We study the use of formal modeling and verification techniques at an early stage in the development of safety-critical automotive products which are originally described in the domain specific architectural language EAST-ADL2. This architectural language only focuses on the structural definition of functional blocks. However, the behavior inside each functional block is not specified and that limits formal modeling and analysis of systems behaviors as well as efficient verification of safety properties. In this paper, we tackle this problem by proposing one modeling approach, which formally captures the behavioral execution inside each functional block and their interactions, and helps to improve the formal modeling and verification capability of EAST-ADL2: the behavior of each elementary function of EAST-ADL2 is specified in UPPAAL Timed Automata. The formal syntax and semantics are defined in order to specify the behavior model inside EAST-ADL2 and their interactions. A composition of the functional behaviors is considered a network of Timed Automata that enables us to verify behaviors of the entire system using the UPPAAL model checker. The method has been demonstrated by verifying the safety of the Brake-by-wire system design.