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27
Routing without regret: On convergence to nash equilibria of regretminimizing algorithms in routing games
 In PODC
, 2006
"... Abstract There has been substantial work developing simple, efficient noregret algorithms for a wideclass of repeated decisionmaking problems including online routing. These are adaptive strategies an individual can use that give strong guarantees on performance even in adversariallychanging envi ..."
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Cited by 47 (6 self)
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Abstract There has been substantial work developing simple, efficient noregret algorithms for a wideclass of repeated decisionmaking problems including online routing. These are adaptive strategies an individual can use that give strong guarantees on performance even in adversariallychanging environments. There has also been substantial work on analyzing properties of Nash equilibria in routing games. In this paper, we consider the question: if each player in a routing game uses a noregret strategy, will behavior converge to a Nash equilibrium? In general games the answer to this question is known to be no in a strong sense, but routing games havesubstantially more structure. In this paper we show that in the Wardrop setting of multicommodity flow and infinitesimalagents, behavior will approach Nash equilibrium (formally, on most days, the cost of the flow will be close to the cost of the cheapest paths possible given that flow) at a rate that dependspolynomially on the players ' regret bounds and the maximum slope of any latency function. We also show that priceofanarchy results may be applied to these approximate equilibria, and alsoconsider the finitesize (noninfinitesimal) loadbalancing model of Azar [2].
Fast convergence to Wardrop equilibria by adaptive sampling methods
 in Proc. 38th Ann. ACM. Symp. on Theory of Comput. (STOC
, 2006
"... We study rerouting policies in a dynamic roundbased variant of a well known game theoretic traffic model due to Wardrop. Previous analyses (mostly in the context of selfish routing) based on Wardrop’s model focus mostly on the static analysis of equilibria. In this paper, we ask the question whethe ..."
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Cited by 43 (8 self)
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We study rerouting policies in a dynamic roundbased variant of a well known game theoretic traffic model due to Wardrop. Previous analyses (mostly in the context of selfish routing) based on Wardrop’s model focus mostly on the static analysis of equilibria. In this paper, we ask the question whether the population of agents responsible for routing the traffic can jointly compute or better learn a Wardrop equilibrium efficiently. The rerouting policies that we study are of the following kind. In each round, each agent samples an alternative routing path and compares the latency on this path with its current latency. If the agent observes that it can improve its latency then it switches with some probability depending on the possible improvement to the better path. We can show various positive results based on a rerouting policy using an adaptive sampling rule that implicitly amplifies paths that carry a large amount of traffic in the Wardrop equilibrium. For general asymmetric games, we show that a simple replication protocol in which agents adopt strategies of more successful agents reaches a certain kind of bicriteria equilibrium within a time bound that is independent of the size and the structure of the network but only depends on a parameter of the latency functions, that we call the relative slope. For symmetric games, this result has an intuitive interpretation: Replication approximately satisfies almost everyone very quickly. In order to achieve convergence to a Wardrop equilibrium besides replication one also needs an exploration component discovering possibly unused strategies. We present a
REPLEX — Dynamic traffic engineering based on Wardrop routing policies
 In Proc. 2nd Conference on Future Networking Technologies (CoNext
, 2006
"... One major challenge in communication networks is the problem of dynamically distributing load in the presence of bursty and hard to predict changes in traffic demands. Current traffic engineering operates on time scales of several hours which is too slow to react to phenomena like flash crowds or BG ..."
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Cited by 20 (4 self)
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One major challenge in communication networks is the problem of dynamically distributing load in the presence of bursty and hard to predict changes in traffic demands. Current traffic engineering operates on time scales of several hours which is too slow to react to phenomena like flash crowds or BGP reroutes. One possible solution is to use load sensitive routing. Yet, interacting routing decisions at short time scales can lead to oscillations, which has prevented load sensitive routing from being deployed since the early experiences in Arpanet. However, recent theoretical results have devised a game theoretical rerouting policy that provably avoids such oscillation and in addition can be shown to converge quickly. In this paper we present REPLEX, a distributed dynamic traffic engineering algorithm based on this policy. Exploiting the fact that most underlying routing protocols support multiple equalcost routes to a destination, it dynamically changes the proportion of traffic that is routed along each path. These proportions are carefully adapted utilising information from periodic measurements and, optionally, information exchanged between the routers about the traffic condition along the path. We evaluate the algorithm via simulations employing traffic loads that mimic actual Web traffic, i. e., bursty TCP traffic, and whose characteristics are consistent with selfsimilarity. The simulations quickly converge and do not exhibit significant oscillations on both artificial as well as real topologies, as can be expected from the theoretical results.
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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Cited by 7 (4 self)
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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.
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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Cited by 5 (0 self)
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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
Tight Bounds for Parallel Randomized Load Balancing
 Computing Research Repository
, 1992
"... We explore the fundamental limits of distributed ballsintobins algorithms, i.e., algorithms where balls act in parallel, as separate agents. This problem was introduced by Adler et al., who showed that nonadaptive and symmetric algorithms cannot reliably perform better than a maximum bin load of Θ ..."
