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This paper deals with specific issues related to the design of distributed embedded systems implemented with mixed, event-triggered and time-triggered task sets, which communicate over bus protocols consisting of both static and dynamic phases. Such systems are emerging as a new standard for automotive applications. We have developed a holistic timing analysis and scheduling approach for this category of systems. Three alternative scheduling heuristics are presented and compared. We have also identified several new design problems characteristic to such hybrid systems. An example related to bus access optimization in the context of a mixed static/dynamic bus protocol is presented. Experimental results prove the efficiency of such an optimization approach.