Max-Min Fair Input-Queued Switching

Fairness in traffic management can improve the isolation between traffic streams, offer a more predictable performance, eliminate transient bottlenecks, mitigate the effect of certain kinds of denial-ofservice attacks, and serve as a critical component of a quality-ofservice strategy to achieve certain guaranteed services such as delay bounds and minimum bandwidths. While fairness in bandwidth allocation over a shared output link has been studied extensively, the desired eventual goal is overall fairness in the use of all the resources in a switch or a router. Several research efforts have attempted to achieve fairness in input-queued switches by one measure or another. However, there has been no uniform framework for evaluating these different strategies. In this report, we formalize the notion of fairness in input-queued switches through a rigorous framework that permits a quantitative evaluation of various strategies for fairness. Based on an extension of the max-min notion of fairness, our framework permits the algorithmic determination of the fair rates to be allocated to the flows through the switch. In addition to proving the correctness of the algorithm, we show that it can be implemented in a distributed fashion to dynamically determine flow rates. We further propose a practical scheduling strategy based on our algorithm. We present simulation results, using both real traffic traces as well synthetic traffic, to evaluate the fairness of a variety of popular scheduling algorithms for input-queued switches. The results show that our scheduling strategy achieves better fairness than other known algorithms for input-queued switches.