Abstract:Serving large language model (LLM) inference in cloud environments requires jointly optimizing model selection, GPU provisioning, parallelism configuration, and workload routing under latency, accuracy, memory, and budget constraints. While mixed-integer linear programming (MILP) can model this problem, its computational cost limits frequent re-optimization under demand variability. Existing heuristics often optimize individual components separately and may become infeasible when system-wide constraints are enforced.
This paper presents a scalable framework for SLO-constrained LLM inference. We formulate the problem as an MILP with a two-phase delay model capturing both prefill and autoregressive decoding under tensor and pipeline parallelism. To solve it efficiently, we develop two constraint-aware heuristics: a Greedy Heuristic (GH) and an Adaptive Greedy Heuristic (AGH). AGH extends GH through multi-start construction, local search, and GPU consolidation. Both methods maintain feasibility through parallelism-aware filtering, cost-based ranking, and adaptive parallelism scaling.
Experiments based on the Azure LLM Inference Trace show that GH generates feasible solutions within one second, while AGH achieves near-optimal performance within three seconds and scales to large instances where exact solvers fail to converge. Under out-of-sample stress with up to 1.5x delay and accuracy inflation, AGH degrades gracefully through provisioned headroom, yielding substantially lower cost and SLO violations than cost-minimal MILP solutions. Across synthetic and real Azure workloads, AGH maintains SLO compliance at significantly lower cost than exact MILP solutions. These results demonstrate that high-quality allocations provide substantial robustness to demand variability while enabling rapid adaptation to workload changes.
From: Jiaming Cheng [view email]
[v1]
Wed, 8 Apr 2026 18:11:09 UTC (1,321 KB)
[v2]
Fri, 5 Jun 2026 07:23:00 UTC (3,471 KB)
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