In this paper, we present a priority-aware scheduling methodology for concurrent application execution on chip multicore processors. Our methodology improves the performance of up to 4 high-priority applications while also preventing resource starvation for low-priority ones by means of progress-aware scheduling. We compare our results with Linux's completely fair scheduler and two state-of-the-art progress aware schedulers. Experimental results on an Intel Xeon Gold 6130 CPU demonstrate an average increase in high-priority application performance of 36.4% over Linux while also maintaining high throughput for low-priority applications. In addition, we show that our methodology achieves high-priority application performance comparable to a state-of-the-art hardware cache partitioning method (Intel's POCAT). Our method achieves average performance within 14.5% to 0.2% of POCAT without the need for hardware support.