An iterative and starvation-free solution for a general class of distributed control problems based on interaction primitives

Abstract

AbstractFor an independent and graphical representation of the constraints in distributed system parts the formalism of Loosely Coupled Systems is recalled. The events in these structures are formally derived from symmetrical bilateral restrictions. How the interaction between neighbouring parts influences processes in these parts is then adequately described by a symmetrical transitional structure (slack of behaviour) in each part. In order also to represent asymmetrical types of influence local excitement relations are introduced by means of which we can determine directions of flow and can force processes to leave a given local state. The formally extended system structures are called Interaction Systems (IS). A solution of the Dining Philosophers' Problem given by Dijkstra in [5] is briefly discussed. In order to demonstrate the flexibility and representational power of our graphical tools we then derive a starvation-free solution for that problem in a stepwise procedure. (We do not assume a global finite-delay property.) We reconsider a general problem for distributed processes which access shared resources [2, 14]. The solution scheme for the special case of Dijkstra's problem applies at once to the general case. The starvation-freeness of the solution is proved