A Game-Theoretic Analysis of Grid Job Scheduling

Computational Grid is a well-established platform that gives an assurance to provide a vast range of heterogeneous resources for high performance computing. Efficient and effective resource management and Grid job scheduling are key requirements in order to optimize the use of the resources and to take full advantage from Grid systems. In this paper, we study the job scheduling problem in Computational Grid by using a game-theoretic approach. Grid resources are usually owned by different organizations which may have different and possibly conflicting concerns. Thus it is a crucial objective to analyze potential scenarios where selfish or cooperative behaviors of organizations impact heavily on global Grid efficiency. To this purpose, we formulate a repeated non-cooperative job scheduling game, whose players are Grid sites and whose strategies are scheduling algorithms. We exploit the concept of Nash equilibrium to express a situation in which no player can gain any profit by unilaterally changing its strategy. We extend and complement our previous work by showing whether, under certain circumstances, each investigated strategy is a Nash equilibrium or not. In the negative case we give a counter-example, in the positive case we either give a formal proof or motivate our conjecture by experimental results supported by simulations and exhaustive search.