4 ms·

They're Poisson distributed, by construction. Queuing service time is actually the go to example when first introducing the Poisson distribution in an intro to

They're Poisson distributed, by construction. Queuing service time is actually the go to example when first introducing the Poisson distribution in an intro to statistics class. No need to make a bet. Anything that can't be negative isn't normally distributed. The bigger issue here, aside from the fact that you may be taking a simple average when you need to be taking a weighted average to aggregate your individual point estimates, as others have pointed out, is that you can estimate a sufficiently symmetric Poisson distribution with a normal distribution, but response latency is not symmetric, specifically because time travel isn't possible and you can't ever get negative response times to balance out the tail events on the right side of the distribution. Tail events with respect to latency can only be bad, not good. They're a bet with a hard cap on winnings but potentially unbounded losses. As such, you really need to consider what the worst case is and the expected frequency of that worst case.

mjb 6y ago
Service latencies are typically not Poisson distributed, partially because their queuing systems are non-trivial, but mostly because there's typically a lot more going on than just queues. For one great deep dive on the topic, check out https://drkp.net/papers/latency-socc14.pdf https://drkp.net/papers/latency-socc14.pdf
- nonameiguess 6y ago
  Thank you, that is quite interesting! As you can see, even though I have an applied math degree, I still can't just analytically infer a distribution. You need empirical results. This reminds me of the Jellyfish network topology for data centers (https://www.researchgate.net/publication/51943691_Jellyfish_Networking_Data_Centers_Randomly https://www.researchgate.net/publication/51943691_Jellyfish_...), where they found completely random route selection to be faster and more scalable than any other existing solution. I suspect, naively, that latency purely from network appliance queueing probably gives a mixture of Poissons in a straight line bus topology. But add in arbitrary routing and the much more complicated schedulers of the servers themselves, and you get no well-behaved distribution at all. It's especially interesting to compare the SLAs given by data center providers that tend to always use 99th or even 99.9th percentile worst case performance, with application metrics using arithmetic averages.
kqr 6y ago
> Anything that can't be negative isn't normally distributed. Human height?

mjb 6y ago

Service latencies are typically not Poisson distributed, partially because their queuing systems are non-trivial, but mostly because there's typically a lot more going on than just queues. For one great deep dive on the topic, check out https://drkp.net/papers/latency-socc14.pdf https://drkp.net/papers/latency-socc14.pdf

nonameiguess 6y ago
Thank you, that is quite interesting! As you can see, even though I have an applied math degree, I still can't just analytically infer a distribution. You need empirical results. This reminds me of the Jellyfish network topology for data centers (https://www.researchgate.net/publication/51943691_Jellyfish_Networking_Data_Centers_Randomly https://www.researchgate.net/publication/51943691_Jellyfish_...), where they found completely random route selection to be faster and more scalable than any other existing solution. I suspect, naively, that latency purely from network appliance queueing probably gives a mixture of Poissons in a straight line bus topology. But add in arbitrary routing and the much more complicated schedulers of the servers themselves, and you get no well-behaved distribution at all. It's especially interesting to compare the SLAs given by data center providers that tend to always use 99th or even 99.9th percentile worst case performance, with application metrics using arithmetic averages.

kqr 6y ago

> Anything that can't be negative isn't normally distributed. Human height?