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