⚡ electrical engineering

Distributive Perimetral Queue Balancing Mechanisms: Towards Equitable Urban Traffic Gating and Fair Perimeter Control

This paper proposes a distributive perimetral queue balancing mechanism that integrates fairness objectives into urban traffic gating, demonstrating through a San Francisco case study that such strategies can maintain system efficiency while significantly improving equitable delay distribution across entry points compared to conventional perimeter control.

Original authors: Kevin Riehl, Lea Künstler, Ying-Chuan Ni, Anastasia Psarou, Shaimaa K. El-Baklish, Anastasios Kouvelas, Michail A. Makridis

Published 2026-04-10

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Kevin Riehl, Lea Künstler, Ying-Chuan Ni, Anastasia Psarou, Shaimaa K. El-Baklish, Anastasios Kouvelas, Michail A. Makridis

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a busy city center, like the Financial District in San Francisco, as a giant, crowded party.

The Problem: The "All-Or-Nothing" Bouncer
Right now, traffic management works a bit like a bouncer at the door of a club who only cares about the total number of people inside. If the club gets too crowded, the bouncer stops letting anyone in. He doesn't care who is waiting outside.

In traffic terms, this is called Perimeter Control. It's a smart system that slows down cars entering a congested zone to keep the inside moving smoothly. But there's a catch: because the bouncer treats everyone the same, some people waiting at the door might be stuck in a massive, hours-long line, while others just a few blocks away get through quickly. It's efficient for the club as a whole, but it feels incredibly unfair to the person stuck in the longest line.

The New Idea: The "Fair Queue" Bouncer
This paper proposes a smarter bouncer. Instead of just looking at the total crowd count, this new system looks at the lines at every single entrance.

Think of it like a restaurant with multiple host stands.

The Old Way: The manager sees the restaurant is full, so they tell all host stands to stop seating people. One stand might have a line of 50 people, while another has only 2. Both get the same "stop" signal.
The New Way: The manager sees the restaurant is full, but notices Stand A has a huge line and Stand B has almost no one. The manager tells Stand A to slow down significantly, but tells Stand B to keep letting people in at a normal pace.

The total number of people entering the restaurant stays the same (so the inside doesn't get too crowded), but the wait times become much more equal. No one is left waiting for hours while others breeze through.

How It Works: Two "Fairness" Rules
The researchers tested two different ways to decide who gets to go in:

The "Proportional" Rule (Aristotle's Way): "If you have a longer line, you get a bigger share of the green light, but not all of it." It's like splitting a pizza based on how hungry everyone is. If you're starving (long queue), you get a bigger slice than someone who just had a snack (short queue).
The "Max-Min" Rule (Rawls' Way): "Let's make sure the person with the worst situation is helped first." Imagine a group of people waiting for a bus. This rule says, "We will keep the bus waiting until the person with the longest wait time gets on, even if it means the person with a short wait has to wait a tiny bit longer." It prioritizes the person suffering the most.

The Results: Everyone Wins
The researchers ran a massive computer simulation of San Francisco's traffic to test this. Here is what they found:

The City Still Runs Smoothly: The new system didn't slow down the city. In fact, traffic flowed just as well as the old "all-or-nothing" system.
The Wait Times Became Fair: The huge gaps between "lucky" intersections and "unlucky" ones disappeared. The lines at the different entrances became much more even.
Less Stress: People waiting at the busiest entrances didn't have to wait as long, and the overall "frustration level" of the traffic network went down.

Why This Matters
Traffic isn't just about math; it's about people. If a traffic system feels unfair, people get angry, they might break the rules, or they might stop trusting the system.

This paper shows that we can have our cake and eat it too: we can keep the city moving efficiently and treat every driver with more fairness. It's a step toward a future where our traffic lights don't just manage cars, but manage the city with a sense of justice.

1. Problem Statement

Urban traffic networks face increasing congestion, leading to reduced speeds, longer travel times, and economic/environmental costs. Perimeter control is a strategy used to regulate vehicle inflow into congested urban regions (zones) to maintain stable traffic conditions.

However, existing perimeter control literature has two primary limitations:

Efficiency-Only Focus: Traditional approaches optimize system-level metrics (e.g., total travel time, network throughput) but often ignore equity. This can result in highly uneven queue distributions at entry points, causing excessive delays for specific origins while others flow smoothly.
Implementation Gap: Most studies rely on macroscopic models that abstract away critical microscopic phenomena like queue spill-backs and gridlock. Furthermore, few strategies have been tested in large-scale, real-time microscopic environments, and only one city (Zurich) has implemented a preliminary approach.

