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Feedback-feedforward Signal Control with Exogenous Demand Estimation in Congested Urban Road Networks

Leonardo Pedroso, Pedro Batista, Markos Papageorgiou

TL;DR

This paper tackles congestion in urban road networks by exploiting the store-and-forward model and existing loop-sensor infrastructure to jointly estimate link occupancy $x_z(k)$ and net exogenous demand $e_z(k)$ in real time. It couples a Kalman-filter-based estimator with a linear-quadratic regulator to produce a feedback-feedforward traffic-signal controller that directly accounts for time-varying exogenous load via a feedforward term. The authors demonstrate, through simulations on the Chania network, that incorporating exogenous-demand estimates yields meaningful performance gains, especially during exogenous surges, and that the approach remains implementable in real time with a single loop detector per link. Overall, the work shows how real-time demand estimation can elevate traffic-responsive control beyond robust-tuning strategies by actively compensating for forecasted disturbances, improving travel-time and queue balance in urban networks.

Abstract

To cope with uncertain traffic patterns and traffic models, traffic-responsive signal control strategies in the literature are designed to be robust to these uncertainties. These robust strategies still require sensing infrastructure to implement traffic-responsiveness. In this paper, we take a novel perspective and show that it is possible to use the already necessary sensing infrastructure to estimate the uncertain quantities in real time. Specifically, resorting to the store-and-forward model, we design a novel network-wide traffic-responsive strategy that estimates the occupancy and exogenous demand in each link, i.e., entering (exiting) vehicle flows at the origins (destinations) of the network or within links, in real time. Borrowing from optimal control theory, we design an optimal linear quadratic control scheme, consisting of a linear feedback term, of the occupancy of the road links, and a feedforward component, which accounts for the varying exogenous vehicle load on the network. Thereby, the resulting control scheme is a simple feedback-feedforward controller, which is fed with occupancy and exogenous demand estimates, and is suitable for real-time implementation. Numerical simulations for the urban traffic network of Chania, Greece, show that, for realistic surges in the exogenous demand, the proposed solution significantly outperforms tried-and-tested solutions that ignore the exogenous demand.

Feedback-feedforward Signal Control with Exogenous Demand Estimation in Congested Urban Road Networks

TL;DR

This paper tackles congestion in urban road networks by exploiting the store-and-forward model and existing loop-sensor infrastructure to jointly estimate link occupancy and net exogenous demand in real time. It couples a Kalman-filter-based estimator with a linear-quadratic regulator to produce a feedback-feedforward traffic-signal controller that directly accounts for time-varying exogenous load via a feedforward term. The authors demonstrate, through simulations on the Chania network, that incorporating exogenous-demand estimates yields meaningful performance gains, especially during exogenous surges, and that the approach remains implementable in real time with a single loop detector per link. Overall, the work shows how real-time demand estimation can elevate traffic-responsive control beyond robust-tuning strategies by actively compensating for forecasted disturbances, improving travel-time and queue balance in urban networks.

Abstract

To cope with uncertain traffic patterns and traffic models, traffic-responsive signal control strategies in the literature are designed to be robust to these uncertainties. These robust strategies still require sensing infrastructure to implement traffic-responsiveness. In this paper, we take a novel perspective and show that it is possible to use the already necessary sensing infrastructure to estimate the uncertain quantities in real time. Specifically, resorting to the store-and-forward model, we design a novel network-wide traffic-responsive strategy that estimates the occupancy and exogenous demand in each link, i.e., entering (exiting) vehicle flows at the origins (destinations) of the network or within links, in real time. Borrowing from optimal control theory, we design an optimal linear quadratic control scheme, consisting of a linear feedback term, of the occupancy of the road links, and a feedforward component, which accounts for the varying exogenous vehicle load on the network. Thereby, the resulting control scheme is a simple feedback-feedforward controller, which is fed with occupancy and exogenous demand estimates, and is suitable for real-time implementation. Numerical simulations for the urban traffic network of Chania, Greece, show that, for realistic surges in the exogenous demand, the proposed solution significantly outperforms tried-and-tested solutions that ignore the exogenous demand.
Paper Structure (16 sections, 4 theorems, 55 equations, 10 figures, 2 tables)

This paper contains 16 sections, 4 theorems, 55 equations, 10 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Statement of Contributions
  3. Organization
  4. Notation
  5. Problem statement
  6. Store-and-forward model
  7. Nonlinear model
  8. Objectives and framework
  9. Estimation of occupancy and exogenous demand
  10. Feedback-feedforward signal control
  11. Simulation results
  12. Synthetic Exogenous Demand Scenario
  13. Realistic Exogenous Demand Scenario
  14. Discussion
  15. Conclusion
  16. ...and 1 more sections

Key Result

Lemma 1

Consider a feasible traffic network characterized by $(\mathcal{G},\mathbf{T},\mathbf{t_0})$ and a minimum complete stage strategy characterized by stage matrix $\mathbf{S}$. Let $\mathbfcal{C}$ be the controllability matrix of the store-and-forward LTI system eq:LTI_saf_cte. Then, $\mathrm{rank}(\m

Figures (10)

  • Figure 1: Scheme of the store-and-forward occupancy dynamics of link $z$.
  • Figure 2: Chania urban traffic network topology graph PedrosoBatistaEtAl2022Saffron.
  • Figure 3: Exogenous demand in some links.
  • Figure 4: Comparison of estimate, ground-truth, and measurement of the occupancy of link $20$.
  • Figure 5: Evolution of the estimate of the exogenous demand on link $20$.
  • ...and 5 more figures

Theorems & Definitions (8)

  • Remark 2.1
  • Lemma 1: PedrosoBatista2021SignalControl
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Lemma 4
  • proof