Load Balancing Game Research Articles

Machine Load Balancing Game with Linear Externalities

Machine Load Balancing Game with Linear Externalities

Nash Social Welfare in Selfish and Online Load Balancing

In load-balancing problems there is a set of clients, each wishing to select a resource from a set of permissible ones to execute a certain task. Each resource has a latency function, which depends on its workload, and a client’s cost is the completion time of her chosen resource. Two fundamental variants of load-balancing problems are selfish load balancing (a.k.a. load-balancing games ), where clients are non-cooperative selfish players aimed at minimizing their own cost solely, and online load balancing , where clients appear online and have to be irrevocably assigned to a resource without any knowledge about future requests. We revisit both problems under the objective of minimizing the Nash Social Welfare , i.e., the geometric mean of the clients’ costs. To the best of our knowledge, despite being a celebrated welfare estimator in many social contexts, the Nash Social Welfare has not been considered so far as a benchmarking quality measure in load-balancing problems. We provide tight bounds on the price of anarchy of pure Nash equilibria and on the competitive ratio of the greedy algorithm under very general latency functions, including polynomial ones. For this particular class, we also prove that the greedy strategy is optimal, as it matches the performance of any possible online algorithm.

Machine load balancing game with linear externalities

The Machine Load Balancing Game with linear externalities is considered. A set of jobs is to be assigned to a set of machines with different latencies depending on their own loads and also loads on other machines. Jobs choose machines to minimize their own latencies. The social cost of a schedule is the maximum delay among all machines, i.e. {\it makespan. For the case of two machines in this model an Nash equilibrium existence is proven and of the expression for the Price of Anarchy is obtained.

Optimal Taxes in Atomic Congestion Games

How can we design mechanisms to promote efficient use of shared resources? Here, we answer this question in relation to the well-studied class of atomic congestion games, used to model a variety of problems, including traffic routing. Within this context, a methodology for designing tolling mechanisms that minimize the system inefficiency (price of anarchy) exploiting solely local information is so far missing in spite of the scientific interest. In this article, we resolve this problem through a tractable linear programming formulation that applies to and beyond polynomial congestion games. When specializing our approach to the polynomial case, we obtain tight values for the optimal price of anarchy and corresponding tolls, uncovering an unexpected link with load balancing games. We also derive optimal tolling mechanisms that are constant with the congestion level, generalizing the results of Caragiannis et al. [8] to polynomial congestion games and beyond. Finally, we apply our techniques to compute the efficiency of the marginal cost mechanism. Surprisingly, optimal tolling mechanism using only local information perform closely to existing mechanism that utilize global information, e.g., Bilò and Vinci [6], while the marginal cost mechanism, known to be optimal in the continuous-flow model, has lower efficiency than that encountered levying no toll. All results are tight for pure Nash equilibria and extend to coarse correlated equilibria.

Computing the Price of Anarchy in Processor Load Balancing Game with Linear Delays

This paper considers a generalization of the processor load balancing game also known as KP-model. A linear delay of a processor may depend on not only its load but on loads of other processors. Players choose processors of different speeds to run their jobs striving to minimize job's delay, i.e., the job completion time on a chosen processor. The social cost is the maximum delay over all processors. We propose a computing algorithm of the exact PoA value which can be applied to estimate the POA visually if its exact analytical expression is not obtained yet or it is rather complicated to figure out its formula.

Design and Implementation of Load Balancing Game Theory for the Efficient Public Cloud

Design and Implementation of Load Balancing Game Theory for the Efficient Public Cloud

The efficiency of Nash equilibria in the load balancing game with a randomizing scheduler

We study the efficiency of Nash equilibria for the load balancing game with a randomizing scheduler. In the game, we are given a set of facilities and a set of players along with a scheduler, where each facility is associated with a linear cost function, and the players are randomly ordered by the scheduler. Each player chooses exactly one of these facilities to fulfill his task, which incurs to him a cost depending on not only the cost function of the facility he chooses and the players who choose the same facility (as in a usual load balancing game), but also his uncertain position in the uniform random ordering. From an individual perspective, each player tries to choose a facility for optimizing his own objective that is determined by a certain decision-making principle. From a system perspective, it is desirable to minimize the maximum cost among all players, which is a commonly used criterion for load balancing. We estimate the price of anarchy and price of stability for this class of load balancing games under uncertainty, provided all players follow one of the four decision-making principles, namely the bottom-out, win-or-go-home, minimum-expected-cost, and minimax-regret principles. Our results show that the efficiency loss of Nash equilibria in these decentralized environments heavily rely on player's attitude toward the uncertainty.

