SLOPE: Decision-Aligned Marginal Resource Allocation for Co-Located LLM Serving

Joint TTFT/E2E violations are terminal outcomes, but an online LLM scheduler must choose variable-duration actions before future arrivals and generation demand are known. Starting from the same latency allowances as the terminal objective, SLOPE jointly designs service valuation and execution-cost learning for online resource allocation. Its central idea is to translate terminal SLO risk into a computable local service comparison: an SLO-normalized potential unifies input progress, phase completion, and decode service, while analysis of the variable-duration service process yields potential removal per unit time as the allocation criterion. SLOPE then identifies marginal resource effects under a common request plan, making candidate comparisons determine both how service value is assessed and which execution-cost differences must be learned. Theoretical analysis establishes a pathwise upper bound on joint violations and a selection-quality guarantee under relative-cost error. Across three model/workload pairs and a 10×–30× sweep of system-normalized TTFT/E2E thresholds, SLOPE improves joint-SLO performance across the evaluated SLO regimes. At the common 20× reference point, it reduces load-averaged joint violations by **15.5%–30.1% relatively** against the best evaluated baseline at each load, with scheduling-call p95 below **2 ms** on Llama 70B. Real-GPU trace analysis and controlled replay further show that planned service can be realized during execution and that cost-aware local choices can yield more jointly successful requests under the same continuation policy, providing empirical mechanism evidence for the allocation criterion.