My actual objective is to simulate logged IPs of web-site users who are all assumed to use dynamically assigned IPs.

There will be two kinds of users:

• good users who only change IP when the ISP assignes a new one
• bad users who will restart their router to obtain a new IP

So what I would like to understand is what assignment mechanics are usually at work here deciding from what pool of IPs one is chosen and whether the probability is uniformly distributed.

I know there is no definite and global answer as this process can be adjusted be the ISP but maybe there is something like a technological frame and common process that allows some plausible assumptions.

UPDATE:

A bad user will restart the router as often as possible if necessary. So here the central question is how many IP changes on average are necessary to end up with a previously used IP.