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Atomic congestion games: fast, myopic and concurrent
"... We study here the effect of concurrent greedy moves of players in atomic congestion games where n selfish agents (players) wish to select a resource each (out of m resources) so that her selfish delay there is not much. Such games usually admit a global potential that decreases by sequential and se ..."
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We study here the effect of concurrent greedy moves of players in atomic congestion games where n selfish agents (players) wish to select a resource each (out of m resources) so that her selfish delay there is not much. Such games usually admit a global potential that decreases by sequential and selfishly improving moves. However, concurrent moves may not always lead to global convergence. On the other hand, concurrent play is desirable because it might essentially improve the system convergence time to some balanced state. The problem of “maintaining ” global progress while allowing concurrent play is exactly what is examined and answered here. We examine two orthogonal settings: (i) A game where the players decide their moves without global information, each acting “freely ” by sampling resources randomly and locally deciding to migrate (if the new resource is better) via a random experiment. Here, the resources can have quite arbitrary latency that is load dependent. (ii) An “organised” setting where the players are prepartitioned into selfish groups (coalitions) and where each coalition does an improving coalitional move. Here the concurrency is among the members of the coalition. In this second setting, the resources have latency functions that are only linearly dependent on the load, since this is the only case so far where a global potential exists. In both cases (i), (ii) we show that the system converges to an “approximate” equilibrium very fast (in
Fast load balancing via bounded best response
, 2008
"... It is known that the dynamics of best response in an environment of noncooperative users may converge to a good solution when users play sequentially, but may cycle far away from the global optimum solution when users play concurrently. We introduce the notion of bounded best response where users r ..."
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It is known that the dynamics of best response in an environment of noncooperative users may converge to a good solution when users play sequentially, but may cycle far away from the global optimum solution when users play concurrently. We introduce the notion of bounded best response where users react with best response subject to rules that are forced locally by the system. We investigate the problem of load balancing tasks on machines in a bipartite graph model and show that the dynamics of concurrent bounded best response converges to a nearoptimum solution quickly, i.e., with polylogarithmic number of rounds. This is in contrast to the concurrent best response dynamics which cycles far away from the optimum and to any sequential dynamics which requires at least a linear number of rounds to get to a reasonable solution.
Conflicting congestion effects in resource allocation games
 In WINE, 2008. [8] Michel Goemans, Vahab Mirrokni, and Adrian Vetta
"... We study strategic resource allocation settings, where jobs are selfinterested players who choose resources with the objective of minimizing their individual cost. Our framework departs from the existing game theoretic models of resource allocation in two fundamental ways. First, while most of the ..."
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We study strategic resource allocation settings, where jobs are selfinterested players who choose resources with the objective of minimizing their individual cost. Our framework departs from the existing game theoretic models of resource allocation in two fundamental ways. First, while most of the previous work has considered cost structures with either negative congestion effects or positive ones, we introduce cost functions that encompass both effects. Second, we do not assume the existence of a fixed set of resources; rather, jobs can always activate new resources, but activating a new resource is costly. Specifically, in our model there is a set of heterogeneous jobs and an unlimited supply of identical resources. The cost of a job is the load on its chosen resource plus its share in the resource’s activation cost, which is proportional to its length. We provide results with respect to equilibrium existence and the inefficiency introduced due to selfinterested behavior. We show that if the resource’s activation cost is shared equally among its users, a pure Nash equilibrium (NE) might not exist. In contrast, under the proportional sharing rule, a pure NE always exists and we provide a polytime algorithm for computing it.
Approximating Wardrop Equilibria with Finitely Many Agents
"... We present efficient algorithms for computing approximate Wardrop equilibria in a distributed and concurrent fashion. Our algorithms are exexuted by a finite number of agents each of which controls the flow of one commodity striving to balance the induced latency over all utilised paths. The set of ..."
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We present efficient algorithms for computing approximate Wardrop equilibria in a distributed and concurrent fashion. Our algorithms are exexuted by a finite number of agents each of which controls the flow of one commodity striving to balance the induced latency over all utilised paths. The set of allowed paths is represented by a DAG. Our algorithms are based on previous work on policies for infinite populations of agents. These policies achieve a convergence time which is independent of the underlying network and depends mildly on the latency functions. These policies can neither be applied to a finite set of agents nor can they be simulated directly due to the exponential number of paths. Our algorithms circumvent these problems by computing a randomised path decomposition in every communication round. Based on this decomposition, flow is shifted from overloaded to underloaded paths. This way, our algorithm can handle exponentially large path collections in polynomial time. Our algorithms are stateless, and the number of communication rounds depends polynomially on the approximation quality and is independent of the topology and size of the network.
Nonadaptive Selfish Routing with Online Demands
, 2007
"... We study the efficiency of selfish routing problems in which traffic demands are revealed online. We go beyond the common Nash equilibrium concept in which possibly all players reroute their flow and form a new equilibrium upon arrival of a new demand. In our model, demands arrive in n sequential ..."
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We study the efficiency of selfish routing problems in which traffic demands are revealed online. We go beyond the common Nash equilibrium concept in which possibly all players reroute their flow and form a new equilibrium upon arrival of a new demand. In our model, demands arrive in n sequential games. In each game, the new demands form a Nash equilibrium and their routings remain unchanged afterwards. We study the problem both with nonatomic and atomic player types and with continuous and nondecreasing latency functions on the edges. For polynomial latency functions, we give constant upper and lower bounds on the competitive ratio of the resulting online routing in terms of the maximum degree, the number of games and in the atomic setting the number of players. In particular, for nonatomic players and affine latency functions we show that the competitive ratio is at most 4n. Finally, we present improved upper bounds for the special n+2 case of two nodes connected by parallel arcs.
