Congestion Games, Load Balancing, and Price of Anarchy (original) (raw)
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Network resource allocation and a congestion game
PROCEEDINGS OF THE ANNUAL ALLERTON …, 2003
We explore the properties of a congestion game where users of a congested resource anticipate the effect of their actions on the price of the resource. When users are sharing a single resource, we show existence and uniqueness of the Nash equilibrium, and establish that the aggregate utility received by the users is at least 3/4 of the maximum possible aggregate utility. We also consider extensions to a network context, where users submit individual payments for each link in the network which they may wish to use. In this network model, we again show that the selfish behavior of the users leads to an aggregate utility which is no worse than 3/4 the maximum possible aggregate utility. We also show that the same analysis extends to a wide class of resource allocation systems where end users simultaneously require multiple scarce resources. These results form part of a growing literature on the "price of anarchy," i.e., the extent to which selfish behavior affects system efficiency.
Conjecture: Existence of Nash Equilibria in Modern Internet Congestion Control
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The Internet’s congestion control landscape is currently in the midst of an unprecedented paradigm shift. A recent measurement study found that BBR, a congestion control algorithm introduced by Google in 2016, has seen rapid adoption and is deployed at more than 20% of the Alexa Top 20,000 websites. Encouraging early deployment results fromGoogle, Dropbox and Spotify suggest that BBR could potentially replace traditional loss-based congestion control algorithms like CUBIC. In this paper, we study the interactions between CUBIC and BBR and show that the underlying interactions can be modeled as a normal form game. Our game-theoretic analysis and testbed measurements suggest that while BBR seems to achieve somewhat better performance than CUBIC on the Internet today, this advantage will decrease as the proportion of BBR flows increases. The distribution of congestion control algorithms on the Internet would likely reach a Nash Equilibrium, where no flow has the incentive to switch fro...
Symmetry in Network Congestion Games: Pure Equilibria and Anarchy Cost
2005
We study computational and coordination efficiency issues of Nash equilibria in symmetric network congestion games. We first propose a simple and natural greedy method that computes a pure Nash equilibrium with respect to traffic congestion in a network. In this algorithm each user plays only once and allocates her traffic to a path selected via a shortest path computation. We then show that this algorithm works for series-parallel networks when users are identical or when users are of varying demands but have the same best response strategy for any initial network traffic. We also give constructions where the algorithm fails if either the above condition is violated (even for series-parallel networks) or the network is not series-parallel (even for identical users). Thus, we essentially indicate the limits of the applicability of this greedy approach. We also study the price of anarchy for the objective of maximum latency. We prove that for any network of m uniformly related links and for identical users, the price of anarchy is \({\it \Theta}({\frac{{\rm log} m}{{\rm log log} m}}\) ).
Tight Bounds for Selfish and Greedy Load Balancing
2006
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 selects to run its job to the server among its permissible servers 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 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 and price of stability 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.
A Model for Load Balancing in Distributed System using∈-Congestion Game
iitg.ernet.in
The use of game theoretic models has been quite successful in describing various cooperative and non-cooperative optimization problems in networks and other domains of computer systems. In this paper we study another application of game theoretic models in the domain of distributed system, where nodes play a game to balance the total processing loads among themselves. We have used congestion gaming model, a model of game theory where many agents compete for allocating some resources, and studied the existence of Nash Equilibria for such types of games. As the classical congestion game is known to be PLS-Complete, we use a slight approximation of it, called the -Congestion game, which converges to -Nash equilibria within finite number of steps under some conditions. Our focus is to define the load balancing problem using the model ofcongestion games and finally provide a greedy algorithm for load balancing in distributed systems. We have simulated our proposed system to show the effect of -congestion game, and the distribution of load at equilibrium state.
2009
While the well-known Transport Control Protocol (TCP) is a de facto standard for reliable communication on the Internet, and performs well in practice, the question “how good is the TCP/IP congestion control algorithm?” is not completely resolved. In this paper, we provide some answers to this question using the competitive analysis framework. First, we prove that for networks with a single bottleneck (or point of congestion), TCP is competitive to the optimal global algorithm in minimizing the user-perceived latency or flow time of the sessions. Specifically, we show that with O(1) times as much bandwidth and O(1) extra time per job, TCP is O(1)competitive against an optimal global algorithm. We motivate the need for allowing TCP to have extra resources by observing that existing lower bounds for non-clairvoyant scheduling algorithms imply that no online, distributed, non-clairvoyant algorithm can be competitive with an optimal offline algorithm if both algorithms were given the sa...
Internet Congestion: A Laboratory Experiment
Experimental Business Research, 2005
Human players and automated players (bots) interact in real time in a congested network. A player's revenue is proportional to the number of successful "downloads" and his cost is proportional to his total waiting time. Congestion arises because waiting time is an increasing random function of the number of uncompleted download attempts by all players. Surprisingly, some human players earn considerably higher profits than bots. Bots are better able to exploit periods of excess capacity, but they create endogenous trends in congestion that human players are better able to exploit. Nash equilibrium does a good job of predicting the impact of network capacity and noise amplitude. Overall efficiency is quite low, however, and players overdissipate potential rents, i.e., earn lower profits than in Nash equilibrium..
A game theoretical study of peering vs transit in the internet
2014 IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS), 2014
We propose a model for network optimization in a non-cooperative game setting with specific reference to the Internet connectivity. We refer to the general model shown in internal report [1], where Autonomous Systems (AS) decisions on link creation and traffic routing are strategically based on realistic interconnection costs, keeping into account the peering/transit dichotomy. Equilibria existence and convergence results were obtained in [1] only for a specific toy problem, while here we study larger scale scenarios which better fit the complex nature of the Internet. We are able to show that equilibria existence and convergence properties still hold for many possible generalizations, yet not all of them, and provide a specific example for which the system enters in a never-ending oscillation. Thanks to the use of simulations we covered those scenarios for which analytic results could not be obtained, thus analyzing a broad variety of general cases which were not studied in [1]. Simulation shows that the system, in the vast majority of cases, converges to an equilibrium. Very interestingly, even in asymmetric scenarios the equilibrium reached suggests that players tend to be symmetric with respect to the peering exchange points and send their asymmetric traffic quota via the transit service providers.
Nash equilibria in load balancing in distributed computer systems
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The use of game theoretical techniques has been quite successful in describing routing in networks, both in road traffic applications as well as in telecommunication networks applications. We study in this paper a third area of applications of such games, which is load balancing in distributed computer systems. One of the most important questions that arise in all applications of routing games is the existence and uniqueness of equilibrium.