Predictability of task execution is paramount for real-time systems so that upper bounds of execution times can be determined via static timing analysis. Static timing analysis on network-on-chip (NoC) processors may result in unsafe underestimations when the underlying communication paths are not considered. This stems from contention on the underlying network when data from multiple sources share parts of a routing path in the NoC. Contention analysis must be performed to provide safe and reliable bounds. In addition, the overhead incurred by contention due to inter- process communication (IPC) can be reduced by mapping tasks to cores in such a way that contention is minimized. This paper makes several contributions to increase pre- dictability of real-time tasks on NoC architectures. First, we contribute a constraint solver that exhaustively maps real- time tasks onto cores to minimize contention and improve predictability. Second, we develop a novel TDMA-like approach to map communication traces into time frames to ensure separation of analysis for temporally disjoint communication. Third, we contribute a novel multi-heuristic ap- proximation, HSolver, for rapid discovery of low contention solutions. HSolver reduces contention by up to 70% when compared with na ̈ıve and constrained exhaustive solutions. We evaluate our experiments using a micro-benchmark of task system IPC on the TilePro64, a real, physical NoC processor with 64 cores. To the best of our knowledge, this is the first work to consider IPC for worst-case time frames to simplify analysis and to measure the impact on actual hardware for NoC-based real-time multicore systems.