Service-Induced Congestion in Memory-Constrained LLM Serving
Authors: Ruicheng Ao, Jing Dong, Gan Luo, David Simchi-Levi
Organizations: Institute for Data, Systems, and Society, Massachusetts Institute of Technology, Cambridge, MA 02139 · Columbia Business School, Columbia University, New York, NY 10027 · School of Mathematical Sciences, Peking University, Beijing, China
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.
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%.
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.
The surge of large language model (LLM) applications on personal devices imposes massive, bursty workloads on cloud serving infrastructure. While prefill-decode disaggregation improves throughput and scalability, memory-bound decode instances often suffer from persistent load imbalance, as output lengths are unknown when requests arrive at the cloud. To address this, we propose MAPS, a Memory-Aware Predictive Scheduling framework tailored for disaggregated LLM serving. MAPS performs device-assisted speculative output length prediction overlapped with cloud-side prefilling, incurring negligible latency overhead. To handle generation uncertainty, MAPS applies uncertainty-aware calibration to derive output-length upper bounds with target coverage, enabling safe scheduling decisions. Building on these bounds, MAPS employs a hierarchical global-local scheduling strategy to mitigate inter-decoder queue buildup and intra-decoder head-of-line blocking. Extensive experiments on two real-world workloads and two LLMs show that MAPS significantly outperforms three state-of-the-art systems, reducing average end-to-end latency by 42.6 and tail latency by up to 84.8.