A scheduling Algorithm based on Potential Game for a Cluster Grid Massimo Orazio Spata, Salvatore Rinaudo A scheduling Algorithm based on Potential Game for a Cluster Grid Massimo Orazio Spata, Salvatore Rinaudo STMicroelectronics, Catania, 95121, Italy massimo.spata@st.com, salvatore.rinaudo@st.com doi: 10.4156/jcit.vol4.issue3.4 Abstract This paper introduces an algorithm whose aim is to increase scheduling efficiency on a distributed system like a Cluster Grid. In order to measure this efficiency, we have classified jobs in homogeneous classes and observed the throughput on homogeneous class of compute server. The scheduler is based on a defined Potential function applied to the Prisoner’s Dilemma problem of the Game Theory and this approach allows avoiding inefficiency caused by generic greedy scheduler policies. Moreover for this kind of games, we have verified that all Nash equilibrium solutions correspond to the Potential Function minimum. Keywords Cluster Grid; Game Theory; Potential Games; Scheduling. 1. Introduction 1.1 The problem and the proposed solution In a distributed system like a cluster grid, it is very difficult to define a transparent system approach to resource management for Grid users; this is due to Grid heterogeneous architectural characteristics. In fact, one of the most important limits of a Grid regards the absolute absence of transparency for the users during job scheduling. To resolve this problem, in this paper “Potential Games” paradigm is proposed for managing Grid resources. Moreover this proposed solution, should supplies an automated synchronization of computational reservation in order to manage concurrent access to shared resources. 1.2 Related studies Prior art related to this research is reported in [1], [2] and [3]. In [1], it is considered the scheduling of n independent jobs on m non-identical machines. The main contributions in this paper include generating schedules in a concrete scheduled space using ideas taken from game theory and multi-agent. In [2], three different methods are compared: Optimal, Nash, and Greedy. The results show that price of anarchy focuses on the worst-case equilibrium solution. We could consider the best Nash solution, the closest to the social optimum, whereas greedy algorithm approach is a myopic strategy, because each client makes the best choice available at the moment. In [3], “Nash Equilibrium” solution paradigm is used to manage Grid resources as in a Microeconomic model, where users make decisions to allocate limited resources, typically as in a Grid where goods or services should be negotiated. But, Game Theory Nash Equilibrium solution for the Prisoner’s Dilemma Problem could become computationally complex, requiring an exponential amount of time, to schedule a job. In order to solve this inefficiency problem, Hart and Mas-Colell have proposed in [10] a characterization of Shapley value (Symmetric Games) through the Potential Function idea. They have been demonstrated that we can found a function P=P(N,v), defined for every game G for every set of player and for which P(0)=0 (normalization condition). The P Function has been named Potential Function because it is a discrete “derivata” version referred to number of players of the Game. The Shapley value for every game associates a vector with n coordinates, obtaining for each game a scalar P, using a single number instead of a vector (exactly as classic Gravitation Theory where Gravitation Potential function for every point associates a scalar ie a number). Moreover for this kind of games, we have verified that all Nash equilibrium solutions correspond to the Potential Function minimum. 2. Strategic Game Form and Nash Equilibrium In [4] a strategic game form G, with two players is: (X,Y,E,h) where: 34