Geometry-Aware Online Scheduling for LLM Serving: From Theoretical Bound to System Practice
Authors: Li Kong, Qi Qi, Yinyu Ye, Zijie Zhou
Abstract
The explosive demand for interactive Large Language Model serving has highlighted the management of the Key-Value cache's dynamic memory footprint as a critical area for performance optimization in inference engines. Modern inference systems overwhelmingly rely on time-centric scheduling heuristics, such as Shortest Job First. However, their theoretical optimality is rooted in traditional schedule modeling, failing to capture the highly dynamic, 2D spatio-temporal geometric growth specific to LLM inference mechanisms. To resolve this, we propose the geometry-aware online scheduling by introducing the Smallest Volume First (SVF) algorithm and its highly efficient variant, 1-bit SVF. Theoretically, we provide a rigorous mathematical foundation for our approach. Via a novel volume-certificate proof, we sharpen SVF's worst-case competitive ratio from the prior best of 48 towards \textbf{3} in the high-concurrency regime of LLM serving. Building upon this core breakthrough, we complete a comprehensive theoretical taxonomy analyzing our algorithms across different traffic scenarios and information availability. Practically, we seamlessly integrate our approach as a plug-and-play layer in vLLM. Extensive evaluations on Llama-3.1 models demonstrate comprehensive performance gains: SVF delivers strong reductions in both average and tail latency, while 1-bit SVF, with merely a single bit information, achieves competitive throughput and latency. This work establishes a theoretically sound and empirically proven approach for resolving memory-constrained scheduling in modern LLM deployments. To facilitate future research, our code is available at https://github.com/Aurora-Kl/Geometry-Aware-Online-Scheduling.git.
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-cache usage, while each generated token further increases memory consumption, creating dynamic memory constraints during autoregressive decoding. Given a backlog of n requests arriving together, the goal is to form mixed prefill and decode batches over time to minimize total end-to-end latency. We show that heterogeneous prompt lengths fundamentally change the scheduling problem: the problem is NP-hard, and standard policies such as first-come-first-served, shortest-output-first, and total-size-based prioritization can have unbounded approximation ratios. We propose Sorted-F, a scheduling algorithm that repeatedly forms feasible batches using an F-metric that balances batch size against downstream decode cost. We prove that Sorted-F achieves a constant-factor approximation guarantee in the offline/backlogged model. We also develop practical implementations, including an exact dynamic program for small instances and scalable local-search and greedy heuristics for larger instances, as well as LP-guided and receding-horizon variants. Experiments on public workloads that combine short conversations and long-document summarization show that F-metric-based scheduling consistently reduces latency relative to standard baselines and remains close to the LP relaxation lower bound for tractable instances.
Efficient scheduling of large language model (LLM) inference tasks is critical for achieving low latency and high throughput, a challenge that is becoming increasingly acute with the rise of reasoning-capable LLMs whose generation lengths are highly variable. Traditional strategies like First Come, First-Serve (FCFS) often suffer from Head-of-Line (HOL) blocking, where long-running tasks delay shorter ones queued behind them. In this paper, we introduce PARS, a prompt-aware LLM task scheduler that mitigates HOL blocking by approximating shortest-job-first (SJF) scheduling through pairwise ranking with a margin ranking loss. PARS effectively predicts response-length-based task ordering directly from prompts, thereby optimizing scheduling decisions with minimal overhead. In addition, it integrates seamlessly with vLLM, a state-of-the-art LLM serving system, for the research community. Extensive experiments across multiple LLM models and real-world inference use cases, including chat, math, and code generation, demonstrate that PARS significantly reduces latency by up to 15.7x compared to the vLLM default scheduler. Cross-model evaluations demonstrate that our design generalizes effectively, allowing effective scheduling across diverse LLMs without requiring model-specific retraining.
LLM serving exhibits extreme length variability, making size-based scheduling difficult in practice. Recent LLM schedulers approximate SJF/SRPT using predicted decode lengths or ranks and primarily report mean-centric metrics such as TTFT and TBT. We show that these prediction-driven policies can be fragile under distribution shifts, bursty arrivals, and GPU memory pressure, while offering limited control over the tail latency (P90-P99) that dominates user experience, even with perfect decode-length knowledge. We introduce a distribution-aware, prediction-free scheduling framework that replaces explicit length prediction with soft priority boosting driven by lightweight statistical signals. Our design co-optimizes scheduling and cache-aware preemption to account for memory-coupled decode dynamics across workload mixes. Evaluated on production and open-source traces, our method reduces P99 TTLT by up to 35-50% relative to SRPT with perfect length knowledge and reduces TTFT by 34-47% across workloads, including reasoning-heavy and chat-heavy tasks. These results demonstrate a robust alternative for optimizing tail latency in online LLM serving.