Suppose to have one server and two queues, say A and B. In both queues arrive jobs with exponential inter-arrival time with rate λ, but only A is connected to the server. The server has an exponential service time with rate μ, but, as said before, can serve only A (So the system composed by **B and the server** is an M/M/1). B enqueues jobs until there are jobs in the A queue and in the server. When the server is idle and A is empty, then B empties. When there will arrive new jobs in the M/M/1 system, then B will continue to enqueue the new jobs as before. What are the mean number of jobs in B queue?
side note: Would be useful to define a rate of "emptiness" (of a M/M/1), supposing the distribution exponential?