High-Throughput Computing (HTC) and Many-Task Computing (MTC) paradigms employ loosely coupled applications which consist of a large number, from tens of thousands to even billions, of independent tasks. To support such large-scale applications, a heterogeneous computing system composed of multiple computing platforms with different types such as supercomputers, grids, and clouds can be used. On allocating heterogeneous resources of the system to multiple users, there arethree important aspects to consider: fairness among users, efficiency for maximizing the system throughput, and user satisfaction for reducing the average user response time. In this paper, we present three resource allocation policies for multi-user and multi-application workloads in a heterogeneous computing system. These three policies are a fairness policy, a greedy efficiency policy, and a fair efficiency policy. We evaluate and compare the performance of the three resource allocation policies over various settings ofa heterogeneous computing system and loosely coupled applications, using simulation based on the trace from real experiments. Our simulation results show that the fair efficiency policy can provide competitive efficiency, with a balanced level of fairness and user satisfaction, compared to the other two resource allocation policies.