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The existing response-time analysis for Controller Area Network (CAN) does not support mixed messages that are scheduled with offsets. Mixed messages are implemented by several high-level protocols for CAN that are used in the automotive industry. We extend the existing offset-based analysis which is applicable to any high-level protocol for CAN that uses periodic, sporadic and mixed transmission of messages. Moreover, we implement the extended analysis as a standalone simulator that will be integrated as a plug-in with the existing industrial tool suite (Rubus-ICE). The experiments, that we performed, indicate that it is possible to achieve up to 4.48% improvement in schedulability when mixed messages are scheduled with offsets.