RouterBench: Routing Benchmark Framework

• RouterBench is a formal benchmarking framework that defines and measures routing system performance, cost efficiency, and quality in AI, networking, and other domains.
• Its methodology employs cost–quality tradeoff analysis, convex hull formation, and multi-objective metrics to rigorously compare routing strategies.
• The framework integrates diverse datasets and evaluation techniques, providing actionable insights for improving LLM routing, classical network systems, vehicle routing, quantum circuits, and VLSI design.

RouterBench is a formal benchmarking framework designed to evaluate the performance, cost efficiency, and robustness of LLM routing systems, as well as a range of other routing and optimization approaches in networking, vehicle routing, quantum circuits, and VLSI design. Its development addresses the need for standardized, systematic comparison of routing strategies across diverse domains, including both classical and AI-based settings. With foundational support for multi-objective analysis, cost-quality tradeoff exploration, and compatibility with large heterogeneous datasets, RouterBench has become an essential research tool for quantifying and diagnosing the strengths, limitations, and risks of routing mechanisms.

1. Definition and Motivation

RouterBench arises from the necessity to objectively measure the effectiveness of routing systems, especially in environments with multiple candidate models or paths, competing resource constraints, and task-specific performance criteria. In the context of LLMs, routers dynamically select one from a pool of models to process a given query, aiming to maximize output quality while minimizing cost. The absence of a unified evaluation protocol has led to the design of RouterBench—a framework that combines rich benchmark datasets (such as over 405k inference results from 11 LLMs (Hu et al., 18 Mar 2024)) and principled cost-quality metrics to rigorously assess routing strategies. Analogous requirements exist in classical networking (TCAM-based IP lookup (Mahini et al., 2010), performance-driven path selection (Apostolaki et al., 2020)), logistics (vehicle and pathfinding benchmarks (Weise et al., 2020, Tricoire, 2021)), and quantum routing (Pina-Canelles et al., 6 Feb 2025), each motivating domain-specific extensions.

2. Framework Architecture and Theoretical Principles

RouterBench formalizes routing evaluation along the cost-quality plane. Each router is modeled as a black-box function, $R_\theta(x) \to \text{LLM}_i$, mapping input $x$ to a candidate LLM under user-defined parameters $\theta$ (including cost constraints). For any LLM $m$ and dataset $D$,

$$c_m = \mathbb{E}[c(\text{LLM}_m(x)) \mid x \in D], \qquad q_m = \mathbb{E}[q(\text{LLM}_m(x)) \mid x \in D]$$

allow quantification of model cost and quality.

RouterBench applies linear interpolation and extrapolation to generate attainable points on the cost-quality frontier, and constructs non-decreasing convex hulls to optimize over possible trade-offs, ensuring monotonic improvements with increasing cost.

A critical scalar metric, Average Improvement in Quality (AIQ), is defined as:

$\text{AIQ}(R_\theta) = \frac{1}{c_{\max} - c_{\min}} \int_{c_{\min}}^{c_{\max}} \text{optimal quality at cost %%%%5%%%%} \, dc$

This enables direct ranking and comparison of routers independent of domain specifics.

3. Benchmark Datasets and Multi-Domain Coverage

RouterBench incorporates datasets spanning:

• LLM routing: 405k+ outcomes from 11 models across 8 task types (reasoning, knowledge, math, coding, RAG, etc.) (Hu et al., 18 Mar 2024).
• Classical IP routing: Telstra routing tables, TCAM configurations, and power-consumption metrics (Mahini et al., 2010).
• Internet path selection: Performance traces, BGP-compatible routing states, and programmable switch deployments (Apostolaki et al., 2020).
• Vehicle routing: Data for 2-opt, Or-opt, LNS, ESPPRC, and maxflow algorithms across multiple programming languages (Tricoire, 2021).
• Quantum device routing: Random circuit ensembles for NISQ architectures, fidelity metrics, and SWAP/circuit depth statistics (Pina-Canelles et al., 6 Feb 2025).

These datasets are compiled, cleaned, and normalized as needed (including one-hot encoding for categorical attributes and log+minmax scaling for heavy-tailed numerical features (Giakatos et al., 2022)).

