A waiting-loss system of type M/M/1/2 is subject to two independent Poisson inputs 1 and 2 with respective intensities λ 1 and λ 2 (type 1- and type 2-customers). An arriving type 1-customer who finds...

A waiting-loss system of type M/M/1/2 is subject to two independent Poisson inputs 1 and 2 with respective intensities λ₁
and λ₂
(type 1- and 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 μ₁
and μ₂.

Describe the behaviour of the system by a homogeneous Markov chain, determine the transition rates, and draw the transition graph.