Abstract. We propose ESREQM (Efficient Sending Rate EstimationQueue Management), a novel active queue management scheme that achieves almost perfect max-min fairness among flows with minimum (constant) per-flow state and a constant number of CPU operations to handle an incoming packet using a single queue with very low buffer requirements. ESREQM estimates sending rates of flows through a history discounting process that allows it to guarantee max-min fairness by automatically adapting parameters. It can also be used to punish non-responsive flows. The per-flow state is limited to a single value per flow, which allows the flow memory to be in SRAM, thereby making packet processing scalable with link speeds. ESREQM results in good link utilization with low buffer size requirements because it provably desynchronizes TCP flows as a by-product. We show our results through a mixture of analysis and simulation. Our scheme does not make assumptions on what transport protocols are used.
We generalize the Cost-Distance problem: Given a set of sites in -dimensional Euclidean space and a weighting over pairs of sites, construct a network that minimizes the cost (i.e. weight) of the network and the weighted distances between all pairs of sites. It turns out that the optimal solution can contain Steiner points as well as cycles. Furthermore, there are instances where crossings optimize the network. We then investigate how trees can approximate the weighted Cost-Distance problem. We show that for any given set of sites and a non-negative weighting of pairs, provided the sum of the weights is polynomial, one can construct in polynomial time a tree that approximates the optimal network within a factor of . Finally, we show that better approximation rates are not possible for trees. We prove this by giving a counter-example. Thus, we show that for this instance that every tree solution differs from the optimal network by a factor .
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