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Characterizing the existence of potential functions in weighted congestion games
 Proc. 2nd Internat. Sympos. Algorithmic Game Theory, volume 5814 of LNCS, pages 97 – 108
, 2009
"... Abstract Since the pioneering paper of Rosenthal a lot of work has been done in order to determine classes of games that admit a potential. First, we study the existence of potential functions for weighted congestion games. Let C be an arbitrary set of locally bounded functions and let G(C) be the ..."
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Abstract Since the pioneering paper of Rosenthal a lot of work has been done in order to determine classes of games that admit a potential. First, we study the existence of potential functions for weighted congestion games. Let C be an arbitrary set of locally bounded functions and let G(C) be the set of weighted congestion games with cost functions in C. We show that every weighted congestion game G ∈ G(C) admits an exact potential if and only if C contains only affine functions. We also give a similar characterization for wpotentials with the difference that here C consists either of affine functions or of certain exponential functions. We finally extend our characterizations to weighted congestion games with facilitydependent demands and elastic demands, respectively.
Distributed Algorithms for QoS Load Balancing ∗
"... We consider a dynamic load balancing scenario in which users allocate resources in a noncooperative and selfish fashion. The perceived performance of a resource for a user decreases with the number of users that allocate the resource. In our dynamic, concurrent model, users may reallocate resources ..."
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We consider a dynamic load balancing scenario in which users allocate resources in a noncooperative and selfish fashion. The perceived performance of a resource for a user decreases with the number of users that allocate the resource. In our dynamic, concurrent model, users may reallocate resources in a roundbased fashion. As opposed to various settings analyzed in the literature, we assume that users have quality of service (QoS) demands. A user has zero utility when falling short of a certain minimum performance threshold and having positive utility otherwise. Whereas various loadbalancing protocols have been proposed for the setting without quality of service requirements, we consider protocols that satisfy an additional locality constraint: The behavior of a user depends merely on the state of the resource it currently allocates. This property is particularly useful in scenarios where the state of other resources is not readily accessible. For instance, if resources represent channels in a mobile network, then accessing channel information may require timeintensive measurements. We consider several variants of the model, where the quality of service demands may depend on the user, the resource, or both. For all cases we present protocols for which the dynamics converge to a state in which all users are satisfied. More importantly, the time to reach such a state scales nicely. It is only logarithmic in the number of users, which makes our protocols applicable in largescale systems.
Distributed Selfish Load Balancing on Networks
"... We study distributed load balancing in networks with selfish agents. In the simplest model considered here, there are n identical machines represented by vertices in a network and m ≫ n selfish agents that unilaterally decide to move from one vetex to another if this improves their experienced load. ..."
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We study distributed load balancing in networks with selfish agents. In the simplest model considered here, there are n identical machines represented by vertices in a network and m ≫ n selfish agents that unilaterally decide to move from one vetex to another if this improves their experienced load. We present several protocols for concurrent migration that satisfy desirable properties such as being based only on local information and computation and the absence of global coordination or cooperation of agents. Our main contribution is to show rapid convergence of the resulting migration process to states that satisfy different stability or balance criteria. In particular, the convergence time to a Nash equilibrium is only logarithmic in m and polynomial in n, where the polynomial depends on the graph structure. Using a slight modification with neutral moves, a perfectly balanced state can be reached after additional time polynomial in n. Inaddition, we show reduced convergence times to approximate Nash equilibria. Finally, we extend our results to networks of machines with different speeds or to agents that have different weights and show similar results for convergence to approximate and exact Nash equilibria. 1
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.
aachen.de
, 2016
"... We consider a dynamic load balancing scenario in which users allocate resources in a noncooperative and selfish fashion. The perceived performance of a resource for a user decreases with the number of users that allocate the resource. In our dynamic, concurrent model, users may reallocate resour ..."
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We consider a dynamic load balancing scenario in which users allocate resources in a noncooperative and selfish fashion. The perceived performance of a resource for a user decreases with the number of users that allocate the resource. In our dynamic, concurrent model, users may reallocate resources in a roundbased fashion. As opposed to various settings analyzed in the literature, we assume that users have quality of service (QoS) demands. A user has zero utility when falling short of a certain minimum performance threshold and having positive utility otherwise. Whereas various loadbalancing protocols have been proposed for the setting without quality of service requirements, we consider protocols that satisfy an additional locality constraint: The behavior of a user depends merely on the state