Dry and wet seasons alternate, with each dry season lasting an exponential time with rate and

Dry and wet seasons alternate, with each dry season lasting an exponential time with rate λ and each wet season an exponential time with rate μ. The lengths of dry and wet seasons are all independent. In addition, suppose that people arrive to a service facility according to a Poisson process with rate v. Those

(a) What is limt→∞N(t)/t?

(b) Find limt→∞E[U(t)].

(c) If all Fi are exponential with rate λ and all Gi are exponential with rate μ, what is P{U(t) = k}?