Java - Test if Random queue is periodic

OK, I have been digging through the www but haven't found a solution to my problem. I will try to explain as best as I can. Please excuse my bad english ;)

I have to create a queue using the class Random. I know this class is only "pseudorandom" but that doesn't matter.

Next I have to test the queue whether it is periodic or not. If it isn't periodic I can continue. I found no algorithm to test the queue on that, and it seems to be rather complicated creating my own. Has anybody of you ever created something similiar or can give me some advice how I can achieve my goal?

Thanks!