Fairness on ramp metering. Extending ALINEA for equitable access and congestion reduction

Fairness on Ramp Metering Extending ALINEA for Equitable Access and Congestion Reduction Yangle Zhan Supervision: Kevin Riehl, Anastasios Kouvelas, Michail Makridis Home University Supervision: Juan Jesús Pérez Master Thesis February 2025 Fairness in Ramp Metering February 2025 Fairness on Ramp Metering Yangle Zhan IVT ETH Zürich CH-8093 Zurich [email protected] Supervision: Kevin Riehl, Anastasios Kouvelas, Michail Makridis IVT ETH Zurich Home University Supervision: Juan Jesús Pérez Barcelona School of Industrial Engineering (ETSEIB) Universitat Politècnica de Catalunya February 2025 Abstract Ramp metering systems effectively reduce freeway congestion but often face public opposition due to inequitable delay distribution among users. This study addresses this challenge by introducing EqALINEA, a fairness-enhanced extension of the ALINEA algorithm designed to balance efficiency and equity in freeway access. Using microsimulations in SUMO, we evaluate ALINEA, Upstream ALINEA, and EqALINEA across both a simplified network and a real-world case study of Barcelona’s Ronda de Dalt corridor. Results indicate that traditional ALINEA prioritizes mainline throughput at the expense of spatial equity, disproportionately delaying on-ramp users near bottlenecks. EqALINEA mitigates these disparities by incorporating fairness constraints, including maximum waiting thresholds and proactive queue management. This approach leads to a more balanced distribution of delays while maintaining overall traffic efficiency within the simulation time. The algorithm adapts effectively to urban environments such as the Ronda de Dalt, where infrastructure limitations and evolving mobility policies require equitable traffic management solutions. This study demonstrates the feasibility of integrating fairness into decentralized ramp metering strategies to improve public acceptance and align with sustainable urban planning objectives. Keywords Keywords; Fairness, Ramp Metering, ALINEA, Traffic Equity, Congestion Management, Urban Mobility. i Fairness in Ramp Metering February 2025 Fairness on Ramp Metering Yangle Zhan IVT ETH Zürich CH-8093 Zurich [email protected] Supervision: Kevin Riehl, Anastasios Kouvelas, Michail Makridis IVT ETH Zurich Home University Supervision: Juan Jesús Pérez Barcelona School of Industrial Engineering (ETSEIB) Universitat Politècnica de Catalunya Februar 2025 Zusammenfassung Zufahrtsdosierung auf Autobahnen (Ramp-Metering-Systeme) reduzieren Staus auf Autobahnen effektiv, stoßen jedoch häufig auf öffentliche Ablehnung aufgrund ungleicher Verzögerungsverteilung unter den Verkehrsteilnehmern. Diese Studie befasst sich mit dieser Herausforderung durch den Entwurf von EqALINEA, einer gerechtigkeitsorientierten Erweiterung des ALINEA-Algorithmus, die Effizienz und Gerechtigkeit (Fairness) beim Autobahnzugang in Einklang bringt. Mithilfe von Mikrosimulationen in SUMO werden ALINEA, Upstream ALINEA und EqALINEA sowohl in einem vereinfachten Netzwerk als auch in einer realen Fallstudie auf der Ronda de Dalt in Barcelona evaluiert. Die Ergebnisse zeigen, dass der traditionelle ALINEA-Algorithmus den Hauptfahrstreifenfluss priorisiert, dabei jedoch die räumliche Gerechtigkeit vernachlässigt, wodurch Nutzer von Zufahrtsrampen, insbesondere an Engstellen, überproportional lange Wartezeiten erleiden. EqALINEA reduziert diese Ungleichheiten durch die Integration von FairnessBeschränkungen, darunter maximale Wartezeitgrenzen und ein proaktives Warteschlangenmanagement. Diese Methode führt zu einer ausgewogeneren Verteilung der Verzögerungen, während die allgemeine Verkehrseffizienz innerhalb der Simulationszeit aufrechterhalten bleibt. Der Algorithmus passt sich wirksam an urbane Umgebungen wie die Ronda de Dalt (Barcelona) an, wo infrastrukturelle Einschränkungen und sich wandelnde Mobilitätspolitiken gerechte Verkehrsmanagementlösungen erfordern. Diese Studie zeigt die Machbarkeit der Integration von Fairness in dezentralisierte RampMetering-Strategien, um die öffentliche Akzeptanz zu verbessern, und mit nachhaltiger Stadtplanung in Einklang zu bringen. Schlüsselwörter Schlüsselwörter; Gerechtigkeit (Fairness), Autobahn-Zufahrtsdosierung (Ramp Metering), ALINEA, Verkehrsgerechtigkeit, Staumanagement, urbane Mobilität. ii Fairness in Ramp Metering February 2025 Contents ListofTables...................................... 3 ListofFigures ..................................... 4 Abbreviations...................................... 5 1 Introduction..................................... 7 1.1 ProblemStatement.............................. 9 1.2 Motivation................................... 12 1.3 ResearchQuestions.............................. 14 1.4 Objectives................................... 15 2 LiteratureReview.................................. 16 2.1 Ramp Metering Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.1.1 Ramp Metering Components . . . . . . . . . . . . . . . . . . . . . 17 2.1.2 Ramp Metering Control Strategies . . . . . . . . . . . . . . . . . 18 2.1.3 Location of Mainline Detector . . . . . . . . . . . . . . . . . . . . 19 2.1.4 Categories of Existing Ramp Metering Algorithms . . . . . . . . . 21 2.2 Fairness in Ramp Metering . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.2.1 Fairness-Considerating Ramp Metering Algorithms . . . . . . . . 29 3 Methodology .................................... 33 3.1 SimulationModels .............................. 33 3.1.1 ToyModel............................... 34 3.1.2 Ronda de Dalt (Barcelona) . . . . . . . . . . . . . . . . . . . . . . 35 3.2 Simulation Demand Models . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.2.1 Toy Model Flow Spawning Strategy . . . . . . . . . . . . . . . . . 42 3.2.2 Ronda de Dalt Model Flow Spawning Strategy . . . . . . . . . . . 44 3.2.3 Vehicle & Driver Population . . . . . . . . . . . . . . . . . . . . . 45 3.3 BenchmarkControllers............................ 49 3.3.1 ALINEA and Upstream ALINEA . . . . . . . . . . . . . . . . . . 49 3.3.2 Component Placement and Data Collection . . . . . . . . . . . . 51 3.3.3 Implementation (ALINEA & Upstream ALINEA) . . . . . . . . . 53 3.4 EqALINEA .................................. 57 3.4.1 EqALINEA Fairness . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.5 EvaluationFramework ............................ 60 1 Fairness in Ramp Metering February 2025 4 ResultsandDiscussion............................... 63 4.1 Traffic Efficiency Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.2 FairnessEvaluation.............................. 65 4.2.1 Gini Coefficient Analysis . . . . . . . . . . . . . . . . . . . . . . . 65 4.2.2 On-Ramp User Experience Analysis . . . . . . . . . . . . . . . . . 67 5 Conclusions ..................................... 73 5.1 Limitations .................................. 74 5.2 Future Research Directions . . . . . . . . . . . . . . . . . . . . . . . . . . 74 6 References...................................... 75 A Appendix & Additional Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 2 Fairness in Ramp Metering February 2025 List of Tables 1 Applications & Previous Work on Ramp Metering . . . . . . . . . . . . . . . . 26 2 Overview Fairness-Considerating Ramp Metering Algorithms . . . . . . . . . . 31 3 Updated Vehicle Type Characteristics . . . . . . . . . . . . . . . . . . . . . . . 48 4 Traffic Efficiency Metrics for Toy Model . . . . . . . . . . . . . . . . . . . . . . 64 5 Traffic Efficiency Metrics for Ronda Model . . . . . . . . . . . . . . . . . . . . 64 6 Gini Coefficients for Toy Model and Ronda De Dalt Model . . . . . . . . . . . 65 7 Average Waiting Time per On-Ramp [s] . . . . . . . . . . . . . . . . . . . . . . 68 8 Maximum Waiting Time per On-Ramp [s] . . . . . . . . . . . . . . . . . . . . 69 9 Merging Rate per On-Ramp [veh/cycle] . . . . . . . . . . . . . . . . . . . . . . 70 10 Number of Vehicles Joined to Highway [veh/ST] . . . . . . . . . . . . . . . . . 71 11 Red Time Assignation per On-Ramp (s) . . . . . . . . . . . . . . . . . . . . . 72 12 Presence of Ramp Metering Worldwide . . . . . . . . . . . . . . . . . . . . . . 81 13 Exit Interval Average Flow (veh/h) . . . . . . . . . . . . . . . . . . . . . . . . 81 14 Comparison of Ramp Metering Algorithms . . . . . . . . . . . . . . . . . . . . 82 3 Fairness in Ramp Metering February 2025 List of Figures 1 Ramp Metering: How it works. . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 Ramp Metering - Top U.S. Metropolitan Areas. . . . . . . . . . . . . . . . . . 11 3 Global Implementation of Ramp Metering (Excluding the United States). . . . 