Many embedded systems operate in multiple modes, where mode switches can be both time- as well as event-triggered. While timing and schedulability analysis of the system when it is operating in a single mode has been well studied, it is always difficult to piece together the results from different modes in order to deduce the timing properties of a multi-mode system. As a result, often certain restrictive assumptions are made, e.g., restricting the time instants at which mode changes might occur. The problem becomes more complex when both time- and event-triggered mode changes are allowed. Further, for complex systems that cannot be described by traditional periodic/sporadic event models (i.e., where event streams are more complex/bursty) modeling multiple modes is largely an open problem. In this paper we propose a model and associated analysis techniques to describe embedded systems that process multiple bursty/complex event/data streams and in which mode changes are both timeand event-triggered. Compared to previous studies, our model is very general and can capture a wide variety of real-life systems. Our analysis techniques can be used to determine different performance metrics, such as the maximum fill-levels of different buffers and the delays suffered by the streams being processed by the system. The main novelty in our analysis lies in how we piece together results from the different modes in order to obtain performance metrics for the full system. Towards this, we propose both – exact, but computationally expensive, as well as safe approximation techniques. The utility of our model and analysis has been illustrated using a detailed smart-phone case study.