batching

Step time is a straight line in batch size, so throughput is a hyperbola with a ceiling. The answer finds the knee in closed form and shows why the ceiling usually comes from the KV cache, not the tensor cores.

Joules per token is power over throughput, and the power term is the one candidates obsess over. The answer shows why the denominator moves the result by about 50x while the numerator is pinned under a datasheet cap.

Doubling the batch raised tokens per second by a third and sent goodput to zero. The answer shows why every sequence in a batch shares one step time, and how to find the batch size that maximizes the number users feel.

Three parts, and most candidates finish one. The algebra fits on a line, the proof fits in three, and the part interviewers remember is the batch size at which the whole trick runs out of spare compute.

The same drafter that triples speed at 3 a.m. costs a third of peak throughput at 6 p.m. if left alone. The answer builds a step-time model for Llama 3.3 70B on eight H100s, derives a draft length per batch bucket, and shows why context length moves the whole table.

The speedup formula has two inputs that vary per request and per moment, and the tail lives where both are bad. The answer computes when speculation turns into a slowdown, shows which requests own the p99, and picks a policy instead of an on/off switch.