12 4 Comparison: Mainline Conditions (with and without Ramp Metering). . . . . . 16 5 Ramp Metering Scheme For Generic Site. . . . . . . . . . . . . . . . . . . . . . 18 6 Mainline Detector Placement. . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 7 ToyModelNetwork. ................................ 34 8 LesRondesdeBarcelona............................... 35 9 Travel Purpose & Vehicle Occupancy: Distribution on Ronda de Dalt. . . . . . 36 10TrafficVolume(Weekday).............................. 36 11 Economic Poles & Urban Centralities. . . . . . . . . . . . . . . . . . . . . . . . 37 12 Traffic Volume Increase on Barcelona’s Ring Roads (2021–2023). . . . . . . . . 39 13 Ronda Dalt Model Network. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 14RondaToyModelNetwork. ............................ 41 15 LOS Criteria For Multi-Lane Highways. . . . . . . . . . . . . . . . . . . . . . . 42 16 ALINEA Working Principle (Scheme). . . . . . . . . . . . . . . . . . . . . . . . 50 17 Ramp Metering Component Placement. . . . . . . . . . . . . . . . . . . . . . . 53 18 Ensuring Sufficient Time for On-Ramp Freeway Entry. . . . . . . . . . . . . . 57 19 Toy model Occupancy Variation J9. . . . . . . . . . . . . . . . . . . . . . . . . 83 20 Toy model Occupancy Variation J10. . . . . . . . . . . . . . . . . . . . . . . . 84 21 Toy model Occupancy Variation J11. . . . . . . . . . . . . . . . . . . . . . . . 85 22 Toy model Average Speeds J9. . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 23 Toy model Average Speeds J10. . . . . . . . . . . . . . . . . . . . . . . . . . . 86 24 Toy model Average Speeds J11. . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4 Fairness in Ramp Metering February 2025 Abbreviations AIMD Additive Increase Multiplicative Decrease AD Average Delay [min/veh] ALINEA Asservissement Linéaire d’Entrée Autoroutière (Linear feedback ramp metering algorithm) AMB Àrea Metropolitana de Barcelona (Barcelona Metropolitan Area) AR Arrival Rate [%] ARMS Advanced Real-time Ramp Metering System AS Average Speed [km/h] DHPC Dual Heuristic Programming Control EqALINEA Equity-oriented ALINEA (proposed fairness-optimized algorithm) GFLC Genetic Fuzzy Logic Control HERO Heuristic Ramp-Metering Coordination ILC Iterative Local Control ITS Intelligent Transport Systems LOS Level of Service METALINE Multi-ramp Traffic Management Algorithm for Efficient Line Integration and Network Efficiency ODMatrix Origin-Destination Matrix PCU Passenger Car Unit RM Ramp Metering SL2015 SUMO’s 2015 Lane Change Model 5 Fairness in Ramp Metering February 2025 ST Simulation Time SWARM System Wide Adaptive Ramp Metering SUMO Simulation of Urban Mobility (traffic simulation software) TAV Total Arrived Vehicles [veh TD Total Delays [h] TDV Total Departed Vehicles [veh/ST] TTD Total Travel Distance [km] TTT Total Travel Time [h] UpALINEA Upstream ALINEA (modified ALINEA with upstream occupancy feedback) VMS Variable Message Signs VSL Variable Speed Limits ZCS Zippered Control Strategy 6 Fairness in Ramp Metering February 2025 can be optimized to balance efficiency with fairness, ensuring that the delays imposed on drivers are equitable. Ramp metering faces several challenges. Studies highlight various obstacles including issues related to geometry, costs, public opposition, heavy ramp volume, and agency support. This is reflected in the United Kingdom’s development of specific guidelines for ramp metering systems, as shown in documents like Ramp Metering Design Manual (Caltrans, 2022) and TD 121 (Agency, 2020). These documents provide appraisal and design requirements for ramp metering. Among these challenges, 58% of the barriers are due to the geometry of existing infrastructure (Mizuta et al., 2014b), such as inadequate acceleration length, closely spaced ramps, and limited sight distances. These geometric limitations make it difficult for vehicles to merge smoothly into mainline traffic, thus complicating the implementation or expansion of ramp metering systems. 13 Fairness in Ramp Metering February 2025 1.3 Research Questions This thesis explores how fairness considerations in ramp metering can be systematically integrated into traffic control strategies without significantly compromising efficiency. To achieve this, the study addresses the following research questions: 1. How do existing ramp metering strategies impact fairness and efficiency? • How do ALINEA and Upstream ALINEA distribute delays among different on-ramp users? •What equity concerns arise from traditional ramp metering strategies? 2. How can fairness be explicitly incorporated into ramp metering control? • How does EqALINEA modify the existing Local ALINEA framework to ensure fairer access? • What mechanisms are introduced in EqALINEA to balance fairness and efficiency? 3. What are the trade-offs between fairness and efficiency in ramp metering? •How does EqALINEA compare to ALINEA and Upstream ALINEA in terms of congestion delay, waiting times on ramp, and merging rate? • Does prioritizing fairness (e.g., reducing extreme waiting times) lead to unintended efficiency losses? 4. How do different fairness principles emerge in ramp metering applications? • Which fairness principles (Egalitarian, Rawlsian, Utilitarian) are explicitly or implicitly applied under EqALINEA? • Does the fairness concept shift depending on the network structure (e.g., Toy Model vs. Ronda Toy Model)? • How does fairness affect different user groups (e.g., local on-ramp users vs. long-distance commuters)? 14 Fairness in Ramp Metering February 2025 1.4 Objectives A comprehensive investigation of the potential and requirements for implementing ramp metering strategies considering fairness is conducted in this thesis. The specific objectives of the project include: 1. Evaluate the fairness of existing ramp metering strategies • Analyze ALINEA and Upstream ALINEA using fairness and efficiency metrics, assessing their impact on delay distribution. • Compare delay disparities across different on-ramps to identify potential equity concerns in metering systems. 2. Develop and implement EqALINEA, a fairness-optimized ramp metering algorithm • Design an enhanced metering strategy that ensures equitable access while preventing excessive congestion. • Implement EqALINEA in SUMO and validate its effectiveness using microsimulation models. 3. Analyze the efficiency-fairness trade-offs in ramp metering • Compare EqALINEA’s performance against benchmark control strategy ALINEA and Upstream ALINEA in both the Toy Model and Ronda Toy Model. • Assess key trade-offs between throughput maximization, congestion reduction, and fairness improvement. 4. Assess the applicability of different fairness principles in ramp metering based on scenario-specific needs. • Identify which fairness concept (e.g., Egalitarian, Rawlsian, Utilitarian) is implicitly or explicitly applied in EqALINEA. • Evaluate how fairness influence equity outcomes for different user groups (e.g., on-ramp users vs. main entry users). 15 Fairness in Ramp Metering February 2025 2 Literature Review In this literature review, I will first examine the components and control strategies of ramp metering to establish a foundational understanding of how these systems work. This will be followed by an exploration of existing ramp metering algorithms to categorize them and provide an overview of their approaches. Finally, I will review algorithms that specifically incorporate fairness considerations, focusing on how they attempt to address issues of inequity in delay distribution. 