Consider buildup of a line at a supermarket. If avg arrival rate equals avg processing rate (1 per min for ex), how long is the line on avg?
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Replying to @fortelabs
are we assuming both arrival & processing are Poisson processes?
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Replying to @calcsam
u mean more or less random? I don't think so because arrival and processing time both = 1/min
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Replying to @fortelabs
sure on average they are 1 /min but what is the distribution? impossible to answer Q without knowing
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Replying to @fortelabs
looks like
@vgr is right, I think this is variance of a random walk. Seems to be E(t) = sqrt(t) / 2: https://docs.google.com/spreadsheets/d/1pJpnCpiw9CVHkAPoIqfpDwD7GL11rKuaCi2lnrTgBjs/edit?usp=sharing …2 replies 0 retweets 3 likes -
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more interested in "how long does it take queue size to get to 6months"
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hmm shouldn't that be about 6^2/2=18 months? About 750k jobs at 1/min arrival frequency...
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