How to exclude local IP from bandwidth usage?

I have a client whose website is sometimes suspended for exceeding his maximum bandwidth.

However, if I look in the statistics of his bandwidth usage, I see that 85% of the traffic is coming from 95.211.203.196. But that is the IP address of the server itself?!

Is local traffic on the server itself (traffic that isn't coming from or going out on the inteet), counted towards the total amount of bandwidth used? That's not right, is it? I mean, only traffic that I have to pay for should be counted towards the total bandwidth used, right?

Am I seeing things wrong here, or is there a way to exclude local traffic from counting towards the total used bandwidth?

PS. I did search for this and in fact found a few hits that talk about this issue. Unfortunately none provided a solution, so that's why I'm asking here...

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