Rational C1 Suboptimal Compensators for Continuous-Time Systems

We prove the optimality of routing policies with limitedstate information that are employed in queueing systems with finitecapacities and customers arriving at arbitrary instants. Using samplepath arguments we show that, on one hand, when service times areexponential and capacities are equal, the round robin policy minimizesthe expected number of losses by any time t and at the same time,maximizes the expected number of departures by t , over all policies thatuse no state information. On the other hand, when service times aredeterministic, a modified round robin policy that makes use of limitedstate information outperforms stochastically all dynamic policies thathave richer state information, in terms of the number of losses and thenumber of departures by t .