Abstract : The Clock Constraint Specification Language (CCSL) is a formal polychronous language based on the notion of logical clock. It defines a set of kernel constraints that can represent both asynchronous and synchronous relations. It was originally developed as part of the UML Profile for MARTE to express causal and temporal constraints of Real-time and Embedded Systems. In this paper, we explore the use of CCSL for modeling scheduling requirements and to conduct schedulability analysis. For this purpose, a dedicated scheduling library of CCSL has been built. This library is endowed with a state-based operational semantics, and is applied to solve issues related to schedulability analysis and latency-insensitive design. We establish schedulability categories and latency-insensitiveness property in the context of the semantics, and solve those issues by using model checking techniques.