Coalitions in Routing Games: A Worst-Case Perspective

We investigate a routing game that allows for the creation of coalitions, within the framework of cooperative game theory. Specifically, we describe the cost of each coalition as its maximin value. This represents the performance that the coalition can guarantee itself, under any (including worst) conditions. We then investigate fundamental solution concepts of the considered cooperative game, namely the core and a variant of the min-max fair nucleolus . We consider two types of routing games based on the agents’ Performance Objectives, namely bottleneck routing games and additive routing games . For bottleneck games, we establish that the core includes all system-optimal flow profiles and that the nucleolus is system-optimal or disadvantageous for the smallest agent in the system. Moreover, we describe an interesting set of scenarios for which the nucleolus is always system-optimal. For additive games, we focus on the fundamental load balancing game of routing over parallel links. We establish that, contrary to bottleneck games, not all system-optimal flow profiles lie in the core. However, we describe a specific system-optimal flow profile that does lie in the core and, under assumptions of symmetry, is equal to the nucleolus.

Selfish load balancing for jobs with favorite machines

This paper studies the load balancing game for the favorite machine model, where each job has a certain set of favorite machines with the shortest processing time for the job. We obtain tight bounds on the Strong Price of Anarchy (strong PoA) for the general favorite machine model and a special case of the model. Our results generalize the well-known bounds on the strong PoA for the unrelated machine and identical machine models.

Efficiency analysis with respect to the unit cost objectives in scheduling games

We study two models of scheduling games: load-balancing games with and without activation costs, respectively. The inefficiency of equilibria is measured with two new and more reasonable social objectives: the maximum and the average of all players’ unit costs, respectively. For each game problem and each social objective, we provide parametric bounds on the PoA and the PoS and conclude that the loss of efficiency of equilibria with the new unit cost objectives is even more severe than that with the traditional objectives which focus on the costs of the players.

Non-cooperative power and latency aware load balancing in distributed data centers

In this paper we propose an algorithm for load balancing in distributed data centers based on game theory. We model the load balancing problem as a non-cooperative game among the front-end proxy servers. We model the operating cost associated with a data center as a weighted linear combination of the energy cost and the latency cost. We propose a non-cooperative load balancing game with the objective of minimizing the operating cost and obtain the structure of Nash equilibrium. Based on this structure, a distributed load balancing algorithm is designed. We compare the performance of the proposed algorithm with the existing approaches. Numerical results demonstrate that the solution achieved by the proposed algorithm approximates the global optimal solution in terms of the cost and it also ensures fairness among the users.

Load Balancing Game With Shadowing Effect for Indoor Hybrid LiFi/RF Networks

Light Fidelity (LiFi) is a recently proposed technology that uses 300 THz visible light spectrum for high speed wireless communications as well as providing illumination. Basically, a LiFi access point (AP) covers only a few square meters, enabling a dense deployment of LiFi APs to improve the network throughput. However, channel blockage and shadowing in conjunction with inter-cell interference compromise the connectivity and system throughput of LiFi networks. In this paper, a network structure that combines LiFi with the conventional radio frequency (RF) system is considered. Users experiencing strong blockages can be switched to the RF system to achieve a higher data rate. In this paper, blockages, random orientation of LiFi receivers, and the user data rate requirement are characterised to model a practical communication scenario. A novel load balancing (LB) scheme based on evolutionary game theory is proposed for hybrid LiFi/RF networks. The performance of the proposed scheme is comprehensively analyzed. Results show that compared to state-of-the-art LB algorithms, the proposed scheme greatly improves user satisfaction levels at reduced computational complexity. Also, an optimal orientation of LiFi receivers and blockage density in hybrid networks would maximize the users quality of service.

