Back-of-the-envelope calculations are often expected in system design questions. They help logically state the parameters influencing a result, and estimating the capacity requires multiple estimations on the way. Also lets us individually state our assumptions.
Eg: Estimate the hardware requirements to set up a system like YouTube.
Eg: Estimate the number of petrol pumps in the city of Mumbai.
Chapters
00:06 Storage Requirements
01:20 Supplementary storage requirements
03:54 Back of Envelope calculations
05:38 Youtube caching estimation
08:58 Youtube video processing estimation
12:14 Conclusion
------STORAGE
Let's start with storage requirements:
About 1 billion active users.
I assume 1/1000 produces a video a day.
Which means 1 million new videos a day.
What's the size of each video?
Assume the average length of a video to be 10 minutes.
Assume a 10 minute video to be of size 1 GB. Or...
A video is a bunch of images. 10 minutes is 600 seconds. Each second has 24 frames. So a video has 25*600 = 150,000 frames.
Each frame is of size 1 MB. Which means (1.5 10^5) (10^6) bytes = 150 GB.
This estimate is very inaccurate, and hence we must either revise our estimate or hope the interviewer corrects us. Normal video of 10 minutes is about 700 MB.
As each video is of about 1GB, we assume the storage requirement per day is 1GB * 1 million = 1 PB.
This is the bare minimum storage requirement to store the original videos. If we want to have redundancy for fault tolerance and performance, we have to store copies. I'll choose 3 copies.
That's 3 petabytes of raw data storage.
What about video formats and encoding? Let's assume a single type of encoding, mp4, and the formats will take a 720p video and store it in 480, 360, 240 and 144p respectively. That means approximately half the video size per codec.
If X is the original storage requirement = 1 PB,
We have X + X/2 + X/4 + X/8 == 2*X.
With redundancy, that's 2X 3 = 6X.
That's 6 PB(processed) + 3PB (raw) == 10 PB of data. About 100 hard drives. The cost of this system is about 1 million per day.
For a 3 year plan, we can expect a 1 billion dollar storage price.
Now let's look at the real numbers:
Video upload speed = 3 * 10^4 minutes per minute.
That's 3 * 10^4 * 1440 video footage per day = 4.5 * 10^7 minutes.
Video encoding can reduce a 1-hour film to 1 GB. So 1 million GB is the requirement. That's 1 PB.
So the original cost is similar to what the real numbers say.
If we are off by order of magnitude, it's good. However, being off by 3 or more orders of magnitude is too much. We can then highlight the following:
Where our assumption was wrong, or
Which factor we didn't take into account.