The Max-Plus Algebra and the Network Calculus

Discrete event dynamic systems (DEDS) are systems whose state transitions are triggered by events that occur at discrete instants of time. The communication networks are examples of this kind of systems. The mathematical constraints of some DEDS can be described more adequately using the max-plus 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. The goal of this article is to improve a systematic use of the max-plus algebra in the formulation and derivation of results on network calculus. To illustrate the introduced methodology, we analyze a window flow controller, a system that controls the traffic admitted by a network in order to limit its backlog in a specified manner