In a heterogeneous distributed system made out of different kinds of computing platforms, for example, supercomputers, gird, and clouds, a two-level scheduling methodology can be utilized to effectively distributed resources of the platforms to clients in the first level, and map tasks of the clients in nodes for every platform in the second-level for executing many-task applications. When scheduling heterogeneous assets, specialist co-ops of the system ought to think about the fairness among various clients and also the system effectiveness. Be that as it may, the fairness can’t be achieved by only distributing an equal amount of resources from every platform to each client. In this project, we examine how to address the fairness issue among different clients in a heterogeneous distributed system. We exhibit three first-level resource allocation approaches of a supplier affinity first policy, an application affinity first strategy, and a platform affinity based round-robin strategy, and two second-level task mapping strategies of a most influenced first policy and a co-runner affinity based round-robin policy. Utilizing trace-based simulations, we assess the execution of different combinations of the first and second level schedulings. Our broad simulation comes about the exhibit that the first level policy assumes an essential part to achieve relatively good fairness.