It is now widely believed that FlexRay will emerge as the predominant protocol for in-vehicle automotive communication systems. As a result, there has been a lot of recent interest in timing and predictability analysis techniques that are specifically targeted towards FlexRay. In this paper we propose a compositional performance analysis framework for a network of electronic control units (ECUs) that communicate via a FlexRay bus. Given a specification of the tasks running on the different ECUs, the scheduling policy used at each ECU, and a specification of the FlexRay bus (e.g. slot sizes and message priorities), our framework can answer questions related to the maximum end-to-end delay experienced by any message, the amount of buffer required at each communication controller and the utilization of the different ECUs and the bus. In contrast to previous timing analysis techniques which analyze the FlexRay bus in isolation, our framework is fully compositional and allows the modeling of the schedulers at the ECUs and the FlexRay protocol in a seamless manner. As a result, it can be used to analyze large systems and does not involve any computationally expensive step like solving an ILP (which previous approaches require). We illustrate our framework using detailed examples and also present results from a Matlab-based implementation.