Dioid of formal power series for the determination of performance parameters of communication networks

Discrete event dynamic systems (DEDS) are systems whose state transitions are triggered by events that occur at discrete instants. The communication networks are examples of this kind of systems. The mathematical constraints of some DEDS can be described more adequately using the dioid algebra. Previous works show that the problem of determining performance bounds for communication networks is simplified if modeled using this algebra. The compilation of existing rules and results on this field is called network calculus (NC). The goal of this article is to propose a dioid of formal power series for the treatment of NC problems. To illustrate the adequacy of the proposed dioid, we analyze a FIFO multiplexer. The results obtained for this particular system represent an extension of previous results.