Understanding CHOKe: throughput and spatial characteristics

A recently proposed active queue management, CHOKe, is stateless, simple to implement, yet surprisingly effective in protecting TCP from UDP flows. We present an equilibrium model of TCP/CHOKe. We prove that, provided the number of TCP flows is large, the UDP bandwidth share peaks at (e+1)/sup -1/=0.269 when UDP input rate is slightly larger than link capacity, and drops to zero as UDP input rate tends to infinity. We clarify the spatial characteristics of the leaky buffer under CHOKe that produce this throughput behavior. Specifically, we prove that, as UDP input rate increases, even though the total number of UDP packets in the queue increases, their spatial distribution becomes more and more concentrated near the tail of the queue, and drops rapidly to zero toward the head of the queue. In stark contrast to a nonleaky FIFO buffer where UDP bandwidth shares would approach 1 as its input rate increases without bound, under CHOKe, UDP simultaneously maintains a large number of packets in the queue and receives a vanishingly small bandwidth share, the mechanism through which CHOKe protects TCP flows

Counter-intuitive throughput behaviors in networks under end-to-end control

It has been shown that as long as traffic sources adapt their rates to aggregate congestion measure in their paths, they implicitly maximize certain utility. In this paper we study some counter-intuitive throughput behaviors in such networks, pertaining to whether a fair allocation is always inefficient and whether increasing capacity always raises aggregate throughput. A bandwidth allocation policy can be defined in terms of a class of utility functions parameterized by a scalar a that can be interpreted as a quantitative measure of fairness. An allocation is fair if alpha is large and efficient if aggregate throughput is large. All examples in the literature suggest that a fair allocation is necessarily inefficient. We characterize exactly the tradeoff between fairness and throughput in general networks. The characterization allows us both to produce the first counter-example and trivially explain all the previous supporting examples. Surprisingly, our counter-example has the property that a fairer allocation is always more efficient. In particular it implies that maxmin fairness can achieve a higher throughput than proportional fairness. Intuitively, we might expect that increasing link capacities always raises aggregate throughput. We show that not only can throughput be reduced when some link increases its capacity, more strikingly, it can also be reduced when all links increase their capacities by the same amount. If all links increase their capacities proportionally, however, throughput will indeed increase. These examples demonstrate the intricate interactions among sources in a network setting that are missing in a single-link topology

A Unique "Nonnegative" Solution to an Underdetermined System: from Vectors to Matrices

This paper investigates the uniqueness of a nonnegative vector solution and the uniqueness of a positive semidefinite matrix solution to underdetermined linear systems. A vector solution is the unique solution to an underdetermined linear system only if the measurement matrix has a row-span intersecting the positive orthant. Focusing on two types of binary measurement matrices, Bernoulli 0-1 matrices and adjacency matrices of general expander graphs, we show that, in both cases, the support size of a unique nonnegative solution can grow linearly, namely O(n), with the problem dimension n. We also provide closed-form characterizations of the ratio of this support size to the signal dimension. For the matrix case, we show that under a necessary and sufficient condition for the linear compressed observations operator, there will be a unique positive semidefinite matrix solution to the compressed linear observations. We further show that a randomly generated Gaussian linear compressed observations operator will satisfy this condition with overwhelmingly high probability

Fast ground-state cooling of mechanical resonator with time-dependent optical cavities

We propose a feasible scheme to cool down a mechanical resonator (MR) in a three-mirror cavity optomechanical system with controllable external optical drives. Under the Born-Oppenheimer (BO) approximation, the whole dynamics of the mechanical resonator and cavities is reduced to that of a time-dependent harmonic oscillator, whose effective frequency can be controlled through the optical driving fields. The fast cooling of the MR can be realized by controlling the amplitude of the optical drives. Significantly, we further show that the ground-state cooling may be achieved via the three-mirror cavity optomechanical system without the resolved sideband condition.Comment: Some references including our previous works on cooling of mechanical resonators are added, and some typos are corrected in this new version. Comments are welcom