Transportation Network Analysis, Volume I: Static and Dynamic Traffic Assignment

TL;DR

Transportation Network Analysis Volume I establishes a rigorous foundation for static and dynamic traffic assignment by formalizing networks, equilibrium concepts, and workable optimization and VI frameworks. It clarifies how link- and path-based representations, together with the Beckmann objective and fixed-point formulations, enable tractable analysis of large-scale road networks while exposing the limitations of static models and motivating dynamic alternatives. The book also surveys network representations, data structures, and foundational algorithms for shortest paths, which underpin traffic assignment solutions, and situates these methods within a broader historical and methodological context. Collectively, this volume provides a comprehensive reference for graduate students and practitioners seeking to understand, formulate, and solve traffic assignment problems, with a planned Volume II addressing transit, freight, and logistics. The approach emphasizes clarity of assumptions, practical data considerations, and the tradeoffs between realism, data requirements, and computational feasibility.

Abstract

This book covers static and dynamic traffic assignment models used in transportation planning and network analysis. Traffic assignment is the final step in the traditional planning process, and recent decades have seen many advances in formulating and solving such models. The book discusses classical solution methods alongside recent ones used in contemporary planning software. The primary audience for the book is graduate students new to transportation network analysis, and to this end there are appendices providing general mathematical background, and more specific background in formulating optimization problems. We have also included appendices discussing more general optimization applications outside of traffic assignment. We believe the book is also of interest to practitioners seeking to understand recent advances in network analysis, and to researchers wanting a unified reference for traffic assignment content. A second volume is currently under preparation, and will cover transit, freight, and logistics models in transportation networks. A free PDF version of the text will always be available online at https://sboyles.github.io/blubook.html. We will periodically post updated versions of the text at this link, along with slides and other instructor resources.

Figures (15)

• Figure 1: Nodes and links in transportation networks.
• Figure 2: Two representations of the same intersection.
• Figure 3: Traffic assignment as interacting systems.
• Figure 4: A more complicated traffic assignment problem, with tolls.
• Figure 5: Schematic of the four-step process.

Theorems & Definitions (2)

• Theorem 2.1
• proof