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

Distributed Optimal Rate-Reliability-Lifetime Tradeoff in Wireless Sensor Networks

The transmission rate, delivery reliability and network lifetime are three fundamental but conflicting design objectives in energy-constrained wireless sensor networks. In this paper, we address the optimal rate-reliability-lifetime tradeoff with link capacity constraint, reliability constraint and energy constraint. By introducing the weight parameters, we combine the objectives at rate, reliability, and lifetime into a single objective to characterize the tradeoff among them. However, the optimization formulation of the rate-reliability-reliability tradeoff is neither separable nor convex. Through a series of transformations, a separable and convex problem is derived, and an efficient distributed Subgradient Dual Decomposition algorithm (SDD) is proposed. Numerical examples confirm its convergence. Also, numerical examples investigate the impact of weight parameters on the rate utility, reliability utility and network lifetime, which provide a guidance to properly set the value of weight parameters for a desired performance of WSNs according to the realistic application's requirements.Comment: 27 pages, 10 figure