Load balancing for dynamic spectrum assignment with local information for secondary users
 In Proc. Symp. Dynamic Spectrum Access Networks (DySPAN
, 2008
"... Abstract—In this paper we study an idealized model of load balancing for dynamic spectrum allocation (DSA) for secondary users using only local information. In our model, each agent is assigned to a channel and may reassign its load in a round based fashion. We present a randomized protocol in which ..."
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Abstract—In this paper we study an idealized model of load balancing for dynamic spectrum allocation (DSA) for secondary users using only local information. In our model, each agent is assigned to a channel and may reassign its load in a round based fashion. We present a randomized protocol in which the actions of the agents depend purely on some cost measure (e. g., latency, inverse of the throughput, etc.) of the currently chosen channel. Since agents act concurrently, the system is prone to oscillations. We show how this can be avoided guaranteeing convergence towards a state in which every agent sustains at most a certain threshold cost (if such a state exists). We show that the system converges quickly by giving bounds on the convergence time towards approximately balanced states. Our analysis in the fluid limit (where the number of agents approaches infinity) holds for a large class of cost functions. We support our theoretical analysis by simulations to determine the dependence on the number of agents. It turns out that the number of agents affects the convergence time only in a logarithmic fashion. The work shows under quite general assumptions that even an extremely large number of users using several hundreds of (virtual) channels can work in a DSA fashion. I.
Distributed load balancing algorithm for adaptive channel allocation for Cognitive Radios
 In Proc. of the 2nd Conf. on Cognitive Radio Oriented Wireless Networks and Communications (CrownCom
, 2007
"... Abstract — The problem of channel allocation has been extensively studied in the context of cellular networks. There is a substantial amount of work in the field of dynamic frequency assignment for WLANs and mesh networks as well. The growing interest in the cognitive radio technology and its capabi ..."
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Abstract — The problem of channel allocation has been extensively studied in the context of cellular networks. There is a substantial amount of work in the field of dynamic frequency assignment for WLANs and mesh networks as well. The growing interest in the cognitive radio technology and its capability to offer more efficient spectrum usage brought this problem back as one of the most popular research topics nowadays. In this paper we present two quite simple to implement, distributed algorithms for selecting channels, in cognitive radio environment, so that the load is distributed (smoothed) over them. I.
Tight Bounds for Randomized Load Balancing on Arbitrary Network Topologies
, 1201
"... We consider the problem of balancing load items (tokens) on networks. Starting with an arbitrary load distribution, we allow in each round nodes to exchange tokens with their neighbors. Thegoalisto achieveadistribution whereall nodeshavenearlythe samenumber of tokens. For the continuous case where t ..."
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We consider the problem of balancing load items (tokens) on networks. Starting with an arbitrary load distribution, we allow in each round nodes to exchange tokens with their neighbors. Thegoalisto achieveadistribution whereall nodeshavenearlythe samenumber of tokens. For the continuous case where tokens are arbitrarily divisible, most load balancing schemes correspond to Markov chains whose convergence is rather wellunderstood in terms of their spectral gap. However, since for many applications load items cannot be divided arbitrarily, we focus on the discrete case where the load is composed of indivisible tokens. Unfortunately, this discretization entails a nonlinear behavior due to its rounding errors, which makes the analysis much harder than in the continuous case. Therefore, it has been a major open problem to understand the limitations of discrete load balancing and its relation to the continuous case. We investigate several randomized protocols for different communication models in the discrete case. Ourresults demonstratethat there is almost no deviationbetween the discrete
ABSNET: Fully Decentralized Runtime Adaptation for Distributed Objects
"... We present a formalized, fully decentralized runtime semantics for a core subset of ABS, a language graph representation of a network infrastructure, with network endpoints represented as graph nodes, and links as arcs with buffers, corresponding to OSI layer 2 interconnects. The key problem we wish ..."
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We present a formalized, fully decentralized runtime semantics for a core subset of ABS, a language graph representation of a network infrastructure, with network endpoints represented as graph nodes, and links as arcs with buffers, corresponding to OSI layer 2 interconnects. The key problem we wish to address is how to allocate computational tasks to nodes so that certain performance objectives are met. To this end, we use the semantics as a foundation for performing networkadaptive task execution via object migration between nodes. Adaptability is analyzed in terms of three Quality of Service objectives: node load, arc load and message latency. We have implemented the key parts of our semantics in a simulator and evaluated how well objectives are achieved for some applicationrelevant choices of network topology, migration procedure and ABS program. The evaluation suggests that it is feasible in a decentralized setting to continually meet both the objective of a nodebalanced task allocation and make headway towards minimizing communication, and thus arc load and message latency. 1
A Learning Perspective on Selfish Behavior in Games
, 2009
"... Computer systems increasingly involve the interaction of multiple selfinterested agents. The designers of these systems have objectives they wish to optimize, but by allowing selfish agents to interact in the system, they lose the ability to directly control behavior. What is lost by this lack of ..."
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Computer systems increasingly involve the interaction of multiple selfinterested agents. The designers of these systems have objectives they wish to optimize, but by allowing selfish agents to interact in the system, they lose the ability to directly control behavior. What is lost by this lack of centralized control? What are the likely outcomes of selfish behavior? In this work, we consider learning dynamics as a tool for better classifying and understanding outcomes of selfish behavior in games. In particular, when such learning algorithms exist and are efficient, we propose “regretminimization” as a criterion for selfinterested behavior and study the systemwide effects in broad classes of games when players achieve this criterion. In addition, we present a general transformation from offline approximation algorithms for linear optimization problems to online algorithms that achieve low regret.