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A Max Pressure Algorithm for Traffic Signals Considering Pedestrian Queues

Hao Liu, Vikash V. Gayah, Michael Levin

TL;DR

The proposed algorithm outperforms both models since the states of both vehicles and pedestrians are taken into consideration to determine signal timings, and it also exhibits the maximum stability property for both vehicles and pedestrians.

Abstract

This paper proposes a novel max-pressure (MP) algorithm that incorporates pedestrian traffic into the MP control architecture. Pedestrians are modeled as being included in one of two groups: those walking on sidewalks and those queued at intersections waiting to cross. Traffic dynamics models for both groups are developed. Under the proposed control policy, the signal timings are determined based on the queue length of both vehicles and pedestrians waiting to cross the intersection. The proposed algorithm maintains the decentralized control structure, and the paper proves that it also exhibits the maximum stability property for both vehicles and pedestrians. Microscopic traffic simulation results demonstrate that the proposed model can improve the overall operational efficiency -- i.e., reduce person travel delays -- under various vehicle demand levels compared to the original queue-based MP (Q-MP) algorithm and a recently developed rule-based MP algorithm considering pedestrians. The Q-MP ignores the yielding behavior of right-turn vehicles to conflicting pedestrian movements, which leads to high delay for vehicles. On the other hand, the delay incurred by pedestrians is high from the rule-based model since it imposes large waiting time tolerance to guarantee the operational efficiency of vehicles. The proposed algorithm outperforms both models since the states of both vehicles and pedestrians are taken into consideration to determine signal timings.

A Max Pressure Algorithm for Traffic Signals Considering Pedestrian Queues

TL;DR

The proposed algorithm outperforms both models since the states of both vehicles and pedestrians are taken into consideration to determine signal timings, and it also exhibits the maximum stability property for both vehicles and pedestrians.

Abstract

This paper proposes a novel max-pressure (MP) algorithm that incorporates pedestrian traffic into the MP control architecture. Pedestrians are modeled as being included in one of two groups: those walking on sidewalks and those queued at intersections waiting to cross. Traffic dynamics models for both groups are developed. Under the proposed control policy, the signal timings are determined based on the queue length of both vehicles and pedestrians waiting to cross the intersection. The proposed algorithm maintains the decentralized control structure, and the paper proves that it also exhibits the maximum stability property for both vehicles and pedestrians. Microscopic traffic simulation results demonstrate that the proposed model can improve the overall operational efficiency -- i.e., reduce person travel delays -- under various vehicle demand levels compared to the original queue-based MP (Q-MP) algorithm and a recently developed rule-based MP algorithm considering pedestrians. The Q-MP ignores the yielding behavior of right-turn vehicles to conflicting pedestrian movements, which leads to high delay for vehicles. On the other hand, the delay incurred by pedestrians is high from the rule-based model since it imposes large waiting time tolerance to guarantee the operational efficiency of vehicles. The proposed algorithm outperforms both models since the states of both vehicles and pedestrians are taken into consideration to determine signal timings.
Paper Structure (19 sections, 4 theorems, 39 equations, 11 figures)

This paper contains 19 sections, 4 theorems, 39 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Traffic dynamics
  3. Vehicle traffic dynamics
  4. Pedestrian dynamics
  5. Max pressure algorithm incorporating pedestrians
  6. Signal control algorithm
  7. Maximum stability property
  8. Stable region
  9. Maximum stability
  10. Numerical simulation
  11. Network setup
  12. Implementation of signal control algorithms
  13. Results
  14. Stable regions
  15. Travel delay
  16. ...and 4 more sections

Key Result

Theorem 1

The proposed PQ-MP algorithm Equations eq:veh_weight--eq:opt stabilizes the queue process if $(\mathbf{d}^{\mathrm{v}}, \mathbf{p}^{\mathrm{in}})\in (\pazocal{D}^0, \pazocal{Q}_{\mathrm{in}}^0)$ and if the distribution of the adjusted saturation flow, $\tilde{C}^{\mathrm{v}}_{h,i,j}(t)$ in Equation

Figures (11)

  • Figure 1: Pedestrian network.
  • Figure 2: Network setup.
  • Figure 3: Signal configuration.
  • Figure 4: Evolution of number of vehicles and pedestrians under Q-MP.
  • Figure 5: Evolution of number of vehicles and pedestrians under rule-based MP.
  • ...and 6 more figures

Theorems & Definitions (9)

  • Definition 1
  • Definition 2
  • Theorem 1: Maximum stability
  • proof
  • Lemma 1
  • Lemma 2
  • proof
  • Lemma 3
  • proof