Incremental optimization of cyclic timed event graphs

We deal with the problem of allocating a given number of tokens, so as to maximize the firing rate of a cyclic event graph with deterministic transition firing delays. We propose an incremental algorithm that is inspired by the algorithm formulated by Panayiotou and Cassandras (1999) for the case of kanban systems. The algorithm can be applied to a special class of nets in which tokens are allocated to places that belong to only one circuit: this class is powerful enough to model kanban systems. We provide necessary and sufficient conditions for the convergence to the optimum also in the case of multiple solutions