A timed Petri net framework to find optimal IRIS schedules

IRIS (increasing reward with increasing service) real-time scheduling appears frequently in real-time control applications such as heuristic control. IRIS requires not only meeting deadlines, but also finding the schedule with the best result (highest reward). In this paper, a framework is presented that uses Timed Petri nets (TPN) to transform an IRIS problem into a dynamic programming (DP) problem, allowing the application of known TPN and DP techniques. In the presented approach, an IRIS problem with tasks having discrete-time optimal parts is transformed into a (possibly unbounded) TPN. Then, the critical path problem of the TPN state graph can be tackled with DP. This approach allows for the IRIS problem multiple constraints and negative rewards.