Scaling LLM Inference Beyond Amdahl`s Limits via Eliminating Non-Scalable Overheads

Deployers of online LLM services usually seek to maximize cluster-wide performance given a fixed number of GPUs. Tensor parallelism (TP) is necessary to fit modern models but scales sub-linearly as the TP degree t grows, due to cross-GPU communication and non-scalable runtime work, as predicted by Amdahl's Law. Conversely, increasing t improves memory efficiency and alleviates KV-cache contention and swapping. We identify and validate an empirical optimal TP degree t_e that balances these effects. We present Albireo, a parallel inference system that raises the attainable t_e by shrinking the non-scalable portion via overlap of scheduling and I/O with compute and sequence-parallel sampling, without changing model architectures. Across models and benchmarks, Albireo achieves up to 1.9x higher throughput, 48% lower latency, 28% higher GPU utilization, and 54% lower energy than vLLM; in production it yields up to 2x higher throughput.