Routing Games with Progressive Filling

Max-min fairness (MMF) is a widely known approach to a fair allocation of bandwidth to each of the users in a network. This allocation can be computed by uniformly raising the bandwidths of all users without violating capacity constraints. We consider an extension of these allocations by raising the bandwidth with arbitrary and not necessarily uniform time-depending velocities (allocation rates). These allocations are used in a game-theoretic context for routing choices, which we formalize in progressive filling games (PFGs). We present a variety of results for equilibria in PFGs. We show that these games possess pure Nash and strong equilibria. While computation in general is NP-hard, there are polynomial-time algorithms for prominent classes of Max-Min-Fair Games (MMFG), including the case when all users have the same source-destination pair. We characterize prices of anarchy and stability for pure Nash and strong equilibria in PFGs and MMFGs when players have different or the same source-destination pairs. In addition, we show that when a designer can adjust allocation rates, it is possible to design games with optimal strong equilibria. Some initial results on polynomial-time algorithms in this direction are also derived

Hierarchical Beamforming: Resource Allocation, Fairness and Flow Level Performance

We consider hierarchical beamforming in wireless networks. For a given population of flows, we propose computationally efficient algorithms for fair rate allocation including proportional fairness and max-min fairness. We next propose closed-form formulas for flow level performance, for both elastic (with either proportional fairness and max-min fairness) and streaming traffic. We further assess the performance of hierarchical beamforming using numerical experiments. Since the proposed solutions have low complexity compared to conventional beamforming, our work suggests that hierarchical beamforming is a promising candidate for the implementation of beamforming in future cellular networks.Comment: 34 page

On Money as a Means of Coordination between Network Packets

In this work, we apply a common economic tool, namely money, to coordinate network packets. In particular, we present a network economy, called PacketEconomy, where each flow is modeled as a population of rational network packets, and these packets can self-regulate their access to network resources by mutually trading their positions in router queues. Every packet of the economy has its price, and this price determines if and when the packet will agree to buy or sell a better position. We consider a corresponding Markov model of trade and show that there are Nash equilibria (NE) where queue positions and money are exchanged directly between the network packets. This simple approach, interestingly, delivers improvements even when fiat money is used. We present theoretical arguments and experimental results to support our claims

Multipath streaming: fundamental limits and efficient algorithms

We investigate streaming over multiple links. A file is split into small units called chunks that may be requested on the various links according to some policy, and received after some random delay. After a start-up time called pre-buffering time, received chunks are played at a fixed speed. There is starvation if the chunk to be played has not yet arrived. We provide lower bounds (fundamental limits) on the starvation probability of any policy. We further propose simple, order-optimal policies that require no feedback. For general delay distributions, we provide tractable upper bounds for the starvation probability of the proposed policies, allowing to select the pre-buffering time appropriately. We specialize our results to: (i) links that employ CSMA or opportunistic scheduling at the packet level, (ii) links shared with a primary user (iii) links that use fair rate sharing at the flow level. We consider a generic model so that our results give insight into the design and performance of media streaming over (a) wired networks with several paths between the source and destination, (b) wireless networks featuring spectrum aggregation and (c) multi-homed wireless networks.Comment: 24 page

Towards Fast-Convergence, Low-Delay and Low-Complexity Network Optimization

Distributed network optimization has been studied for well over a decade. However, we still do not have a good idea of how to design schemes that can simultaneously provide good performance across the dimensions of utility optimality, convergence speed, and delay. To address these challenges, in this paper, we propose a new algorithmic framework with all these metrics approaching optimality. The salient features of our new algorithm are three-fold: (i) fast convergence: it converges with only $O(\log(1/\epsilon))$ iterations that is the fastest speed among all the existing algorithms; (ii) low delay: it guarantees optimal utility with finite queue length; (iii) simple implementation: the control variables of this algorithm are based on virtual queues that do not require maintaining per-flow information. The new technique builds on a kind of inexact Uzawa method in the Alternating Directional Method of Multiplier, and provides a new theoretical path to prove global and linear convergence rate of such a method without requiring the full rank assumption of the constraint matrix