Modeling and response time evaluation of Ethernet-based automation systems using Max-plus algebra

Abstract—In this paper, a new approach to evaluate the response time in Ethernet-based automation systems using client server protocols, is presented. It is based on modeling the behaviour of the system using timed event graphs and the resulting state representation in Max-Plus algebra. First, an algorithm for tracking the frames in the architecture and giving the response time relative to any occurring event is explicated. Subsequently, analytical formulas for direct calculus of this delay are obtained. Finally, experimental measurements taken on a laboratory platform are used to check the validity of the method. Hence, the interest and effectiveness of our results become obvious. They can be used a posteriori to assess the delays in an existing architecture or a priori during the design phase to fulfill the time requirements of a control system. I