This work deals with the scheduling problem of a directed acyclic graph with interprocessor communication delays. The objective is to minimize the makespan, taking into account the contention in the network induced by the message routing. We propose two heuristics for solving the scheduling and routing problems onto arbitrary networks, taking into consideration the access con icts to links during the task scheduling. Both heuristics signi cantly improve the performance of the algorithms which do not consider the contention in the network. The comparison of these heuristics is done on problems with di erent granularity levels in regard to execution times and number of needed processors.