The core problem addressed is how to integrate fairness objectives into perimeter control without sacrificing the efficiency gains provided by traditional gating mechanisms.

2. Methodology

A. Framework & Case Study

Control Basis: The authors build upon a feedback-based gating algorithm (using PI controllers) that adjusts the green ratio ( $r^E$ ) at perimeter intersections based on the difference between current vehicle accumulation ( $n_i$ ) and a target accumulation ( $n^T_i$ ).
Case Study: A large-scale, demand-calibrated microsimulation of the San Francisco Financial District.
- Scale: 3 interacting zones, 46 signalized intersections, 284 induction loop detectors, and 131 lane-area detectors.
- Demand: 125,000+ trips over 24 hours, calibrated using mesoscopic models.
- Simulation: Implemented in SUMO with 10 different random seeds to ensure robustness.

B. Proposed Mechanism: Distributive Queue Balancing

The authors propose an extension to the standard gating algorithm. Instead of assigning an identical green ratio to all perimeter intersections of a zone, the system redistributes the total admissible inflow budget ( $R_{avail}$ ) based on local queue conditions.

The process involves:

Budget Calculation: The zone-level controller determines the total available green time budget ( $R_{avail}$ ) required to maintain the target accumulation.
Local Requests: Each perimeter intersection $j$ calculates a requested green ratio ( $\hat{r}^E_j$ ) based on its local queue length ( $l_j$ ).
Allocation Rules: The total budget is distributed among intersections using two distinct distributive allocation rules:
- Proportional (Aristotelian) Balancing: Allocates green time proportional to the queue length. Intersections with longer queues receive a larger share, reflecting a "need-based" or Prioritarian fairness ideology.
  - Formula: $\hat{r}^E_j \propto l_j$
- Max-Min (Rawlsian) Balancing: Uses an iterative algorithm to maximize the minimum allocation. It prioritizes the "worst-off" intersections (those with the longest queues) until their requests are met, ensuring no intersection is starved. This reflects Rawlsian fairness ideology.

3. Key Contributions

Integration of Fairness: Explicitly incorporates distributive principles (Proportional and Max-Min) into feedback-based perimeter control, moving beyond purely efficiency-driven optimization.
Microscopic Validation: Demonstrates the feasibility of these strategies in a high-resolution, large-scale microsimulation environment (San Francisco), addressing the gap between theoretical macroscopic models and real-world implementation.
Computational Efficiency: The proposed mechanism is computationally lightweight, making it compatible with real-time signal control systems.
Multi-Zone Compatibility: The framework is designed to work within multi-zone gating architectures where zones share border intersections.

4. Results

The study compared three scenarios: Uncontrolled, Standard Gating, and Queue Balancing (Proportional & Max-Min).

A. Efficiency Gains (Standard Gating)

Conventional perimeter control successfully stabilized vehicle accumulation near capacity.
Performance: Increased average network flow by ~13% and average speed by ~16% compared to the uncontrolled scenario.
Trade-off: While efficiency improved, standard gating slightly increased average queue lengths (+5.7%) and maximum queue lengths (+2.6%) compared to the uncontrolled case, as it prioritizes aggregate flow over local distribution.

B. Fairness & Equity Improvements (Queue Balancing)

The proposed balancing mechanisms matched the efficiency gains of standard gating while significantly improving equity metrics:

Proportional Balancing:
- Reduced average queue lengths by 8.25%.
- Reduced average loss times (delay) by 6.49%.
- Improved dispersion (Egalitarian fairness) by reducing the standard deviation of queues and delays.
Max-Min Balancing:
- Excelled in worst-case scenarios (Rawlsian fairness).
- Reduced maximum queue lengths by 7.19%.
- Reduced maximum loss times by 3.73%.
Overall: Both mechanisms achieved queue homogenization, ensuring that congestion was distributed more evenly across entry points rather than concentrating on specific origins.

5. Significance

Social Robustness: The paper argues that traffic control strategies perceived as unfair face political resistance and behavioral adaptations (e.g., rerouting, signal violations). By integrating fairness, ITS solutions can achieve higher user acceptance and long-term viability.
Philosophical Application: It successfully translates abstract fairness ideologies (Aristotelian proportionality and Rawlsian max-min) into concrete, actionable traffic control algorithms.
Future Implementation: The results suggest that equitable perimeter control is not only theoretically possible but practically feasible in real-time, microscopic environments. This paves the way for smarter, more socially responsible Intelligent Transportation Systems (ITS).

Conclusion: The proposed framework demonstrates that it is possible to maintain high system efficiency while significantly improving the equitable distribution of traffic delays, offering a robust path forward for urban traffic management in congested cities.