In the Soft Real-Time System scheduling process with the processor is a critical task. The system schedules the processes on a processor in a time interval, and hence the processes get chance to executes on the processor. Priority-driven scheduling algorithms are sub-categorized into mainly two categories called Static Priority and Dynamic Priority Scheduler. Critical Analysis of more static and dynamic priority scheduling algorithms have been discussed in this paper. This paper has covered the static priority algorithms like Rate Monotonic (RM) and Shortest Job First (SJF) and the dynamic priority algorithms like Earliest Deadline First (EDF) and Least Slack Time First (LST). These all algorithms have been analyzed with preemptive process set and this paper has considered all the process set are periodic. This paper has also proposed a hybrid approach for efficient scheduling. In a critical analysis, it has been observed that while scheduling in underload situation dynamic priority algorithms perform well and even EDF also make sure that all process will meet their deadline. However, in an overload situation, the performance of dynamic priority algorithms reduce quickly, and most of the task will miss its deadline, whereas static priority scheduling algorithms miss a few deadlines, even it is possible to schedule all processes in underload situation, whereas in an overload situation, the static algorithms perform well compared to the dynamic scheduler. This paper is proposing one Hybrid algorithm call S_LST which uses the concept of LST and SJF scheduling algorithm. This algorithm has been applied to the periodic task set, and observations are registered. We have observed the Success Ratio (SR) & Effective CPU Utilization (ECU) and compared all algorithms in the same conditions. It is noted that instead of using LST and SJF as an independent algorithm, Hybrid algorithm S_LST performs well in underload and overload scenario. Practical investigations have been led on a huge dataset. Data Set consists of the 7000+ process set, and each process set has one to nine processes and load varies between 0.5 to 5. It has been tried on 500-time unit to approve the rightness everything being equal.