In order to avoid missing any new conversations you can set up several notifications. Move to settings of your account and find "Notifications" tab.
For each site you can set alerts which will notify you about new messages in following conversations:
There are three types of notiications:
Desktop- notifications in browser and Windows-app;
Push- notification in Android-app;
Email- notifications which operator will receive on his email.
When a new conversation appears all operators will receive notification about it automatically. After assigning this conversation to one of operators only he will receive notifications about it.
Configuring browser notifications
Google Chrome, Yandex Browser