We study the design of risk-sensitive online algorithms, in which risk measures are used in the competitive analysis of randomized online algorithms. We introduce the CVaR$_\delta$-competitive ratio ($\delta$-CR) using the conditional value-at-risk of an algorithm’s cost, which measures the expectation of the $(1-\delta)$-fraction of worst outcomes against the offline optimal cost, and use this measure to study three online optimization problems: continuous-time ski rental, discrete-time ski rental, and one-max search. The structure of the optimal $\delta$-CR and algorithm varies significantly between problems: we prove that the optimal $\delta$-CR for continuous-time ski rental is $2-2^{-\Theta(\frac{1}{1-\delta})}$, obtained by an algorithm described by a delay differential equation. In contrast, in discrete-time ski rental with buying cost $B$, there is an abrupt phase transition at $\delta = 1 - \Theta(\frac{1}{\log B})$, after which the classic deterministic strategy is optimal. Similarly, one-max search exhibits a phase transition at $\delta = \frac{1}{2}$, after which the classic deterministic strategy is optimal; we also obtain an algorithm that is asymptotically optimal as $\delta \todown 0$ that arises as the solution to a delay differential equation.

There has been growing interest in employing neural networks (NNs) to directly solve constrained optimization problems with low run-time complexity. However, it is non-trivial to ensure NN solutions strictly satisfy problem constraints due to inherent NN prediction errors. Existing feasibility-ensuring methods are either computationally expensive or lack performance guarantee. In this paper, we propose Homeomorphic Projection as a low-complexity scheme to guarantee NN solution feasibility for optimization over a general set homeomorphic to a unit ball, covering all compact convex sets and certain classes of non-convex sets. The idea is to (i) learn a minimum distortion homeomorphic mapping between the constraint set and a unit ball using a bi-Lipschitz invertible NN (INN), and then (ii) perform a simple bisection operation concerning the unit ball such that the INN-mapped final solution is feasible with respect to the constraint set with minor distortion-induced optimality loss. We prove the feasibility guarantee and bounded optimality loss under mild conditions. Simulation results, including those for non-convex AC-OPF problems in power grid operation, show that homeomorphic projection outperforms existing methods in solution feasibility and run-time complexity while achieving similar optimality loss.

There has been growing interest in employing neural network (NN) to directly solve constrained optimization problems with low run-time complexity. However, it is non-trivial to ensure NN solutions strictly satisfying problem constraints due to inherent NN prediction errors. Existing feasibility-ensuring methods either are computationally expensive or lack performance guarantee. In this paper, we propose homeomorphic projection as a low-complexity scheme to guarantee NN solution feasibility for optimization over a general set homeomorphic to a unit ball, covering all compact convex sets and certain classes of nonconvex sets. The idea is to (i) learn a minimum distortion homeomorphic mapping between the constraint set and a unit ball using an invertible NN (INN), and then (ii) perform a simple bisection operation concerning the unit ball so that the INN-mapped final solution is feasible with respect to the constraint set with minor distortion-induced optimality loss. We prove the feasibility guarantee and bound the optimality loss under mild conditions. Simulation results, including those for non-convex AC-OPF problems in power grid operation, show that homeomorphic projection outperforms existing methods in solution feasibility and run-time complexity, while achieving similar optimality loss.

This paper investigates the online station assignment for (commercial) electric vehicles (EVs) that request battery swapping from a central operator, i.e., in the absence of future information a battery swapping service station has to be assigned instantly to each EV upon its request. Based on EVs’ locations, the availability of fully-charged batteries at service stations in the system, as well as traffic conditions, the assignment aims to minimize cost to EVs and congestion at service stations. Inspired by a polynomial-time offline solution via a bipartite matching approach, we develop an efficient and implementable online station assignment algorithm that provably achieves the tight (optimal) competitive ratio under mild conditions. Monte Carlo experiments on a real transportation network by Baidu Maps show that our algorithm performs reasonably well on realistic inputs, even with a certain amount of estimation error in parameters.

Bufferbloat is a phenomenon in computer networks where large router buffers are frequently filled up, resulting in high queueing delay and delay variation. More and more delay-sensitive applications on the Internet have made this phenomenon a pressing issue. Interacting with the Transmission Control Protocol (TCP), active queue management (AQM) algorithms run on routers play an important role in combating bufferbloat. However, AQM algorithms have not been widely deployed due to complicated manual parameter tuning. Moreover, they are often designed and analyzed based on network models with a single bottleneck link, rendering their performance and stability unclear in multi-bottleneck networks. In this paper, we propose a general framework to combat bufferbloat in multi-bottleneck networks. We first present an equilibrium analysis for a general multi-bottleneck TCP/AQM system and provide sufficient conditions for the uniqueness of an equilibrium point in the system. We then decompose the system into single-bottleneck subsystems and derive sufficient conditions for the local asymptotic stability of the subsystems. Using our framework, we develop an algorithm to compute the equilibrium point of the system. We further present a case study to analyze the stability of the recently proposed Controlled Delay (CoDel) in multi-bottleneck networks and devise Self-Tuning CoDel to improve the system stability. Extensive numerical and packet-level simulation results not only verify our theoretical studies but also show that our proposed Self-Tuning CoDel significantly stabilizes queueing delay in multi-bottleneck networks, thereby mitigating bufferbloat.

Bufferbloat is a phenomenon where router buffers are constantly being filled, resulting in high queueing delay and delay variation. Larger buffer size and more delay-sensitive applications on the Internet have made this phenomenon a pressing issue. Active queue management (AQM) algorithms, which play an important role in combating bufferbloat, have not been widely deployed due to complicated manual parameter tuning. Moreover, AQM algorithms are often designed and analyzed based on models with a single bottleneck link, rendering their performance and stability unclear in multi-bottleneck networks. In this paper, we propose a general framework to combat bufferbloat in multi-bottleneck networks. We first conduct an equilibrium analysis for a general multi-bottleneck TCP/ AQM system and develop an algorithm to compute the equilibrium point. We then decompose the system into single-bottleneck subsystems and derive sufficient conditions for the local asymptotic stability of the subsystems. Using the proposed framework, we present a case study to analyze the stability of the recently proposed Controlled Delay (CoDel) in multi-bottleneck networks and devise Self-tuning CoDel to improve the system stability and performance. Extensive simulation results show that Self-tuning CoDel effectively stabilizes queueing delay in multi-bottleneck scenarios, and thus contributes to combating bufferbloat.

We propose an online algorithm for solving optimal power flow (OPF) problems on radial networks where the controllable devices continuously interact with the network that implicitly computes a power flow solution given a control action. Collectively the controllable devices and the network implement a gradient projection algorithm for the OPF problem in real time. The key design feature that enables this approach is that the intermediate iterates of our algorithm always satisfy power flow equations and operational constraints. This is achieved by explicitly exploiting the network to implicitly solve power flow equations for us in real time at scale. We prove that the proposed algorithm converges to the set of local optima and provide sufficient conditions under which it converges to a global optimum. We derive an upper bound on the suboptimality gap of any local optimum. This bound suggests that any local minimum is almost as good as any strictly feasible point. We explain how to greatly reduce the gradient computation in each iteration by using approximate gradient derived from linearized power flow equations. Numerical results on test networks, ranging from 42-bus to 1990-bus, show a great speedup over a second-order cone relaxation method with negligible difference in objective values.

It has been recently discovered that heavy-tailed completion times can result from protocol interaction even when file sizes are light-tailed. A key to this phenomenon is the use of a restart policy where if the file is interrupted before it is completed, it needs to restart from the beginning. In this paper, we show that fragmenting a file into pieces whose sizes are either bounded or independently chosen after each interruption guarantees light-tailed completion time as long as the file size is light-tailed; i.e., in this case, heavy-tailed completion time can only originate from heavy-tailed file sizes. If the file size is heavy-tailed, then the completion time is necessarily heavy-tailed. For this case, we show that when the file size distribution is regularly varying, then under independent or bounded fragmentation, the completion time tail distribution function is asymptotically bounded above by that of the original file size stretched by a constant factor. We then prove that if the distribution of times between interruptions has nondecreasing failure rate, the expected completion time is minimized by dividing the file into equal-sized fragments; this optimal fragment size is unique but depends on the file size. We also present a simple blind fragmentation policy where the fragment sizes are constant and independent of the file size and prove that it is asymptotically optimal. Both these policies are also shown to have desirable completion time tail behavior. Finally, we bound the error in expected completion time due to error in modeling of the failure process.

