Napkin Problem 2

Nov 2019

This is an edition of the Napkin Math newsletter, where you'll receive an occassional problem to practise your order-of-magnitude calculations. You can subscribe through email.

Fellow computer-napkin-mathers, it’s time for napkin problem #2. The last problem’s solution you’ll find at the end! I’ve updated sirupsen/napkin-math with last week’s tips and tricks–consult that repo if you need a refresher. My goal for that repo is to become a great resource for napkin calculations in the domain of computers. My talk from SRECON’s video was published this week, you can see it here.

Problem #2: Your SSD-backed database has a usage-pattern that rewards you with a 80% page-cache hit-rate (i.e. 80% of disk reads are served directly out of memory instead of going to the SSD). The median is 50 distinct disk pages for a query to gather its query results (e.g. InnoDB pages in MySQL). What is the expected average query time from your database?

Reply to this email with your answer, happy to provide you mine ahead of time if you’re curious.

Solution to this problem is available in the next edition

Last Problem’s Solution

Question: How much will the storage of logs cost for a standard, monolithic 100,000 RPS web application?

Answer: First I jotted down the basics and convert them to scientific notation for easy calculation ~1 *10^3 bytes/request (1 KB), 9 * 10^4 seconds/day, and 10^5 requests/second. Then multiplied these numbers into storage per day: 10^3 bytes/request * 9 * 10^4 seconds/day * 10^5 requests/second = 9 * 10^12 bytes/day = 9 Tb/day. Then we need to use the monthly cost for disk storage from sirupsen/napkin-math (or your cloud’s pricing calculator) – $0.01 GB/month. So we have 9 Tb/day * $0.01 GB/month. We do some unit conversions (you could do this by hand to practise, or on Wolframalpha) and get to $3 * 10^3 per month, or $3,000 per month. Most of those who replied got somewhere between $1,000 and $10,000 – well within an order of magnitude!