I want to manage a team which developers themselves now support the software produced. Developers are the only people who know how to fix the problems.

The problem is that when something goes wrong the customer calls me as PM and want me to solve the problem asap. Sometimes I try to fix it myself and sometimes I should find other senior developer to solve it. And this is bothering especially when I (or the developer) am at home or on holiday! In most cases the problem cannot be postponed to the next working day and should be fixed immediate. Some can be solved temporarily (for example by resetting the service) and some need more knowledge. Now I think a support team is needed but I don't know how to define the roles. What they should do ? What they should know about the software ? Should they have the knowledge like developers?