1,020 research outputs found
A Study of Problems Modelled as Network Equilibrium Flows
This thesis presents an investigation into selfish routing games from three main perspectives. These three areas are tied together by a common thread that runs through the main text of this thesis, namely selfish routing games and network
equilibrium flows. First, it investigates methods and models for nonatomic selfish routing and then develops algorithms for solving atomic selfish routing games. A number of algorithms are introduced for the atomic selfish routing problem, including dynamic programming for a parallel network and a metaheuristic tabu search. A piece-wise mixed-integer linear programming problem is also presented which allows standard solvers to solve the atomic selfish routing problem. The connection between the atomic selfish routing problem, mixed-integer linear programming and the multicommodity
flow problem is explored when constrained by unsplittable flows or flows that are restricted to a number of paths. Additionally, some novel probabilistic online learning algorithms are presented and compared with the equilibrium solution given by the potential function of the nonatomic selfish routing game. Second, it considers multi-criteria extensions of selfish routing and the inefficiency
of the equilibrium solutions when compared with social cost. Models are presented that allow exploration of the Pareto set of solutions for a weighted sum model (akin to the social cost) and the equilibrium solution. A means by which
these solutions can be measured based on the Price of Anarchy for selfish routing games is also presented. Third, it considers the importance and criticality of components of the network (edges, vertices or a collection of both) within a selfish routing game and the impact of their removal. Existing network science measures and demand-based measures
are analysed to assess the change in total travel time and issues highlighted. A new measure which solves these issues is presented and the need for such a measure is evaluated.
Most of the new findings have been disseminated through conference talks and journal articles, while others represent the subject of papers currently in preparation
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
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