BIAS OPTIMALITY IN CONTROLLED QUEUING-SYSTEMS

This paper studies an admission control M/M/1 queueing system. It show s that the only gain (average) optimal stationary policies with gain a nd bias which satisfy the optimality equation are of control limit typ e, that there are at most two and, if then are two, they occur consecu tively. Conditions are provided which ensure the existence of two gain optimal control limit policies and are illustrated with an example. T he main result is that bias optimality distinguishes these two gain op timal policies and that the larger of the two control limits is the un ique bias optimal stationary policy. Consequently it is also Blackwell optimal. This result is established by appealing to the third optimal ity equation of the Markov decision process and some observations conc erning the structure of solutions of the second optimality equation.