A Packet Dropping Mechanism for Efficient Operation of M/M/1 Queues with Selfish Users

We consider a fundamental game theoretic problem concerning selfish users contributing packets to an M/M/1 queue. In this game, each user controls its own input rate so as to optimize a desired tradeoff between throughput and delay. We first show that the original game has an inefficient Nash Equilibrium (NE), with a Price of Anarchy (PoA) that scales linearly or worse in the number of users. In order to improve the outcome efficiency, we propose an easily implementable mechanism design whereby the server randomly drops packets with a probability that is a function of the total arrival rate. We show that this results in a modified M/M/1 queueing game that is an ordinal potential game with at least one NE. In particular, for a linear packet dropping function, which is similar to the Random Early Detection (RED) algorithm used in Internet Congestion Control, we prove that there is a unique NE. We also show that the simple best response dynamic converges to this unique equilibrium. Finally, for this scheme, we prove that the social welfare (expressed either as the summation of utilities of all players, or as the summation of the logarithm of utilities of all players) at the equilibrium point can be arbitrarily close to the social welfare at the global optimal point, i.e. the PoA can be made arbitrarily close to 1. We also study the impact of arrival rate estimation error on the PoA through simulations.Comment: This work is an extended version of the conference paper: Y. Gai, H. Liu and B. Krishnamachari, "A packet dropping-based incentive mechanism for M/M/1 queues with selfish users", the 30th IEEE International Conference on Computer Communications (IEEE INFOCOM 2011), China, April, 201

Distributed Game Theoretic Optimization and Management of Multichannel ALOHA Networks

The problem of distributed rate maximization in multi-channel ALOHA networks is considered. First, we study the problem of constrained distributed rate maximization, where user rates are subject to total transmission probability constraints. We propose a best-response algorithm, where each user updates its strategy to increase its rate according to the channel state information and the current channel utilization. We prove the convergence of the algorithm to a Nash equilibrium in both homogeneous and heterogeneous networks using the theory of potential games. The performance of the best-response dynamic is analyzed and compared to a simple transmission scheme, where users transmit over the channel with the highest collision-free utility. Then, we consider the case where users are not restricted by transmission probability constraints. Distributed rate maximization under uncertainty is considered to achieve both efficiency and fairness among users. We propose a distributed scheme where users adjust their transmission probability to maximize their rates according to the current network state, while maintaining the desired load on the channels. We show that our approach plays an important role in achieving the Nash bargaining solution among users. Sequential and parallel algorithms are proposed to achieve the target solution in a distributed manner. The efficiencies of the algorithms are demonstrated through both theoretical and simulation results.Comment: 34 pages, 6 figures, accepted for publication in the IEEE/ACM Transactions on Networking, part of this work was presented at IEEE CAMSAP 201

Intervention in Power Control Games With Selfish Users

We study the power control problem in wireless ad hoc networks with selfish users. Without incentive schemes, selfish users tend to transmit at their maximum power levels, causing significant interference to each other. In this paper, we study a class of incentive schemes based on intervention to induce selfish users to transmit at desired power levels. An intervention scheme can be implemented by introducing an intervention device that can monitor the power levels of users and then transmit power to cause interference to users. We mainly consider first-order intervention rules based on individual transmit powers. We derive conditions on design parameters and the intervention capability to achieve a desired outcome as a (unique) Nash equilibrium and propose a dynamic adjustment process that the designer can use to guide users and the intervention device to the desired outcome. The effect of using intervention rules based on aggregate receive power is also analyzed. Our results show that with perfect monitoring intervention schemes can be designed to achieve any positive power profile while using interference from the intervention device only as a threat. We also analyze the case of imperfect monitoring and show that a performance loss can occur. Lastly, simulation results are presented to illustrate the performance improvement from using intervention rules and compare the performances of different intervention rules.Comment: 33 pages, 6 figure

A Comprehensive Survey of Potential Game Approaches to Wireless Networks

Potential games form a class of non-cooperative games where unilateral improvement dynamics are guaranteed to converge in many practical cases. The potential game approach has been applied to a wide range of wireless network problems, particularly to a variety of channel assignment problems. In this paper, the properties of potential games are introduced, and games in wireless networks that have been proven to be potential games are comprehensively discussed.Comment: 44 pages, 6 figures, to appear in IEICE Transactions on Communications, vol. E98-B, no. 9, Sept. 201