2.1 Ramp Metering Systems Ramp meters are traffic signals placed on freeway on-ramps to control the frequency of vehicles merging onto the freeway. By managing the flow of traffic entering the freeway and dispersing groups of vehicles that complicate merging, these signals contribute to reducing overall congestion. As shown in Figure 4, vehicles from nearby roads form a queue behind the stop line on the ramp. They are then released onto the freeway in flows or batches of vehicles based on the specific ramp metering control strategies in place. Figure 4: Comparison: Mainline Conditions (with and without Ramp Metering). (a) Freeway Without Ramp Metering. (b) Freeway With Ramp Metering. Source: Washington State Department of Transportation 16 Fairness in Ramp Metering February 2025 2.1.1 Ramp Metering Components Ramp metering has evolved significantly from its earliest form, where a policeman would manually direct traffic entering a freeway (Demiral and Celikoglu, 2011). Today, it involves sophisticated, intelligent, technological systems designed to optimize traffic flow between on-ramp vehicles and mainline freeway traffic. These systems are composed of the following key components: • Signal Heads: These can be two-section or three-section signals. Two-section heads feature green and red lights, while three-section heads include a yellow light, providing more familiar cues to drivers. The signal heads manage when vehicles can proceed onto the freeway. • Detectors: Sensor equipment (loop detectors) monitors traffic conditions both on the ramps and the mainline. Ramp detectors ensure that the signal only turns green when a vehicle is present at the stop line. Queue detectors can monitor the length of the line waiting to enter the freeway, while other detectors assess traffic flow on the freeway itself to determine the optimal metering rate. These detectors are typically connected directly to the ramp controller. • Signage: Signs play a crucial role in guiding drivers. They should be placed at the start of the ramp and near the signal to provide clear instructions. Additional signs upstream or with adaptive screens can alert drivers if the ramp is being actively metered, helping to manage expectations and improve compliance with the system. Together, these components ensure smooth and efficient ramp metering, minimizing congestion and improving freeway safety. 17 Fairness in Ramp Metering February 2025 Figure 5: Ramp Metering Scheme For Generic Site. Source: Highways Agency (2008) 2.1.2 Ramp Metering Control Strategies RM employs various control strategies to manage traffic effectively. Mainly three types of Ramp Metering Control systems can be distinguished: • Local system: This approach makes ramp metering decisions independently for each ramp, considering only the traffic conditions at the specific ramp and its immediate freeway entry point, without taking into account the traffic conditions across the entire network. • System-wide control / Coordinated system: This approach coordinates ramp meters across multiple on-ramps and the entire freeway system. It adopts a holistic strategy by using data from various ramps and freeway sections to manage traffic flow across a larger area. Although more complex, it can better distribute traffic 18 Fairness in Ramp Metering February 2025 and reduce congestion on the main road. • Integrated system: This approach extends beyond ramp metering by integrating various traffic control measures, such as signal timing, ramp metering, and route guidance through Variable Message Signs (VMS). The goal is to optimize overall traffic flow by utilizing a range of tools and strategies to manage freeway traffic more effectively. Based on the control philosophy, there are two categories of control schemes: • Pre-timed control: This is the simplest control strategy, but it provides the least effective results. It relies on pre-determined, static timing for the ramp signal, with the metering rate set based on historical traffic patterns rather than real-time data. It’s simple but less flexible, as it doesn’t adjust to current traffic conditions. • Traffic-responsive control: This strategy dynamically adjusts the metering rate based on real-time traffic conditions. By utilizing detectors to monitor traffic flow, speed, and congestion both on the ramp and the freeway, the system can respond to fluctuations and optimize traffic flow more effectively. 2.1.3 Location of Mainline Detector Ramp metering systems rely on strategically placed detectors to monitor traffic conditions and inform control decisions. A critical design choice is the placement of mainline detectors, which are typically categorized as upstream or downstream relative to the merging area (Figure 6). • Upstream detectors are positioned before the merging zone to monitor approaching freeway traffic. These detectors enable proactive control by predicting congestion propagation and adjusting metering rates preemptively. • Downstream detectors are placed after the merging area to directly observe congestion levels at the bottleneck. This reactive approach prioritizes stabilizing downstream traffic flow, as seen in strategies like ALINEA, which uses downstream occupancy to regulate ramp inflows. 19 Fairness in Ramp Metering February 2025 Figure 6: Mainline Detector Placement. Source: van Lindonk (2020) The choice between upstream and downstream detector placement significantly impacts algorithm behavior because: 1. Upstream detectors: •Allow proactive control, anticipating congestion before it occurs. •Enable better queue management on the ramp. •Provide more immediate response to changes in ramp demand. 2. Downstream detectors: •Measure the actual impact of merging traffic on mainline flow •Can detect congestion formation more directly •Allow for feedback control based on the resulting traffic state after merging This fundamental distinction explains why different algorithms adopt specific detector configurations, as systematically compared in Table 14 by Luaibi et al. (2023). The table highlights how upstream detector-based strategies prioritize congestion prevention while downstream-focused approaches excel at bottleneck stabilization. Upstream placement tends to favor responsive local control, while downstream placement is often used in algorithms aiming for optimal mainline flow conditions. The choice influences the algorithm’s responsiveness, control strategy, and overall effectiveness in managing traffic flow. 20 Fairness in Ramp Metering February 2025 2.1.4 Categories of Existing Ramp Metering Algorithms Ramp metering algorithms can be categorized into four different types (Zhang et al., 2001) based on the combination of control strategies and the degree to which they incorporate local and system-wide traffic conditions. 1. Isolated algorithms: Each on-ramp operates independently, meaning that its metering rate is determined based only on the traffic conditions at that specific ramp. These conditions can include factors like vehicle flow, occupancy, travel speed, and potentially any queue overflow that builds up on the ramp itself. • Zone Algorithm 2 :This algorithm regulates freeway traffic by dividing the roadway into zones and assigning each a calculated metering rate to maintain the target density. The assigned rate is distributed among the ramps based on predetermined factors, adjusting entry flow to minimize congestion. • ALINEA 3 :The ALINEA algorithm adjusts the metering rate using occupancy data collected from a downstream detector on the freeway. Every few seconds, the algorithm calculates the difference between the current occupancy and a target threshold. It then updates the metering rate to reduce this difference, aiming to keep freeway traffic below a congestion threshold. • Local metering using neural networks: This adaptive ramp metering approach leverages neural network models to determine metering rates for individual ramps. Unlike traditional algorithms that rely on pre-set thresholds or simple feedback mechanisms, neural networks can learn complex patterns in traffic flow by analyzing historical and real-time data. This enables the system to predict optimal metering rates based on a variety of traffic conditions, such as ramp occupancy, mainline traffic density, and speed. 2. Cooperative algorithms: These algorithms coordinate the metering rates of multiple on-ramps along a freeway. Unlike isolated ramp metering, where each ramp operates independently, cooperative algorithms utilize data from neighboring ramps and overall freeway conditions to collaboratively adjust metering rates. This approach helps prevent both bottleneck congestion and spillback at critical ramps, optimizing traffic flow not only at individual ramps but across the entire freeway. 2 Stratified Zone Metering: Variant of Zone metering, that using real-time density data for more precise control. 3 Extension of ALINEA: Smaragdis et al. (2004) proposed three more modifications FL-ALINEA, UP-ALINEA and X-ALINEA/Q to improving the performance in various scenarios. 