How fast can messages be published to PubNub channels?

Messages can be published as fast as needed, however there is a soft limit on max throughput since messages will be discarded if the subscriber cannot keep pace with the publisher. For example, if you publish 200 messages at once (before the subscriber had a chance to downloaded any), the subscriber may not receive the first 100 messages because PubNub message queue (by default) has a limit of 100 messages stored in memory.  Also, see these guidelines for publishing messages reliably to a channel.