Multipath TCP (MP-TCP) has the potential to greatly improve application performance by using multiple paths transparently. We propose a fluid model for a large class of MP-TCP algorithms and identify design criteria that guarantee the existence, uniqueness, and stability of system equilibrium. We clarify how algorithm parameters impact TCP-friendliness, responsiveness, and window oscillation and demonstrate an inevitable tradeoff among these properties. We discuss the implications of these properties on the behavior of existing algorithms and motivate our algorithm Balia (balanced linked adaptation), which generalizes existing algorithms and strikes a good balance among TCP-friendliness, responsiveness, and window oscillation. We have implemented Balia in the Linux kernel. We use our prototype to compare the new algorithm to existing MP-TCP algorithms.

Energy expenditure has become a significant fraction of data center operating costs. Recently, “geographical load balancing” has been proposed to reduce energy cost by exploiting the electricity price differences across regions. However, this reduction of cost can paradoxically increase total energy use. We explore whether the geographical diversity of Internet-scale systems can also provide environmental gains. Specifically, we explore whether geographical load balancing can encourage use of “green” renewable energy and reduce use of “brown” fossil fuel energy. We make two contributions. First, we derive three distributed algorithms for achieving optimal geographical load balancing. Second, we show that if the price of electricity is proportional to the instantaneous fraction of the total energy that is brown, then geographical load balancing significantly reduces brown energy use. However, the benefits depend strongly on dynamic energy pricing and the form of pricing used.

We formulate optimal power flow problem for unbalanced multiphase radial networks. We show that there is an equivalent single-phase mesh network that has a radial structure at the macro-level and a clique structure corresponding to each line in the radial network. Existing sufficient conditions for exact semidefinite relaxation are therefore applicable to unbalanced multiphase networks. In particular, they imply that if a semidefinite relaxation is exact over each of the cliques in the mesh equivalent network, then it is exact for the entire network.

Most mobile devices today come with multiple access interfaces, \emph{e.g.}, 4G and WiFi. Multipath TCP (MP-TCP) can greatly improve network performance by exploiting the connection diversity of multiple access interfaces, at the expense of higher energy consumption. In this paper, we design MP-TCP algorithms for mobile devices by jointly considering the performance and energy consumption. We consider two main types of mobile applications: realtime applications that have a fixed duration and file transfer applications that have a fixed data size. For each type of applications, we propose a two-timescale algorithm with theoretical guarantee on the performance. We present simulation results that show that our algorithms can reduce energy consumption by up to 22$\%$ without sacrificing throughput compared to a baseline MP-TCP algorithm.

The combination of loss-based TCP and drop-tail routers often results in full buffers, creating large queueing delays. The challenge with parameter tuning and the drastic consequence of improper tuning have discouraged network administrators from enabling AQM even when routers support it. To address this problem, we propose a novel design principle for AQM, called the pricing-link-by-time (PLT) principle. PLT increases the link price as the backlog stays above a threshold β, and resets the price once the backlog goes below β. We prove that such a system exhibits cyclic behavior that is robust against changes in network environment and protocol parameters. While β approximately controls the level of backlog, the backlog dynamics are invariant for β across a wide range of values. Therefore, β can be chosen to reduce delay without undermining system performance. We validate these analytical results using packet-level simulation.

Demand response is crucial for the incorporation of renewable energy into the grid. In this paper, we focus on a particularly promising industry for demand response: data centers. We use simulations to show that, not only are data centers large loads, but they can provide as much (or possibly more) flexibility as large-scale storage if given the proper incentives. However, due to the market power most data centers maintain, it is difficult to design programs that are efficient for data center demand response. To that end, we propose that prediction-based pricing is an appealing market design, and show that it outperforms more traditional supply function bidding mechanisms in situations where market power is an issue. However, prediction-based pricing may be inefficient when predictions are inaccurate, and so we provide analytic, worst-case bounds on the impact of prediction error on the efficiency of prediction-based pricing. These bounds hold even when network constraints are considered, and highlight that prediction-based pricing is surprisingly robust to prediction error.

Many existing fluid-flow models of the Internet congestion control algorithms make simplifying assumptions on the effects of buffers on the data flows. In particular, they assume that the flow rate of a TCP flow at every link in its path is equal to the original source rate. However, a fluid flow in practice is modified by the queueing processes on its path, so that an intermediate link will generally not see the original source rate. In this paper, a more accurate model is derived for the behavior of the network under a congestion controller, which takes into account the effect of buffering on output flows. It is shown how this model can be deployed for some well-known service disciplines such as first-in-first-out and generalized weighted fair queueing. Based on the derived model, the dual and primal-dual algorithms are studied under the common pricing mechanisms, and it is shown that these algorithms can become unstable. Sufficient conditions are provided to guarantee the stability of the dual and primal-dual algorithms. Finally, a new pricing mechanism is proposed under which these congestion control algorithms are both stable.

The optimal power flow (OPF) problem seeks to control the power generation/consumption to minimize the generation cost, and is becoming important for distribution networks. OPF is nonconvex and a second-order cone programming (SOCP) relaxation has been proposed to solve it. We prove that after a "small" modification to OPF, the SOCP relaxation is exact under a "mild" condition. Empirical studies demonstrate that the modification to OPF is "small" and that the "mild" condition holds for all test networks, including the IEEE 13-bus test network and practical networks with high penetration of distributed generation.

Multi-path TCP (MP-TCP) has the potential to greatly improve application performance by using multiple paths transparently. We propose a fluid model for a large class of MP-TCP algorithms and identify design criteria that guarantee the existence, uniqueness, and stability of system equilibrium. We characterize algorithm parameters for TCP-friendliness and prove an inevitable tradeoff between responsiveness and friendliness. We discuss the implications of these properties on the behavior of existing algorithms and motivate a new design that generalizes existing algorithms. We use ns2 simulations to evaluate the proposed algorithm and illustrate its superior overall performance.

For mitigating the urgency of constructing power plant, alleviating supply pressure of power company, electricity scheduling of customers is a very important issue, wherein to promote demand response is a key factor. The demand response is mainly through electricity price publicized by utility company to guide customers in electricity scheduling, and by use of price negotiating mechanism, to reach mutual benefits for both sides of demand and supply. The paper proposes a method of minimizing tariff for customers through changing elastic load use time intervals where customers' electricity use time is divided into inelastic and elastic intervals by electricity use characteristics. In the paper, customer's one day electricity used is assumed to conduct simulation, by genetic algorithm, comparing variations among scheduling and tariff under different electricity use limitation situations. As shown in the results, it is found that through elastic load use time interval changes, minimum tariff objective can be reached, and feasibility of the proposed method is verified.

Rate adaptation and power control are two key resource allocation mechanisms in multiuser wireless networks. In the presence of interference, how do we jointly optimize end-to-end source rates and link powers to achieve weighted max-min rate fairness for all sources in the network? This optimization problem is hard to solve as physical layer link rate functions are nonlinear, nonconvex, and coupled in the transmit powers. We show that the weighted max-min rate fairness problem can, in fact, be decoupled into separate fairness problems for flow rate and power control. For a large class of physical layer link rate functions, we characterize the optimal solution analytically by a nonlinear Perron-Frobenius theory (through solving a conditional eigenvalue problem) that captures the interaction of multiuser interference. We give an iterative algorithm to compute the optimal flow rate that converges geometrically fast without any parameter configuration. Numerical results show that our iterative algorithm is computationally fast for both the Shannon capacity, CDMA, and piecewise linear link rate functions.

Various link bandwidth adjustment mechanisms are being developed to save network energy. However, their interaction with congestion control can significantly reduce network throughput, and is not well understood. We firstly put forward a framework to study this interaction, and then propose an easily implementable dynamic bandwidth adjustment (DBA) mechanism for the links. In DBA, each link updates its bandwidth according to an integral control law to match its average buffer size with a target buffer size. We prove that DBA reduces link bandwidth without sacrificing throughput---DBA only turns off excess bandwidth---in the presence of congestion control. Preliminary ns2 simulations confirm this result.

Renewable energy such as solar and wind generation will constitute an important part of the future grid. As the availability of renewable sources may not match the load, energy storage is essential for grid stability. In this paper we investigate the feasibility of integrating solar photovoltaic (PV) panels and wind turbines into the grid by also accounting for energy storage. To deal with the fluctuation in both the power supply and demand, we extend and apply stochastic network calculus to analyze the power supply reliability with various renewable energy configurations. To illustrate the validity of the model, we conduct a case study for the integration of renewable energy sources into the power system of an island off the coast of Southern California. In particular, we asses the power supply reliability in terms of the average Fraction of Time that energy is Not-Served (FTNS).

Recent advances in network coding have shown great potential for efficient information multicasting in communication networks, in terms of both network throughput and network management. In this paper, the problem of flow control at end-systems for network-coding-based multicast flows is addressed. Optimization-based models are formulated for network resource allocation, based on which two sets of decentralized controllers at sources and links/nodes for congestion control are developed for wired networks with given coding subgraphs and without given coding subgraphs, respectively. With random network coding, both sets of controllers can be implemented in a distributed manner, and work at the transport layer to adjust source rates and at network layer to carry out network coding. The convergence of the proposed controllers to the desired equilibrium operating points is proved, and numerical examples are provided to complement the theoretical analysis. The extension to wireless networks is also briefly discussed.

