In this paper, an analytic model is proposed for the performance evaluation of vehicular safety related services in the dedicated short range communications (DSRC) system on highways. The generation and service of safety messages in each vehicle is modeled by a generalized M/G/1 queue. The overall model is a set of interacting M/G/1 queues, one queue for each vehicle. The interaction is that the server is shared as it is the contention medium. To make the model scalable, we use semi-Markov process (SMP) model to capture the shared server's behavior from one tagged vehicle's perspective, where the medium contention and back off behavior for this vehicle and influences from other vehicles are considered. Furthermore, this SMP interacts with the tagged vehicle's own M/G/1 queue through fixed-point iteration. The proof for the existence, uniqueness and convergence of the fixed point is provided. Based on the fixed-point solution, performance indices including mean transmission delay, packet delivery ratio (PDR), and packet reception ratio (PRR) are derived. Analytic-numeric results are verified through extensive simulations under various network parameters. Compared with the existing models, the proposed SMP model facilitates the impact analysis of hidden terminal problem on the PDR and PRR computation in a more precise manner.