An apparatus and method implement a No-Per-Connection-Timestamp Discrete-Rate Scheduler with Pivot Session which does not strictly require the computation and storage of any scheduling-related information per connection, not even a single bit, but only maintains one variable service rate and one timestamp per rate FIFO queue. In a first embodiment, the pivot-session-based scheduler does not make use of per-connection scheduling information, and further embodiments maintain a single scheduling-related bit per connection. The scheduler achieves near-optimal delay bounds, and fairness indices (both SFI and WFI) that are almost identical to those of the discrete-rate scheduler with per-connection timestamps.