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Cited by 5 (0 self)
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We explore the fundamental limits of distributed ballsintobins algorithms, i.e., algorithms where balls act in parallel, as separate agents. This problem was introduced by Adler et al., who showed that nonadaptive and symmetric algorithms cannot reliably perform better than a maximum bin load of Θ(loglogn/logloglogn) within the same number of rounds. We present an adaptive symmetric algorithm that achieves a bin load of two in log ∗ n + O(1) communication rounds using O(n) messages in total. Moreover, larger bin loads can be traded in for smaller time complexities. We prove a matching lower bound of (1−o(1))log ∗ n on the time complexity of symmetric algorithms that guarantee small bin loads at an asymptotically optimal message complexity of O(n). The essential preconditions of the proof are (i) a limit of O(n) on the total number of messages sent by the algorithm and (ii) anonymity of bins, i.e., the port numberings of balls are not globally consistent. In order to show that our technique yields indeed tight bounds, we provide for each assumption an algorithm violating it, in turn achieving a constant maximum bin load in constant time. As an application, we consider the following problem. Given a fully connected graph of n nodes, where each node needs to send and receive up to n messages, and in each round each node may send one message over each link, deliver all messages as quickly as possible to their destinations. We give a simple and robust algorithm of time complexity O(log ∗ n) for this task and provide a generalization to the case where all nodes initially hold arbitrary sets of messages. Completing the picture, we give a less practical, but asymptotically optimal algorithm terminating within O(1) rounds. All these bounds hold with high probability.
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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Cited by 4 (3 self)
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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.
SLAOriented Management of Containers for Hosting Stateful Web Services
 in proceedings of the 3rd IEEE International Conference on eScience and Grid Computing
, 2007
"... ServiceOriented Architectures provide integration of interoperability for independent and loosely coupled services. Web services and the associated new standards such as WSRF are frequently used to realise such ServiceOriented Architectures. In such systems, autonomic principles of selfconfigurat ..."
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Cited by 3 (2 self)
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ServiceOriented Architectures provide integration of interoperability for independent and loosely coupled services. Web services and the associated new standards such as WSRF are frequently used to realise such ServiceOriented Architectures. In such systems, autonomic principles of selfconfiguration, selfoptimisation, selfhealing and selfadapting are desirable to ease management and improve robustness. In this paper we focus on the extension of the self management and autonomic behaviour of a WSRF container connected by a structured P2P overlay network to monitor and rectify its QoS to satisfy its SLAs. The SLA plays an important role during two distinct phases in the lifecycle of a WSRF container. Firstly during service deployment when services are assigned to containers in such a way as to minimise the threat of SLA violations, and secondly during maintenance when violations are detected and services are migrated to other containers to preserve QoS. In addition, as the architecture has been designed and built using standardised modern technologies and with high levels of transparency, conventional web services can be deployed with the addition of a SLA specification. 1.
Concurrent Imitation Dynamics in Congestion Games
, 2008
"... Imitating successful behavior is a natural and frequently applied approach to trust in when facing scenarios for which we have little or no experience upon which we can base our decision. In this paper, we consider such behavior in atomic congestion games. We propose to study concurrent imitation dy ..."
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Cited by 3 (3 self)
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Imitating successful behavior is a natural and frequently applied approach to trust in when facing scenarios for which we have little or no experience upon which we can base our decision. In this paper, we consider such behavior in atomic congestion games. We propose to study concurrent imitation dynamics that emerge when each player samples another player and possibly imitates this agents ’ strategy if the anticipated latency gain is sufficiently large. Our main focus is on convergence properties. Using a potential function argument, we show that our dynamics converge in a monotonic fashion to stable states. In such a state none of the players can improve its latency by imitating somebody else. As our main result, we show rapid convergence to approximate equilibria. At an approximate equilibrium only a small fraction of agents sustains a latency significantly above or below average. In particular, imitation dynamics behave like fully polynomial time approximation schemes (FPTAS). Fixing all other parameters, the convergence time depends only in a logarithmic fashion on the number of agents. Since imitation processes are not innovative they cannot discover unused strategies. Furthermore, strategies may become extinct with nonzero probability. For the case of singleton games, we show that the probability of this event occurring is negligible. Additionally, we prove that the social cost of a stable state reached by our dynamics is not much worse than an optimal state in singleton congestion games with linear latency function. Finally, we discuss how the protocol can be extended such that, in the long run, dynamics converge to a Nash equilibrium.
Engineering an Autonomic Container for WSRFbased Web Services
 in proceedings of the 15th International Conference on Advanced Computing and Communication (ADCOM
, 2007
"... This paper presents an autonomic Web Service Resource Framework (WSRF) container that enables selfconfiguration using IBM’s autonomic computing (AC) architecture and resolves Quality of Service (QoS) problems through service migration. The migration manager bases its decisions on an overall health s ..."
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Cited by 2 (2 self)
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This paper presents an autonomic Web Service Resource Framework (WSRF) container that enables selfconfiguration using IBM’s autonomic computing (AC) architecture and resolves Quality of Service (QoS) problems through service migration. The migration manager bases its decisions on an overall health status metric (Hmetric). The Hmetric characterises the health of a service container. A unified AC sensor/effector interface, protocol, and metric summarization allows us to build up a hierarchical WSRF container structure to create a virtualized WSRF container. 1.