Public clouds provide Infrastructure as a Service (IaaS) to users who do not own sufficient compute resources. It faces the problem of the scheduling tasks to meet the peak demand while preserving Quality-of-Service (QoS). Randomized selection of resources and allocated the tasks and execute within the given start and end time. And also allocated the task to the resources based on workload and payment process. Each resource had the cost to work. The primary objective is to minimize the time overlapping of the tasks assigned to a given resource.And another one is to maximize the time overlapping among tasks assigned to different resources. We use the Fair Scheduling algorithm to perform this process to select the resource based on task workload. Each task has a strict deadline to meet, so that the resource allocation problem can be considered as a deadline constrained task scheduling (DCTS) one. An integer programming formulation of the DCTS problem is established, with the objective of maximizing the profit of the private cloud on the premise of guaranteeing QoS. while increases exponentially with the growth of the number of tasks, using the fair scheduling process based scheduling approach is proposed to solve this problem. It will increase the profit and also increase the problems of nontrivial size.