All of the things I mentioned are things that you can get away without but eventually scale forces you to tackle. Each of those things brings with it additional cost without increasing the throughput.
This shouldn't be too novel an idea: consider a normal supply curve: cost per unit tends to go up with volume.
> All of the things I mentioned are things that you can get away without but eventually scale forces you to tackle. Each of those things brings with it additional cost without increasing the throughput.
That doesn't mean it costs more than O(n).
Let's say you start off with 100 workers providing 100 units of support, and 20 workers of overhead.
Let's say doubling support means you need double the existing workers, plus double the existing overhead, plus 20 more workers to handle new kinds of overhead.
So 120 x 2 + 20 = 260 workers for 200 units of support.
Then 260 x 2 + 20 = 540 workers for 400 units of support.
The percentage of overhead grows every single time we double the number of workers.
And yet if you do the math, you see that the overhead never goes over 40%. And it was already 20% when we started, so that extra amount isn't hard to afford at all.
Despite growing every stage, it's still O(n). The dominating factor is linear.
Obviously those numbers are just an example. But the point is that you have to look at how much the costs increase. Even if it's theoretically faster than linear, if the overhead only grows a moderate amount as you grow from a thousand support workers to a billion support workers then it's not an excuse. It's within a small fudge factor of linear for all real-world numbers.
> This shouldn't be too novel an idea: consider a normal supply curve: cost per unit tends to go up with volume.
Only in the short term. In the long term, production ramps up until the price is pretty close, and on top of that economies of scale drop the price by a significant amount.
All of the things I mentioned are things that you can get away without but eventually scale forces you to tackle. Each of those things brings with it additional cost without increasing the throughput.
This shouldn't be too novel an idea: consider a normal supply curve: cost per unit tends to go up with volume.