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Dynamic Pedestrian Traffic Assignment with Link Transmission Model for Bidirectional Sidewalk Networks

Tanapon Lilasathapornkit, Meead Saberi

TL;DR

This paper addresses the challenge of planning urban walking networks under bidirectional pedestrian flows by developing a simulation-based dynamic pedestrian traffic assignment (DPTA) framework that combines dynamic user equilibrium route choice with a link transmission model loading procedure. It introduces a pedestrian-specific travel-time function (pVDF) and a three-dimensional triangular bidirectional fundamental diagram, paired with a first-order node model to reproduce self-organization and shockwave phenomena. Key contributions include a bidirectional DUE formulation, a calibrated 3D bidirectional FD, a compatible node model, and validation across a small grid, a long corridor, and a large-scale Sydney CBD sidewalk network, demonstrating realistic congestion dynamics and path-switching behavior. The framework offers a scalable tool for planning and managing pedestrian infrastructure, enabling more accurate assessment of bidirectional crowd dynamics and informing investment and operations at city scale.

Abstract

Planning assessment of the urban walking infrastructure requires appropriate methodologies that can capture the time-dependent and unique microscopic characteristics of bidirectional pedestrian flow. In this paper, we develop a simulation-based dynamic pedestrian traffic assignment (DPTA) model specifically formulated for walking networks (e.g. sidewalks) with bidirectional links. The model consists of a dynamic user equilibrium (DUE) based route choice and a link transmission model (LTM) for network loading. The formulated DUE adopts a pedestrian volume delay function (pVDF) taking into account the properties of bidirectional pedestrian streams such as self-organization. The adopted LTM uses a three-dimensional triangular bidirectional fundamental diagram as well as a generalized first-order node model. The applicability and validity of the model is demonstrated in hypothetical small networks as well as a real-world large-scale network of sidewalks in Sydney. The model successfully replicates formation and propagation of shockwaves in walking corridors and networks due to bidirectional effects.

Dynamic Pedestrian Traffic Assignment with Link Transmission Model for Bidirectional Sidewalk Networks

TL;DR

This paper addresses the challenge of planning urban walking networks under bidirectional pedestrian flows by developing a simulation-based dynamic pedestrian traffic assignment (DPTA) framework that combines dynamic user equilibrium route choice with a link transmission model loading procedure. It introduces a pedestrian-specific travel-time function (pVDF) and a three-dimensional triangular bidirectional fundamental diagram, paired with a first-order node model to reproduce self-organization and shockwave phenomena. Key contributions include a bidirectional DUE formulation, a calibrated 3D bidirectional FD, a compatible node model, and validation across a small grid, a long corridor, and a large-scale Sydney CBD sidewalk network, demonstrating realistic congestion dynamics and path-switching behavior. The framework offers a scalable tool for planning and managing pedestrian infrastructure, enabling more accurate assessment of bidirectional crowd dynamics and informing investment and operations at city scale.

Abstract

Planning assessment of the urban walking infrastructure requires appropriate methodologies that can capture the time-dependent and unique microscopic characteristics of bidirectional pedestrian flow. In this paper, we develop a simulation-based dynamic pedestrian traffic assignment (DPTA) model specifically formulated for walking networks (e.g. sidewalks) with bidirectional links. The model consists of a dynamic user equilibrium (DUE) based route choice and a link transmission model (LTM) for network loading. The formulated DUE adopts a pedestrian volume delay function (pVDF) taking into account the properties of bidirectional pedestrian streams such as self-organization. The adopted LTM uses a three-dimensional triangular bidirectional fundamental diagram as well as a generalized first-order node model. The applicability and validity of the model is demonstrated in hypothetical small networks as well as a real-world large-scale network of sidewalks in Sydney. The model successfully replicates formation and propagation of shockwaves in walking corridors and networks due to bidirectional effects.
Paper Structure (14 sections, 14 equations, 17 figures, 3 tables)

This paper contains 14 sections, 14 equations, 17 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Route choice model
  4. Dynamic User Equilibrium.
  5. Link travel time function
  6. Turning fraction
  7. Dynamic network loading
  8. Link Model
  9. Node Model
  10. Numerical Experiments
  11. Small grid network
  12. Long corridor
  13. Large-scale real network application: Sydney footpath network
  14. Conclusion

Figures (17)

  • Figure 1: An overview of the proposed DPTA model.
  • Figure 2: Three dimensional bidirectional fundamental diagram based on (a) a logistic function (b) a power function (c) the function proposed by flotterod2015bidirectional. Grey points represent empirical data used for calibration (d) A comparison between three FDs for unidirectional flow when density ratio $\rho _{a}$ = 1.
  • Figure 3: A node model example
  • Figure 4: Small network demonstration: (a) the grid network structure. Pink circles represent nodes and gray lines with arrows represent directional links. (b) The demand profile for scenarios 1 and 3 with unidirectional flows. The black line represents demand from node 1 to node 9. (c) The demand profile for scenario 2 with bidirectional flows. The black line represents demand from node 1 to node 9 and the orange line represents demand from node 8 to node 4.
  • Figure 5: The convergence pattern in scenario 1, 2, and 3.
  • ...and 12 more figures