A generalized framework for achieving max-min fairness

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Fairness in traffic management improves the isolation between traffic streams, offers a more predictable performance, eliminates transient bottlenecks, mitigates the effect of certain kinds of denial-of-service attacks, and serves as a critical component of a quality-of-service 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 of the network. Several research efforts have attempted to achieve fairness in the allocation of a single resource. However, there has been no uniform framework to achieve overall fairness in systems with multiple resources. This dissertation proposes a framework that achieves overall fairness in the allocation of multiple resources to contending users wherein each user contends for a different, but not necessarily disjoint, subset of the set of available resources. Based on an extension of the notion of bottleneck links, we present a constructive principle that enables us to iteratively determine the max-min fair allocation of resources. This principle leads to the development of the Fair Resource Algorithm (FRA) that, as we prove, achieves max-min fairness. Two applications of the FRA algorithm are presented. The first is in an input-queued switch based on the virtual-output-queueing architecture wherein each flow shares the bandwidth at its input and output ports with other flows. We present an ideal algorithm as well as a practical and distributed version for implementation in input-queued switches. We show, via simulations using both real gateway traffic traces and synthetically generated traffic, that our algorithm is significantly fairer than other popular algorithms and does not incur any performance overhead. We also describe an application of the FRA algorithm to wireless networks. In a wireless network, the shared and non-exclusive nature of the wireless medium does not permit a clear characterization of resources. We model the network as a graph and formulate the problem of achieving max-min fair allocations as graph coloring problems. We introduce the notion of contention zones as resources and present a version of the FRA algorithm that provably achieves max-min fairness. The above formulation also offers insights that lead to the development of two practical algorithms that operate locally on each node using information that is readily available. We show, via simulations, that these algorithms achieve both better fairness and performance as compared to the IEEE 802.11b standard.