Suggest you consider exploring the Real-Time Specification for Java (RTSJ). While it is not a traditional environment for constructing real-time software, it is an up-and-coming technology with a lot of interest. Even better, you can witness some of the ongoing debate about what matters and what doesn't in real-time systems.
Sun's JavaRTS is freely available for download, and has some interesting demonstrations available to show deterministic behavior, and show off their RT garbage collector.
In terms of a specific project, I suggest you start simple: 1) Build a work-generator that you can tune to consume a given amount of CPU time; 2) Put this into a framework that can produce a distribution of work-generator tasks (as threads, or as chunks of work executed in a thread) and a mechanism for logging the work produced; 3) Produce charts of the execution time, sojourn time, deadline, slack/overrun of these tasks versus their priority; 4) demonstrate that tasks running in the context of real-time threads (vice timesharing) behave differently.
Bonus points if you can measure the overhead in the scheduler by determining at what supplied load (total CPU time produced by your work generator tasks divided by wall-clock time) your tasks begin missing deadlines.