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Selection of the Speed Command Distance for Improved Performance of a Rule-Based VSL and Lane Change Control

Tianchen Yuan, Faisal Alasiri, Petros A. Ioannou

TL;DR

This work analyzes how the distance to the upstream variable speed limit (VSL) zone, $L_0$, affects closed-loop freeway control with a multi-section CTM that accounts for capacity drop and bounded acceleration. It derives a lower bound on $L_0$ to ensure congestion is absorbed before downstream traffic reaches the bottleneck, and provides a piecewise rule-based VSL design that matches the upstream inflow to bottleneck capacity, complemented by a lane-change controller to mitigate capacity drop. A stability analysis shows exponential convergence of densities to the equilibrium after congestion clearance, and microscopic simulations on an I-710-like network validate the bound and demonstrate mobility and emission benefits when $L_0$ satisfies or exceeds the bound, particularly under high demand. The results offer a practical design tool for tuning $L_0$ and show that concentrating control upstream can outperform a front-loaded feedback-linearization VSL in heavy-traffic scenarios, with implications for integration with ramp metering in more complex networks.

Abstract

Variable Speed Limit (VSL) control has been one of the most popular techniques with the potential of smoothing traffic flow, maximizing throughput at bottlenecks, and improving mobility and safety. Despite the substantial research efforts in the application of VSL control, few studies have looked into the effect of the VSL sign distance from the point of an accident or a bottleneck. In this paper, we show that this distance has a significant impact on the effectiveness and performance of VSL control. We propose a rule-based VSL strategy that matches the outflow of the upstream VSL zone with the bottleneck capacity based on a multi-section Cell Transmission Model (CTM). Then, we consider the distance of the upstream VSL zone as a control variable and perform a comprehensive analysis of its impact on the performance of the closed-loop traffic control system based on the multi-section CTM. We develop a lower bound that this distance needs to satisfy in order to guarantee homogeneous traffic density across sections and reduce bottleneck congestion. The bound is verified analytically and demonstrated using microscopic simulation of traffic on I-710 in Southern California. The simulations are used to quantify the benefits on mobility, safety and emissions obtained by selecting the upstream VSL zone distance to satisfy the analytical lower bound. The developed lower bound is a design tool which can be used to tune and improve the performance of VSL controllers.

Selection of the Speed Command Distance for Improved Performance of a Rule-Based VSL and Lane Change Control

TL;DR

This work analyzes how the distance to the upstream variable speed limit (VSL) zone, , affects closed-loop freeway control with a multi-section CTM that accounts for capacity drop and bounded acceleration. It derives a lower bound on to ensure congestion is absorbed before downstream traffic reaches the bottleneck, and provides a piecewise rule-based VSL design that matches the upstream inflow to bottleneck capacity, complemented by a lane-change controller to mitigate capacity drop. A stability analysis shows exponential convergence of densities to the equilibrium after congestion clearance, and microscopic simulations on an I-710-like network validate the bound and demonstrate mobility and emission benefits when satisfies or exceeds the bound, particularly under high demand. The results offer a practical design tool for tuning and show that concentrating control upstream can outperform a front-loaded feedback-linearization VSL in heavy-traffic scenarios, with implications for integration with ramp metering in more complex networks.

Abstract

Variable Speed Limit (VSL) control has been one of the most popular techniques with the potential of smoothing traffic flow, maximizing throughput at bottlenecks, and improving mobility and safety. Despite the substantial research efforts in the application of VSL control, few studies have looked into the effect of the VSL sign distance from the point of an accident or a bottleneck. In this paper, we show that this distance has a significant impact on the effectiveness and performance of VSL control. We propose a rule-based VSL strategy that matches the outflow of the upstream VSL zone with the bottleneck capacity based on a multi-section Cell Transmission Model (CTM). Then, we consider the distance of the upstream VSL zone as a control variable and perform a comprehensive analysis of its impact on the performance of the closed-loop traffic control system based on the multi-section CTM. We develop a lower bound that this distance needs to satisfy in order to guarantee homogeneous traffic density across sections and reduce bottleneck congestion. The bound is verified analytically and demonstrated using microscopic simulation of traffic on I-710 in Southern California. The simulations are used to quantify the benefits on mobility, safety and emissions obtained by selecting the upstream VSL zone distance to satisfy the analytical lower bound. The developed lower bound is a design tool which can be used to tune and improve the performance of VSL controllers.

Paper Structure

This paper contains 14 sections, 2 theorems, 25 equations, 9 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Multi-Section Cell Transmission Model
  4. Control Design
  5. Rule-Based Variable Speed Limit Control
  6. Analysis of VSL Zone Distance
  7. Lane Change Control
  8. Stability Analysis
  9. Numerical Simulations
  10. Simulation Network and Parameter Selection
  11. Performance Measurements
  12. Microscopic Simulations
  13. Proposed VSL vs. Feedback-Linearization VSL
  14. Conclusion

Key Result

Theorem 1

Consider the freeway bottleneck control problem with a constant demand $d \geq (1-\epsilon_0)C_d$ and VSL commands given by (eq:v0_VSLcommand) and (eq:vi_VSLcommand). The propagation of the traffic congestion at the bottleneck can be completely absorbed by the low-density area created by the VSL con where $\rho_i$ is the measured density of section $i$, for $i=0,1,2,...,N$. $C_d$ is the downstream

Figures (9)

  • Figure 1: Representation of a motorway stretch within the multi-section CTM framework with the VSL control.
  • Figure 2: Triangular fundamental diagram under VSL Control. The red curve represents the supply function. The blue curve represents the demand function.
  • Figure 3: The behavior of flow curves with time when the VSL is activated.
  • Figure 4: The I-710 simulation network.
  • Figure 5: Fundamental diagram of the simulation network with (red) and without (blue) incident.
  • ...and 4 more figures

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Theorem 2
  • proof