Scalable Joint Resource Allocation for SLO-Constrained LLM Inference in Heterogeneous GPU Clouds

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.