1980s (mid): Alphanumeric display pagers were introduced. They could send a text message through a digital network and initiate in a variety of ways, including operator dispatch, IXO (a device used for sending alphanumeric pages via Telelocator Alphanumeric Protocol (TAP)), and computer.
Motorola OPTRX is an Alphanumeric Pager released by Motorola in 1984.

What about having Pagers, where we can send small text messages to players who are either online/offline?
The text messages could be limited to certain amount of characters for realism.
A player can send a message using a command, for example
/page <name> <msg>A player can check their messages
/pager. This will list any unread messages. Once a message is received, it is deleted automatically.
What do you think?