Upper Bound for Delay Densities

Abstract

In networked control systems, sensors and actuators are connected via networks to the controller platform. Contrary to direct links, delays vary in a more or less wide range in network links. Hence, delays are one of the key issues in the design process of a networked control system. Therefore, obtaining safe upper bounds is essential to guarantee the desired behavior of the system. On the other hand, the bounds should be as tight as possible. Large overestimations result in over-dimensioned platforms and networks. A common approach is to assume the occurrence of the worst case response time (WCRT) for all transmissions. This simplifies the design process as the WCRT can be derived directly from the platform model. Though, it contains inherently large overestimations. A more accurate approach is featured by delay densities. By not treating each event individually, delay densities give a description of the timing behavior within intervals. Additionally, the method is not limited to strictly periodic events. In this paper, we propose a method for deriving an upper bound from a platform description in Real-Time-Calculus.