OS Services Booking has the option to allow you to integration your Booking system with Google Calendar. It works like this way: When customer makes the booking request with one Employee in your OSB system. The appointment will be added to Gcalendar of that employee, and if that booking request is cancelled or removed by administrator or customer, the appointment on Employee’s Gcalendar will be removed.

You can read more about this feature through this documentation: http://joomdonationdemo.com/osservicesbooking/documentation/integrations/gcalendar-integration