On-Line End-to-End Congestion Control

Congestion control in the current Internet is accomplished mainly by TCP/IP. To understand the macroscopic network behavior that results from TCP/IP and similar end-to-end protocols, one main analytic technique is to show that the the protocol maximizes some global objective function of the network traffic. Here we analyze a particular end-to-end, MIMD (multiplicative-increase, multiplicative-decrease) protocol. We show that if all users of the network use the protocol, and all connections last for at least logarithmically many rounds, then the total weighted throughput (value of all packets received) is near the maximum possible. Our analysis includes round-trip-times, and (in contrast to most previous analyses) gives explicit convergence rates, allows connections to start and stop, and allows capacities to change.Comment: Proceedings IEEE Symp. Foundations of Computer Science, 200

A Fast Distributed Stateless Algorithm for α\alpha-Fair Packing Problems

Over the past two decades, fair resource allocation problems have received considerable attention in a variety of application areas. However, little progress has been made in the design of distributed algorithms with convergence guarantees for general and commonly used $\alpha$-fair allocations. In this paper, we study weighted $\alpha$-fair packing problems, that is, the problems of maximizing the objective functions (i) $\sum_j w_j x_j^{1-\alpha}/(1-\alpha)$ when $\alpha > 0$, $\alpha \neq 1$ and (ii) $\sum_j w_j \ln x_j$ when $\alpha = 1$, over linear constraints $Ax \leq b$, $x\geq 0$, where $w_j$ are positive weights and $A$ and $b$ are non-negative. We consider the distributed computation model that was used for packing linear programs and network utility maximization problems. Under this model, we provide a distributed algorithm for general $\alpha$ that converges to an $\varepsilon-$approximate solution in time (number of distributed iterations) that has an inverse polynomial dependence on the approximation parameter $\varepsilon$ and poly-logarithmic dependence on the problem size. This is the first distributed algorithm for weighted $\alpha-$fair packing with poly-logarithmic convergence in the input size. The algorithm uses simple local update rules and is stateless (namely, it allows asynchronous updates, is self-stabilizing, and allows incremental and local adjustments). We also obtain a number of structural results that characterize $\alpha-$fair allocations as the value of $\alpha$ is varied. These results deepen our understanding of fairness guarantees in $\alpha-$fair packing allocations, and also provide insight into the behavior of $\alpha-$fair allocations in the asymptotic cases $\alpha\rightarrow 0$, $\alpha \rightarrow 1$, and $\alpha \rightarrow \infty$.Comment: Added structural results for asymptotic cases of \alpha-fairness (\alpha approaching 0, 1, or infinity), improved presentation, and revised throughou

Computational Aspects of Game Theory and Microeconomics

The purpose of this thesis is to study algorithmic questions that arise in the context of game theory and microeconomics. In particular, we investigate the computational complexity of various economic solution concepts by using and advancing methodologies from the fields of combinatorial optimization and approximation algorithms. We first study the problem of allocating a set of indivisible goods to a set of agents, who express preferences over combinations of items through their utility functions. Several objectives have been considered in the economic literature in different contexts. In fair division theory, a desirable outcome is to minimize the envy or the envy-ratio between any pair of players. We use tools from the theory of linear and integer programming as well as combinatorics to derive new approximation algorithms and hardness results for various types of utility functions. A different objective that has been considered in the context of auctions, is to find an allocation that maximizes the social welfare, i.e., the total utility derived by the agents. We construct reductions from multi-prover proof systems to obtain inapproximability results, given standard assumptions for the utility functions of the agents. We then consider equilibrium concepts in games. We derive the first subexponential algorithm for computing approximate Nash equilibria in $2$-player noncooperative games and extend our result to multi-player games. We further propose a second algorithm based on solving polynomial equations over the reals. Both algorithms improve the previously known upper bounds on the complexity of the problem. Finally, we study game theoretic models that have been introduced recently to address incentive issues in Internet routing. A polynomial time algorithm is obtained for computing equilibria in such games, i.e., routing schemes and payoff allocations from which no subset of agents has an incentive to deviate. Our algorithm is based on linear programming duality theory. We also obtain generalizations when the agents have nonlinear utility functions.Ph.D.Committee Chair: Lipton, Richard; Committee Member: Ding, Yan; Committee Member: Duke, Richard; Committee Member: Randall, Dana; Committee Member: Vazirani, Vija