21 Fairness in Ramp Metering February 2025 • Helper ramp algorithm: This method integrates local traffic-responsive control with a central override mechanism to achieve coordinated, system-wide management. On-ramps are organized into groups, each assigned predefined metering rates that dynamically adjust based on local traffic conditions. If the queue at a particular ramp surpasses a set threshold, the central override activates to adjust the metering rate, aiming to prevent excessive queue buildup and congestion spillback. When the issue persists, the algorithm applies more restrictive metering rates upstream to further alleviate congestion. • Linked-ramp algorithm: Each ramp’s metering rate is determined by subtracting the upstream traffic flow from a predefined target flow rate. When one ramp’s metering rate reaches its minimum level due to congestion, upstream ramps are also required to reduce their metering rates to maintain coordinated flow. 3. Competitive algorithms: These algorithms calculate two sets of metering rates for each ramp: one based on local traffic conditions (e.g., traffic flow, speed, occupancy at the ramp) and another based on system-wide or corridor-level conditions (e.g., congestion levels or flow on adjacent ramps and the mainline). The more restrictive of these two rates is then selected and implemented at each ramp. • Compass algorithm: This algorithm adjusts on-ramp metering rates using real-time freeway data and predefined thresholds for occupancy and traffic volume. By monitoring local and downstream mainline conditions, Compass selects the most restrictive metering rate to prevent congestion, while also employing queue spillback detection to ensure that ramp queues do not disrupt adjacent surface roads. This system can operate in both automated and manual modes, allowing traffic managers flexibility to override automated settings as needed for incident response or special conditions. • Bottleneck algorithm: This algorithm is specifically designed to manage traffic flow near congestion-prone areas, or "bottlenecks," on a freeway. It operates by balancing the incoming traffic demand upstream of a ramp with the capacity available at the downstream bottleneck, adjusting the metering rate at on-ramps accordingly. When congestion begins to form, the algorithm reduces metering rates for all ramps in the affected zone, coordinating entry rates to prevent an overload at the bottleneck. Additionally, it incorporates a queue management system that adjusts metering rates if ramp queues exceed a set threshold, preventing spillback onto surface streets. 22 Fairness in Ramp Metering February 2025 Egalitarian fairness in ramp metering would seek to provide equal wait times for all drivers, ensuring that no one ramp or user is prioritized over another. This approach would standardize metering rates across all ramps so that all drivers experience the same level of access, regardless of their location or vehicle type. This principle sacrifices some efficiency in favor of strict equality, distributing wait times uniformly across users. Diorthotic fairness refers to fairness in systems where individuals actively interact and influence resource allocation through mechanisms such as markets or pricing. In this framework, users make decisions based on their preferences and constraints, such as budgets or willingness to pay, with outcomes emerging from these interactions. Examples include congestion pricing or toll systems, where drivers choose whether to pay for prioritized access. However, in this study the scope does not include those factors and primary operates within a dianemetic fairness framework. So, this study focuses exclusively on the dianemetic fairness aspects of resource allocation in traffic management. 2.2.1 Fairness-Considerating Ramp Metering Algorithms The trade-off between efficiency and fairness in freeway ramp metering has been a recurring theme in the literature (Kotsialos and Papageorgiou (2001); Levinson et al. (2002)). As observed in these studies, the most efficient ramp metering strategies often achieve their objectives at the cost of equity, creating a fundamental tension in ramp control. The most efficient ramp control logic tends to prioritize free-flow conditions on the freeway mainline, benefiting the majority of commuters while heavily restricting access at specific on-ramps. This approach minimizes congestion but concentrates delays at certain entry points, making it less equitable. While this strategy may satisfy engineering standards for efficiency, it risks low public acceptance due to perceived unfairness. To mitigate these issues, coordination of on-ramp meters is frequently employed, not only to prevent freeway queues but also to distribute delays more evenly. Although formal theoretical models for equity in ramp control are limited, practical measures aimed at enhancing fairness have evolved over time in real-world applications. For instance, maximum queue length constraints, originally intended to prevent spillovers onto local streets, also serve to limit excessive wait times for ramp users. Many strategies further incorporate minimum and maximum metering rate limits to achieve a more balanced 29 Fairness in Ramp Metering February 2025 distribution of delays. Some systems, like Denver’s “helper algorithm,” Lipp et al. (1991) adjust upstream metering rates to relieve congestion on heavily restricted downstream ramps. Similarly, the Minnesota Zonal and Stratified Zonal algorithms impose maximum delay limits to ensure that no driver experiences disproportionately long waits at a single ramp. The following Table 2 provides a comparison of various studies that examine the aspect of fairness in ramp metering algorithms. 30 Fairness in Ramp Metering February 2025 Table 2: Overview Fairness-Considerating Ramp Metering Algorithms Name Study Description and Key Features Fairness Principle Efficiency vs. Fairness Trade-Off Strengths Limitations Parameters Balancing Efficiency and Equity of Ramp Meters Zhang and Levinson (2005) BEEX is a ramp metering algorithm that minimizes weighted travel time, assigning higher weights to longer wait times at on-ramps to balance efficiency with equity. It uses an adjustable equity coordination factor to distribute delays more evenly across ramps. Real-time data is used to identify bottlenecks and adjust ramp metering rates. Utilitarian (Freeway drivers) with Harsanyian (On-ramp drivers) -Allows a tunable balance between efficiency and equity by adjusting the equity coordination factor. -Higher values increase fairness but may reduce efficiency. -Prioritizes freeway mainline efficiency, keeping it at or below capacity. -Possible spillover onto local streets -Does not proactively address equity for on-ramp users. -Average On-Ramp Waiting Time A Pareto-Optimization Approach for a Fair Ramp Metering Li et al. (2016) This algorithm achieves fair ramp metering by minimizing both total system delay (freeway and on-ramp) and spatial inequity in delay distribution across on-ramps. It uses a Pareto-optimal multi-objective optimization approach, with a spatial equity index to compare delays, dynamically finding solutions based on desired equity-efficiency balance. Egalitarian (On-ramp drivers) with Harsanyian (Freeway drivers) -Balances system efficiency (minimizing total delay) with equity by generating a Pareto front of solutions, allowing trade-offs between objectives. -Ensures fairer delay distribution across ramp groups -Provides Pareto-optimal solutions for decision-makers. -Prioritizing equity may reduce freeway efficiency. -Spatial equity index does not account for temporal equity. -Total Travel Delay (veh·h) and Equity Index An Analysis on Efficiency and Equity of Fixed-Time Ramp Metering Kesten et al. (2013) FTRM uses fixed signal timings based on historical traffic data to control on-ramp inflows and manage freeway capacity, without real-time adjustments. The strategy was tested in VISSIM on a congested corridor, focusing on impacts to delays and speeds. Fairness was assessed by variability: lower variability in speed or delay means a fairer system. The study shows that applying FTRM makes conditions less fair for on-ramp drivers. Egalitarian (equal treatment for all vehicles, regardless of needs or locations) -Efficiency gains on the mainline may come at the expense of increased delays at on-ramps; -Equity outcome depends on specific measures used (e.g., delay vs. speed). -Simple to implement and cost-effective compared to dynamic metering; -Improves mainline efficiency. -Possible spillover onto local streets; -Lacks real-time adaptability; -May worsen equity for ramp users. -Spot Speed -Space Mean Speed -Delay Coordinated Ramp Metering with Equity Consideration Using Reinforcement Learning Lu et al. (2017) RAS-EQ uses reinforcement learning (RL) to optimize ramp metering, balancing traffic efficiency and user equity by dynamically adjusting metering rates based on efficiency (total time spent) and equity (even delay distribution). Utilizes asymmetric cell transmission model (ACTM) for traffic flow and adjusts based on efficiency and equity reward functions. Utilitarian (Freeway drivers) with Egalitarian (On-ramp drivers) -Allows adjustment via parameter δto weigh efficiency and equity; higher δvalues improve equity at the cost of some efficiency. -Highly