A large class of embedded systems today which concurrently execute numerous independent QoS sensitive applications like streaming audio and video, web browsing, email, interactive gaming etc. Have proportional share schedulers at their heart as the principal resource multiplexing strategy. However, producing schedulers that have both low scheduling overheads as well as good proportional share allocation accuracy have proved to be a daunting task. On one hand, we have schemes that provide optimal task allocation fairness accuracy, but generally suffer scheduling overheads that are at least logarithmic to the number of tasks. On the other hand there are O (1) complexity round-robin based algorithms, but they generally fail to provide good fairness properties. This paper presents Partitioned Proportional Round-Robin (PPRR), a two level hierarchical O (1) proportional share scheduler that achieves near optimal fairness accuracy while executing a mix of jobs with varying priorities in most practical scenarios. Simulation based experimental results reveal that even on systems containing up to 50 tasks with skewed execution rate requirements, a PPRR scheduler with just eight groups is able to provide less than about one percent deviation per task with respect to their ideal execution rates.