# Meet Alice. Alice is impatient.

DevFeed: [Meet Alice. Alice is impatient.](<https://devfeed.tech/articles/meet-alice-alice-is-impatient-12598.md>)

Original publisher: [Read original article](<http://brooker.co.za/blog/2026/06/19/waiting.html>)

Author: Marc Brooker

Published: 2026-06-19T00:00:00Z

Content type: article

Language: en

Sources: [Marc Brooker's Blog](<https://devfeed.tech/sources/marc-brooker-s-blog.md>), [Marc Brooker's Blog](<https://devfeed.tech/sources/marc-brooker-s-blog-2.md>)

Topics: [Latency](<https://devfeed.tech/topics/latency.md>), [Web](<https://devfeed.tech/topics/web.md>), [Code](<https://devfeed.tech/topics/code.md>), [Server](<https://devfeed.tech/topics/server.md>)

Tags: [code](<https://devfeed.tech/tags/code.md>), [latency](<https://devfeed.tech/tags/latency.md>), [metrics](<https://devfeed.tech/tags/metrics.md>), [outage](<https://devfeed.tech/tags/outage.md>), [reasoning](<https://devfeed.tech/tags/reasoning.md>), [recovery](<https://devfeed.tech/tags/recovery.md>), [server](<https://devfeed.tech/tags/server.md>), [time](<https://devfeed.tech/tags/time.md>), [web](<https://devfeed.tech/tags/web.md>)

## AI overview

The article explains why customers may perceive web-service latency and outages as much longer than service-side averages suggest. It uses the inspection paradox to show that people disproportionately encounter longer events, presents a formula for the customer-observed mean recovery time, and describes a simulator based on median and p99 values.

## Source excerpt

Meet Alice. Alice is impatient. What do you mean? Meet Alice. Alice uses your web service. Alice, like most humans, measures her time in seconds and minutes. Alice says your service is slow. You tell Alice that the mean request to your service completes in 100ms, but Alice says that her mean wait time is 1s. You're both right. Meet Alex. Alex uses your web service. Alex, like most humans, measures his time in seconds and minutes. Alex says that when you have outages, they last a long time and he gets really annoyed. You tell Alex that your MTTR is less than 1 minute. Alex says that he sees the mean outage lasting 1 hour. Again, you're both right. What's going on? What's going on is that you're measuring time in requests, or in outages, and Alex and Alice are measuring time in seconds and minutes. When you have a long pause or a long outage, Alex and Alice sample that outage multiple times (maybe because they have multiple customers angry at them). The number of times they experience the outage is proportional to the length of the outage. But you only count that as one. More technically, what's going on here is the inspection paradox. Alex and Alice don't experience your latency distribution $f(t)$, they experience a t-weighted version of it. If you have a MTTR or mean request time of $\mathbb{E}[X]$, Alex and Alice experience a mean recovery time $\mathbb{E}_a[X]$ where $\mathbb{E}_a[X] = \frac{\mathbb{E}[X^2]}{2 \mathbb{E}[X]} = \frac{1}{2} \left( \mathbb{E}[X] + \frac{\mathrm{Var}(X)}{\mathbb{E}[X]} \right)$. Let's play with this with a little simulation. Plug in your median latency (or recovery time), and 99th percentile latency (or recovery time), we'll fit a log-normal distribution to it, and then plot both what your service metrics see and what your customers see. Median: ms p99: ms What your service sees (mean): - ms. What your customers experience (mean): - ms. For example, put in 30 as the median (let's ignore the milliseconds and pretend these are minutes