efficient for freeway flow by prioritizing mainline efficiency. -Better ensure fairer distribution of delays among groups of ramps. -SD of TWT does not account for temporal equity among vehicles arriving at different times. -Requires significant computational resources for training. -SD of TWT -Total Time Spent (TTS) Efficiency and Equity Performance of a Coordinated Ramp Metering Algorithm Li et al. (2016) This algorithm modifies HERO to incorporate a combined index of efficiency (total travel time) and equity (Gini coefficient) to balance objectives. The Gini coefficient measures spatial equity to ensure balanced delay distribution across ramps, tested in AIMSUN simulation. Utilitarian (greater-good focus) with Egalitarian elements (using Gini for spatial equity) -Allows tunable adjustments to prioritize either efficiency or equity; -Gini coefficient provides balanced delay distribution. -Ensures equitable delay distribution across ramps, maintaining mainline efficiency. -May slightly reduce efficiency if equity objective is weighted heavily; -Focuses on spatial equity without temporal considerations. -Total Travel Time (TTT), -Gini Coefficient New Horizontal Equity Measure for Ramp Meters Amini et al. (2016) A horizontal equity measure implemented with HERO, assigning delays based on individual contributions to congestion using vehicle O-D data. Delays are proportionately assigned according to each vehicle’s impact on downstream bottlenecks, tested in hypothetical microsimulation. Aristotelian (proportional delays based on congestion contribution) -Enhances freeway flow and fairness by delaying high-impact vehicles, though it may increase metering rates for ramps with high downstream impact. -Provides more equitable delays by penalizing high-impact ramps, potentially improving public acceptance. -Requires real-time O-D data; -Low-impact vehicles may face delays if queued behind high-impact vehicles. -Normalized Gini coefficient Efficiency versus Fairness in Network-Wide Ramp Metering Kotsialos and Papageorgiou (2001) AMOC dynamically adjusts metering rates based on traffic demands and ramp storage, balancing freeway efficiency with ramp equity. Real-time data is used for adjustments, and queue constraints prevent excessive delays, tested on the Amsterdam ring-road. Utilitarian (Freeway drivers) with Harsanyian (On-ramp drivers) -Prioritizes mainline efficiency by focusing metering at ramps near bottlenecks. When queue constraints are active, AMOC sacrifices some freeway throughput to reduce excessive ramp delays and avoid spillover. -Maximizes freeway flow while applying queue constraints for fairer delay distribution. -Fairness is secondary to efficiency, lacking a specific fairness objective function, which may result in unequal treatment for different ramps. -Spatial equity (Queue Length) Measuring the equity and efficiency of ramp meters Levinson et al. (2004) Co-EOAX minimizes total weighted travel time by applying non-linear weights to ramp delays, balancing efficiency and equity without requiring O-D data. The Global On-Ramp Grouping Factor X enables flexibility in adjusting equity, tested in AIMSUN. Utilitarian (Freeway drivers) with Egalitarian (On-ramp drivers) Higher X values improve equity by distributing delays more evenly across ramps but may reduce freeway throughput. -Simplifies equity adjustments without O-D data, facilitating easier implementation. -Limited by pre-set X values; -Higher equity settings may lower mainline efficiency. -Total Weighted Travel Time (WTT) -Group Factor X Source: Self-compiled data. 31 Fairness in Ramp Metering February 2025 The concept of equity in ramp metering is fundamental to gaining public acceptance and ensuring successful implementation. Ramp metering inherently involves trade-offssome drivers benefit from improved freeway flow, while others, particularly those delayed at on-ramps, may feel disadvantaged or even harmed by increased waiting times. This raises an important question: What is fairness, who benefits and who is disadvantaged, and how much, compared to a system without ramp metering? Furthermore, if the system sacrifices the equity of on-ramp drivers to improve the overall corridor efficiency, What is the equity-efficiency trade-off ratio in ramp metering, specifically quantifying the degree of delay imposed on on-ramp drivers to achieve improvements in overall corridor efficiency? Freeways were initially built for intercity travel, but over time, they have evolved to meet the needs of local commuters as well. This shift prompts a reevaluation of whether long-distance travel should remain a primary policy focus, or if it would be justifiable to reduce some freeway efficiency to enhance access for on-ramp users, particularly in areas near to bottlenecks. As we can observe from previous research, studies have increasingly shifted focus from solely maximizing freeway efficiency (utilitarian fairness) to recognizing and addressing the equity of on-ramp drivers (egalitarian fairness), even if it means compromising efficiency to some extent. The majority of those studies use coordinated, traffic-responsive ramp metering, which is not only complex but also costly to implement, and it does not directly address users’ equity concerns. For this reason, this research aims to explore whether ramp-metered systems genuinely benefit or disadvantage those delayed at ramps, particularly users joining near bottlenecks. To do this, both the ALINEA algorithm and a modified version of ALINEA will be implemented in a real-case simulation using SUMO. This approach will assess the tangible impacts on user experience, exploring both the efficiency and fairness of ramp metering from a user-centered perspective. 32 Fairness in Ramp Metering February 2025 3 Methodology This chapter describes the methodology used in this thesis, which consists of developing simulation models, implementing benchmark controllers, designing an optimized ramp metering algorithm, and evaluating its performance. To systematically analyze ramp metering strategies, the study employs microscopic traffic simulation models, which allow for detailed vehicle-level interactions. These simulations help in evaluating both fairness and efficiency of different ramp metering techniques. The following sections provide an overview of the simulation models used, the benchmark controllers implemented, the proposed optimization approach, and the evaluation framework: • Simulation Models: This section describes the toy model, which serves as a simplified test environment, and the real-world case study on the Ronda de Dalt in Barcelona. • Benchmark Controllers: The standard ALINEA and Upstream ALINEA ramp metering strategies are explained, along with details on sensor placements and algorithmic logic. • Proposed Algorithm: The optimized EqALINEA strategy is introduced, detailing how it improves congestion management and fairness in traffic flow distribution. • Evaluation Framework: The methodology for assessing fairness and efficiency is outlined, including performance metrics and comparative analysis between different control strategies. 3.1 Simulation Models This section presents the two simulation environments used in this study: • A Toy Model: Serves as a controlled test environment to evaluate ramp metering strategies in a simplified setting before applying them to real-world conditions. • A Real-World Case Study: Focused on the Ronda de Dalt, a major urban freeway in Barcelona, where real traffic conditions are simulated. The toy model allows for rapid experimentation and testing of different control strategies 33 Fairness in Ramp Metering February 2025 without the complexities of real-world calibration. Once key insights are obtained, the methodologies are applied to the more complex Ronda de Dalt scenario to assess their effectiveness in real-world traffic conditions. 3.1.1 Toy Model The toy model is a simplified traffic simulation used to investigate the fundamental dynamics of ramp metering under controlled conditions. It provides a structured test environment to validate the efficiency and fairness of metering strategies before deploying them in real-world networks. The network consists of a 4.1 km freeway segment with a maximum speed of 100 km/h (27.78 m/s) and three 500-meter-long on-ramps at 1.0 km, 2.0 km, and 3.0 km from the mainline’s starting point. Each on-ramp is equipped with: •Aramp metering signal, located 250 meters before the merge nose. •Ademand loop and passage loop to measure inflows. • Atraffic sensor 40 meters downstream 4 of each merge point to record mainline occupancy. Toy Model Network To regulate ramp metering, the ALINEA control strategy is applied, adjusting metering rates based on real-time occupancy levels. The toy model’s network layout is shown in Fig. 7. Figure 7: Toy Model Network. 