Recently there has been a growing interest in models and methods targeted towards the (co)design of stream processing applications; e.g. those for audio/video processing. Streams processed by such applications tend to be highly bursty and exhibit a high data-dependent variability in their processing requirements. As a result, classical event and service models such as periodic, sporadic, etc. can be overly pessimistic when dealing with such applications. In this paper, we present a new model called Event Count Automata (ECA) for capturing the timing properties of such streams. Our model can be used to cleanly formulate properties relevant to stream processing on heterogeneous multiprocessor architectures, such as buffer overflow/underflow constraints. It can also provide the basis for developing analysis methods to compute delay/timing properties of the processed streams under different scheduling policies. Our ECAs, though similar in flavor to timed and hybrid automata, have a different semantics, are more light-weight, and are specifically suited for modeling stream processing applications and architectures. We present the basic aspects of this model and illustrate its modeling potential. We then apply it in a specific stream processing setting and develop an analysis technique based on the formalism of Colored Petri Nets (CPNs). Finally, we validate our modeling and analysis techniques with the help of preliminary experimental results generated using the CPN simulation tool.