We have recently introduced a new feature called smart notifications for agents within the portal itself which would give real-time audible notifications about new tickets and updates on the ones you are working on. You can open the Notification Center by clicking on the bell icon in the navigation bar next to the icons on the right end of it.
You could choose the ones you want to get these alerts for by clicking on the gear icon in the notification center that gives you the preferences. You could enable desktop notifications in this window.
Muting is possible by turning on the "silent notifications" within the Preferences tab.