Analysis of preemptive periodic real-time systems using the (max, plus) algebra with applications in robotics

We present the model of a system of periodic real-time tasks with fixed priorities, preemption and synchronization, performed by a robot controller, using marked graphs. Then, with the help of the (max, plus) algebra, we derive simple tests to check real-time constraints on those tasks such as response times and the respect of deadlines. This method takes into account the precedence and synchronization constraints and is not limited to a particular scheduling policy.