Almost all existing fluid models of congestion control assume that the fluid flow at the output of a link is the same as the fluid flow at the input of the link. This means that all links in the path of a flow see the original source rate. In reality, a fluid flow is modified by the queueing processes on its path, so that an intermediate link will generally not see the original source rate. In this paper, we propose a simple model that explicitly takes into account of the effect of buffering on output flows. We study the dual and primal-dual algorithms that use implicit feedback and show that, while they are always asymptotically stable if feedback delay is ignored, they can be unstable in the new model.

Energy expenditure has become a significant fraction of data center operating costs. Recently, "geographical load balancing" has been suggested to reduce energy cost by exploiting the electricity price differences across regions. However, this reduction of cost can paradoxically increase total energy use.

This paper studies the optimization of a multicell multiple-input-single-output (MISO) downlink system in which each base station serves multiple users, and each user is served by only one base station. First, we consider the problem of maximizing the minimum weighted signal-to-interference-plus-noise ratio (SINR) of all users subject to a single weighted-sum power constraint, where the weights can represent relative power costs of serving different users in each cell. We apply concave Perron-Frobenius theory to propose a joint power control and linear beamforming algorithm which converges geometrically fast to the optimal solution. As a by-product, we resolve an open problem of convergence of a previously proposed algorithm by Wiesel, Eldar, and Shamai in 2006. Next, we study the max-min weighted SINR problem subject to multiple weighted-sum power constraints and we show that it can be decoupled into its associated single-constrained subproblems.

Spectrum management is used to improve performance in multiuser communication system, e.g., cognitive radio or femtocell networks, where multiuser interference can lead to data rate degradation. We study the nonconvex NP-hard problem of maximizing a weighted sum rate in a multiuser Gaussian interference channel by power control subject to affine power constraints. By exploiting the fact that this problem can be restated as an optimization problem with constraints that are spectral radii of specially crafted nonnegative matrices, we derive necessary and sufficient optimality conditions and propose a global optimization algorithm based on the outer approximation method. Central to our techniques is the use of nonnegative matrix theory, e.g., nonnegative matrix inequalities and the Perron-Frobenius theorem. We also study an inner approximation method and a relaxation method that give insights to special cases. Our techniques and algorithm can be extended to a multiple carrier system model, e.g., OFDM system or receivers with interference suppression capability.

This paper is concerned with understanding the connection between the existing Internet congestion control algorithms and the optimal control theory. The available resource allocation controllers are mainly devised to derive the state of the system to a desired equilibrium point and, therefore, they are oblivious to the transient behavior of the closed-loop system. To take into account the real-time performance of the system, rather than merely its steady-state performance, the congestion control problem should be solved by maximizing a proper utility functional as opposed to a utility function. For this reason, this work aims to investigate what utility functionals the existing congestion control algorithms maximize. In particular, it is shown that there exist meaningful utility functionals whose maximization leads to the celebrated primal, dual and primal/dual algorithms. An implication of this result is that a real network problem may be solved by regarding it as an optimal control problem on which some practical constraints, such as a real-time link capacity constraint, are imposed.

It has been recently discovered that heavy-tailed file completion time can result from protocol interaction even when file sizes are light-tailed. A key to this phenomenon is the RESTART feature where if a file transfer is interrupted before it is completed, the transfer needs to restart from the beginning. In this paper, we show that independent or bounded fragmentation produces light-tailed file completion time as long as the file size is light-tailed, i.e., in this case, heavy-tailed file completion time can only originate from heavy-tailed file sizes. If the file size is heavy-tailed, then the file completion time is clearly heavy-tailed. For this case, we show that when the file size distribution is regularly varying, then under independent or bounded fragmentation, the completion time tail distribution function is asymptotically upper bounded by that of the original file size stretched by a constant factor. We then prove that if the failure distribution has non-decreasing failure rate, the expected completion time is minimized by dividing the file into equal sized fragments; this optimal fragment size is unique but depends on the file size. We also present a simple blind fragmentation policy where the fragment sizes are constant and independent of the file size and prove that it is asymptotically optimal. Finally, we bound the error in expected completion time due to error in modeling of the failure process.

Motivated partially by a control-theoretic viewpoint, we propose a game-theoretic model, calledrandom access game, for contention control. We characterize Nash equilibria of random access games, study their dynamics, and propose distributed algorithms (strategy evolutions) to achieve Nash equilibria. This provides a general analytical framework that is capable of modeling a large class of system-wide quality-of-service (QoS) models via the specification of per-node utility functions, in which system-wide fairness or service differentiation can be achieved in a distributed manner as long as each node executes a contention resolution algorithm that is designed to achieve the Nash equilibrium. We thus propose a novel medium access method derived from carrier sense multiple access/collision avoidance (CSMA/CA) according to distributed strategy update mechanism achieving the Nash equilibrium of random access game. We present a concrete medium access method that adapts to a continuous contention measure called conditional collision probability, stabilizes the network into a steady state that achieves optimal throughput with targeted fairness (or service differentiation), and can decouple contention control from handling failed transmissions. In addition to guiding medium access control design, the random access game model also provides an analytical framework to understand equilibrium and dynamic properties of different medium access protocols.

This paper develops a new model that describes the queueing process of a communication network when data sources use window flow control. The model takes into account the burstiness in sub-round-trip time (RTT) timescales and the instantaneous rate differences of a flow at different links. It is generic and independent of actual source flow control algorithms. Basic properties of the model and its relation to existing work are discussed. In particular, for a general network with multiple links, it is demonstrated that spatial interaction of oscillations allows queue instability to occur even when all flows have the same RTTs and maintain constant windows. The model is used to study the dynamics of delay-based congestion control algorithms. It is found that the ratios of RTTs are critical to the stability of such systems, and previously unknown modes of instability are identified. Packet-level simulations and testbed measurements are provided to verify the model and its predictions.

When heterogeneous congestion control protocols that react to different pricing signals share the same network, the current theory based on utility maximization fails to predict the network behavior. The pricing signals can be different types of signals such as packet loss, queueing delay, etc, or different values of the same type of signal such as different ECN marking values based on the same actual link congestion level. Unlike in a homogeneous network, the bandwidth allocation now depends on router parameters and flow arrival patterns. It can be non-unique, suboptimal and unstable. InTang(“Equilibrium of heterogeneous congestion control: Existence and uniqueness,”IEEE/ACM Trans. Netw., vol. 15, no. 4, pp. 824–837, Aug. 2007), existence and uniqueness of equilibrium of heterogeneous protocols are investigated. This paper extends the study with two objectives: analyzing the optimality and stability of such networks and designing control schemes to improve those properties. First, we demonstrate the intricate behavior of a heterogeneous network through simulations and present a framework to help understand its equilibrium properties. Second, we propose a simple source-based algorithm to decouple bandwidth allocation from router parameters and flow arrival patterns by only updating a linear parameter in the sources' algorithms on a slow timescale. It steers a network to the unique optimal equilibrium. The scheme can be deployed incrementally as the existing protocol needs no change and only new protocols need to adopt the slow timescale adaptation.

This paper investigates the network performance loss of using only single-path routing when multiple paths are available. The performance metric is the aggregate utility achieved by the joint optimization of congestion control and routing. As computing the exact loss for a general network topology is NP-hard, we develop analytical bounds on this "cost of not splitting". Our bound is independent of the number of source-destination pairs when the latter one is larger than the number of links in a network. We also propose a vertex projection method and combine it with branch-and-bound to provide progressively tighter bounds on the performance loss. Numerical examples are used to show the effectiveness of our approximation technique.

MaxNet TCP is a congestion control protocol that uses explicit multi-bit signalling from routers to achieve desirable properties such as high throughput and low latency. In this paper we present an implementation of an extended version of MaxNet. Our contributions are threefold. First, we extend the original algorithm to give both provable stability and rate fairness. Second, we introduce the MaxStart algorithm which allows new MaxNet connections to reach their fair rates quickly. Third, we provide a Linux kernel implementation of the protocol. With no overhead but 24-bit price signals, our implementation scales from 32 bit/s to 1 peta-bit/s with a 0.001% rate accuracy. We confirm the theoretically predicted properties by performing a range of experiments at speeds up to 1 Gbit/sec and delays up to 180 ms on the WAN-in-Lab facility.

A novel continuous time fluid flow model of the dynamics of the interaction between ACK-clocking and the link buffer is presented. A fundamental integral equation relating the instantaneous flow rate and the window dynamics is derived. Properties of the model, such as well-posedness and stability, are investigated. Packet level experiments verify that this new model is more accurate than existing models, correctly predicting qualitatively different behaviors, for example when round trip delays are heterogeneous.

