This paper presents an approach to build a communication behavioural semantic model for heterogeneous distributed systems that include synchronous and asynchronous communications. Since each node of such system has its own physical clock, it brings the challenges of correctly specifying the system's time constraints. Based on the logical clocks proposed by Lamport and CCSL proposed by Aoste team in INRIA as well as pNets from Oasis team in INRIA, we develop timed-pNets to model communication behaviour for distributed systems. Timed-pNets are tree style hierarchical structures. Each node is associated with a timed specification which consists of a set of logical clocks and some relations on clocks. The leaves are represented by timed-pLTSs and non-leaf nodes are represented by timed-pNets including some holes which are filled by leaves or non-leaf nodes. Both timed-pLTSs and timed-pNets node can be translated to timed specifications. All these notions and methods are illustrated on a simple use-case of car insertion from the area of Intelligent Transportation Systems (ITS) and then TimeSquare tool is used to simulate and check the validity of our model.