A combination of game theory and genetic algorithm for load balancing in distributed computer systems

High demand of computation and communication in recent decades has increased the importance of distributed computer systems. Because of the heterogeneity of resources, resource management is one of the main challenges in designing distributed computer systems. In this paper, a new method has been proposed for solving load balancing problem in distributed computer systems using game theory and a genetic algorithm. The load balancing problem has been modelled as a non-cooperative game among users of the system. The payoff function of players was computed using an introduced parameter in order to decrease the users' expected response time. Certain Nash equilibriums are unstable in a multi agent problem. Thus, a genetic algorithm based on the concept of Nash equilibrium is used for solving the load balancing game. Simulation results show the performance of the proposed load balancing algorithm in terms of the expected response time and fairness index as parameters in evaluating the performance of load balancing algorithms.

A combination of game theory and genetic algorithm for load balancing in distributed computer systems

High demand of computation and communication in recent decades has increased the importance of distributed computer systems. Because of the heterogeneity of resources, resource management is one of the main challenges in designing distributed computer systems. In this paper, a new method has been proposed for solving load balancing problem in distributed computer systems using game theory and a genetic algorithm. The load balancing problem has been modelled as a non-cooperative game among users of the system. The payoff function of players was computed using an introduced parameter in order to decrease the users' expected response time. Certain Nash equilibriums are unstable in a multi agent problem. Thus, a genetic algorithm based on the concept of Nash equilibrium is used for solving the load balancing game. Simulation results show the performance of the proposed load balancing algorithm in terms of the expected response time and fairness index as parameters in evaluating the performance of load balancing algorithms.

How Good is Bargained Routing?

In the context of networking, research has focused on non-cooperative games, where the selfish agents cannot reach a binding agreement on the way they would share the infrastructure. Many approaches have been proposed for mitigating the typically inefficient operating points. However, in a growing number of networking scenarios, selfish agents are able to communicate and reach an agreement. Hence, the degradation of performance should be considered at an operating point of a cooperative game. Accordingly, our goal is to lay foundations for the application of the cooperative game theory to fundamental problems in networking. We explain our choice of the Nash bargaining scheme (NBS) as the solution concept, and introduce the price of selfishness (PoS), which considers the degradation of performance at the worst NBS. We focus on the fundamental load balancing game of routing over parallel links. First, we consider agents with identical performance objectives. We show that, while the price of anarchy (PoA) here can be large, through bargaining, all agents, and the system, strictly improve their performance. Interestingly, in a two-agent system or when all the agents have identical demands, we establish that they reach social optimality. We then consider agents with different performance objectives and demonstrate that the PoS and PoA can be unbounded, yet we explain why both measures are unsuitable. Accordingly, we introduce the price of heterogeneity (PoH), as an extension of the PoA. We establish an upper bound on the PoH and indicate its further motivation for bargaining. Finally, we discuss network design guidelines that follow from our findings.

Generalized mirror descents in congestion games

Different types of dynamics have been studied in repeated game play, and one of them which has received much attention recently consists of those based on “no-regret” algorithms from the area of machine learning. It is known that dynamics based on generic no-regret algorithms may not converge to Nash equilibria in general, but to a larger set of outcomes, namely coarse correlated equilibria. Moreover, convergence results based on generic no-regret algorithms typically use a weaker notion of convergence: the convergence of the average plays instead of the actual plays. Some work has been done showing that when using a specific no-regret algorithm, the well-known multiplicative updates algorithm, convergence of actual plays to equilibria can be shown and better quality of outcomes in terms of the price of anarchy can be reached for atomic congestion games and load balancing games. Are there more cases of natural no-regret dynamics that perform well in suitable classes of games in terms of convergence and quality of outcomes that the dynamics converge to?We answer this question positively in the bulletin-board model by showing that when employing the mirror-descent algorithm, a well-known generic no-regret algorithm, the actual plays converge quickly to equilibria in nonatomic congestion games. This gives rise to a family of algorithms, including the multiplicative updates algorithm and the gradient descent algorithm as well as many others. Furthermore, we show that our dynamics achieves good bounds on the outcome quality in terms of the price-of-anarchy type of measures with two different social costs: the average individual cost and the maximum individual cost.Finally, the bandit model considers a probably more realistic and prevalent setting with only partial information, in which at each time step each player only knows the cost of her own currently played strategy, but not any costs of unplayed strategies. For the class of atomic congestion games, we propose a family of bandit algorithms based on the mirror-descent algorithms previously presented, and show that when each player individually adopts such a bandit algorithm, their joint (mixed) strategy profile quickly converges with implications.