Resource Allocation in Wireless Networks: Theory and Applications

Limited wireless resources, such as spectrum and maximum power, give rise to various resource allocation problems that are interesting both from theoretical and application viewpoints. While the problems in some of the wireless networking applications are amenable to general resource allocation methods, others require a more specialized approach suited to their unique structural characteristics. We study both types of the problems in this thesis. We start with a general problem of alpha-fair packing, namely, the problem of maximizing sum_j {w_j f_α(x_j)}, where w_j > 0, ∀j, and (i) f_α(x_j)=ln(x_j), if α = 1, (ii) f_α(x_j)= {x_j^(1-α)}/{1-α}, if α ≠ 1,α > 0, subject to positive linear constraints of the form Ax ≤ b, x ≥ 0, where A and b are non-negative. This problem has broad applications within and outside wireless networking. We present a distributed algorithm for general alpha that converges to an epsilon-approximate solution in time (number of distributed iterations) that has an inverse polynomial dependence on the approximation parameter epsilon and poly-logarithmic dependence on the problem size. This is the first distributed algorithm for weighted alpha-fair packing with poly-logarithmic convergence in the input size. We also obtain structural results that characterize alpha-fair allocations as the value of alpha is varied. These results deepen our understanding of fairness guarantees in alpha-fair packing allocations, and also provide insights into the behavior of alpha-fair allocations in the asymptotic cases when alpha tends to zero, one, and infinity. With these general tools on hand, we consider an application in wireless networks where fairness is of paramount importance: rate allocation and routing in energy-harvesting networks. We discuss the importance of fairness in such networks and cases where our results on alpha-fair packing apply. We then turn our focus to rate allocation in energy harvesting networks with highly variable energy sources and that are used for applications such as monitoring and tracking. In such networks, it is essential to guarantee fairness over both the network nodes and the time slots and to be as fair as possible -- in particular, to require max-min fairness. We first develop an algorithm that obtains a max-min fair rate assignment for any routing that is specified at the input. Then, we consider the problem of determining a "good'' routing. We consider various routing types and either provide polynomial-time algorithms for finding such routings or prove that the problems are NP-hard. Our results reveal an interesting trade-off between the complexities of computation and implementation. The results can also be applied to other related fairness problems. The second part of the thesis is devoted to the study of resource allocation problems that require a specialized approach. The problems we focus on arise in wireless networks employing full-duplex communication -- the simultaneous transmission and reception on the same frequency channel. Our primary goal is to understand the benefits and complexities tied to using this novel wireless technology through the study of resource (power, time, and channel) allocation problems. Towards that goal, we introduce a new realistic model of a compact (e.g., smartphone) full-duplex receiver and demonstrate its accuracy via measurements. First, we focus on the resource allocation problems with the objective of maximizing the sum of uplink and downlink rates, possibly over multiple orthogonal channels. For the single-channel case, we quantify the rate improvement as a function of the remaining self-interference and signal-to-noise ratios and provide structural results that characterize the sum of uplink and downlink rates on a full-duplex channel. Building on these results, we consider the multi-channel case and develop a polynomial time algorithm which is nearly optimal in practice under very mild restrictions. To reduce the running time, we develop an efficient nearly-optimal algorithm under the high SINR approximation. Then, we study the achievable capacity regions of full-duplex links in the single- and multi-channel cases. We present analytical results that characterize the uplink and downlink capacity region and efficient algorithms for computing rate pairs at the region's boundary. We also provide near-optimal and heuristic algorithms that "convexify'' the capacity region when it is not convex. The convexified region corresponds to a combination of a few full-duplex rates (i.e., to time sharing between different operation modes). The analytical results provide insights into the properties of the full-duplex capacity region and are essential for future development of fair resource allocation and scheduling algorithms in Wi-Fi and cellular networks incorporating full-duplex

On-line end-to-end congestion control

Congestion control in the current Internet is accomplished mainly by TCP/IP. To understand the macroscopic network behavior that results from TCP/IP and similar end-to-end protocols, one main analytic technique is to show that the the protocol maximizes some global objective function of the network traffic. We analyze a particular end-to-end MIMD (Multiplicative-Increase, Multiplicative-Decrease) protocol. We show that if all users of the network use the protocol and all connections last for at least logarithmically many rounds, then the total weighted throughput (value of all packets received) is near the maximum possible. Our analysis includes round-trip-times and (in contrast to most previous analyses) gives explicit convergence rates, allows connections to start and stop and allows capacities to change