This paper studies window flow control focusing on bridging the gap between microscopic factors such as burstiness in sub-RTT timescales, and observable macroscopic properties such as steady state bandwidth sharing and flow level stability. Using new models, we analytically capture notable effects of microscopic behavior on macroscopic quantities. For loss-based protocols, we calculate the loss synchronization rate for different flows and use it to quantitatively explain the unfair bandwidth sharing between paced and unpaced TCP flows. For delay-based protocols, we show that the ratios of round trip delays are critical to the stability of the system. These results deepen the fundamental understanding of congestion control systems. Packet level simulations are used to verify our theoretical claims.

In this paper, we generalize the random access game model, and show that it provides a general gametheoretic framework for designing contention based medium access control. We extend the random access game model to the network with multiple contention measure signals, study the design of random access games, and analyze different distributed algorithms achieving their equilibria. As examples, a series of utility functions is proposed for games achieving the maximum throughput in a network of homogeneous nodes. In a network with n traffic classes, an N-signal game model is proposed which achieves the maximum throughput under the fairness constraint among different traffic classes. In addition, the convergence of different dynamic algorithms such as best response, gradient play and Jacobi play under propagation delay and estimation error is established. Simulation results show that game model based protocols can achieve superior performance over the standard IEEE 802.11 DCF, and comparable performance as existing protocols with the best performance in literature.

We study a model for peer-to-peer file sharing. The goal is to distribute a file from a server to multiple peers. We assume the upload capacity of each peer is the only bottleneck. We examine the finish times of peers under different transmission strategies. Pareto optimality, min-max finish time, and optimal average finish time of the model are studied. We believe the results provide fundamental insights into practical peer-to-peer systems such as BitTorrent.

Recent advances in network coding have shown great potential for efficient information multicasting in communication networks, in terms of both network throughput and network management. In this paper, we address the problem of rate control at end-systems for network coding based multicast flows. We develop two adaptive rate control algorithms for the networks with given coding subgraphs and without given coding subgraphs, respectively. With random network coding, both algorithms can be implemented in a distributed manner, and work at transport layer to adjust source rates and at network layer to carry out network coding. We prove that the proposed algorithms converge to the globally optimal solutions for intra-session network coding. Some related issues are discussed, and numerical examples are provided to complement our theoretical analysis.

TCP/IP can be interpreted as a distributed primal-dual algorithm to maximize aggregate utility over source rates. It has recently been shown that an equilibrium of TCP/IP, if it exists, maximizes the same delay-insensitive utility over both source rates and routes, provided pure congestion prices are used as link costs in the shortest-path calculation of IP. In practice, however, pure dynamic routing is never used and link costs are weighted sums of both static as well as dynamic components. In this paper, we introduce delay-sensitive utility functions and identify a class of utility functions that such a TCP/IP equilibrium optimizes. We exhibit some counter-intuitive properties that any class of delay-sensitive utility functions optimized by TCP/IP necessarily possess. We prove a sufficient condition for global stability of routing updates for general networks. We construct example networks that defy conventional wisdom on the effect of link cost parameters on network stability and utility.

This paper presents a link model which captures the queue dynamics when congestion windows of TCP sources change. By considering both the self-clocking and the link integrator effects, the model is a generalization of existing models and is shown to be more accurate by both open loop and closed loop packet level simulations. It reduces to the known static link model when flows' round trip delays are similar, and approximates the standard integrator link model when the heterogeneity of round trip delays is significant. We then apply this model to the stability analysis of FAST TCP. It is shown that FAST TCP flows over a single link are always linearly stable regardless of delay distribution. This result resolves the notable discrepancy between empirical observations and previous theoretical predictions. The analysis highlights the critical role of self-clocking in TCP stability and the scalability of FAST TCP with respect to delay. The proof technique is new and less conservative than the existing ones.

Many modern massively distributed systems deploy thousands of nodes to cooperate on a computation task. Network congestions occur in these systems. Most applications rely on congestion control protocols such as TCP to protect the systems from congestion collapse. Most TCP congestion control algorithms use packet loss as signal to detect congestion. In this paper, we study the packet loss process in sub-round-trip-time (sub-RTT) timescale and its impact on the loss-based congestion control algorithms. Our study suggests that the packet loss in sub-RTT timescale is very bursty. This burstiness leads to two effects. First, the sub-RTT burstiness in packet loss process leads to complicated interactions between different loss-based algorithms. Second, the sub-RTT burstiness in packet loss process makes the latency of data transfers under TCP hard to predict. Our results suggest that the design of a distributed system has to seriously consider the nature of packet loss process and carefully select the congestion control algorithms best suited for the distributed computation environments.

We propose a jointly opportunistic source coding and opportunistic routing (OSCOR) protocol for correlated data gathering in wireless sensor networks. OSCOR improves data gathering efficiency by exploiting opportunistic data compression and cooperative diversity associated with wireless broadcast advantage. The design of OSCOR involves several challenging issues across different network protocol layers. At the MAC layer, sensor nodes need to coordinate wireless transmission and packet forwarding to exploit multiuser diversity in packet reception. At the network layer, in order to achieve high diversity and compression gains, routing must be based on a metric that is dependent on not only link-quality but also compression opportunities. At the application layer, sensor nodes need a distributed source coding algorithm that has low coordination overhead and does not require the source distributions to be known. OSCOR provides practical solutions to these challenges incorporating a slightly modified 802.11 MAC, a distributed source coding scheme based on network coding and Lempel-Ziv coding, and a node compression ratio dependent metric combined with a modified Dijkstra's algorithm for path selection. We evaluate the performance of OSCOR through simulations, and show that OSCOR can potentially reduce power consumption by over 30% compared with an existing greedy scheme, routing driven compression, in a 4 × 4 grid network.

Network protocols in layered architectures have historically been obtained on anad hocbasis, and many of the recent cross-layer designs are also conducted through piecemeal approaches. Network protocol stacks may instead be holistically analyzed and systematically designed as distributed solutions to some global optimization problems. This paper presents a survey of the recent efforts towards a systematic understanding of “layering” as “optimization decomposition,” where the overall communication network is modeled by a generalized network utility maximization problem, each layer corresponds to a decomposed subproblem, and the interfaces among layers are quantified as functions of the optimization variables coordinating the subproblems. There can be many alternative decompositions, leading to a choice of different layering architectures. This paper surveys the current status of horizontal decomposition into distributed computation, and vertical decomposition into functional modules such as congestion control, routing, scheduling, random access, power control, and channel coding. Key messages and methods arising from many recent works are summarized, and open issues discussed. Through case studies, it is illustrated how “Layering as Optimization Decomposition” provides a common language to think about modularization in the face of complex, networked interactions, a unifying, top-down approach to design protocol stacks, and a mathematical theory of network architectures.

In this paper we present the motivation, the design, and a recent demonstration of the UltraLight testbed at SC|05. The goal of the Ultralight testbed is to help meet the data-intensive computing challenges of the next generation of particle physics experiments with a comprehensive, network- focused approach. UltraLight adopts a new approach to networking: instead of treating it traditionally, as a static, unchanging and unmanaged set of inter-computer links, we are developing and using it as a dynamic, configurable, and closely monitored resource that is managed from end-to-end. To achieve its goal we are constructing a next-generation global system that is able to meet the data processing, distribution, access and analysis needs of the particle physics community. In this paper we will first present early results in the various working areas of the project. We then describe our experiences of the network architecture, kernel setup, application tuning and configuration used during the bandwidth challenge event at SC|05. During this Challenge, we achieved a record-breaking aggregate data rate in excess of 150 Gbps while moving physics datasets between many Grid computing sites.

In this paper we present the design and implementation of the mission-oriented USLHCNet for HEP research community and the UltraLight network testbed. The design philosophy for these networks is to help meet the data-intensive computing challenges of the next generation of particle physics experiments with a comprehensive, network-focused approach. Instead of treating the network as a static, unchanging and unmanaged set of intercomputer links, we are developing and using it as a dynamic, configurable, and closely monitored resource that is managed from end-to-end. In this paper we will present our work in the various areas of the project including infrastructure construction, protocol research and application development. Our goal is to construct a next-generation global system that is able to meet the data processing, distribution, access and analysis needs of the particle physics community.

