Scheduling real-time task graphs on cluster platforms requires efficient utilization of the cluster's resources in order to satisfy the deadlines of the tasks. In this paper, we introduce a new approach to schedule real-time tandem task graphs on a computer cluster. Our approach aims at minimizing the communication time needed to transfer data among the cluster's nodes respecting all the limitations imposed by cluster's network (e.g., limited connectivity of the network topology and limited bandwidth of the communication links). This communication time represents an extra overhead that is added to the execution time of the tasks; hence, an additional processing power is needed to satisfy tasks' deadlines. Minimizing this communication time helps utilize the processing power of the cluster's processors efficiently, and consequently minimize rejection rate of the tasks. We evaluate the performance of our approach through a set of simulation experiments running on heterogeneous cluster environments. The results show that our approach considerably improves acceptance rate of the applications on the cluster.