Online scheduling: generalized pinwheel problem

Consider a non-preemptive infinite horizon service system with a single server characterized by a service time and a maximum allowable time between consecutive services. A rigorous Markov Decision Process formulation is provided in order to develop a dynamic programming algorithm for determining a feasible schedule. The constraints are then relaxed in order to invoke a semi-MDP. This semi-MDP is used to generate a non-randomized policy which generates a schedule of jobs. An algorithm that searches this schedule for a subsequence which is feasible and can be implemented periodically is presented.