exponential) rates of four and two customers an hour.
(a) What proportion of customers enter the system?
(b) What proportion of entering customers receive service from B?
(c) What is the average number of customers in the system?
(d) What is the average amount of time that an entering customer spends in the system?