Long lived is aka - Elephant flow. Short lived is aka Runt flows. So for a shared output buffer aka Tomahawk IV the buffer can be considered as occupied buffer(alpha) and unoccupied buffer( 1-alpha). Buffer sizes for N flows are sized to BW*Tdelay / sqrt(N). This can be termed as McKeown's second equation. Runt flows typically coexist with other Runt flows in the buffer. If alpha is the occupancy ratio of a buffer, arriving runt flows are split evenly on (1- alpha)* cumulative buffer size. One term that will show up in Buffer sizing analytical models is the square root of Window size for TCP. The Delay BW product - is 2.5GB for 100Gbps with 200ms RTT so its too huge for any Networking SOC. This becomes a lot smaller when N - number of flows increases , for N=10,000 the delay BW product can be 100 times smaller and still the 100G link will perform.
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