4Adequate distance at the Boulevard Périphérique in Paris Papageorgiou et al. (1991). 34 Fairness in Ramp Metering February 2025 3.1.2 Ronda de Dalt (Barcelona) The Ronda de Dalt is one of the most critical road infrastructures in Barcelona. Unlike traditional highways that primarily serve intercity commuters, the Ronda de Dalt plays a multifunctional role by managing urban, metropolitan, and regional traffic within a dense urban environment. Figure 8: Les Rondes de Barcelona. Characteristics of the Ronda / Ronda de Dalt Along with the Ronda Litoral, the Ronda de Dalt forms part of Barcelona’s primary ring road system, Les Rondes, which were constructed to improve citywide mobility by redistributing vehicle flows away from the urban core. Their impact is particularly evident in the way they have reorganized traffic distribution in and around Barcelona. The Rondes play eight fundamental roles in the city’s transportation system (Barcelona Regional, 2019): • Les Rondes connecten: The Rondes facilitate mobility between Barcelona and its surrounding municipalities, serving both occupational and personal travel purposes. According to traffic data, 69% of trips are occupational (primarily work-related), while 31% are personal (including rendezvous, shopping and leisure). Additionally, 65% of vehicles have a single occupant, highlighting the dominance of private car 35 Fairness in Ramp Metering February 2025 usage in daily mobility Figure 9: Travel Purpose & Vehicle Occupancy: Distribution on Ronda de Dalt. • Les Rondes distribueixen: The Rondes distribute traffic flows, reducing congestion in the city center. Of the 536,000 vehicles entering Barcelona daily, 60% are absorbed by the Rondes, easing pressure on main urban roads like Gran Via, Diagonal, Meridiana, and Via Augusta. Beyond regional traffic distribution, the Rondes also structure local mobility, connecting neighborhoods that have limited public transport accessibility, particularly for metropolitan and regional connections. • Les Rondes canalitzen: The Rondes function as high-capacity urban roads, distinct from conventional highways. Their design incorporates frequent entry and exit points, steeper gradients, and a sinuous layout, prioritizing integration with the existing urban fabric. Originally planned to respond to local mobility needs, their final alignment was shaped by residential demands, ensuring accessibility for surrounding neighborhoods. However, these design choices also influence traffic intensity, speed, and congestion dynamics, making the Rondes a hybrid characteristics between highways and urban streets. Figure 10: Traffic Volume (Weekday). 36 Fairness in Ramp Metering February 2025 • Les Rondes cohabiten: The Rondes intersect densely populated urban areas, influencing the daily lives of approximately 310,000 residents. The surrounding neighborhoods exhibit high socioeconomic contrasts, ranging from areas with higher purchasing power to some of Barcelona’s most vulnerable districts, particularly in mountainous zones. Despite these disparities, the Rondes form part of daily mobility routes** for residents, connecting them to essential services such as supermarkets, healthcare centers, childcare facilities, and community spaces. • Les Rondes contaminen: The Rondes contribute to air pollution and noise emissions, posing environmental challenges that need to be addressed through sustainable mobility solutions. • Les Rondes condicionen: The Rondes act as a physical and social boundary, limiting cross-neighborhood connectivity and influencing urban development. They define the transition between the city and natural spaces like Collserola, Besòs, and Llobregat, shaping land use and accessibility. • Les Rondes evolucionen: The Rondes must adapt to evolving mobility needs, balancing private vehicle use with sustainable alternatives. Public policies increasingly prioritize public transport and non-motorized mobility, aiming to reduce car dependency and its negative externalities. • Les Rondes enllacen: Initially designed as peripheral infrastructure, the Rondes have redefined Barcelona’s urban boundaries, linking the city center with its metropolitan surroundings. Today, they connect major economic hubs, healthcare facilities, universities, and sports areas, integrating Barcelona within a broader regional framework. Figure 11: Economic Poles & Urban Centralities. 37 Fairness in Ramp Metering February 2025 Why the Simulation Focuses on Ronda de Dalt (Direction Llobregat) This study specifically simulates the Llobregat-bound direction of the Ronda de Dalt. The selection was influenced by the following factors: • Personal Commute Experience: Over the past two years, this section has been part of the researcher’s daily commute, providing direct insights into its traffic behavior and congestion patterns. • Persistent Congestion and Increasing Demand: The Llobregat-bound direction is one of the most congested urban highways in Barcelona, frequently reaching saturation levels, especially during peak hours. Despite a 19% reduction in traffic in Barcelona’s central avenues, the Ronda de Dalt has experienced a steady increase in demand. In the past two years alone, traffic along this corridor has grown by 10.62% (see Fig. 12), intensifying pressure on existing infrastructure. •Infrastructure Limitations: Unlike other metropolitan highways, the Ronda de Dalt was built within a constrained urban footprint, with narrow lanes, frequent onramps, and limited emergency shoulders. Physical expansion is unfeasible/unrealistic, as noted by Javier Ortigosa, head of the Metropolitan Urban Planning Office, who states that "the urban fabric sets the limit—expanding the Ronda would not reduce congestion, as vehicles still need to enter restricted city areas." Furthermore, sustainable mobility policies, aimed at discouraging private vehicle use in Barcelona, have inadvertently shifted more congestion to the Rondes, reinforcing the need for demand-side solutions like ramp metering. • Policy and Urban Mobility Objectives: The Barcelona City Council has actively pursued policies to reduce private vehicle dependency in favor of sustainable mobility options, such as public transport and green corridors. However, a significant portion of commuters continue to rely on cars, leading to a paradox where traffic restrictions in the city center push more vehicles onto the Rondes. 38 Fairness in Ramp Metering February 2025 –A2 – Off-ramp (1 lane). –A3 – Off-ramp (1 lane). –A4 – Off-ramp (1 lane). –A5 – Mainline exit (3 lanes). •Sequence : – E1 - A1 - A2E2 - A3 - E3 - A4 - E4 - E4b - A5 - E5 - Dynamic Flow Replication Based on Traffic Intensity: To replicate realistic traffic variations throughout the morning peak period, flow spawning follows the observed traffic intensity pattern (see Fig. 10) over the course of a weekday. • The spawning rate is updated every 10 minutes to reflect real-time changes in traffic demand. • The simulation period starts at 06:00 AM and ends at 09:00 AM, covering the morning congestion buildup. A total simulation time of 10.800 seconds. • Peak congestion is expected to occur around 08:00 AM, in alignment with real-world traffic patterns. 3.2.3 Vehicle & Driver Population To simulate realistic driving behaviors, the simulation utilizes ten vehicle types, divided into five passenger car categories and five motorcycle categories. These vehicle types are characterized by varying levels of driving aggressiveness, which influence acceleration, deceleration, lane-changing tendencies, and overall interaction with surrounding traffic. The simulation now implements the SL2015 lane change model which introduces a more dynamic and realistic representation of lane-changing behaviors based on driver aggressiveness, cooperation, and anticipation. Vehicle Type Classification: • Vehicles are categorized into five aggression levels (aggr1 to aggr5), ranging from least to most aggressive. Higher aggression levels correspond to reduced reaction times, increased impatience, faster speed adaptation, and riskier lane-changing behavior, including lane-splitting for motorcycles. The key characteristics of each vehicle type are summarized in Table 3. 