This paper presents a formal model of concurrent systems to represent scopes of communication channel names precisely. The model presented here is an extension of multiset rewriting system. We represent a concurrent system consists of a number of processes and messages using a bipartite directed acyclic graph. Each process or message corresponds to a source node of the graph. Names used for communication channel in the system are sink nodes. We represent the scopes of names in the system using edges of the graph. The operational semantics of the system is given as a labeled transition system. It is possible to represent local names that their scope are not nested using this model. We define an equivalence relation that two systems are equivalent not only in their behavior but extrusions of scopes of names.