In order to understand QPS for Google we can look at the # of queries handles by Google per day and then infer the QPS from the daily data assuming a uniform distribution.
I would like to take a top-down approach and understand how many queries are down across the world per day. Also, assuming that by queries specifically, we are referring to searches on Google.com and not via other Google services.
The world population is 7B and 50% of those have access to the internet.
Thus we have about 3.5B people and it is also safe to assume that anyone who has touched internet also uses Google.
Of the above 3.5B we can assume that:
1. 20% of them are in the developed world. (700M)
2. 60% are from developing countries (2.1B)
3. 20% of them are from underdeveloped countries. (700M)
We can also assume that users in developed countries have access to high-speed internet thus we can assume that the number of queries they do is quite high. While I work in tech and run several dozen google queries per day, it is not true for most people to query so often. Based on my experience I think the range is very wide and thus I will choose 5 as the avg number of queries per day per user.
For developed countries, this number will be a lot lesser as not many people have access to smart phones. Thus I am assuming the number of queries in the developed world is a lot lesser. Assuming its 40% of developed world. 2 queries per user per day
For underdeveloped countries, this will be even lesser and maybe more like 0.25 queries per day per user.
Based on the above we can evaluate queries for each part of the world:
Developed --> 700M * 5 queries per day --> 3.5B queries per day
Developing --> 2.1B * 2 --> 4.2B queries per day
Underdeveloped --> 700M * 0.25 --> 350M queries per day
Thus total query per day --> 3.5B + 4.2B + 350M ~ 7.8B queries per day --(A)
Thus, total queries per second --> (A)/(24*60*60)
Note: I am not feeling very confident about my choice of how I arrived at 5 queries per user per day in a developed country. Any suggestions on how to best estimate the daily queries in developed, developing, and underdeveloped countries?