A New Model for Selfish Routing

Lücking, Thomas; Mavronicolas, Marios; Monien, Burkhard; Rode, Manuel

doi:10.1007/978-3-540-24749-4_48

Cited by 57 publications

(55 citation statements)

References 30 publications

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“…Finally, we should contrast this work with [8] which (in the model from [7]) studies "quadratic social cost", a sum of individual costs weighted by the task weights. That measure of social cost is the same as ours in the case where all task weights are equal, but in general leads to very different results for social optima and coordination ratio, even in the special case of identical resources.…”

Section: Alternative Models and Related Workmentioning

confidence: 95%

Utilitarian resource assignment

Berenbrink

Goldberg

et al. 2006

Journal of Discrete Algorithms

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This paper studies a resource allocation problem introduced by Koutsoupias and Papadimitriou. The scenario is modelled as a multiple-player game in which each player selects one of a finite number of known resources. The cost to the player is the total weight of all players who choose that resource, multiplied by the "delay" of that resource. Recent papers have studied the Nash equilibria and social optima of this game in terms of the L ∞ cost metric, in which the social cost is taken to be the maximum cost to any player. We study the L 1 variant of this game, in which the social cost is taken to be the sum of the costs to the individual players, rather than the maximum of these costs. We give bounds on the size of the coordination ratio, which is the ratio between the social cost incurred by selfish behavior and the optimal social cost; we also study the algorithmic problem of finding optimal (lowest-cost) assignments and Nash Equilibria. Additionally, we obtain bounds on the ratio between alternative Nash equilibria for some special cases of the problem.

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Section: Alternative Models and Related Workmentioning

confidence: 95%

Utilitarian resource assignment

Berenbrink

Goldberg

et al. 2006

Journal of Discrete Algorithms

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“…It is an interesting open problem whether the conjecture holds for the case of identical users and arbitrary capacities. Finally, conjectures motivated by and similar to the Fully Mixed Nash Equilibrium Conjecture were recently formulated and studied in an intensive way for several variants of the KP model [4], [8], [9], [17], [19]. For an advocate of conjectures related to the fully mixed Nash equilibrium, we refer the reader to the recent survey [12].…”

Section: Epiloguementioning

confidence: 97%

The Price of Selfish Routing

Mavronicolas

Spirakis

2007

Algorithmica

Self Cite

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We study the problem of routing traffic through a congested network. We focus on the simplest case of a network consisting of m parallel links. We assume a collection of n network users; each user employs a mixed strategy, which is a probability distribution over links, to control the shipping of its own assigned traffic. Given a capacity for each link specifying the rate at which the link processes traffic, the objective is to route traffic so that the maximum (over all links) latency is minimized. We consider both uniform and arbitrary link capacities.How much decrease in global performance is necessary due to the absence of some central authority to regulate network traffic and implement an optimal assignment of traffic to links? We investigate this fundamental question in the context of Nash equilibria for such a system, where each network user selfishly routes its traffic only on those links available to it that minimize its expected latency cost, given the network congestion caused by the other users. We use the Coordination Ratio, originally defined by Koutsoupias and Papadimitriou [16], as a measure of the cost of lack of coordination among the users; roughly speaking, the Coordination Ratio is the ratio of the expectation of the maximum (over all links) latency in the worst possible Nash equilibrium, over the least possible maximum latency had global regulation been available.Our chief instrument is a set of combinatorial Minimum Expected Latency Cost Equations, one per user, that characterize the Nash equilibria of this system. These are linear equations in the minimum expected latency costs, involving the user traffics, the link capacities, and the routing pattern determined by the mixed strategies. In turn, we solve these equations in the case of fully mixed strategies, where each user assigns its traffic with a strictly positive probability to every link, to derive the first existence and uniqueness results for fully mixed Nash equilibria in this setting. Through a thorough analysis and characterization of fully mixed Nash equilibria, we obtain tight upper bounds of no worse than O(ln n/ln ln n) on the Coordination Ratio for (i) the case of uniform capacities and arbitrary traffics and (ii) the case of arbitrary capacities and identical traffics.

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“…The social cost of the total latency has been studied in [6,10,24,33]. The authors in [24] study symmetric load balancing games with linear latency functions and show tight bounds on the price of anarchy of 4/3 for different servers and 9/8 for identical servers with weighted clients. The price of anarchy of symmetric load balancing games with polynomial or convex latency functions is studied in [20,21].…”

Section: Load Balancing Gamesmentioning

confidence: 99%

Tight Bounds for Selfish and Greedy Load Balancing

et al. 2010

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We study the load balancing problem in the context of a set of clients each wishing to run a job on a server selected among a subset of permissible servers for the particular client. We consider two different scenarios. In selfish load balancing, each client is selfish in the sense that it chooses, among its permissible servers, to run its job on the server having the smallest latency given the assignments of the jobs of other clients to servers. In online load balancing, clients appear online and, when a client appears, it has to make an irrevocable decision and assign its job to one of its permissible servers. Here, we assume that the clients aim to optimize some global criterion but in an online fashion. A natural local optimization criterion that can be used by each client when making its decision is to assign its job to that server Algorithmica (2011) 61:606-637 607 that gives the minimum increase of the global objective. This gives rise to greedy online solutions. The aim of this paper is to determine how much the quality of load balancing is affected by selfishness and greediness.We characterize almost completely the impact of selfishness and greediness in load balancing by presenting new and improved, tight or almost tight bounds on the price of anarchy of selfish load balancing as well as on the competitiveness of the greedy algorithm for online load balancing when the objective is to minimize the total latency of all clients on servers with linear latency functions. In addition, we prove a tight upper bound on the price of stability of linear congestion games.

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A New Model for Selfish Routing

Cited by 57 publications

References 30 publications

Utilitarian resource assignment

Utilitarian resource assignment

The Price of Selfish Routing

Tight Bounds for Selfish and Greedy Load Balancing

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