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, non-clairvoyant 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.
KeywordsFair scheduling Game theory Algorithm
This work is partly supported by Polish National Science Center Sonata grant UMO-2012/07/D/ST6/02440
- 1.Carroll, T.E., Grosu, D.: Divisible load scheduling: an approach using coalitional games. In: Proceedings of the ISPDC (2007)Google Scholar
- 5.Feitelson, D.G.: Parallel workloads archive. http://www.cs.huji.ac.il/labs/parallel/workload/
- 6.Goyal, P., Vin, H.M., Chen, H.: Start-time fair queueing: a scheduling algorithm for integrated services packet switching networks. In: Proceedings of the SIGCOMM, pp. 157–168 (1996)Google Scholar
- 8.Gulati, A., Ahmad, I., Waldspurger, C.A.: PARDA: proportional allocation of resources for distributed storage access. In: FAST Proceedings, February 2009Google Scholar
- 12.Mashayekhy, L., Grosu, D.: A merge-and-split mechanism for dynamic virtual organization formation in grids. In: PCCC Proceedings, pp. 1–8 (2011)Google Scholar
- 13.Mishra, D., Rangarajan, B.: Cost sharing in a job scheduling problem using the Shapley value. In: Proceedings of the EC, pp. 232–239 (2005)Google Scholar
- 16.Rzadca, K., Trystram, D., Wierzbicki, A.: Fair game-theoretic resource management in dedicated grids. In: CCGRID Proceedings (2007)Google Scholar
- 17.Skowron, P., Rzadca, K.: Non-monetary fair scheduling – cooperative game theory approach. In: SPAA (see also the extended arxiv version) (2013)Google Scholar
- 18.Wang, Y., Merchant, A.: Proportional-share scheduling for distributed storage systems. In: FAST Proceedings, pp. 4–4 (2007)Google Scholar