Richard Southwell

Atomic congestion games on graphs and their applications in networking

In this paper, we introduce and analyze the properties of a class of games, the atomic congestion games on graphs (ACGGs), which is a generalization of the classical congestion games. In particular, an ACGG captures the spatial information that is often ignored in a classical congestion game. This is useful in many networking problems, e.g., wireless networks where interference among the users heavily depends on the spatial information. In an ACGG, a players payoff for using a resource is a function of the number of players who interact with it and use the same resource. Such spatial information can be captured by a graph. We study fundamental properties of the ACGGs: under what conditions these games possess a pure strategy Nash equilibrium (PNE), or the finite improvement property (FIP), which is sufficient for the existence of a PNE. We show that a PNE may not exist in general, but that it does exist in many important special cases including tree, loop, or regular bipartite networks. The FIP holds for important special cases including systems with two resources or identical payoff functions for each resource. Finally, we present two wireless network applications of ACGGs: power control and channel contention under IEEE 802.11.

Spectrum mobility games

Cognitive radio gives users the ability to switch channels and make use of dynamic spectrum opportunities. However, switching channels takes time, and may affect the quality of a users transmission. When a cognitive radio users channel becomes unavailable, sometimes it may be better waiting until its current channel becomes available again. Motivated by the recent FCC ruling on TV white space, we consider the scenario where cognitive radio users are given the foreknowledge of channel availabilities. Using this information, each user must decide when and how to switch channels. The users wish to exploit spectrum opportunities, but they must take account of the cost of switching channels and the congestion that comes from sharing channels with one another. We model the scenario as a game which, as we show, is equivalent to a network congestion game in the literature after proper and non-trivial transformations. This allows us to design a protocol which the users can apply to find Nash equilibria in a distributed manner. We further evaluate how the performance of the proposed schemes depends on switching cost using real channel availability measurements.

Convergence Dynamics of Resource-Homogeneous Congestion Games

Many resource sharing scenarios can be modeled as congestion games. A nice property of congestion games is that simple dynamics are guaranteed to converge to Nash equilibria. Loose bounds on the convergence time are known, but exact results are difficult to obtain in general. We investigate congestion games where the resources are homogeneous but can be player-specific. In these games, players always prefer less used resources. We derive exact conditions for the longest and shortest convergence times. We also extend the results to games on graphs, where individuals only cause congestions to their neighbors. As an example, we apply our results to study cognitive radio networks, where selfish users share wireless spectrum opportunities that are constantly changing. We demonstrate how fast the users need to be able to switch channels in order to track the time-variant channel availabilities.

Convergence Dynamics of Graphical Congestion Games

Graphical congestion games provide powerful models for a wide range of scenarios where spatially distributed individuals share resources. Understanding when graphical congestion game dynamics converge to pure Nash equilibria yields important engineering insights into when spatially distributed individuals can reach a stable resource allocation. In this paper, we study the convergence dynamics of graphical congestion games where players can use multiple resources simultaneously. We show that when the players are free to use any subset of resources the game always converges to a pure Nash equilibrium in polynomial time via lazy best response updates. When the collection of sets of resources available to each player is a matroid, we show that pure Nash equilibria may not exist in the most general case. However, if the resources are homogenous, the game can converge to a Nash equilibrium in polynomial time.

Congestion-Aware DNS for Integrated Cellular and Wi-Fi Networks

Intelligent network selection plays an important role in achieving an effective data offloading in the integrated cellular and Wi-Fi networks. However, previously proposed network selection schemes mainly focused on offloading as much data traffic to Wi-Fi as possible, without systematically considering the Wi-Fi network congestion and the ping-pong effect, both of which may lead to a poor overall user quality of experience. Thus, in this paper, we study a more practical network selection problem by considering both the impacts of the network congestion and switching penalties. More specifically, we formulate the users’ interactions as a Bayesian network selection game (NSG) under the incomplete information of the users’ mobilities. We prove that it is a Bayesian potential game and show the existence of a pure Bayesian–Nash equilibrium that can be easily reached. We then propose a distributed network selection (DNS) algorithm based on the network congestion statistics obtained from the operator. Furthermore, we show that computing the optimal centralized network allocation is an NP-hard problem, which further justifies our distributed approach. Simulation results show that the DNS algorithm achieves the highest user utility and a good fairness among users, as compared with the on-the-spot offloading and cellular-only benchmark schemes.

Physical interference model based spectrum sharing with generalized spatial congestion games

With the rapid development of heterogeneous wireless technologies, the issue of how selfish wireless users can share spectrum is becoming increasingly relevant. In this paper we introduce the generalized spatial congestion game (GSCG), and use it to model wireless spectrum sharing over a large area. The idea behind the GSCG is to think of the players as vertices in a weighted graph. The amount of congestion two players cause each other (when they use the same resource) is determined by the weight of the edge linking them. The GSCG is more suitable for modeling spectrum sharing than many previously considered models, because one can select the edge weights and payoff functions to correspond with several practical interference models (such as the physical interference model). We focus on determining which GSCGs possess pure Nash equilibria (i.e., mutually acceptable resource allocations), and how selfish players can organize themselves into pure Nash equilibria.