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Resources of a multi-user system in multi-processor online scheduling areshared by competing users in which fairness is a major performance criterionfor resource allocation. Fairness ensures equality in resource sharing amongthe users. According to our knowledge, fairness based on the user's objectivehas neither been comprehensively studied nor a formal fairness model has beenwell defined in the literature. This motivates us to explore and define a newmodel to ensure algorithmic fairness with quantitative performance measuresbased on optimization of the user's objective. In this paper, we propose a newmodel for fairness in Multi-user Multi-processor Online SchedulingProblem(MUMPOSP). We introduce and formally define quantitative fairnessmeasures based on user's objective by optimizing makespan for individual userin our proposed fairness model. We also define the unfairness of deprived usersand absolute fairness of an algorithm. We obtain lower bound results for theabsolute fairness for m identical machines with equal length jobs. We show thatour proposed fairness model can serve as a framework for measuring algorithmicfairness by considering various optimality criteria such as flow time and sumof completion times.

A New Fairness Model based on User's Objective for Multi-user Multi-processor Online Scheduling