Cyclic Scheduling: Diophantine Problems Perspective

Cyclic scheduling concerns of rules aimed at resources assignment as to minimize a given objective function, e.g. the cycle of order execution, feasible timetabling. Such kind of problems belongs to a class of the NP-hard ones. Moreover, assuming integer character of data domain it belongs to the class of Diophantine problems that implies their undecidability. In that context, the contribution emphasizes benefits derived from Diophantine problems perspective while focuses on cyclic steady state reachability problem. The conditions sufficient for periodic behaviour of a system composed of sequential, repetitive processes are the main objective. The relationship between system resource constraints and an initial state as well as priority rules allocation is investigated. Finally, the conditions assuring steady state behavior of the system controlled by distributed set of dispatching rules are discussed.