In chip multiprocessor (CMP) systems with multi-application workloads, communication and memory access both play an important role in influencing system performance. Intelligently prioritizing network packets and memory requests can notably improve system throughput. But with increasing workload diversity in CMPs, applying the same request prioritization rules across the chip can lead to sub-optimal results. In this paper, we propose a novel heterogeneous prioritization framework for CMPs in which two different packet prioritization approaches are proposed and applied to network-on-chip (NoC) routers. A new ranking scheme for classifying an application’s criticality is also proposed. We evaluate our framework using a detailed cycle-accurate full system event-driven simulator. Our experimental results show that the proposed framework outperforms fair prioritization techniques by up to 12.6% as well as other application-specific techniques from prior literature by up to 6.9% for various multi-application workloads.