Heuristic scheduling algorithms designed based on properties of optimal algorithm for soft real-time tasks

A soft real-time task is one whose completion time is recommended by a specific deadline. However, should the deadline be missed, such a task is not considered to have failed; only the later it finishes, the higher the penalty that is paid. For a set of soft real-time tasks that are to be scheduled on a single machine, our objective is to minimize the total penalty paid. Since the problem is NP-hard, it is not known whether an optimal schedule can be found in polynomial time. We prove four properties of any optimal scheduling algorithm for the problem. Then, we derive a number of heuristic algorithms which hold the properties obtained herein. The heuristic algorithms differ in the way that the tasks priorities are assigned. These algorithms assign priorities by using functions of task execution times, penalty factors or deadlines. Numerical simulations are presented to compare the penalty to be paid by each algorithm.