4. Evaluation Methodologies and Comparative Analysis

RouterBench implements diverse routing strategies for comparative performance analysis:

• Predictive routers using supervised regression or classification models to estimate cost and accuracy per candidate; selection via trade-off parameter $\lambda$ in $score_{ij} = \lambda P_{ij} - \text{cost}_j$ (Hu et al., 18 Mar 2024, Somerstep et al., 5 Feb 2025).
• Cascading routers invoking models in cost order until a judge function with error $\varepsilon$ aborts or escalates (Hu et al., 18 Mar 2024).
• Minimax plug-in routers solving $$\hat{g}_\mu(x) = \arg\min_m \sum_k \mu_k [\hat\Phi(x)]_{m,k}$$ for a convex combination of risk metrics $\mu$ (Somerstep et al., 5 Feb 2025).
• Structured and contrastively trained routers (RadialRouter) using RadialFormer for embedding query–LLM relations, optimized via combined KL divergence and query-query contrastive loss (Jin et al., 4 Jun 2025).
• Benchmarks against naive, zero, and oracle routers that select LLMs solely based on best expected cost-quality values.

Results are aggregated on the cost–quality plane, with convex hulls and Pareto frontiers highlighting trade-offs. For instance, RadialRouter achieves 9.2% improvement in “Balance” trade-off and 5.8% in “Cost First” routing compared to standard baselines on RouterBench (Jin et al., 4 Jun 2025).

5. Diagnostic Tools and Robustness Assessment

RouterBench has been extended to DRSC/DSC-style evaluation (Kassem et al., 20 Mar 2025) with metrics:

• Proportion of queries routed to strong models,

$$P_{\text{strong}} = \frac{N_{\text{strong}}}{N_{\text{total}}} \times 100$$

• Categorical breakdown for coding, translation, math, factual, privacy, and adversarial prompts, revealing inefficiencies in category-based heuristics.
• Privacy and safety risk analysis via PUPA and adversarial query subsets, testing for backdoor vulnerability and jailbreaking risk.
• Sensitivity and calibration tests (robustness to query perturbation), showing that keyword presence can flip routing decisions up to 98% of the time, indicating superficial complexity estimation.

6. Extensions Beyond LLMs

RouterBench methodologies have direct analogs in classical routing domains:

• Power-efficient TCAM architectures evaluated for mean enabled bits per search (MEPS) and Power Optimization Factor (POF), becoming benchmarking standards for search-related power consumption (Mahini et al., 2010).
• Performance-driven BGP routing monitored using P4-enabled switches with memory-efficient counters and real-time control plane optimization, enabling sub-second adaptive routing (Apostolaki et al., 2020).
• Vehicle and generic pathfinding optimization using multi-objective evolutionary algorithms (NSGA-II, NSGA-III, d-NSGA-II) and Pareto-front indicators (IGD+) (Weise et al., 2020).
• Quantum circuit routing in NISQ devices benchmarked for SWAP count, circuit depth overhead, and overall fidelity, demonstrating up to 84% fidelity improvement using advanced SABRE variants (Pina-Canelles et al., 6 Feb 2025).
• VLSI routing and RL-based environments (XRoute) evaluated for solution quality via wirelength, via count, and design rule violations, using reinforcement learning algorithms versus search-based methods (Zhou et al., 2023).

7. Impact, Limitations, and Prospects

RouterBench formalizes cross-domain routing evaluation, driving advances in efficiency, security, and practical deployment. Its general framework enables calibration, diagnosis, and comparison of complex routing systems under real-world cost, latency, and robustness constraints. Limitations include sensitivity to benchmark selection, the need for high-quality labeled data for supervised approaches, and domain-specific requirements for truly representative performance metrics. Active areas include incorporation of latency and throughput metrics, privacy/safety auditing, dynamic pool adaptation strategies, and hybrid algorithmic–learning methods. As routing problems, both in AI and communication systems, grow in complexity, RouterBench provides the scalable infrastructure necessary for principled, reproducible benchmarking and systematic improvement.