The scheduling theory of Heemstra de Groot et al. is supplemented by extending the Final Matrixs usefulness beyond finding iteration bounds, critical loops and subcritical loops of recursive data flow graphs (RDFGs) to scheduling. DFG is a special case of Petri nets (PN). Hence we apply the cycle time theory of PN to the scheduling of DFG. Contributions include: (1) development of explicit formulas for slack time, scheduling ranges and update, and static rate-optimal time scheduling based on entries of the final matrix; (2) development of a fastest processor assignment algorithm based on the rate-optimal static scheduling without unfolding while considering abnormal cases in which iteration bounds are fractional or smaller than some node execution times; (3) discovery of a new anomaly in addition to the above two cases; (4) development of a user-friendly Final-matrix based Integration Tool (FIT) to view critical and subcritical loops, iteration bounds, scheduling ranges, and level and processor assignment diagrams based on a single tool final matrix rather than other tools; (5) elimination of redundant steps such as the construction of inequality graphs; (6) development of a proof showing that the ALAP and ASAP fixed-time schedulings satisfy the firing rule; and (7) thousand-fold faster (linear time complexity) processing compared to others and use of fewer processors in the case of large DFGs.
Journal of Information Science and Engineering, 16(3), 391-422