When heterogeneous congestion control protocols that react to different pricing signals (e.g. packet loss, queueing delay, ECN marking etc.) share the same network, the current theory based on utility maximization fails to predict the network behavior. Unlike in a homogeneous network, the bandwidth allocation now depends on router parameters and flow arrival patterns. It can be non-unique, inefficient and unfair. This paper has two objectives. First, we demonstrate the intricate behaviors of a heterogeneous network through simulations and present a rigorous framework to help understand its equilibrium efficiency and fairness properties. By identifying an optimization problem associated with every equilibrium, we show that every equilibrium is Pareto efficient and provide an upper bound on efficiency loss due to pricing heterogeneity. On fairness, we show that intra-protocol fairness is still decided by a utility maximization problem while inter-protocol fairness is the part over which we don't have control. However it is shown that we can achieve any desirable inter-protocol fairness by properly choosing protocol parameters. Second, we propose a simple slow timescale source-based algorithm to decouple bandwidth allocation from router parameters and flow arrival patterns and prove its feasibility. The scheme needs only local information.

Abstract — This paper considers jointly optimal design of cross-layer congestion control, routing and scheduling for ad hoc wireless networks. We first formulate the rate constraint and scheduling constraint using multicommodity flow variables, and formulate resource allocation in networks with fixed wireless channels (or single-rate wireless devices that can mask channel variations) as a utility maximization problem with these con-straints. By dual decomposition, the resource allocation problem naturally decomposes into three subproblems: congestion control, routing and scheduling that interact through congestion price. The global convergence property of this algorithm is proved. We next extend the dual algorithm to handle networks with time-varying channels and adaptive multi-rate devices. The stability of the resulting system is established, and its performance is characterized with respect to an ideal reference system which has the best feasible rate region at link layer. We then generalize the aforementioned results to a general model of queueing network served by a set of interdependent parallel servers with time-varying service capabilities, which models many design problems in communication networks. We show that for a general convex optimization problem where a subset of variables lie in a polytope and the rest in a convex set, the dual-based algorithm remains stable and optimal when the constraint set is modulated by an irreducible finite-state Markov chain. This paper thus presents a step toward a systematic way to carry out cross-layer design in the framework of “layering as optimization decomposition ” for time-varying channel models. I.

Network protocols in layered architectures have historically been obtained primarily on an ad-hoc basis. Recent research has shown that network protocols may instead be holistically analyzed and systematically designed as distributed solutions to some global optimization problems in the form of Network Utility Maximization (NUM), providing insight into what they optimize and structures of the network protocol stack. This paper presents a short survey of the recent efforts towards a systematic understanding of 'layering' as 'optimization decomposition', where the overall communication network is modeled by a generalized NUM problem, each layer corresponds to a decomposed subproblem, and the interfaces among layers are quantified as functions of the optimization variables coordinating the sub-problems. Different decompositions lead to alternative layering architectures. We summarize several examples of horizontal decomposition into distributed computation and vertical decomposition into functional modules such as congestion control, routing, scheduling, random access, power control, and coding.

When heterogeneous congestion control protocols that react to different pricing signals share the same network, the resulting equilibrium may no longer be interpreted as a solution to the standard utility maximization problem. We prove the existence of equilibrium in general multi-protocol networks under mild assumptions. For almost all networks, the equilibria are locally unique, and finite and odd in number. They cannot all be locally stable unless it is globally unique. Finally, we show that if the price mapping functions that map link prices to effective prices observed by the sources are similar, then global uniqueness is guaranteed.

We present a model for the joint design of congestion control and media access control (MAC) for ad hoc wireless networks. Using contention graph and contention matrix, we formulate resource allocation in the network as a utility maximization problem with constraints that arise from contention for channel access. We present two algorithms that are not only distributed spatially, but more interestingly, they decompose vertically into two protocol layers where TCP and MAC jointly solve the system problem. The first is a primal algorithm where the MAC layer at the links generates congestion (contention) prices based on local aggregate source rates, and TCP sources adjust their rates based on the aggregate prices in their paths. The second is a dual subgradient algorithm where the MAC sub-algorithm is implemented through scheduling link-layer flows according to the congestion prices of the links. Global convergence properties of these algorithms are proved. This is a preliminary step towards a systematic approach to jointly design TCP congestion control algorithms and MAC algorithms, not only to improve performance, but more importantly, to make their interaction more transparent.

We prove that the XCP equilibrium solves a constrained max-min fairness problem by identifying it with the unique solution of a hierarchy of optimization problems, namely those solved by max-min fair allocation, but solved by XCP under an additional constraint. We describe an algorithm to compute this equilibrium and derive a lower and upper bound on link utilization. While XCP reduces to max-min allocation at a single link, in a network the additional constraint can cause a flow to receive an arbitrarily small fraction of its max-min allocation. We present simulation results to confirm our analytical findings.

When heterogeneous congestion control protocols that react to different pricing signals share the same network, the resulting equilibrium may no longer be interpreted as a solution to the standard utility maximization problem. We prove the existence of equilibrium under mild assumptions. Then we show that multi-protocol networks whose equilibria are locally non-unique or infinite in number can only form a set of measure zero. Multiple locally unique equilibria can arise in two ways. First, unlike in the single-protocol case, the set of bottleneck links can be non-unique with heterogeneous protocols even when the routing matrix has full row rank. The equilibria associated with different sets of bottleneck links are necessarily distinct. Second, even when there is a unique set of bottleneck links, network equilibrium can still be non-unique, but is always finite and odd in number. They cannot all be locally stable unless it is globally unique. Finally, we provide various sufficient conditions for global uniqueness. Numerical examples are used throughout the paper to illustrate these results.

We introduce a discrete-time model of FAST TCP that fully captures the effect of self-clocking and compare it with the traditional continuous-time model. While the continuous-time model predicts instability for homogeneous sources sharing a single link when feedback delay is large, experiments suggest otherwise. Using the discrete-time model, we prove that FAST TCP is locally asymptotically stable in general networks when all sources have a common round-trip feedback delay, no matter how large the delay is. We also prove global stability for a single bottleneck link in the absence of feedback delay. The techniques developed here are new and applicable to other protocols.

Recently, there has been a surge in research activities that utilize the power of recent developments in nonlinear optimization to tackle a wide scope of work in the analysis and design of communication systems, touching every layer of the layered network architecture, and resulting in both intellectual and practical impacts significantly beyond the earlier frameworks. These research activities are driven by both new demands in the areas of communications and networking, and new tools emerging from optimization theory. Such tools include new developments of powerful theories and highly efficient computational algorithms for nonlinear convex optimization, as well as global solution methods and relaxation techniques for nonconvex optimization.Optimization theory can be used to analyze, interpret, or design a communication system, for both forward-engineering and reverse-engineering. Over the last few years, it has been successfully applied to a wide range of communication systems, from the high speed Internet core to wireless networks, from coding and equalization to broadband access, and from information theory to network topology models. Some of the theoretical advances have also been put into practice and started making visible impacts, including new versions of TCP congestion control, power control and scheduling algorithms in wireless networks, and spectrum management in DSL broadband access networks.Under the theme of optimization and control of communication networks, this Hot Topic Session consists of five invited talks covering a wide range of issues, including protocols, pricing, resource allocation, cross layer design, traffic engineering in the Internet, optical transport networks, and wireless networks.

Layered architecture is one of the most fundamental and influential structures of network design. Can we integrate the various protocol layers into a single coherent theory by regarding them as carrying out an asynchronous distributed primal-dual computation over the network to implicitly solve a global optimization problem? Different layers iterate on different subsets of the decision variables using local information to achieve individual optimalities, but taken together, these local algorithms attempt to achieve a global objective. Such a theory will expose the interconnection between protocol layers and can be used to study rigorously the performance tradeoff in protocol layering as different ways to distribute a centralized computation. In this talk, we describe some preliminary work towards this goal and discuss some of the difficulties of this approach.

This paper is aimed at designing a congestion control system that scales gracefully with network capacity, providing high utilization, low queueing delay, dynamic stability, and fairness among users. The focus is on developing decentralized control laws at end-systems and routers at the level of fluid-flow models, that can provably satisfy such properties in arbitrary networks, and subsequently approximate these features through practical packet-level implementations. Two families of control laws are developed. The first "dual" control law is able to achieve the first three objectives for arbitrary networks and delays, but is forced to constrain the resource allocation policy. We subsequently develop a "primal-dual" law that overcomes this limitation and allows sources to match their steady-state preferences at a slower time-scale, provided a bound on round-trip-times is known. We develop two packet-level implementations of this protocol, using 1) ECN marking, and 2) queueing delay, as means of communicating the congestion measure from links to sources. We demonstrate using ns-2 simulations the stability of the protocol and its equilibrium features in terms of utilization, queueing and fairness, under a variety of scaling parameters.

TCP-AQM can be interpreted as distributed primal-dual algorithms to maximize aggregate utility over source rates. We show that an equilibrium of TCP/IP, if exists, maximizes aggregate utility over both source rates and routes, provided congestion prices are used as link costs. An equilibrium exists if and only if this utility maximization problem and its Lagrangian dual have no duality gap. In this case, TCP/IP incurs no penalty in not splitting traffic across multiple paths. Such an equilibrium, however, can be unstable. It can be stabilized by adding a static component to link cost, but at the expense of a reduced utility in equilibrium. If link capacities are optimally provisioned, however, pure static routing, which is necessarily stable, is sufficient to maximize utility. Moreover single-path routing again achieves the same utility as multipath routing at optimality.

