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 that arrive during a dry season are allowed to enter; those that arrive during a wet season are lost. Let Nl (t) denote the number of lost customers by time t .

(a) Find the proportion of time that we are in a wet season.

(b) Is {Nl (t ), t ≥ 0} a (possibly delayed) renewal process?

(c) Find limt→∞

Nl (t)

t .