There is a special setting which makes chat buttons act as offline if there are too many people waiting in queue. You can find the "Max queue length" setting on the Overview screen when editing a chat button:
How does it work
you can set a different limit in each chat button and when the queue in the button's department becomes larger (or equal) than the defined limit the button will act as if no one was available on chat. So the button will be either hidden completely, or its offline variant will be displayed and the customer will be able to leave an offline message. When the queue drops below the limit the button will be again displayed as online.
Using this functionality you could control how your buttons on different pages of your website are displayed. For example, if you don't like the idea of a new potential customer, who is starting his chat from a pricing page, to see that he is number 42 in queue, you can set the queue limit for the pricing button to 10. When there will be 10 or more people in the button department's queue this button will be hidden. In the same time customers contacting you for example from your knowledgebase will be able to wait their turn in queue.
By default the limit is set to 10 people in department queue for each existing or new button. The limit can be set from 1 to 100 people. It can't be completely disabled. The button state cannot be changed if the website is already loaded, so if a customer had an online button loaded and the queue limit increased in the meantime, he will be presented with an offline form when clicking the online button.