LLM Serving Optimization with Variable Prefill and Decode Lengths

We study offline scheduling for large language model (LLM) serving under a fixed KV-cache memory budget, where requests have heterogeneous prompt (prefill) and response (decode) lengths. Prompt tokens determine initial KV usage, and each generated token increases memory by one unit. Given a backlog of n requests arriving together, we schedule mixed prefill and decode batches to minimize total end-to-end latency. We show that heterogeneity in prompt lengths makes the problem computationally intractable and that widely used heuristics such as first-come-first-served and shortest-first can be arbitrarily suboptimal. We propose Sorted-F, which repeatedly forms feasible batches using a new selection metric that balances batch size against downstream decode cost, and prove it achieves a constant-factor guarantee on total latency. We further develop practical variants -- an exact solver for small instances and fast heuristics for larger ones -- and evaluate them on a public workload spanning short conversations and long-document summarization, where they consistently reduce average latency relative to standard baselines. Our results highlight that during peak-hour tidal backlogs, greedy GPU packing or short-request prioritization can perform poorly when prompt lengths vary widely, and provide a principled, tunable framework for designing production batch schedulers and planning capacity in memory-constrained LLM serving systems.