The IP Address Paradox

[Ryan_Todd]

Original thread:
"What is the strangest issue with a robot you have ever seen?"

This thread:
I read the following post (full text in the above thread), and it got me thinking.

Originally Posted by Aaron.Graeve

Lone Star this year (I was FTAA). One robot refused to connect to the Driver Station, and the Driver Station refused to connect to FMS. As it was practice day, we were willing to take extra time and figure out what the issue was.

...snip...

Fast forward 30 minutes, still no progress. We have re-run FMS pre-start at least 4 times; the 5 other robots come up fine, but this Driver Station and robot refuse to budge. The team is understandably panicking that they may not be able to compete at all. As a shot in the dark, I turn to the FTA and ask if the Field could be getting a 10.41.*.* IP address from the convention center. As it turns out, the field was getting a 10.41.255.* address with a subnet that conflicted with the 10.41.55.* addresses that the team needed to use.

5 minutes later, the problem is resolved and both of the teams laptops are working fine. The Field exterior IP address is usually checked during setup day for possible conflicts, but must have been missed for some reason. The team was extremely grateful for the resolution and was patient and helpful the entire time.

TL;DR:
A 1 in ~650,000 chance that the FMS wants your IP as its IP.

(emphasis mine)


That may sound like it's practically impossible, but I'm pretty sure that's not the case.

For a quick refresher of the concepts involved, here's a closely related example from your everyday life: The Birthday Paradox.

Anyhow, I was struck with inspiration...
This is just the kind of question that can only be answered one way: MATH!

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If there is a "1 in ~650,000 chance" that any given team will experience an IP address conflict with the FMS, then there's a ~(1 - (1 / 650,000)) = ~99.99985% chance that any given team will *not* experience such a conflict at any given event.

Note: I'm electing to work backwards from this number, as opposed to using the probability of a conflict (1/650,000) directly; otherwise, we'd pretty much end up solving for the Nth root of the number of molecules in an unladen swallow.

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Since the FRC rule for assigning team IP addresses means that we don't have to worry about conflicts *between* teams, the odds of a conflict happening at an event with 66 teams are best expressed as (1 - (~0.9999985 ^ 66)) = ~0.01015%.

Also note that my actual math uses way more sig-figs than I've shown in this post. Since all of this math is only based on rough numbers in the first place, however, this works out just fine.

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That may sound pretty unlikely, but what happens if we expand all of the way out to the scope of an entire FRC season? We'll need to know the number of times an FMS received a new IP address, and the number of teams that connected to each of these IPs.

Counting events with multiple competition fields like MSC and CMP, teams competed on a freshly configured FMS no less than 137 times this past season; depending on whether or not each FMS got a new IP on Saturday morning, there may have been as many as 272 unique IP addresses used by competition FMS setups this season (note that the Einstein fields only operated for one day each). Of course, this ignores any possible field resets mid-day due to technical difficulties!

As for the number of teams that connected to each FMS, I can't seem to find a solid number for the average number of teams per FMS. Since I didn't feel like making a Dropbox account just to pull up Jaci's Data Dump, I just spent a few minutes clicking around the event results listing at random; this (completely unscientific) survey pointed to an average around 50.

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Taking all these numbers together, we get a lower estimate somewhere around (1 - ((0.9999985 ^ 50) ^ 137)) = 1.05% and an upper estimate around (1 - ((0.9999985 ^ 50) ^ 272)) = 2.07%.

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TL; DR:
There was at least a 1% chance of a robot-to-FMS IP conflict happening to somebody during the 2016 competition season; still not exactly likely, but well within the realm of possibility.

Now, how many shared birthdays do we have among this year's robots?