An explicit solution to a tandem queueing model

We consider two queues in tandem, each with an exponential server, and with deterministic arrivals to the first queue. We obtain an explicit solution for the steady state distribution of the process (N-1(t), N-2(t), Y(t)), wh ere N-j(t) is the queue length in the jth queue and Y(t) measures the time elapsed since the last arrival. Then we obtain the marginal distributions o f (N-1(t), N-2(t)) and of N-2(t) We also evaluate the solution in various l imiting cases, such as heavy traffic.