5.1. Jobs arrive at a certain service system according to a Poisson process of rate A. The server will accept an arriving customer only if it is idle at the time of arrival. Potential customers arriving when the system is busy are lost. Suppose that the service times are independent random variables with mean service time A. Show that the long run fraction of time that the server is idle is 1/(1 + Aμ). What is the long run fraction of potential customers that are lost?