Efficient Scheduling Focusing on the Duality of MPL Representation

A max-plus linear (MPL) representation for describing the behavior of a repetitious execution system with a MIMO-FIFO structure is proposed. A conventional MPL form is required to recalculate the representation matrices by each job when applied to systems whose processing times differ by each job. Approximately twice the calculation volume is required to obtain the earliest and latest times using conventional MPL compared with our proposed MPL representation. This work assigns the state variables to events other than conventional ones, reduces the number of independent system parameters in representation matrices, and improves the form to schedule efficiently, even when applied to systems whose processing times differ by each job. The derived equations are similar to the dual system in modern control theory, which means that the calculation load for scheduling can be reduced remarkably comparing with the conventional method