jspoelstra

jspoelstra

# Utility function to use within AzureML for calculating useful account-level performance metrics
# for transaction fraud detection models. Each metric is calculated as a function of the score-cutoff
# used. These include:
#
#   Account Detection Rate (ADR): what fraction of the fraud accounts received a score above the 
#                                 threshold at some point after the fraud started
#   Value Detection Rate (VDR):   From the point in time that the fist transaction scored above 
#                                 the threshold, what fraction of the losses could have been prevented.
#
# This code specifically calculates the effect of delayed action: it will calculate VDR for various scenarios,

jspoelstra

How many pings to wake every server?

By Jacob Spoelstra
_{Research and drafting assistance by Grok.}

Several years ago a colleague asked me a question that looked like a five-minute calculation and was not.

We have 100 servers behind a load balancer. An incoming ping is sent to a server chosen uniformly at random. The servers sleep until pinged. If they are all asleep, how many pings do we need to send to have a 95% chance of having woken every one of them?

The naive answers are wrong in instructive ways. A hundred pings is nowhere near enough: the chance of covering all 100 servers in 100 pings is about $10^{-42}$. The expected number of pings is only about 519, but the mean is not a 95% guarantee. The distribution is skewed — the last few servers take most of the time — so the 95th percentile sits well above the mean.