Extending the concept of Round Robin algorithm (RR) to incorporate user or system defined priority and consider the case of different arrival times of process and suggesting a novel approach that minimizes context switching overhead, average waiting time and turnaround time. Approach: We calculate Optimum Priority 'OP' for each process which determines the order of execution of processes, Optimum Service Time 'OST' for each process which determines time of execution of process in a single round and execute the processes in RR fashion using the calculated parameters. Results: Based on experiments and calculations, the proposed algorithm is successful in reducing afore mentioned problems. Conclusion: Our proposed algorithm can be effective in priority based systems where burst time and arrival time can be easily predicted.