The Bandwidth–Delay Product Knee notebook

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The Bandwidth–Delay Product Knee

A single-bottleneck model separates the inflight data that sustains throughput from the extra data that adds queueing delay.

Static single-bottleneck fluid accounting with declared capacity, RTT, and buffer; not BBR implementation, loss-rate measurement, or current-version benchmark.

The code uses Python 3 and the standard library. Saved output is from the checked CPU run.

capacity_bps = 100_000_000
capacity_bytes_s = capacity_bps / 8
base_rtt_s = 0.040
buffer_bytes = 500_000
bdp_bytes = capacity_bytes_s * base_rtt_s

def model(offered_bytes):
    admitted = min(offered_bytes, bdp_bytes + buffer_bytes)
    excess = offered_bytes - admitted
    queued = max(admitted - bdp_bytes, 0.0)
    rtt = base_rtt_s + queued / capacity_bytes_s
    delivery = min(capacity_bytes_s, admitted / base_rtt_s)
    assert abs(admitted / rtt - delivery) < 1e-6
    assert queued <= buffer_bytes and excess >= 0
    return delivery * 8 / 1e6, rtt * 1000, queued, excess

print(f"BDP={bdp_bytes:.0f} bytes; buffer={buffer_bytes} bytes")
observations = []
for offered in [125_000, 500_000, 750_000, 1_500_000]:
    rate, rtt, queue, excess = model(offered)
    observations.append((rate, rtt))
    print(f"offered={offered:7d} rate={rate:6.1f}Mbps RTT={rtt:5.1f}ms "
          f"queue={queue:.0f} excess={excess:.0f} bytes")

assert max(rate for rate, _ in observations) == 100.0
assert min(rtt for _, rtt in observations) == 40.0
print("Static fluid-model consistency checks: passed")

BDP=500000 bytes; buffer=500000 bytes
offered= 125000 rate=  25.0Mbps RTT= 40.0ms queue=0 excess=0 bytes
offered= 500000 rate= 100.0Mbps RTT= 40.0ms queue=0 excess=0 bytes
offered= 750000 rate= 100.0Mbps RTT= 60.0ms queue=250000 excess=0 bytes
offered=1500000 rate= 100.0Mbps RTT= 80.0ms queue=500000 excess=500000 bytes
Static fluid-model consistency checks: passed

Sources

BBR: Congestion-Based Congestion Control (2016): https://research.google/pubs/bbr-congestion-based-congestion-control-2/
Original BBR paper, author text in Stanford course archive: https://web.stanford.edu/class/cs244/papers/bbr.pdf

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Download full experiment notebook