Multiple applications that execute concurrently on heterogeneous platforms compete for CPU and network resources. In this paper we consider the problem of scheduling applications to ensure fair and efficient execution on master-worker platforms where the communication is restricted to a tree embedded in the network. The goal of the scheduling is to obtain the best throughput while enforcing some fairness between applications. We show how to derive an asymptotically optimal periodic schedule by solving a linear program expressing all problem constraints. For single-level trees, the optimal solution can be analytically computed. For large-scale platforms, gathering the global knowledge needed by the linear programming approach might be unrealistic. One solution is to adapt the multi-commodity flow algorithm of Awerbuch and Leighton, but it still requires some global knowledge. Thus, we also investigates heuristic solutions using only local information, and test them via simulations. The best of our heuristics achieves the optimal performance on about two-thirds of our test cases, but is far worse in a few cases.