Review of volume-delay functions integrating traditional models and emerging AI technologies

[Purposes] Link Performance Functions (LPFs) underpin the estimation of travel times, delays, and congestion in transportation network models. As multimodal systems become increasingly data-rich and feature Connected and Automated Vehicles (CAVs), Electric Vehicles (EVs), and complex queuing phenomena, traditional LPFs face limitations in accuracy, physical consistency, and real-time adaptability. This review synthesizes the evolution of LPFs to address these modern challenges and to bridge theoretical foundations, diverse data sources, and artificial intelligence (AI) techniques. [Methods] We conduct a systematic literature survey of over 270 peer-reviewed studies, covering (i) classical empirical forms (e.g., BPR, Davidson), (ii) theory-driven models (fundamental-diagram and fluid-queue approaches), and (iii) AI-augmented frameworks (LSTM, GNN, Transformer, and physics-informed learning). Models are classified by their mathematical assumptions, data requirements, integration with Dynamic Traffic Assignment tools, and support for multimodal flow interactions. We further evaluate each class against emerging criteria: queuing dynamics, CAV/EV impacts, data fusion complexity, and computational tractability, with the following [Highlights]: (1) emergence of hybrid physics-machine learning (ML) models that enforce conservation laws while leveraging large-scale probe and sensor data; (2) critical gaps in AI-related methods evaluation: reliance on point-error metrics rather than system-level Key Performance Indicators (KPIs) (e.g., network delay, throughput, queue length, bottleneck durations). By bridging theory, data, and AI, this review maps the current landscape of LPFs, highlights open research directions (e.g., fully differentiable LPFs, uncertainty quantification, real-time adaptation), and provides a roadmap for developing robust, transparent models suited to next-generation multimodal transportation networks. (3) Physics-Informed Neural Networks (PINNs) achieve superior predictive accuracy in travel time estimation while maintaining physical consistency, demonstrating clear advantages over both traditional LPFs and other data-driven approaches.