Individuals arrive two at a time to a 2 server queueing station, with the pairs arriving at times distributed according to a Poisson process with rate λ. A pair will only enter the system if it finds both servers are free. In that case, one member of the pair enters service with server 1 and the other with server 2.

Service times at server i are exponential with rate μi , i = 1, 2.

(a) Find the rate at which pairs enter the system.

(b) Find the proportion of time exactly one of the servers is busy.