Optimal surplus capacity utilization in polling systems via fluid models

We discuss the idea of differential fairness in polling systems. One such example scenario is: primary customers demand certain Quality of Service (QoS) and the idea is to utilize the surplus server capacity to serve a secondary class of customers. We use achievable region approach for this. Towards this, we consider a two queue polling system and study its `approximate achievable region´ using a new class of delay priority kind of schedulers. We obtain this approximate region, via a limit polling system with fluid queues. The approximation is accurate in the limit when the arrival rates and the service rates converge towards infinity while maintaining the load factor and the ratio of arrival rates fixed. We show that the set of proposed schedulers and the exhaustive schedulers form a complete class: every point in the region is achieved by one of those schedulers. It is well known that exhaustive service policy optimizes system performances like unfinished work. In this paper, we show that it is also optimal from the perspective of individual queues. We further pose two constrained optimization problems: a) admission control, wherein the arrival rates of secondary customers is optimally designed; b) maximizing the revenue considering the losses when secondary arrival rate is fixed. We finally show that exhaustive service discipline at each queue turns out to be optimal.