Call admission methods for admitting connections into ATM/IP networks having a plurality of communication channels are disclosed. An overbooking technique is utilized which distinguishes among the different service classes. Each service class is assigned an overbooking factor. The call admission is determined based on the overbooking factor assigned to the class and the effective bandwidth for that service class. In addition, methods are disclosed for performing appropriate bookkeeping, i.e., updating and maintaining information concerning the state of the system.