You can set the Default Queue and the max number of simultaneous Chats an Agent can handle in Channels > Chat > Queue Settings.

Default Queue

The default queue is the queue that is automatically assigned to new Chat Departments when they are created.

Maximum Simultaneous Chats

You can define how many Chats Agents can handle simultaneously in the Chat queue settings. This is a global setting which will apply to all Agents and queues.

If the all relevant Agents are at their maximum Chat capacity, the User can still initiate a Chat but they'll be advised that you are searching for an Agent until the next representative is available to accept the new Chat.

If no Agent becomes available within the period defined in your Messenger Chat Settings the User will have the option to either submit a Ticket through Messenger, submit a Ticket through your main contact form or be shown 'busy' message.