Flow-Controlled Scheduling for LLM Inference with Provable Stability Guarantees

The rapid adoption of large language models (LLMs) has created significant challenges for efficient inference at scale. Unlike traditional workloads, LLM inference is constrained by both computation and the memory overhead of key-value (KV) caching, which accelerates decoding but quickly exhausts GPU memory. In this paper, we introduce the first queueing-theoretic framework that explicitly incorporates both computation and GPU memory constraints into the analysis of LLM inference. Based on this framework, we derive rigorous stability and instability conditions that determine whether an LLM inference service can sustain incoming demand without unbounded queue growth. This result offers a powerful tool for system deployment, potentially addressing the core challenge of GPU provisioning. By combining an estimated request arrival rate with our derived stable service rate, operators can calculate the necessary cluster size to avoid both costly over-purchasing and performance-violating under-provisioning. We further validate our theoretical predictions through extensive experiments in real GPU production environments. Our results show that the predicted stability conditions are highly accurate, with deviations typically within 10%.

In large language model (LLM) serving, each request accumulates persistent graphics processing unit (GPU) memory during service as its key-value cache grows with every generated token. Under high concurrency, aggregate memory usage therefore increases endogenously over time: the service process itself creates future capacity pressure. When memory capacity is exceeded, systems evict active requests, discarding cached state and restarting them later, which wastes computation and reduces throughput. We develop a discrete-time dynamical model of memory-constrained LLM inference that captures admission, memory growth, and eviction under continuous batching. In the saturated-input regime, the system admits both eviction-free fixed points and limit cycles with evictions. For homogeneous workloads, we show that the eviction-free equilibrium is unstable and that, except for a Lebesgue-measure-zero exact-capture set, the system converges to a unique worst-case limit cycle that is asymptotically stable outside this exceptional set, with throughput losses as large as 50%. For heterogeneous workloads, we prove a stability criterion in the two-class common-input setting and explain how the survival-polynomial mechanism generalizes to multiple classes and heterogeneous-input lengths. Under an input-dominated scaling regime, coprime decoding lengths stabilize the eviction-free equilibrium, while non-coprime lengths create synchronized modes that drive instability. These results characterize when workload heterogeneity desynchronizes completions and helps stabilize memory-constrained serving. More broadly, we identify service-induced congestion as a structural instability mechanism and derive scheduling design principles for sustaining high throughput.

Serverless inference is emerging as an efficient deployment model for Large Language Models (LLMs) due to its ability to elastically scale resources, improve GPU utilization through resource sharing, and reduce infrastructure costs. However, existing approaches primarily optimize time to first token (TTFT) while overlooking inter-token latency (ITL), a key determinant of user experience during response generation. We observe that LLM inference comprises a computation-intensive prefill stage and a bandwidth-bound decode stage, where admitting new requests can disrupt ongoing decoding and increase latency. To address this, we propose Token Window Pacing (TWP), a closed-loop scheduling framework that leverages runtime feedback from ITL, queue depth, and workload characteristics to regulate request admission at the token level instead of the batch level. TWP dynamically adjusts a selfregulating token window and incorporates chunk-based prefill to minimize interference from incoming requests. Experiments on realistic serverless workloads show that TWP delivers stable TTFT, significantly reduces latency spikes, lowers P99 tail latency, minimizes ITL variation, and improves throughput by up to 45% over ServerlessLLM and 58% over conventional schedulers. These results demonstrate that feedback-driven tokenlevel scheduling enables stable, high-throughput serverless LLM inference without modifying the underlying model.