Suppose customers arrive to a two server system according to a Poisson process with rate , and

Suppose customers arrive to a two server system according to a Poisson process with rate λ, and suppose that each arrival is, independently, sent either to server 1 with probability α or to server 2 with probability 1 − α. Suppose the service time at server i is exponential with rate μi , i = 1, 2.

(a) Find W(α), the average amount of time a customer spends in the system.

(b) If λ = 1 and μi = i, i = 1, 2, find the value of α that minimizes W(α).