# Position: LLM Serving Needs Mathematical Optimization and Algorithmic Foundations, Not Just Heuristics

arXiv: https://arxiv.org/abs/2605.01280 · HTML: https://mlsanity.com/paper/2605.01280/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Serving systems and request scheduling, one of 12 directions in Efficient LLM inference and serving.
- Builds on 27 of its 57 references that are in the map.
- First posted on arXiv 2 May 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, 27 of 27)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding](https://mlsanity.com/paper/2006.16668/) (2020)
- [SGLang: Efficient Execution of Structured Language Model Programs](https://mlsanity.com/paper/2312.07104/) (2023)
- [Mixture-of-Experts with Expert Choice Routing](https://mlsanity.com/paper/2202.09368/) (2022)
- [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)
- [Auxiliary-Loss-Free Load Balancing Strategy for Mixture-of-Experts](https://mlsanity.com/paper/2408.15664/) (2024)
- [Competitive caching with machine learned advice](https://mlsanity.com/paper/1802.05399/) (2018)
- [Llumnix: Dynamic Scheduling for Large Language Model Serving](https://mlsanity.com/paper/2406.03243/) (2024)
- [DynamoLLM: Designing LLM Inference Clusters for Performance and Energy Efficiency](https://mlsanity.com/paper/2408.00741/) (2024)
- [SpotServe: Serving Generative Large Language Models on Preemptible Instances](https://mlsanity.com/paper/2311.15566/) (2023)
- [ServerlessLLM: Low-Latency Serverless Inference for Large Language Models](https://mlsanity.com/paper/2401.14351/) (2024)
- [Don't Stop Me Now: Embedding Based Scheduling for LLMs](https://mlsanity.com/paper/2410.01035/) (2024)
- [Simple and Fast Algorithm for Binary Integer and Online Linear Programming](https://mlsanity.com/paper/2003.02513/) (2020)
- [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)
- [ModServe: Modality- and Stage-Aware Resource Disaggregation for Scalable Multimodal Model Serving](https://mlsanity.com/paper/2502.00937/) (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)
- [ElasticMM: Efficient Multimodal LLMs Serving with Elastic Multimodal Parallelism](https://mlsanity.com/paper/2507.10069/) (2025)
- [LLM Serving Optimization with Variable Prefill and Decode Lengths](https://mlsanity.com/paper/2508.06133/) (2025)
- [An Inquiry into Datacenter TCO for LLM Inference with FP8](https://mlsanity.com/paper/2502.01070/) (2025)

## Built on by (most cited first, 1 of 1)

- [Tackling the Data-Parallel Load Balancing Bottleneck in LLM Serving: Practical Online Routing at Scale](https://mlsanity.com/paper/2605.06113/) (2026)

## Abstract (arXiv)

This position paper argues that LLM inference serving has outgrown generic heuristics and now demands mathematical optimization and algorithmic foundations. Despite rapid advances in serving systems such as vLLM and SGLang, their algorithmic cores remain largely unchanged from classical distributed computing: request routing uses join-shortest-queue or round-robin, scheduling defaults to FIFO, and KV cache eviction follows LRU. These general-purpose policies ignore the distinctive structure of LLM inference--dynamically growing KV cache memory, prefill-decode phase asymmetry, unknown output lengths, and continuous batching constraints. We contend that the field must develop mathematical models capturing these characteristics, enabling the design of algorithms with provable performance guarantees across diverse workloads, rather than heuristics that may succeed in some scenarios but fail unpredictably in others. Emerging work at the intersection of operations research and ML systems demonstrates that principled methods can match or exceed heuristic performance while providing theoretical guarantees. We call on the community to recognize algorithmic design for LLM serving as a research frontier.