Is there any standard equation for the cost to process n items through a pipeline of fixed cost stages? Maybe from queuing theory? Like t_total(n) = t_single + t_worst*(n - 1) where t_single is the sum of the stage costs and t_worst is cost of the most expensive stage?
It doesn't matter how you count, you just have to count the same. So if you want t_single to be 8, your example has to be 11. Either way, my formula works correctly for your example as far as I can tell, so it is not a case where the formula fails?
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I think you are right and I am wrong. I also tried with 3 items and various combinations of stage lengths, but I'm not able to make it last any longer or shorter. Seems like it doesn't matter that there could be various "other bottlenecks". Far from a proof though. :/
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I think a proof is not too hard. We may try it and see. But it still doesn't change the fact that I feel like this should have been proved before, and it should probably have a name, like "Milton's Conjecture" or "Bonham's Law" or something.
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