An advance over the prior art is achieved through an efficient method for an admission control algorithm and a scheduling mechanism that complement each other in providing the following three classes of service. A first class of service is termed Class 1 where users specify a nominal amount of bandwidth desired. A second, lower tier service class is termed Class 2, wherein users specify a nominal and minimum amount of bandwidth desired when entering into a network connection. A third server class is Class 3, where Class 3 users are treated as best effort users. For Class 1 users the methodology of the present invention provides a guaranteed nominal amount of bandwidth. The admission control procedure ensures that Class 1 users are admitted only if resources exist to satisfy the nominal bandwidth requirements of the Class 1 users. Class 2 users are admitted if resources exist to satisfy the minimum bandwidth requirements of the user. Class 2 users are served with a bandwidth of up to their nominal bandwidths if there is capacity left after serving the Class 1 users with their nominal capacities. Class 3 users are served only if the Class 2 users have received their nominal bandwidths.