Ask HN: How big companies handle big queues?

I would like to know how big companies handle big queues. For example, if there are 1M users and each sends one message and it all happens almost at the same time within few seconds timeframe.

It means 1M messages need to reach other 1M users and 1M push notifications need to be sent. I presume all those requests go to the queue so the response is returned faster and user experience is better.

But how do those companies handle 1M queue jobs, since most of those messages need to reach other users almost in realtime, without much delay.