On the Optimal Open-loop Control Policy for Deterministic and Exponential Polling Systems

In this article, we consider deterministic ~both fluid and discrete! polling systems with N queues with infinite buffers and we show how to compute the best polling sequence ~minimizing the average total workload!+ With two queues, we show that the best polling sequence is always periodic when the system is stable and forms a regular sequence+ The fraction of time spent by the server in the first queue is highly noncontinuous in the parameters of the system ~arrival rate and service rate! and shows a fractal behavior+ Moreover, convexity properties are shown and are used in a generalization of the computation of the optimal control policy ~in open loop! for the stochastic exponential case+