Tighter bounds on the inefficiency ratio of stable equilibria in load balancing games

In this paper we study the inefficiency ratio of stable equilibria in load balancing games introduced by Asadpour and Saberi (2009). We prove tighter lower and upper bounds of 7/6 and 4/3, respectively. This improves over the best known bounds for the problem (19/18 and 3/2, respectively). Equivalently, the results apply to the question of how well the optimum for the L2-norm can approximate the L∞-norm (makespan) in identical machines scheduling.

PERFORMANCE OF NON-COOPERATIVE ROUTING OVER PARALLEL NON-OBSERVABLE QUEUES

Autonomic computing is emerging as a significant new approach to the design of computer services. Its goal is the development of services that are able to manage themselves with minimal direct human intervention, and, in particular, are able to sense their environment and to tune themselves to meet end-user needs. However, the impact on performance of the interaction between multiple uncoordinated self-optimizing services is not yet well understood. We present some recent results on a non-cooperative load-balancing game which help to better understand the result of this interaction. In this game, users generate jobs of different services, and the jobs have to be processed on one of the servers of a computing platform. Each service has its own dispatcher which probabilistically routes jobs to servers so as to minimize the mean processing cost of its own jobs. We first investigate the impact of heterogeneity in the amount of incoming traffic routed by dispatchers and present a result stating that, for a fixed amount of total incoming traffic, the worst-case overall performance occurs when each dispatcher routes the same amount of traffic. Using this result we then study the so-called Price of Anarchy (PoA), an oft-used worst-case measure of the inefficiency of non-cooperative decentralized architectures. We give explicit bounds on the PoA for cost functions representing the mean delay of jobs when the service discipline is PS or SRPT. These bounds indicate that significant performance degradations can result from the selfish behavior of self-optimizing services. In practice, though, the worst-case scenario may occur rarely, if at all. Some recent results suggest that for the game under consideration the PoA is an overly pessimistic measure that does not reflect the performance obtained in most instances of the problem.

Load rebalancing games in dynamic systems with migration costs

We consider the following dynamic load balancing game: Given an initial assignment of jobs to identical parallel machines, the system is modified; specifically, some machines are added or removed. Each job's cost is the load on the machine it is assigned to; thus, when machines are added, jobs have an incentive to migrate to the new unloaded machines. When machines are removed, the jobs assigned to them must be reassigned. Consequently, other jobs might also benefit from migrations. In our job-extension penalty model, for a given extension parameterδ≥0, if the machine on which a job is assigned to in the modified schedule is different from its initial machine, then the job's processing time is extended by δ.We provide answers to the basic questions arising in this model. Namely, the existence and calculation of a Nash Equilibrium and a Strong Nash Equilibrium, and their inefficiency compared to an optimal schedule. Our results show that the existence of job-migration penalties might lead to poor stable schedules; however, if the modification is a result of a sequence of improvement steps or, better, if the sequence of improvement steps can be supervised in some way (by forcing the jobs to play in a specific order) then any stable modified schedule approximates well an optimal one.Our work adds two realistic considerations to the study of job scheduling games: the analysis of the common situation in which systems are upgraded or suffer from failures, and the practical fact according to which job migrations are associated with a cost.

Offload Decision Models and the Price of Anarchy in Mobile Cloud Application Ecosystems

With the maturity of technologies, such as HTML5 and JavaScript, and with the increasing popularity of cross-platform frameworks, such as Apache Cordova, mobile cloud computing as a new design paradigm of mobile application developments is becoming increasingly more accessible to developers. Following this trend, future on-device mobile application ecosystems will not only comprise a mixture of native and remote applications, but also include multiple hybrid mobile cloud applications. The resource competition in such ecosystems and its impact over the performance of mobile cloud applications has not yet been studied. In this paper, we study this competition from a game theoretical perspective and examine how it affects the behavior of mobile cloud applications. Three offload decision models of cooperative and non-cooperative nature are constructed and their efficiency compared. We present an extension to the classic load balancing game to model the offload behaviors within a non-cooperative environment. Mixed-strategy Nash equilibria are derived for the non-cooperative offload game with complete information, which further quantifies the price of anarchy in such ecosystems. We present simulation results that demonstrate the differences between each decision model’s efficiency. Our modeling approach facilitates further research in the design of the offload decision engines of mobile cloud applications. Our extension to the classic load balancing game broadens its applicability to real-life applications.