Coloured Petri Nets for Temporal Performance Evaluation of Distributed Control Systems—Application to a FIFO Queue

Abstract

Temporal performances (like response time) of distributed control systems must be measurable for critical systems. The delay and reliability requirements require us to develop an exhaustive method to evaluate these performances through the most accurate models, such as (max,+) algebra combined with timed event graphs. Among the common mechanisms encountered in a distributed control system, the FIFO policy remains one of the most used and cannot be modeled with timed event graphs. We show that the formalism of timed coloured Petri nets described in the (max,+) algebra can model the FIFO queue of a Programmable Logic Controller communication module. We also aim to reveal some exciting features of coloured Petri nets when analytically evaluating temporal performances. We present, therefore, a Timed Coloured Petri net modeling the emptying of a FIFO queue with a periodic task, and the formulas of delays associated with the induced system of (max, +) equations. We also test the consistency of our bounds in a numerical application of our model with positive results.