Fairness and efficiency for polling models with the κ-gated service discipline
We study a polling model in which we want to achieve a balance between the fairness of the waiting times and the efficiency of the system. For this purpose, we introduce a novel service discipline: the κ-gated service discipline. It is a hybrid of the classical gated and exhausted disciplines, and consists of using κ_i consecutive gated service phases at queue i before the server switches to the next queue. The advantage of this discipline is that the parameters κ_i can be used to balance fairness and efficiency. We derive the distributions and means of the waiting times, a pseudo conservation law for the weighted sum of the mean waiting times, and the fluid limits of the waiting times. Our goal is to optimize the κ_i so as to minimize the differences in the mean waiting times, i.e. to achieve maximal fairness, without giving up too much on the efficiency of the system. From the fluid limits we derive a heuristic rule for setting the κ_i. In a numerical study, the heuristic is shown to perform well in most cases.
© 2012 Elsevier B. V. Received 14 December 2010. Revised 9 February 2012. Accepted 10 February 2012. Available online 13 March 2012. The authors would like to thank Marko Boon for assistance with the Mathematica implementation used in the numerical analysis, and for comments on an earlier version of this manuscript. The authors would also like to thank Erik Winands for his fruitful suggestion to use fluid heuristics.