A scheduler and method for use in ATM and packet communication systems applies a no-per-connection-timestamp discrete-rate scheduling technique which does not require the computation and storage of one timestamp per connection, and only maintains a single timestamp per supported service rate. The elimination of the per-connection timestamps has no negative effect on the delay bounds guaranteed by the scheduler. The total implementation cost of such schedulers which approximate the Generalized Processor Sharing (GPS) policy is reduced, since there is less complexity involved in maintaining and sorting the timestamps for all connections.