This paper presents Random Early Detection (RED) gate-ways for congestion avoidance in packet-switched networks. The gateway detects incipient congestion by com-puting the average queue size. The gateway could notify connections of congestion either by dropping packets ar-riving at the gateway or by setting a bit in packet headers. When the average queue size exceeds a preset threshold,the gateway drops or marks each arriving packet with a certain probability, where the exact probability is a func-tion of the average queue size. RED gateways keep the average queue size low while allowing occasional bursts of packets in the queue. During congestion, the probability that the gateway notifies a particular connection to reduce its window is roughly proportional to that connection's share of the bandwidth throughthe gateway. RED gateways are designed to accompany a transport-layer congestion control protocol such as TCP.The RED gateway has no bias against bursty traffic and avoids the global synchronization of many connectionsdecreasing their window at the same time. Simulations of a TCP/IP network are used to illustrate the performance of RED gateways.

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Chernoff--Hoeffding bounds are fundamental tools used in bounding the tail probabilities of the sums of bounded and independent random variables. We present a simple technique which gives slightly better bounds than these, and which more importantly requires only limited independence among the random variables, thereby importing a variety of standard results to the case of limited independence for free. Additional methods are also presented, and the aggregate results are sharp and provide a better understanding of the proof techniques behind these bounds. They also yield improved bounds for various tail probability distributions and enable improved approximation algorithms for jobshop scheduling. The "limited independence" result implies that a reduced amount of randomness and weaker sources of randomness are sufficient for randomized algorithms whose analyses use the Chernoff--Hoeffding bounds, e.g., the analysis of randomized algorithms for random sampling and oblivious packet routi...

. In this paper we study small depth circuits that contain threshold gates (with or without weights) and parity gates. All circuits we consider are of polynomial size. We prove several results which complete the work on characterizing possible inclusions between many classes defined by small depth circuits. These results are the following: 1. A single threshold gate with weights cannot in general be replaced by a polynomial fan-in unweighted threshold gate of parity gates. 2. On the other hand it can be replaced by a depth 2 unweighted threshold circuit of polynomial size. An extension of this construction is used to prove that whatever can be computed by a depth d polynomial size threshold circuit with weights can be computed by a depth d + 1 polynomial size unweighted threshold circuit, where d is an arbitrary fixed integer. 3. A polynomial fan-in threshold gate (with weights) of parity gates cannot in general be replaced by a depth 2 unweighted threshold circuit of polynomial size...

... In this paper we continue the development of a modelling approach which attempts to integrate these several time-scales, and illustrate its application to the analysis of a family of simple and robust measurement-based admission controls. A subsidiary aim of the paper is to shed light on the relationship between the admission control proposed for ATM networks by Gibbens et al [9] and that proposed for controlled-load Internet services by Floyd [7]. We shall see that their common origin in Chernoff bounds allows the definition of a simple and general family of admission controls, capable of tailoring for several implementation scenarios.

We investigate the relative power of the common random string model vs. the private random string model in communication complexity. We show that the two model are essentially equal. Keywords: communication complexity, randomness, theory of computation. Communication complexity is a model of computation where two parties, each with an input, want to mutually compute a Boolean function that is defined on pairs of inputs. Formally, let f : X \Theta Y 7! f0; 1g be a Boolean function. The communication problem for f is the following two-player game. Player A gets x 2 X and player B gets y 2 Y . Their goal is to compute f(x; y). They have unlimited computational power and a full description of f , but they don't know each other's input. They determine the output value by exchanging messages. Let n, the length of the input, be log(jXjjY j). A protocol for computing f is a pair of algorithms (one for each player) according to which the players send binary messages. A protocol proceeds in ...

This paper considers measurement-based admissions control procedures for Controlled-Load services [Wro96]. First, we discuss some of the factors that reduce the requirements on a measurement-based admissions control procedure in an Internet environment with a strong mix of realtime and data traffic. Next, we discuss measurement-based admissions control procedures for Controlled-Load services that are based on the approach of equivalent capacity. Finally, we show some measurements of audio traffic for small audioconferences, and discuss why such traffic could be among the most problematic for measurement-based admissions control procedures. 1 Introduction This paper makes several observations about measurement-based admissions control procedures for Controlled-Load services [Wro96]. We begin with a general discussion of the factors that would allow a measurement-based admissions control procedure to succeed even in the presence of traffic that is difficult to predict. Next, we discuss ...

In this paper it is shown by several examples that probability metrics are a useful tool to study the asymptotic behaviour of (stochastic) recursive algorithms. The basic idea of this approach is to find a `suitable ' probability metric which yields contraction properties of the transformations describing the limits of the algorithm. In order to demonstrate the wide range of applicability of this contraction method we investigate examples from various fields, some of them have been analyzed already in the literature.

Based on recent results for multi-armed bandit problems, we propose an adaptive sampling algorithm that approximates the optimal value of a finite horizon Markov decision process (MDP) with infinite state space but finite action space and bounded rewards. The algorithm adaptively chooses which action to sample as the sampling process proceeds, and it is proven that the estimate produced by the algorithm is asymptotically unbiased and the worst possible bias is bounded by a quantity that converges to zero at rate O � � H ln N N,whereHis the horizon length and N is the total number of samples that are used per state sampled in each stage. The worst-case running-time complexity of the algorithm is O((|A|N) H), independent of the state space size, where |A | is the size of the action space. The algorithm can be used to create an approximate receding horizon control to solve infinite horizon MDPs.

In this paper we present a polynomial time approximation algorithm for designing a multicast overlay network. The algorithm finds a solution that satisfies capacity and reliability constraints to within a constant factor of optimal, and cost to within a logarithmic factor. The class of networks that our algorithm applies to includes the one used by Akamai Technologies to deliver live media streams over the Internet. In particular, we analyze networks consisting of three stages of nodes. The nodes in the first stage are the sources where live streams originate. A source forwards each of its streams to one or more nodes in the second stage, which are called reflectors. A reflector can split an incoming stream into multiple identical outgoing streams, which are then sent on to nodes in the third and final stage, which are called the sinks. As the packets in a stream travel from one stage to the next, some of them may be lost. The job of a sink is to combine the packets from multiple instances of the same stream (by reordering packets and discarding duplicates) to form a single instance of the stream with minimal loss. We assume that the loss rate between any pair of nodes in the network is known, and that losses between different pairs are independent, but discuss extensions in which some losses may be correlated.