Priority-aware networks-on-chip (NoCs) are used in industry to achieve predictable latency under different workload conditions. These NoCs incorporate deflection routing to minimize queuing resources within routers and achieve low latency during low traffic load. However, deflected packets can exacerbate congestion during high traffic load since they consume the NoC bandwidth. State-of-the-art analytical models for priority-aware NoCs ignore deflected traffic despite its significant latency impact during congestion. This paper proposes a novel analytical approach to estimate end-to-end latency of priority-aware NoCs with deflection routing under bursty and heavy traffic scenarios. Experimental evaluations show that the proposed technique outperforms alternative approaches and estimates the average latency for real applications with less than 8% error compared to cycle-accurate simulations.