Performance analysis of timed event graphs with multipliers using (min, +) algebra

We are interested in the performance evaluation of timed event graphs with multipliers. The dynamical equation modelling such graphs are nonlinear in (min,+) algebra. This nonlinearity is due to multipliers and prevents from applying usual performance analysis results. As an alternative, we propose a linearization method in (min,+) algebra of timed event graphs with multipliers. From the obtained linear model, we deduce the cycle time of these graphs. Lower and upper linear approximated models are proposed when linearization condition is not satisfied.