1,172 research outputs found
Load Balancing Congestion Games and their Asymptotic Behavior
A central question in routing games has been to establish conditions for the
uniqueness of the equilibrium, either in terms of network topology or in terms
of costs. This question is well understood in two classes of routing games. The
first is the non-atomic routing introduced by Wardrop on 1952 in the context of
road traffic in which each player (car) is infinitesimally small; a single car
has a negligible impact on the congestion. Each car wishes to minimize its
expected delay. Under arbitrary topology, such games are known to have a convex
potential and thus a unique equilibrium. The second framework is splitable
atomic games: there are finitely many players, each controlling the route of a
population of individuals (let them be cars in road traffic or packets in the
communication networks). In this paper, we study two other frameworks of
routing games in which each of several players has an integer number of
connections (which are population of packets) to route and where there is a
constraint that a connection cannot be split. Through a particular game with a
simple three link topology, we identify various novel and surprising properties
of games within these frameworks. We show in particular that equilibria are non
unique even in the potential game setting of Rosenthal with strictly convex
link costs. We further show that non-symmetric equilibria arise in symmetric
networks. I. INTRODUCTION A central question in routing games has been to
establish conditions for the uniqueness of the equilibria, either in terms of
the network topology or in terms of the costs. A survey on these issues is
given in [1]. The question of uniqueness of equilibria has been studied in two
different frameworks. The first, which we call F1, is the non-atomic routing
introduced by Wardrop on 1952 in the context of road traffic in which each
player (car) is infinitesimally small; a single car has a negligible impact on
the congestion. Each car wishes to minimize its expected delay. Under arbitrary
topology, such games are known to have a convex potential and thus have a
unique equilibrium [2]. The second framework, denoted by F2, is splitable
atomic games. There are finitely many players, each controlling the route of a
population of individuals. This type of games have already been studied in the
context of road traffic by Haurie and Marcotte [3] but have become central in
the telecom community to model routing decisions of Internet Service Providers
that can decide how to split the traffic of their subscribers among various
routes so as to minimize network congestion [4]. In this paper we study
properties of equilibria in two other frameworks of routing games which exhibit
surprisin
Load Balancing Congestion Games and Their Asymptotic Behavior
International audienc
Price of Anarchy in Bernoulli Congestion Games with Affine Costs
We consider an atomic congestion game in which each player participates in
the game with an exogenous and known probability , independently
of everybody else, or stays out and incurs no cost. We first prove that the
resulting game is potential. Then, we compute the parameterized price of
anarchy to characterize the impact of demand uncertainty on the efficiency of
selfish behavior. It turns out that the price of anarchy as a function of the
maximum participation probability is a nondecreasing
function. The worst case is attained when players have the same participation
probabilities . For the case of affine costs, we provide an
analytic expression for the parameterized price of anarchy as a function of
. This function is continuous on , is equal to for , and increases towards when . Our work can be interpreted as
providing a continuous transition between the price of anarchy of nonatomic and
atomic games, which are the extremes of the price of anarchy function we
characterize. We show that these bounds are tight and are attained on routing
games -- as opposed to general congestion games -- with purely linear costs
(i.e., with no constant terms).Comment: 29 pages, 6 figure
Load Balancing via Random Local Search in Closed and Open systems
In this paper, we analyze the performance of random load resampling and
migration strategies in parallel server systems. Clients initially attach to an
arbitrary server, but may switch server independently at random instants of
time in an attempt to improve their service rate. This approach to load
balancing contrasts with traditional approaches where clients make smart server
selections upon arrival (e.g., Join-the-Shortest-Queue policy and variants
thereof). Load resampling is particularly relevant in scenarios where clients
cannot predict the load of a server before being actually attached to it. An
important example is in wireless spectrum sharing where clients try to share a
set of frequency bands in a distributed manner.Comment: Accepted to Sigmetrics 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
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