Users would pay a fee to communicate with any person (recipient) set up on the system. The price would be dependent on market rate, i.e. more for popular people, such as to reduce the volume to a level that the recipients would cope with. The recipients signing up for the service would guarantee to read (or watch, or listen to, etc) a certain number of messages per month.
It might also be interesting to introduce the option for a (possibly partial) refund for relevant communication, i.e. messages that the recipient actually benefitted from receiving. There would likely be sufficient unwanted messages in the service that such a costs of refunds could be born, and the chance of a refund for relevant communication would also stoke demand in the user-base.