Cyberpower UK

Looking for a way to automate the ending of chats where customers have been idle for some time. 
In an ideal world staff would have time to monitor all chats and do this manually but, realistically, this doesn't happen for us and I'm sure doesn't happen for others - especially at this time of year.
I think it would be useful to be able to automate 'nudge' messages where customers have been idle for a given time, and then to automate the ending of the chat when the idleness continues beyond a certain time.