Concurrency in Real-Time Distributed Systems

This thesis is concerned with the modeling and the analysis of distributed real-time systems. In distributed systems, components can evolve independently and communicate with each other. Concurrent actions are performed by different components without influencing each other. The time constraints in distributed real-time systems create complex dependencies between the components and the events that occur. In the previous studies of distributed real-time systems, the distributed aspects are often left aside. This thesis explores these aspects. Our work is based on two formalisms: time Petri nets and networks of timed automata, and is divided into two parts. In the first part, we highlight the differences between centralized and distributed timed systems. We compare the main formalisms and their extensions, with a novel approach that focuses on the preservation of concurrency. In particular, we show how to translate a time Petri net into a network of timed automata with the same distributed behavior. We then study the problem of shared clocks in networks of timed automata: when one considers the implementation of a model on a multi-core architecture, shared clocks require communications that are not explicitly described. We show how to avoid shared clocks while preserving the distributed behavior, when this is possible. In the second part, we focus on formalizing the dependencies between events in partial order representations of the executions of Petri nets and time Petri nets. Occurrence nets is one of these partial order representations, and their structure directly provides the causality, conflict and concurrency relations between events. However, we show that, even in the untimed case, some logical dependencies between event occurrences are not directly described by these structural relations. After having formalized these logical dependencies, we solve the following synthesis problem: from a formula that describes a set of runs, build an associated occurrence net. Then we study the logical relations in a simplified timed setting and show that time creates complex dependencies between event occurrences. These dependencies can be used to define a canonical unfolding, for this particular timed setting.