45 Fairness in Ramp Metering February 2025 Each vehicle type is defined by specific behavioral parameters, as detailed below. •Lane Change Strategy and Cooperation – lcStrategic: Determines how early a vehicle plans a lane change. Higher values result in earlier decision-making to switch lanes strategically. – lcCooperative: Controls the willingness to yield to merging vehicles. Lower values indicate less cooperative behavior, making lane changes more competitive. – lcSpeedGain: Defines how eager a vehicle is to change lanes for speed benefits. Higher values lead to more frequent lane changes to maintain optimal speed. – lcKeepRight: Determines the willingness to follow keep-right rules. Higher values result in earlier lane changes to the right, while 0 disables this behavior. – lcPushy: Defines the willingness to force a lane change even if gaps are tight. Higher values indicate more aggressive behavior. •Sublane and Lateral Behavior (Specific to SL2015) – lcSublane: Controls the eagerness to use lateral positioning within a lane. Higher values indicate more frequent small lateral shifts, which is especially relevant for motorcycles. – minGapLat: Specifies the minimum lateral gap between vehicles when using sublane positioning. – lcPushyGap: Defines the minimum lateral gap required for an aggressive lane change. •Lane Change Timing and Impatience – lcTimeToImpatience: Specifies the time required for a vehicle to reach its maximum impatience level when its lane change is blocked. A lower value leads to quicker aggressive behavior. – lcImpatience: Adjusts lcPushy and lcAssertive dynamically, meaning that vehicles become more aggressive over time if they cannot change lanes. •Acceleration and Deceleration Behavior – accel (m/s²): Defines the maximum acceleration rate, affecting how quickly vehicles reach higher speeds. – decel (m/s²): Defines the maximum deceleration (braking) capacity of a vehicle. 46 Fairness in Ramp Metering February 2025 •Maximum Speed and Speed Adaptation – speedFactor: Multiplier of the default speed limit. A value of 1.0 means the vehicle follows the speed limit exactly, while lower values indicate slower driving tendencies. – speedDev: Adds variability to vehicle speeds, ensuring more realistic driving behavior by simulating different driver tendencies. 47 Fairness in Ramp Metering February 2025 Table 3: Updated Vehicle Type Characteristics Param car1 car2 car3 car4 car5 mot1 mot2 mot3 mot4 mot5 vClass P P P P P M M M M M speedFactor 0.80 0.85 0.90 0.95 1.00 0.85 0.90 0.93 0.95 1.00 speedDev 0.08 0.09 0.10 0.12 0.15 0.07 0.08 0.09 0.10 0.10 tau 5.0 4.5 3.5 3.0 2.5 4.0 3.5 3.0 2.5 1.5 impatience 2.0 2.5 3.0 3.5 4.0 2.0 2.8 3.8 4.5 5.0 lcImpatience 1.0 1.5 2.0 2.5 3.0 1.2 1.8 2.4 3.0 3.6 lcCooperative 0.5 0.3 0.2 0.1 0.0 0.5 0.3 0.2 0.1 0.0 lcStrategic 60 40 25 15 5 50 35 20 10 5 lcSpeedGain 7.0 8.0 9.0 10.0 11.0 8.0 9.0 10.0 11.0 10.0 lcKeepRight 0.6 0.5 0.3 0.2 0.0 0.6 0.4 0.3 0.15 0.0 lcPushy 1.2 1.8 2.2 2.6 3.0 1.5 2.0 2.5 3.0 3.5 lcPushyGap 0.5 0.4 0.3 0.2 0.1 0.5 0.4 0.3 0.2 0.1 lcSublane 6.0 5.0 4.0 3.0 2.0 5.0 4.0 3.0 2.0 1.0 lcAssertive 2.0 2.8 3.5 4.2 5.0 2.5 3.0 3.8 4.5 6.0 lcTimeToImpatience 15 12 9 6 3 15 12 9 6 3 lcSigma 0.4 0.6 0.8 1.0 1.2 0.5 0.7 0.9 1.1 1.3 minGapLat 0.8 0.6 0.5 0.4 0.3 0.6 0.5 0.4 0.3 0.2 maxSpeed 35 35 40 40 45 25 30 35 40 50 accel 1.8 2.2 2.5 2.8 3.0 3.5 4.0 4.5 5.0 6.0 decel 3.0 4.0 5.0 6.0 8.0 4.5 6.0 7.0 9.0 12.0 48 Fairness in Ramp Metering February 2025 3.3 Benchmark Controllers Benchmark controllers are implemented to provide a reference for evaluating ramp metering strategies. This study considers ALINEA and Upstream ALINEA, two widely applied ramp metering techniques, to assess their impact on traffic dynamics and compare their performance with the proposed EqALINEA strategy. 3.3.1 ALINEA and Upstream ALINEA Why ALINEA and Upstream ALINEA as Benchmark Controllers? Since this thesis focuses on fairness in ramp metering, the objective is to implement a widely used and efficient control strategy as a baseline for comparison. ALINEA was selected because it is one of the most commonly applied local ramp metering algorithms, providing a solid foundation for the development and analysis of EqALINEA from a fairness perspective. However, ALINEA faces two critical limitations: •Neglect of Fairness Considerations: ALINEA prioritizes mainline throughput but does not explicitly consider equity among road users. Vehicles at upstream on-ramps, particularly those near bottlenecks often endure disproportionate delays, as the algorithm allows unrestricted inflow when perceived downstream conditions appear uncongested. •Spatial Sensing Constraints - No Upstream Feedback: ALINEA relies solely on downstream sensors, making it incapable of detecting congestion propagation upstream of the merge point. Merging conflicts at the ramp itself may create queues extending backward (upstream), yet if the downstream occupancy remains below the threshold, the system fails to trigger restrictive metering. This feedback loop can intensify congestion instead of mitigating it. 49 Fairness in Ramp Metering February 2025 Figure 16: ALINEA Working Principle (Scheme). Source: Gregurić et al. (2016) Given these challenges, Upstream ALINEA was also selected as a benchmark because it extends ALINEA’s logic by using upstream occupancy measurements, allowing earlier congestion detection and better delay distribution across multiple ramps. This decision is further justified by three key factors: 1. Case Study Context: The Ronda de Dalt in Barcelona is a non-traditional urban highway, characterized by frequent on-ramps, constrained geometry, and mixed traffic dynamics, as discussed in Section 3.1.2. The applicability of traditional highway metering strategies must be reconsidered in such an urban setting. 2. Lack of a Standardized Detector Placement for ALINEA: There is no specify optimal sensor locations, ALINEA has been applied with varied sensor placements in different case studies: • Luaibi et al. (2023) found that 300m downstream from the merge nose provided an optimal critical occupancy detection point. • Papageorgiou et al. (1991) placed sensors 40m downstream at the Boulevard Périphérique in Paris and 400m downstream in Amsterdam. These variations indicate that ALINEA’s sensor placement is not universally defined and choosing the optimum position for the downstream detectors’ station is difficult. 3. Precedent from Other Control Strategies: Many others ramp metering approaches incorporate upstream occupancy to enhance control effectiveness. Table 14 summarizes existing strategies that utilize upstream information. Following this 50 Fairness in Ramp Metering February 2025 approach, implementing Upstream ALINEA represents a natural extension in the development of ALINEA-based strategies. These controllers serve two primary objectives: 1. Establishing a Performance Baseline - The evaluation of ALINEA and Upstream ALINEA provides a reference for assessing the effectiveness of EqALINEA. By simulating these controllers under identical traffic conditions, their capacity to reduce congestion and control freeway access can be systematically compared. 2. Assessing Traffic Efficiency and Fairness - Local ALINEA control strategy is designed to maximize mainline efficiency, but it does not explicitly consider fairness among road users, particularly on-ramp vehicles, which may experience excessive delays specially for those users near to the botterneck. Upstream ALINEA extends ALINEA’s logic by incorporating upstream occupancy to prevent congestion from propagating; however, it does not fully address fairness concerns. Evaluating these controllers allows for an analysis of: •Their effectiveness in managing freeway capacity or throughput. •The impact on on-ramp vehicle delays. • The extent to which fairness improvements could be achieved without compromising efficiency. The following sections describe the sensor configurations, control logic, and operational principles of ALINEA and Upstream ALINEA, which serve as the foundation for developing a ramp metering approach with a focus on fairness. 3.3.2 Component Placement and Data Collection Types of Detectors Used The simulation employs LaneArea (e2) detectors from SUMO to collect real-time traffic data for ramp metering operations. Providing key traffic parameters, including occupancy, speed, queue length, and metering flow per signal cycle. •Occupancy: The percentage of the detector’s length that is occupied by vehicles. •Speed: The average velocity of detected vehicles over detectors. 