Customers arrive to a single server system in accordance with a Poisson process with rate . Arrivals

Customers arrive to a single server system in accordance with a Poisson process with rate λ. Arrivals only enter if the server is free. Each customer is either a type 1 customer with probability p or a type 2 customer with probability 1 − p. The time it takes to serve a type i customer is exponential with rate

μi , i = 1, 2. Find the average amount of time an entering customer spends in the system.