Recently, we have introduced a new graph product, motivated by applications in the context of synchronising periodic real-time processes. This vertex-removing synchronised product (VRSP) is based on modifications of the well-known Cartesian product, and closely related to the synchronised product due to Wöhrle and Thomas. Here, we recall the definition of the VRSP and use it to define two different decompositions of graphs. Although our main results apply to directed labelled acyclic multigraphs, the VRSP can also be used to decompose any undirected graph of order at least 4 into two smaller graphs.
In this paper, the performance gain obtained by combining parallel peri- odic real-time processes is elaborated. In certain single-core mono-processor configurations, for example, embedded control systems in robotics comprising many short processes, process context switches may consume a considerable amount of the available processing power. For this reason, it can be advantageous to combine processes, to reduce the number of context switches and thereby increase the performance of the application. As we consider robotic applications only, often consisting of processes with identical periods, release times and deadlines, we restrict these configurations to periodic real-time processes executing on a single-core mono-processor. By graph-theoretical concepts and means, we provide necessary and sufficient conditions so that the number of context switches can be reduced by combining synchronising processes.
Reading and writing is modelled in CSP using actions containing the sym- bols ? and !. These reading and writing actions are synchronous and there is a one- to-one relationship between occurrences of pairs of these actions. It is cumbersome to ease the restriction of synchronous execution of the read and write actions. For this reason we introduce the half-asynchronous parallel operator that acts on actions con- taining the symbols ¿ and ¡ and study the impact on a Vertex Removing Synchronised Product.