We describe FAST TCP, a new TCP congestion control algorithm for high-speed long-latency networks, from design to implementation. We highlight the approach taken by FAST TCP to address the four difficulties, at both packet and flow levels, which the current TCP implementation has at large windows. We describe the architecture and characterize the equilibrium and stability properties of FAST TCP. We present experimental results comparing our first Linux prototype with TCP Reno, HSTCP, and STCP in terms of throughput, fairness, stability, and responsiveness. FAST TCP aims to rapidly stabilize high-speed long-latency networks into steady, efficient and fair operating points, in dynamic sharing environments, and the preliminary results are promising.

We analyze the effects of price estimation error in a dual-gradient optimization flow control scheme, and characterize the performance of the algorithm in this case. By treating estimation error as inexactness of the gradient, we utilize sufficient conditions for convergence subject to bounded error to characterize the long-term dynamics of the link utilization in terms of a region, which the trajectory enters in finite time. We explicitly find bounds for this region under a particular quantization error model, and provide simulation results to verify the predicted behavior of the system. Finally, we analyze the effects of the stepsize on the convergence of the algorithm, and provide analytical and numerical results, which suggest a particular choice for this parameter.

This paper describes the tradeoff between fairness criteria of different allocation policies and throughput in a general network. A class of utility functions parameterized by a scalar defines a bandwidth allocation policy. An allocation is fair if the scalar is large and efficient if the aggregate source rate is large. The conjecture depends on the network topology in terms of routing and link capacities. A fairer allocation is always more efficient.

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.

In this paper, we investigate how to design AQM with a low-pass filter (average queuing) in supporting TCP based on the well-known AIMD dynamic model sharing a common bottleneck router. Since we formulate the AQM design problem for the given TCP as a state-space model, we get two interesting and important results: (1) we derive PD-type (proportional-derivative) AQM structure is derive in terms of queue length which supports the conjecture in the literature that the AQM RED is not enough to control TCP dynamic behavior, where RED can be classified as P-type AQM structure; (2) we propose a delay-dependent AQM structure to compensate for delays in congestion measure explicitly from the knowledge of RTT, capacity and number of sources, where the previous AQMs RED, REM/PI and AVQ are delay-independent controls. As one trial to obtain stabilizing gains of the proposed structures, we minimize a LQ (linear quadratic) cost of the transients on average-queue length, average-queue length rate, jitter in the rate and the loss probability. Finally, we illustrate the above theoretical results through ns simulations for TCP Reno.

This paper is aimed at designing a congestion control system that scales gracefully with network capacity, providing high utilization, low queueing delay, dynamic stability, and fairness among users. In earlier work we had developed fluid-level control laws that achieve the first three objectives for arbitrary networks and delays, but were forced to constrain the resource allocation policy. In this paper we extend the theory to include dynamics at TCP sources, preserving the earlier features at fast time-scales, but permitting sources to match their steady-state preferences, provided a bound on round-trip-times is known. We develop two packet-level implementations of this protocol, using (i) ECN marking, and (ii) queueing delay, as means of communicating the congestion measure from links to sources. We discuss parameter choices and demonstrate using ns-2 simulations the stability of the protocol and its equilibrium features in terms of utilization, queueing and fairness. We also demonstrate the scalability of these features to increases in capacity, delay, and load, in comparison with other deployed and proposed protocols.

A recently proposed active queue management, CHOKe, is stateless, simple to implement, yet surprisingly effective in protecting TCP from UDP flows. As UDP rate increases, even though the number of UDP packets in the queue rises, its bandwidth share eventually drops to zero, in stark contrast to the behavior of a regular FIFO buffer. We derive a detailed model of CHOKe that accurately predicts this, and other behaviors of CHOKe, and validate the model with simulations. Its key features are the incorporation of the feedback equilibrium of TCP with dropping probability and the spatial characteristics of the queueing process. CHOKe produces a "leaky buffer" where packets can be dropped as they move toward the head of the queue. This leads to a spatially nonuniform distribution of packets and their velocity, and makes it possible for a flow to simultaneously maintain a large number of packets in the queue and receive a vanishingly small bandwidth share. This is the main mechanism through which CHOKe protects TCP from UDP flows.

TCP-AQM protocol can be interpreted as distributed primal-dual algorithms over the Internet to maximize aggregate utility. In this paper, we study whether TCP-AQM together with shortest-path routing can maximize utility with appropriate choice of link cost, on a slower timescale, over both source rates and routes. We show that this is generally impossible because the addition of route maximization makes the problem NP-hard. We exhibit an inevitable tradeoff between routing instability and utility maximization. For the special case of ring network, we prove rigorously that shortest-path routing based purely on congestion prices is unstable. Adding a sufficiently large static component to link cost, stabilizes it, but the maximum utility achievable by shortest-path routing decreases with the weight on the static component. We present simulation results to illustrate that these conclusions generalize to general network topology, and that routing instability can reduce utility to less than that achievable by the necessarily stable static routing.

This paper presents a case study of the 10-Gigabit Ethernet (10GbE) adapter from Intel R . Specifically, with appropriate optimizations to the configurations of the 10GbE adapter and TCP, we demonstrate that the 10GbE adapter can perform well in local-area, storage-area, system-area, and wide-area networks. For local-area, storage-area, and system-area networks in support of networks of workstations, network-attached storage, and clusters, respectively, we can achieve over 7-Gb/s end-to-end throughput and 12-µs end-to-end latency between applications running on Linux-based PCs. For the wide-area network in support of grids, we broke the recently-set Internet2 Land Speed Record by 2.5 times by sustaining an end-to-end TCP/IP throughput of 2.38 Gb/s between Sunnyvale, California and Geneva, Switzerland (i.e., 10,037 kilometers) to move over a terabyte of data in less than an hour. Thus, the above results indicate that 10GbE may be a cost-effective solution across a multitude of computing environments.

A recently proposed active queue management, CHOKe, aims to protect TCP from UDP flows. Simulations have shown that as UDP rate increases, its bandwidth share initially rises but eventually drops. We derive an approximate model of CHOKe and show that, provided the number of TCP flows is large, the UDP bandwidth share peaks at (e+1)-1 = 0.269 when the UDP input rate is slightly larger than the link capacity, and drops to zero as UDP input rate tends to infinity, regardless of the TCP algorithm.

We propose a duality model of end-to-end congestion control and apply it to understanding the equilibrium properties of TCP and active queue management schemes. The basic idea is to regard source rates as primal variables and congestion measures as dual variables, and congestion control as a distributed primal-dual algorithm over the Internet to maximize aggregate utility subject to capacity constraints. The primal iteration is carried out by TCP algorithms such as Reno or Vegas, and the dual iteration is carried out by queue management algorithms such as DropTail, RED or REM. We present these algorithms and their generalizations, derive their utility functions, and study their interaction.

REM (random exponential marking) is an active queue management algorithm that is designed to achieve a desirable equilibrium, without explicit consideration to its dynamic property especially in the presence of feedback delay. We provide sufficient conditions for REM to be locally stable around an equilibrium, in a multi-link multi-source setting, when sources have identical delay of one or two-step discrete time.

We demonstrate that the dynamic behavior of queue and average window is determined predominantly by the stability of TCP/RED, not by AIMD probing nor noise traffic. We develop a general multi-link multi-source model for TCP/RED and derive a local stability condition in the case of a single link with heterogeneous sources. We validate our model with simulations and illustrate the stability region of TCP/RED. These results suggest that TCP/RED becomes unstable when delay increases, or more strikingly, when link capacity increases. The analysis illustrates the difficulty of setting RED parameters to stabilize TCP: they can be tuned to improve stability, but only at the cost of large queues even when they are dynamically adjusted. Finally, we present a simple distributed congestion control algorithm that maintains stability for arbitrary network delay, capacity, load and topology.

It is well known that optimal server placement is NP-hard. We present an approximate model for the case when both clients and servers are dense, and propose a simple server allocation and placement algorithm based on high-rate vector quantization theory. The key idea is to regard the location of a request as a random variable with probability density that is proportional to the demand at that location, and the problem of server placement as source coding, i.e., to optimally map a source value (request location) to a codeword (server location) to minimize distortion (network cost). This view has led to a joint server allocation and placement algorithm that has a time-complexity that is linear in the number of clients. Simulations are presented to illustrate its performance.

