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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.

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if you shut it down it just before your IP lease expires, and wait until it is expired before you boot it back up, you have a slightly improved chance of getting a new one. –  Frank Thomas Nov 1 '13 at 19:40
    
I once fetched distance data from Google maps and for that purpose I restarted the router about 10 to 20 times to bypass the limit and each and every time I received a new IP. But I guess this depends on the ISP (Vodafone in my case) and where you live and what pool of IPs is available. –  Raffael Nov 1 '13 at 19:44
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AFAIK, IP addresses are given to the devices (perhaps using their MAC address) by the ISP. It isn't as resetting it would do any good, the last say is with the ISP. –  Doktoro Reichard Nov 1 '13 at 19:44
    
I know from my own experience that obtaining a new IP after router restart is very likely. But this experience of likeliness is depending on my specific ISPs and location I guess. –  Raffael Nov 1 '13 at 19:46
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As others have said it depends on the ISP. Some ISP operate a IP pool in a round-robin fashion, with addresses increasing (until the top of the pool is reached and it start back to the bottom again). So reconnecting will never give you the same IP address (unless your old number happens to be the only one free) Others allocate from the bottom of the pool and if, as happens quite often all the numbers below you are in use, your old number will be the lowest available number and you will be given it. Others work with leases where you will be given the same number unless this lease expires. –  sgmoore Nov 1 '13 at 20:48

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