Arc Inria

Most large distributed systems, such as embedded systems, systems on chip, Local Area Networks or sensor networks are meant to function under hard safety constraints. One may distinguish two main classes of constraints. The first set of constraints concerns the functional behavior of the system. The techniques used to make sure that the behavior of the system is correct range from formal proof theory and software verifications to testing tools. The second main set of constraints concerns the temporal behavior of the system. In a closed system where all events are controllable, these time guarantees are often given by scheduling techniques under real time constrains [LL73] or model-checking on timed automata [LBW97]. However, most modern distributed embedded systems are more or less open systems where some exogenous non-controllable processes are involved. In this framework, one of the most promising technique to provide deterministic guarantees is the Network Calculus. It can be seen as a set of formulas and techniques which have been developed in the last 10 years or so that allow the designers of distributed systems to get certified bounds on response times as well as buffer capacities [Cha00b, BT00]. The main idea of the theory is to model traffic between the nodes by cumulative arrival curves: A(t) is the amount of traffic at a given node up to time t. The service provided at a node is modeled by a cumulative service curve: S(t) is the quantity of service available up to time t. As for the time constraints, they are often seen as constraint functions f and g on A and S respectively, limiting the amount of activity on any interval of time: