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cmuratori's profile
Casey Muratori
Casey Muratori
Casey Muratori
@cmuratori

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Casey Muratori

@cmuratori

I'm worried that the baby thinks people can't change.

Seattle
caseymuratori.com
Joined March 2009

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    Casey Muratori‏ @cmuratori Mar 15

    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?

    1:15 PM - 15 Mar 2021
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    4 replies 0 retweets 10 likes
      1. Casey Muratori‏ @cmuratori Mar 15

        (I am of course just making that equation up, but I assume it would look something like that).

        1 reply 0 retweets 3 likes
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      2. Rik‏ @IsntTrivial Mar 15
        Replying to @cmuratori

        max(t_i) * (n-1) + sum(t_i) is a lower bound and tight in case max(t_i) = t_0. Upper bound is sum(t_i)*n which is tight in case there's only one stage. Neither *has* to be tight though. Don't think a general formula exists.

        1 reply 0 retweets 0 likes
      3. Casey Muratori‏ @cmuratori Mar 15
        Replying to @IsntTrivial

        Where are you getting those bounds from, though? Why would it matter if max(t_i) is on t_0 or anywhere else?

        1 reply 0 retweets 0 likes
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      2. Josh Tobin‏ @rjoshtobin Mar 15
        Replying to @cmuratori

        Pretty sure you are exactly right - this would make a great awful interview question. Proof sketch: consider the distance between two adjacent items over time. Distance starts out as zero, easy to see max is exactly t_worst.

        1 reply 0 retweets 0 likes
      3. Josh Tobin‏ @rjoshtobin Mar 15
        Replying to @rjoshtobin @cmuratori

        When an item finishes, the next item will be exactly t_max behind it - since after the biggest task, the gap between any two items is exactly t_max.

        0 replies 0 retweets 1 like
      4. End of conversation
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      2. André Rodrigues‏ @afpr252 Mar 16
        Replying to @cmuratori

        Took me a while to reach the same conclusions... There are a couple of assumptions though: each stage can only process one item at a time; an item enters a stage as soon as possible, meaning that all items must be ready to be processed before the pipeline starts.

        2 replies 0 retweets 0 likes
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