Performance optimization for timed weighted marked graphs under infinite server semantics

This paper deals with the performance optimization of resource allocation systems with the aim of maximizing the system's throughput under a given budget for acquiring resources. Resources are assumed to be renewable, i.e., they are not consumed by the operations and become available again after they have been released. The systems under consideration are modeled by a subclass of timed Petri nets called deterministic timed weighted marked graphs. In addition, we take into account infinite server semantics, i.e., the degree of self-concurrency of each transition is infinite. We propose an approach that provides an optimal solution, but has a high computational cost. For this reason, we also present two different approaches that can find suboptimal solutions with a reduced computational cost. The performances of the proposed approaches are compared by means of numerical simulations.