Customers arriving at a bank according to a homogeneous Poisson process with intensity = 0.2. Two bank tellers are on duty. Each customer joins the queue and is serviced immediately upon emptying of the queue. Suppose that the service times of the customers are independent and exponentially distributed random variables with parameter = 5. Let Y (t) denote the number of customers in the process of being served at time t. Determine

(a) the time of explosion;

(b) P(Y (t) = 4) for large t;

(c) P(Y (t) = 0) for large t;

(d) the period of the embedded chain.