TTEthernet is an Ethernet-based synchronized network technology compliant with the AFDX standard. It supports safety-critical applications by defining different traffic classes: Time-Triggered (TT), Rate-Constrained (RC), and Best-Effort traffic. The synchronization is managed through the AS6802 protocol, which defines so-called Protocol Control Frames (PCFs) to synchronize the local clock of each device. In this paper, we analyze the synchronization protocol to assess the impact of the PCFs on TT and RC traffic. We propose a method to decrease the impact of PCFs on TT and a new Network Calculus model to compute RC delay bounds with the influence of both PCF and TT traffic. We finish with a performance evaluation to i) assess the impact of PCFs, ii) show the benefits of our method in terms of reducing the impact of PCFs on TT traffic and iii) prove the necessity of taking the PCF traffic into account to compute correct RC worst-case delays and provide a safe system.