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Time-Sensitive Networking (TSN) is a set of amendments that extend Ethernet to support distributed safety-critical and real-time applications in the industrial automation, aerospace and automotive areas. TSN integrates multiple traffic types and supports interactions in several combinations. In this paper we consider the configuration supporting Scheduled Traffic (ST) traffic scheduled based on Gate-Control-Lists (GCLs), Audio-Video-Bridging (AVB) traffic according to IEEE 802.1BA that has bounded latencies, and Best-Effort (BE) traffic, for which no guarantees are provided. The paper extends the timing analysis method to multiple AVB classes and proofs the credit bounds for multiple classes of AVB traffic, respectively under frozen and non-frozen behaviors of credit during guard band (GB). They are prerequisites for non-overflow credits of Credit-Based Shaper (CBS) and preventing starvation of AVB traffic. Moreover, this paper proposes an improved timing analysis method reducing the pessimism for the worst-case end-to-end delays of AVB traffic by considering the limitations from the physical link rate and the output of CBS. Finally, we evaluate the improved analysis method on both synthetic and real-world test cases, showing the significant reduction of pessimism on latency bounds compared to related work, and presenting the correctness validation compared with simulation results. We also compare the AVB latency bounds in the case of frozen and non-frozen credit during GB. Additionally, we evaluate the scalability of our method with variation of the load of ST flows and of the bandwidth reservation for AVB traffic.