Does the Round-Robin functionality work only during business hours?

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The round robin feature or the automatic assignment functionality would work whenever the icon next to the profile photo is togged on. This is not tied to the business hours. 

As of now, this feature will work irrespective of the portal's business hours. Even if the agent turns on auto ticket assignment during non-business hours, the system will continue assigning the tickets to that agent. 

A workaround would be to not give the agent the permission to turn on the automatic assignment by unchecking "Allow agents to change their availability for automatic ticket assignment" - this would give the admins to control the ticket assignment and could manually switch on round robin during business hours in Dashboard -> Available agents -> ticket assignment.