# Service-Induced Congestion in Memory-Constrained LLM Serving

arXiv: https://arxiv.org/abs/2606.15555 · HTML: https://mlsanity.com/paper/2606.15555/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Serving systems and request scheduling, one of 12 directions in Efficient LLM inference and serving.
- Builds on 12 of its 40 references that are in the map.
- First posted on arXiv 14 Jun 2026.

## Placed in

- Efficient LLM inference and serving / [Serving systems and request scheduling](https://mlsanity.com/inference/serving-systems-and-request-scheduling/)

## Builds on (most cited first, 12 of 12)

- [DistServe: Disaggregating Prefill and Decoding for Goodput-optimized Large Language Model Serving](https://mlsanity.com/paper/2401.09670/) (2024)
- [Splitwise: Efficient generative LLM inference using phase splitting](https://mlsanity.com/paper/2311.18677/) (2023)
- [SARATHI: Efficient LLM Inference by Piggybacking Decodes with Chunked Prefills](https://mlsanity.com/paper/2308.16369/) (2023)
- [Fast Distributed Inference Serving for Large Language Models](https://mlsanity.com/paper/2305.05920/) (2023)
- [Online Scheduling for LLM Inference with KV Cache Constraints](https://mlsanity.com/paper/2502.07115/) (2025)
- [Optimizing LLM Inference: Fluid-Guided Online Scheduling with Memory Constraints](https://mlsanity.com/paper/2504.11320/) (2025)
- [Throughput-Optimal Scheduling Algorithms for LLM Inference and AI Agents](https://mlsanity.com/paper/2504.07347/) (2025)
- [Adaptively Robust LLM Inference Optimization under Prediction Uncertainty](https://mlsanity.com/paper/2508.14544/) (2025)
- [A Universal Load Balancing Principle and Its Application to Large Language Model Serving](https://mlsanity.com/paper/2601.17855/) (2026)
- [Queueing, Predictions, and LLMs: Challenges and Open Problems](https://mlsanity.com/paper/2503.07545/) (2025)
- [Distributed Load Balancing with Workload-Dependent Service Rates](https://mlsanity.com/paper/2411.17103/) (2024)
- [Large-Scale LLM Inference with Heterogeneous Workloads: Prefill-Decode Contention and Asymptotically Optimal Control](https://mlsanity.com/paper/2602.02987/) (2026)

## Abstract (arXiv)

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.