Performance evaluation of discrete event systems involving Henstock-Kurzweil integral

This paper presents a study on the performance of flexible manufacturing systems (FMSs), by using discrete event system (DES) models, considering resource losses modelled by a parameter entitled coverage factor. We conclude that the resources cell loss distribution between the tasks of a FSM is a real function that cannot be integrated, in order to calculate its primitive, in the classical sense of Riemann or Lebesgue, but only in the sense of Henstock-Kurzweil integral. Our result allows one to study more general processes where highly oscillatory functions occur. The method used to deduce the function describing the resources cell loss distribution is compared with a classical method related in the literature, respectively rational interpolants. An example has been constructed to emphasize what we believe to be, new approaches.