Fair Share Is Not Enough: Measuring Fairness in Scheduling with Cooperative Game Theory

We consider the problem of fair scheduling in a multi-organizational system in which organizations contribute their own resources to the global pool and the jobs to be processed on the common resources. We consider on-line, nonclairvoyant scheduling of sequential jobs without preemption. To ensure that the organizations are willing to cooperate the scheduling algorithm must be fair. To characterize fairness, we use a cooperative game theory approach. The contribution of an organization is computed based on how this organization influences the utility (which can be any metric, e.g., flow time, turnaround, resource allocation) of all organizations. Formally, the contribution of the organization is its Shapley value in the cooperative game. The scheduling algorithm should ensure that the contributions of the organizations are close to their utilities. Our previous work proves that this problem is NP-hard and hard to approximate. In this paper we propose a heuristic scheduling algorithm for the fair scheduling problem. We experimentally evaluate the heuristic and compare its fairness to fair share, round robin and the exact exponential algorithm. Our results show that fairness of the heuristic algorithm is close to the optimal. The difference between our heuristic and the fair share algorithm is more visible on longer traces with more organizations. These results show that assigning static target shares (as in the fair share algorithm) is not fair in multi-organizational systems and that instead dynamic measures of organizations’ contributions should be used. keywords: fair scheduling, game theory, algorithm