# Queueing-Aware Optimization of Reasoning Tokens for Accuracy-Latency Trade-offs in LLM Servers

arXiv: https://arxiv.org/abs/2601.10274 · HTML: https://mlsanity.com/paper/2601.10274/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 18 of its 24 references that are in the map.
- First posted on arXiv 15 Jan 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 18 of 18)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [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)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Efficiently Scaling Transformer Inference](https://mlsanity.com/paper/2211.05102/) (2022)
- [Confident Adaptive Language Modeling](https://mlsanity.com/paper/2207.07061/) (2022)
- [CRUXEval: A Benchmark for Code Reasoning, Understanding and Execution](https://mlsanity.com/paper/2401.03065/) (2024)
- [Deja Vu: Contextual Sparsity for Efficient LLMs at Inference Time](https://mlsanity.com/paper/2310.17157/) (2023)
- [Response Length Perception and Sequence Scheduling: An LLM-Empowered LLM Inference Pipeline](https://mlsanity.com/paper/2305.13144/) (2023)
- [AlpaServe: Statistical Multiplexing with Model Parallelism for Deep Learning Serving](https://mlsanity.com/paper/2302.11665/) (2023)
- [A Queueing Theoretic Perspective on Low-Latency LLM Inference with Variable Token Length](https://mlsanity.com/paper/2407.05347/) (2024)

## Abstract (arXiv)

We consider a single large language model (LLM) server that serves a heterogeneous stream of queries belonging to N distinct task types. Queries arrive according to a Poisson process, and each type occurs with a known prior probability. For each task type, the server allocates a fixed number of internal thinking tokens, which determines the computational effort devoted to that query. The token allocation induces an accuracy-latency trade-off: the service time follows an approximately affine function of the allocated tokens, while the probability of a correct response exhibits diminishing returns. Under a first-in, first-out (FIFO) service discipline, the system operates as an M/G/1 queue, and the mean system time depends on the first and second moments of the resulting service-time distribution. We formulate a constrained optimization problem that maximizes a weighted average accuracy objective penalized by the mean system time, subject to architectural token-budget constraints and queue-stability conditions. The objective function is shown to be strictly concave over the stability region, which ensures existence and uniqueness of the optimal token allocation. The first-order optimality conditions yield a coupled projected fixed-point characterization of the optimum, together with an iterative solution and an explicit sufficient condition for contraction. Moreover, a projected gradient method with a computable global step-size bound is developed to guarantee convergence beyond the contractive regime. Finally, integer-valued token allocations are attained via rounding of the continuous solution, and the resulting performance loss is evaluated in simulation results.