Threshold properties of optimal policies in queueing networks with imperfect information

Optimal routing policies for queueing networks under imperfect information are treated by discrete time dynamic programming. It is proved that certain inequalities in terms of information measures can be propagated from one epoch to the next; hence, an inductive argument shows that threshold policies are optimal under mild conditons on the instantaneous costs, and that the total cost is convex and monotone. Two examples are provided. The first deals with a tandem queue having inputs to both work stations, and only inferential information available on the the state of the second station. The second considers optimal routing for incoming customers to a G/M/m queue when the observations are both delayed and subject to random errors.