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An equilibrium-seeking search algorithm for integrating large-scale activity-based and dynamic traffic assignment models

Serio Agriesti, Claudio Roncoli, Bat-hen Nahmias-Biran

TL;DR

The results suggest that the proposed iterative approach does perform well, reaching equilibrium between demand and supply in a limited number of iterations thanks to its perturbation techniques.

Abstract

This paper proposes an iterative methodology to integrate large-scale behavioral activity-based models with dynamic traffic assignment models. The main novelty of the proposed approach is the decoupling of the two parts, allowing the ex-post integration of any existing model as long as certain assumptions are satisfied. A measure of error is defined to characterize a search space easily explorable within its boundaries. Within it, a joint distribution of the number of trips and travel times is identified as the equilibrium distribution, i.e., the distribution for which trip numbers and travel times are bound in the neighborhood of the equilibrium between supply and demand. The approach is tested on a medium-sized city of 400,000 inhabitants and the results suggest that the proposed iterative approach does perform well, reaching equilibrium between demand and supply in a limited number of iterations thanks to its perturbation techniques. Overall, 15 iterations are needed to reach values of the measure of error lower than 10%. The equilibrium identified this way is then validated against baseline distributions to demonstrate the goodness of the results.

An equilibrium-seeking search algorithm for integrating large-scale activity-based and dynamic traffic assignment models

TL;DR

The results suggest that the proposed iterative approach does perform well, reaching equilibrium between demand and supply in a limited number of iterations thanks to its perturbation techniques.

Abstract

This paper proposes an iterative methodology to integrate large-scale behavioral activity-based models with dynamic traffic assignment models. The main novelty of the proposed approach is the decoupling of the two parts, allowing the ex-post integration of any existing model as long as certain assumptions are satisfied. A measure of error is defined to characterize a search space easily explorable within its boundaries. Within it, a joint distribution of the number of trips and travel times is identified as the equilibrium distribution, i.e., the distribution for which trip numbers and travel times are bound in the neighborhood of the equilibrium between supply and demand. The approach is tested on a medium-sized city of 400,000 inhabitants and the results suggest that the proposed iterative approach does perform well, reaching equilibrium between demand and supply in a limited number of iterations thanks to its perturbation techniques. Overall, 15 iterations are needed to reach values of the measure of error lower than 10%. The equilibrium identified this way is then validated against baseline distributions to demonstrate the goodness of the results.
Paper Structure (15 sections, 5 equations, 17 figures, 4 tables)

This paper contains 15 sections, 5 equations, 17 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Assumptions and theoretical background
  4. Definition of a measure of error (MoE)
  5. Characterization of the search space and equilibrium search
  6. A heuristic algorithm solution to a local search problem
  7. Case Study
  8. The activity-based model
  9. The traffic assignment model
  10. Numerical results
  11. First set of iterations: Search space characterization
  12. Second set of iterations: Perturbation
  13. Stability of the equilibrium
  14. Summary of the baseline results and validation
  15. Conclusions

Figures (17)

  • Figure 1: The proposed iterative approach - the gray thread represents the data exchange
  • Figure 2: Assumption 1: Inverse correlation between travel time ($tt$) and number of trips ($n$) - For each OD pair, an increase in travel time (from iteration i1 to iteration i2 - through fa,x) results in a lower number of trips and vice-versa (i2 to i1 through fb)
  • Figure 3: Network effects at a crossing
  • Figure 4: Area comparison between iteration 1 and 2
  • Figure 5: First round of iterations - morning (left) and afternoon peak (right); perturbed iterations shaded in light blue
  • ...and 12 more figures