Hm, really hard to say, but it is doable IMHO. Particle systems are not SO complicated, it's not a whole rendering engine.
I seriously think that you COULD make a first working prototype in like two weeks if you really wanted. And then have time to improve it and make those performance tests.
But maybe I'm too optimistic Also it depends on how much time do you have, if you have only evenings after school, it may be harder.
I think I would have around 4-6 hours effective time per day. I am quite hesitant whether it's enough to finish everything in time, but I really want to do this for my thesis (instead of some other potential topics that came up in my mind).
Hopefully I can create particle systems that's not too complex utilizing compute shader, but sufficient enough for performance test.
That's really hard to tell without knowing how good in learning you are. I would bet some people could do it in a week (or course not the whole thesis, just to learn and make a working simple compute shader particle system). And many people wouldn't learn it in years.
Also, how flexible/universal should the system be? Is it supposed to have some kind of configuration (via a dialog or some "script" file) for different kinds of particle behaviour and appearance (flames, rain, show, smoke, sparks, missile trails etc)?
And against what are you planning to compare the performance advantage? Against a CPU particle system?
I am not going to use any external script in this case.
Yeah, comparing it with general particle systems which is computed by the CPU.