On-chip networks (NoCs) used in multiprocessor systems-on-chips (MPSoCs) pose significant challenges to both on-line (dynamic) and off-line (static) real-time scheduling approaches. They have large numbers of potential contention points, have limited internal buffering capabilities, and network control operates at the scale of small data packets. Therefore, efficient resource allocation requires requires scalable algorithms working on hardware models with a level of detail that is unprecedented in real-time scheduling. We consider here a static scheduling approach, and we target massively parallel processor arrays (MPPAs), which are MPSoCs with large numbers (hundreds) of processing cores. We first identify and compare the hardware mechanisms supporting precise timing analysis and efficient resource allocation in existing MPPA platforms. We determine that the NoC should ideally provide the means of enforcing a global communications schedule that is computed off-line (before execution) and which is synchronized with the scheduling of computations on processors. On the software side, we propose a novel allocation and scheduling method capable of synthesizing such global computation and communication schedules covering all the execution, communication, and memory resources in an MPPA. To allow an efficient use of the hardware resources, our method takes into account the specificities of MPPA hardware and implements advanced scheduling techniques such as software pipelining and pre-computed preemption of data transmissions. We evaluate our technique by mapping two signal processing applications, for which we obtain good latency, throughput, and resource use figures.