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How are critical security updates installed on systems which you cannot afford to reboot but the update requires a reboot. For example, services/businesses that are required to run 24x7 with zero downtime, e.g. Amazon.com or Google.

There are various utilities in different operating systems which allow hot-patching of running code. An example of this would be kpatch and livepatch features of Linux which allow patching the running kernel without interrupting its operations. Its capabilities are limited and can only make trivial changes to the kernel, but this is often sufficient for mitigating a number of critical security issues until time can be found to do a proper fix. This kind of technique in general is called dynamic software updating.

I should point out though that the sites with virtually no downtime (high-availability) are not so reliable because of live-patching, but because of redundancy. Whenever one system goes down, there will be a number of backups in place that can immediately begin routing traffic or processing requests with no delay. There are a large number of different techniques to accomplish this. The level of redundancy provides significant uptime measured in nines. A three nine uptime is 99.9%. Four nine uptime is 99.99%, etc. The "holy grail" is five nines, or 99.999% uptime. Many of the services you listed have five nine availability due to their redundant backup systems spread throughout the world.