EXERCISE 1.

Show by the reversibility technique that the output process of an M/M/1/N queue (of which the capacity is limited to N) is Poisson if the customers who are refused are sent directly to the output. Then show that if the refused customers are not counted in the output process this is not Poisson.

EXERCISE 2.

Show that in a Jackson network in which a customer leaving a station has zero probability of returning, all the streams are Poisson and the network as a whole takes the form of a reversible process.