Jobs arrive at a processing center in accordance with a Poisson process with rate A. However, the center has waiting space for only N jobs and so an arriving job finding N others waiting goes away. At most 1 job per day can be processed, and the processing of this job must start at the beginning of the day. Thus, if there are any jobs waiting for processing at the beginning of a day, then one of them is processed that day, and if no jobs are waiting at the beginning of a day then no jobs are processed that day. Let X, denote the number of jobs at the center at the beginning of day n.

(a) Find the transition probabilities of the Markov chain {X,, n = 0}.

(b) Is this chain ergodic? Explain.

(c) Write the equations for the stationary probabilities.