A waiting-loss system of type \(M / M / 1 / 2\) is subject to two independent Poisson inputs 1 and 2 with respective intensities \(\lambda_{1}\) and \(\lambda_{2}\), which are referred to as type 1and type 2-customers. An arriving type 1-customer who finds the server busy and the waiting places occupied displaces a possible type 2-customer from its waiting place (such a type 2-customer is lost), but ongoing service of a type 2-customer is not interrupted. When a type 1-customer and a type 2-customer are waiting, then the type 1 -customer will always be served first, regardless of the order of their arrivals. The service times of type 1 - and type 2-customers are independent and have exponential distributions with respective parameters \(\mu_{1}\), and \(\mu_{2}\).

Describe the behavior of the system by a homogeneous Markovchain, determine the transition rates, and draw the transition graph.