It is well known that optimal server placement is NP-hard. We present an approximate model for the case when both clients and servers are dense, and propose a simple server allocation and placement algorithm based on high-rate vector quantization theory. The key idea is to regard the location of a request as a random variable with probability density that is proportional to the demand at that location, and the problem of server placement as source coding, i.e., to optimally map a source value (request location) to a code-word (server location) to minimize distortion (network cost). This view has led to a joint server allocation and placement algorithm that has a time-complexity that is linear in the number of clients. Simulations are presented to illustrate its performance.

We view congestion control as a distributed primal--dual algorithm carried out by sources and links over a network to solve a global optimization problem. We describe a multilink multisource model of the TCP Vegas congestion control mechanism. The model provides a fundamental understanding of delay, fairness and loss properties of TCP Vegas. It implies that Vegas stabilizes around a weighted proportionally fair allocation of network capacity when there is sufficient buffering in the network. It clarifies the mechanism through which persistent congestion may arise and its consequences, and suggests how we might use REM active queue management to prevent it. We present simulation results that validate our conclusions.

Destination-based forwarding in traditional IP routers has not been able to take full advantage of multiple paths that frequently exist in Internet service provider networks. As a result, the networks may not operate efficiently, especially when the traffic patterns are dynamic. This paper describes a multipath adaptive traffic engineering mechanism, called MATE, which is targeted for switched networks such as multiprotocol label switching (MPLS) networks. The main goal of MATE is to avoid network congestion by adaptively balancing the load among multiple paths based on measurement and analysis of path congestion. MATE adopts a minimalist approach in that intermediate nodes are not required to perform traffic engineering or measurements besides normal packet forwarding. Moreover MATE does not impose any particular scheduling, buffer management, or a priori traffic characterization on the nodes. This paper presents an analytical model, derives a class of MATE algorithms, and proves their convergence. Several practical design techniques to implement MATE are described. Simulation results are provided to illustrate the efficacy of MATE under various network scenarios.

Active routing permits individual customers, network managers, or network owners to control the paths that their data takes through the network. The objective is to allow routing mechanisms that provide quality of service (QoS), mobility, etc., to be quickly deployed, without waiting for standards, and to allow different routing mechanisms, that provide similar services, to compete. The current work on label switching (MPLS) can also be used to give high level customers, such as virtual private networks (VPNs), more control over their paths. We show how active routing can extend the capabilities of MPLS. We address several implementation issues, including pricing and distributed sandboxes. Pricing or policing must be used to limit the resources that customers acquire, in order to encourage them to use network resources economically. Sandboxes must be used to limit the resources that the participants acquire, in order to limit the harm that they can inflict on other participants. Active routing creates a free market system where network providers compete to sell their resources and implementers compete to sell their active routing programs. We establish a framework to quantitatively compare networks and service providers. As an example, we route Internet protocol (IP) telephony over combinations of circuit and packet networks.

We proposed earlier a flow control algorithm derived from solving the dual of a welfare maximization problem. The algorithm however requires communication between network links and sources that is not achievable on the current Internet. We then extended the basic algorithm to a random early marking (REM) scheme which can be implemented using only binary feedback. We proposed a new price computation algorithm for REM and present simulation results to illustrate its superior performance over the previous versions.

We propose an optimization based flow control for the Internet called random early marking (REM). In this paper we propose and evaluate an enhancement that attempts to speed up the convergence of REM in the face of large feedback delays. REM can be regarded as an implementation of an optimization algorithm in a distributed network. The basic idea is to treat the optimization algorithm as a discrete time system and apply linear control techniques to stabilize its transient. We show that the modified algorithm is stable globally and converges exponentially locally. This algorithm translates into an enhanced REM scheme and we illustrate the performance improvement through simulation.

We have proposed earlier watermarking text documents by slightly shifting certain text lines. Such a text line represents a noisy channel, and marking represents the transmission of a signal through this channel. The power of the signal represents the size of the shift and must be small for the marks to be imperceptible. We formulate the channel capacity under a constraint or individual signal power. We show that to achieve the capacity, the shifts should be normally distributed, have maximum power, and adjacent shifts should be negatively correlated.

Consider a set of users sharing a network node under an allocation scheme that provides each user with a fixed minimum and a random extra amount of bandwidth and buffer. Allocations and prices are adjusted to adapt to resource availability and user demands. Equilibrium is achieved when all users optimize their utility and demand equals supply for nonfree resources. We analyze two models of user behavior. We show that at equilibrium expected return on purchasing variable resources can be higher than that on fixed resources. Thus users must balance the marginal increase in utility due to higher return on variable resources and the marginal decrease in utility due to their variability. For the first user model we further show that at equilibrium where such tradeoff is optimized all users hold strictly positive amounts of variable bandwidth and buffer. For the second model we show that if both variable bandwidth and buffer are scarce then at equilibrium every user either holds both variable resources or none.

We consider how to allocate bandwidth in a multicast tree so as to optimize some global measure of performance. In our model each receiver has a budget to be used for bandwidth reservation on links along its path from the source, and each link has a cost function depending on the amount of total bandwidth reserved at the link by all receivers using that link. We formulate and solve a problem of allocating bandwidth in the multicast tree such that the sum of link costs is minimized.

Each copy of a text document can be made different in a nearly invisible way by repositioning or modifying the appearance of different elements of text, i.e., lines, words, or characters. A unique copy can be registered with its recipient, so that subsequent unauthorized copies that are retrieved can be traced back to the original owner. In this paper we describe and compare several mechanisms for marking documents and several other mechanisms for decoding the marks after documents have been subjected to common types of distortion. The marks are intended to protect documents of limited value that are owned by individuals who would rather possess a legal than an illegal copy if they can be distinguished. We describe attacks that remove the marks and countermeasures to those attacks. An architecture is described for distributing a large number of copies without burdening the publisher with creating and transmitting the unique documents. The architecture also allows the publisher to determine the identity of a recipient who has illegally redistributed the document, without compromising the privacy of individuals who are not operating illegally. Two experimental systems are described. One was used to distribute an issue of the IEEE Journal on Selected Areas in Communications, and the second was used to mark copies of company private memoranda.

We propose an optimization approach to flow control where the objective is to maximize the aggregate source utility over their transmission rates. We view network links and sources as processors of a distributed computation system to solve the dual problem using a gradient projection algorithm. In this system, sources select transmission rates that maximize their own benefits, utility minus bandwidth cost, and network links adjust bandwidth prices to coordinate the sources' decisions. We allow feedback delays to be different, substantial, and time varying, and links and sources to update at different times and with different frequencies. We provide asynchronous distributed algorithms and prove their convergence in a static environment. We present measurements obtained from a preliminary prototype to illustrate the convergence of the algorithm in a slowly time-varying environment. We discuss its fairness property.

Available bit rate (ABR) sources react to network feedback by adjusting their transmission rates. Most schemes fall into one of two types depending on what is fed back and where the control decision is made. Explicit congestion notification schemes allow sources to make control decisions but only with incomplete information on congestion. Explicit rate schemes use more accurate congestion information but make the control decision inside the network without regard to the different desires of various sources. We propose an optimization approach that attempts to combine the advantage of both types of scheme. The objective is to maximize the total utility of all sources over their transmission rates. The dual problem suggests treating network links and ABR sources as processors in a distributed computation system to solve the dual problem using the gradient projection algorithm. In this system ABR sources select transmission rates that maximize their own benefits and network links adjust bandwidth prices to coordinate the sources' decisions. We show how to implement such a system using features defined in the ABR standard. We provide an asynchronous distributed algorithm for links and sources and illustrate their behavior with preliminary simulation results.

We relate burstiness (or indifference) curves for stochastic traffic flows to the quality they experience under the allocation of the resources of bandwidth and buffer space. We use this relation to explore the quality experienced by merged flows under various rules for allocating resources to them, including one motivated by the controlled load service specification. We show how cost structures on the resources can be used to encourage optimal use of shared resources amongst heterogeneous flows.

Consider a set of connections sharing a network node under an allocation scheme that provides each connection with a fixed minimum and a random extra amount of bandwidth and buffer. Allocations and prices are adjusted to adapt to resource availability and user demands. We consider two scenarios of user behavior. In the first scenario a connection purchases an allocation to maximize its expected utility in such a way that the resource cost of the new allocation, and hence its connection charge, remains the same as that for the old allocation. In the second scenario this budget constraint is relaxed and a connection tries to maximize its benefit, expected utility minus the resource cost. Equilibrium is achieved when all connections achieve their optimality and demand equals supply for non-free resources. We show that at equilibrium expected return on purchasing variable resources can be higher than that on fixed resources. Thus connections must balance the marginal increase in utility due to higher return on variable resources and the marginal decrease in utility due to their variability. We further show that in equilibrium where such tradeoff is optimized all connections hold strictly positive amounts of variable bandwidth and buffer.

