Customers arrive at a service station, manned by a single server who serves at an exponential rate μ1, at a Poisson rate λ. After completion of service the customer then joins a second system where the server serves at an exponential rate μ2. Such a system is called a tandem or sequential queueing system.

Assuming that λ<μi , i = 1, 2, determine the limiting probabilities.

Hint: Try a solution of the form Pn,m = Cαnβm, and determine C,α,β.