I'm working with a queue with exponential service times with rate $1/\mu$. There are two customers in the queue and when they are served they rejoin the queue exponentially with rate $1/\lambda$.
Now, how can I calculate the probability that there is 1 customer in the queue at a random moment in time, and the probability that there is 1 customer in the queue upon arrival of a customer.
[I'm preparing for an exam and this question was used last year]