A text document typically consists of a collection of regular structures such as words, lines, and paragraphs, a slight movement of which seems less perceptible than, say, dithering of the document image. We exploit this property to watermark formatted text documents by shifting slightly certain lines and words in order to discourage illicit distribution. We analyze two methods for reliable document identification in the presence of severe distortions introduced by photocopying, facsimile transmission, and other processing. The correlation method uses document profiles directly for detection. To eliminate the effect of certain distortions, the centroid method bases its decision on the distances between the centroids of adjacent profile blocks. We present the maximum likelihood detectors for both methods and evaluate their relative performance. Our analysis indicates that line-shift generally has a smaller error than word-shift detection, and that the correlation detector outperforms the centroid detector provided certain distortions can be accurately compensated for before detection is attempted. These results have been applied to implement a marking and identification system and preliminary experimental results have been very promising.

A way to discourage illicit reproduction of copyrighted or sensitive documents is to watermark each copy before distribution. A unique mark is embedded in the text whose recipient is registered. The mark can be extracted from a possibly noisy illicit copy, identifying the registered recipient. Most image marking techniques are vulnerable to binarization attack and, hence, not suitable for text marking. We propose a different approach where a text document is marked by shifting certain text lines slightly up or down or words slightly left or right from their original positions. The shifting pattern constitutes the mark and is different on different copies. In this paper we develop and evaluate a method to detect such minute shifts. We describe a marking and identification prototype that implements the proposed method. We present preliminary experimental results which suggest that centroid detection performs remarkably well on line shifts even in the presence of severe distortions introduced by printing, photocopying, scanning, and facsimile transmission.

Summary form only given. Electronic documents are more easily copied and redistributed than paper documents. This is a major impediment to electronic publishing. Illegal redistribution can be discouraged by placing unique marks in each copy and registering the copy with the original recipient. If an illegal copy is discovered, the original recipient can be identified. We describe several invisible techniques for encoding information in text documents. We also describe a marking system, for electronic publishing, that is scalable to large numbers of users.

In earlier work we have formulated a collusion problem that determines whether it is possible for a set of colluders to collectively discover a target set of information, starting from their initial knowledge, and have presented a complete solution for a special case of the problem. In this paper we present an algorithm that solves the general case. Given a collusion problem the algorithm determines whether it has a solution, and if it does, computes one. A solution to the collusion problem is a method with which the colluders can uncover the hidden information. Communications protocols that employ cryptographic techniques are increasingly used to protect privacy as well as to communicate. A cryptographic protocol defines a process by which information is transferred among some users while hidden from others. The algorithm presented can be used to determine whether a subset of protocol users can discover, during or after the protocol's execution, the information that is designed to be hidden from them.

Communications networks are traditionally used to bring information together. They can also be used to keep information apart in order to protect personal privacy. A cryptographic protocol specifies a process by which some information is transferred among some users and hidden from others. We show how to implement anonymous credit cards using simple cryptographic protocols. We pose, and solve, a collusion problem which determines whether it is possible for a subset of users to discover information that is designed to be hidden from them during or after execution of the anonymous credit card protocol.

Modern computer networks make it possible to distribute documents quickly and economically by electronic means rather than by conventional paper means. However, the widespread adoption of electronic distribution of copyrighted material is currently impeded by the ease of unauthorized copying and dissemination. In this paper we propose techniques that discourage unauthorized distribution by embedding each document with a unique codeword. Our encoding techniques are indiscernible by readers, yet enable us to identify the sanctioned recipient of a document by examination of a recovered document. We propose three coding methods, describe one in detail, and present experimental results showing that our identification techniques are highly reliable, even after documents have been photocopied.>

This paper describes a communications networking technique for funds transfer which combines the privacy of cash transactions with the security, record-keeping and charging mechanisms of credit cards. The scheme uses a communications network and cryptographic protocols to separate information. The company that extends credit to the individual and collects the bill does not have access to the specific purchases, and the shop that sells the merchandise is convinced that it will be paid without learning the individual's identity.

A major impediment to the widespread adoption of services for electronic distribution of copyrighted material is the ease with which illicit copies can be made and disseminated. In this paper, we describe feature coding techniques to mark document images with codes that are indiscernible by readers but can be decoded by document feature analysis techniques. These codes can be used to trace the source of errant documents. We propose three coding methods: line-shift coding, word-shift coding, and character coding. We describe how the coding features are found, inserted, and decoded. Finally, we show preliminary experimental results indicating robustness of the line-shift coding method where decoding can be performed even from images of up to ten generations of photocopying.

Modern computer networks make it possible to distribute documents quickly and economically by electronic means rather than by conventional paper means. However, the widespread adoption of electronic distribution of copyrighted material is currently impeded by the ease of illicit copying and dissemination. The authors propose techniques that discourage illicit distribution by embedding each document with a unique codeword. The encoding techniques are indiscernible by readers, yet enable one to identify the sanctioned recipient of a document by examination of a recovered document. The authors propose three coding methods, describe one in detail, and present experimental results showing that their identification techniques are highly reliable, even after documents have been photocopied.>

The authors propose a microeconomic approach to service provisioning in ATM networks. The provisioning procedure consists of two algorithms, one executed by the network and the other by individual users. The network offers directly for rent its bandwidth and buffers. Users purchase freely resources to meet their desired quality based on their own traffic parameters and delay requirements. The network periodically adjusts resource prices based on user requests monitored in the previous period. They describe the networks adjustment scheme and users' decision rule, and show that under the proposed price adjustment scheme, in order to minimize their own service cost, individual users will indeed request amounts of resources that optimize a measure of overall network performance. Since this approach does not require the network to know user traffic and delay parameters, it does not mandate traffic policing on the part of the network.>

A probabilistic approach to conformance testing of protocols containing unobservable transitions is proposed. It is said that an implementation conforms to its specification if their observable behavior is probabilistically the same, when both are subject to the same random environment simulated by the tester. Under the randomized inputs, faults in unobservable transitions may manifest themselves in certain statistics measurable from the implementation, and hence can be detected by comparing these measurements against the desirable statistics computed from the specification. The sensitivity of the nonconformance criterion to the uncertainty in our knowledge of desirable statistics is also studied. The conventional testing of protocols without unobservable transitions uses mismatch in outputs to detect faults. Here, one relies, in addition, on mismatch in the dynamics of the protocol under input randomization.>

An exact analysis of the dynamic behavior of IGRP, an adaptive shortest-path routing algorithm, is performed. The distance metric is a weighted sum of traffic-sensitive and traffic-insensitive delay components. The optimality and stability of the protocol is related to the ratio of the weights. In particular, it is shown that if the traffic-sensitive component is not given enough weight, then starting from any initial routing, the subsequent routings after finitely many update periods will oscillate between two worst cases. Otherwise, the successive routings will converge to the unique equilibrium routing. It is also shown that load sharing among routes whose distances are within a threshold of the minimum distance helps stabilize the dynamic behavior.>

A framework for studying a stream of traffic or a message as it is transferred over an asynchronous transfer mode (ATM) connection was previously proposed by the authors (1991). A message is modeled as a deterministic fluid flow, and an ATM node is modeled as a server that allocates bandwidth among concurrent messages. The key concept is that of the burstiness curve of an incoming message, which gives the buffer size needed if the message is served at rate mu . It is shown there that the fixed rate, the leaky bucket, and the affine server are burst reducing. The burstiness bound for each of these servers is presented. A sequence of identical affine servers is related to a fixed rate server, and it is suggested how quality-of-service parameters can usefully be based on the burstiness curve.>

The authors formulate and solve a problem of allocating resources among competing services differentiated by user traffic characteristics and maximum end-to-end delay. The solution leads to an alternative approach to service provisioning in an ATM network, in which the network offers directly for rent its bandwidth and buffers and users purchase freely resources to meet their desired quality. Users make their decisions based on their own traffic parameters and delay requirements and the network sets prices for those resources. The procedure is iterative in that the network periodically adjusts prices based on monitored user demand, and is decentralized in that only local information is needed for individual users to determine resource requests. The authors derive the network's adjustment scheme and the users' decision rule and establish their optimality. Since the approach does not require the network to know user traffic and delay parameters, it does not require traffic policing on the part of the network.>

The authors describe a performance study of a trial switched multimegabit data service (SMDS) link (intended for inter-LAN connection) from the perspective of customers evaluating the feasibility of the link for some target applications. The goals were to take all measurements on the customer premises and to develop a methodology general enough to be used by customers to evaluate the link. The authors measured a lightly loaded system and developed a model of the SMDS connection suitable for evaluating applications via analysis or simulation. They document their methodology and present the SMDS connection delay values as well as a likely breakdown of the constituents of that delay. They used these data to create a simulation model and to simulate a simple application. In the trial configuration, where geographical distances were small, SMDS network delay was one of the notable components of end-to-end delay in the SMDS connection. However, for most packets, throughput is limited by the T1 capacity for transmitting SMDS cells, not by the SMDS network capacity.>