51 Fairness in Ramp Metering February 2025 •Queue Length: The length of vehicles waiting on ramps. •Metered flow: measuring the number of vehicles that has left on-ramp. Signage, Detector’s Location, and Functions Ramp Metering Signage - Ramp metering in the simulation is controlled using traffic signals that regulate vehicle entry onto the freeway. The signals operate based on control strategy algorithms, dynamically adjusting green time durations to control the number of vehicles merging onto the mainline. The metering rate, which determines the share of green time within each control cycle (e.g., every 30 seconds or 1 minute), is recalculated at the end of each interval based on real-time traffic conditions, ensuring adaptive regulation of ramp inflows. • Traffic Light Placement for Toy Model: Positioned 250 meters upstream of the merge nose on each on-ramp. • Traffic Light Placement for Ronda de Dalt: Positioned 30 meters upstream of the merge nose on each on-ramp. The detectors are strategically placed to capture relevant traffic conditions. The main categories of sensors and their functions are as follows: •Up-Ramp Detector: – Placed before the ramp metering signal to monitor the total length of waiting vehicles and assess on-ramp demand. – Provides input for determining the required metering rate adjustments based on congestion levels for EqALINEA control strategy. •Down-Ramp Detector: –Placed after the Ramp metering signal, tracking the merging flow rates. •Downstream Freeway Detectors: –Placed 40 meters after the merge point (or "merge nose") to monitor freeway congestion. – These detectors supply occupancy data to ALINEA, which regulates ramp metering based on freeway conditions. •Upstream Freeway Detectors: – Positioned a hundred meters before the ramps (specific to Upstream ALINEA). – Used to anticipate congestion formation and regulate ramp metering accordingly, preventing congestion from propagating. 52 Fairness in Ramp Metering February 2025 Figure 17: Ramp Metering Component Placement. Source: Own Souce 3.3.3 Implementation (ALINEA & Upstream ALINEA) The ALINEA algorithm is implemented through the alinea_control function, which adjusts the ramp metering signal timings based on real-time traffic conditions. Below is an explanation of how the formula is applied in the code: 53 Fairness in Ramp Metering February 2025 ALINEA Control Logic The fundamental control equation: r(k) = r(k−1) + KR[ˆo−oout(k)] (1) Where: •r(k): Metering rate at the current time cycle. •r(k-1): Metering rate from the previous time cycle. •KR : Control gain parameter (veh/h). In real-life experiments, a value of 70 veh/h was found effective. For simulation with a 1-minute cycle period, it is normalized as KR = 70/60 veh/min. It influences how aggressively the algorithm adjusts the metering rate in response to changes in traffic conditions. •ˆo: Target occupancy (set to 20% in this study). •oout ( k ): Measured downstream occupancy (Exit_O_Measured) at the current time step. Implementation Details with Traci 1def alinea_control(intersection, Q_previous_rate, O_Target, Exit_O_Measured, green_shares):,→ 2""" 3Alinea ramp metering control logic. 4 5Parameters: 6intersection: Ramp metering location ID 7Q_previous_rate: Previous flow rate for metering control 8O_Target: Target freeway occupancy 9Exit_O_Measured: Measured downstream occupancy 10 - green_shares: Previous green time allocation list 11 12 Returns: 13 - Q_rate: Updated metering rate 14 - GREEN_SHARE: Adjusted green time allocation 15 """ 16 Q_rate =Q_previous_rate +Kr *(O_Target -Exit_O_Measured) 17 54 Fairness in Ramp Metering February 2025 tions, quantifying trip completion efficiency. • Total Travel Time (s): Sum of time taken by vehicles to reach destinations, with lower values indicating efficient routing. • Total Travel Distance (km): Total distance traveled by vehicles, where shorter distances suggest minimal detours due to congestion. • Average Speed of Vehicles(km/h): Mean speed of vehicles, reflecting overall traffic fluidity for completed trips. • Total Delays (s): Sum of additional time spent due to congestion or metering, directly quantifying congestion’s impact. • Average Delay per Vehicle (min/veh): Deviation between actual travel time and free-flow travel time, measuring the time experienced per vehicle due to congestion based on different scenario. • Mainline Occupancy (%): The proportion of road space occupied by vehicles at a given time, used to measure congestion levels. High occupancy indicates congestion; optimal occupancy ensures smooth flow (e.g., 10–20% is ideal for free-flow conditions). • Average Free-Flow Difference (s): Deviation between actual travel time and free-flow travel time. 2. Fairness Considerations: How equitably the metering delays are distributed among on-ramp users. As mentioned in Section 3.4.1, in this study we combine Rawlsian fairness with egalitarian fairness; our aim is to minimize variability in the delay metrics across ramps, which translates into a lower Gini coefficient. • Gini Coefficient: Inequality measure (0–1) for delays among completed trips, with 0 = perfect fairness. (Egalitarian Fairness) • Average Waiting Time per On-Ramp (s): Mean delay experienced by vehicles at each on-ramp, identifying bottlenecks. (Harsanyian Fairness) • Merging Rate per On-Ramp (veh/cycle): Vehicles entering the freeway per cycle from each on-ramp, ensuring no ramp is disproportionately restricted. • Number of Vehicles Joined to Highway (veh): Total vehicles entering via each on-ramp, ensuring demand is met without bias. 61 Fairness in Ramp Metering February 2025 • Max On-Ramp Waiting Time (s): Longest delay experienced at any single on-ramp, highlighting worst-case inequities. (Rawlsian Fairness) • Red time assignation per On-Ramp (s/%): Duration/percentage of red signals per on-ramp, balancing metering restrictions equitably. 62 Fairness in Ramp Metering February 2025 4 Results and Discussion This section presents the simulation results and evaluates the impact of ALINEA, Upstream ALINEA, and EqALINEA on traffic efficiency and fairness. The analysis is based on two simulation models, previously introduced in Section 3.2, which represent different levels of network complexity and traffic demand. To ensure clarity, the results are presented in a layered approach: •General trends are first analyzed using the Toy Model. • The key differences observed in the more complex Ronda de Dalt Model are then highlighted. •Comparative tables and visual overlays complement redundant data presentations. 4.1 Traffic Efficiency Analysis The effectiveness of the benchmark control strategies in managing freeway congestion is evaluated using the traffic efficiency metrics outlined in Section 3.5. The performance of ALINEA and Upstream ALINEA is then compared against the proposed EqALINEA algorithm to assess improvements in traffic flow, delay reduction, and overall system efficiency. The analysis is conducted over different simulation durations (ST = Simulation Time) for each model. The initial phase is considered as transitory responde period, where the system gradually gradually fills with vehicles ans stabilizes. To ensure the accurate evaluation, only the steady-state portion of the simulation is analyzed: •Toy Model: ST = 1000s to 3000s •Ronda Toy Model: ST = 1000s to 10800s The traffic efficiency metrics reveal distinct performance trends across control strategies in both the Toy and Ronda models. 63 Fairness in Ramp Metering February 2025 Table 4: Traffic Efficiency Metrics for Toy Model Metric NoControl ALINEA UpALINEA EqALINEA TDV (veh/ST) 1795 1657 1601 2097 TAV (veh/ST) 1212 1211 1209 1219 AR (%) 67.52 73.08 75.52 58.13 TTT (h) 294 256 223 277 TTD (km) 4636 4714 4891 4910 AS (km/h) 15.7 18.4 21.9 17.7 TD (h) 240 205 171 210 AD (min/veh) 8.02 7.42 6.41 6.01 Table 5: Traffic Efficiency Metrics for Ronda Model Metric NoControl ALINEA UpALINEA EqALINEA TDV (veh/ST) 11090 10731 10558 10402 TAV (veh/ST) 10285 10125 9989 9942 AR (%) 92.74 94.35 94.61 95.58 TTT (h) 2182 1761 1648 1454 TTD (km) 36654 39923 40932 41150 AS (km/h) 16.8 22.7 24.8 28.3 TD (h) 1706 1247 1123 927 AD (min/veh) 9.23 6.97 6.38 5.35 In the Toy Model, ALINEA and Upstream ALINEA (UpALINEA) exhibit measurable improvements over the NoControl baseline. ALINEA reduces total delays (TD) by 14.6% (240 h to 205 h) and increases the arrival rate (AR) by 5.6 percentage points (67.5% to 73.1%). UpALINEA further enhances these outcomes, lowering delays by 28.8% (240 h to 171 h) and achieving the highest AR (75.5%). However, EqALINEA demonstrates a contrasting trend: its AR declines to 58.1%, and total travel time (TTT) increases marginally (277 h vs. NoControl’s 294 h). This divergence arises from EqALINEA’s prioritization of equitable merging, which reduces per-vehicle delays (AD: 6.01 min/veh vs. NoControl’s 8.02 min/veh) but increases queuing at specific on-ramps (e.g., J11), leading to higher system-wide vehicle accumulation. In the Ronda Model, all strategies outperform NoControl, with EqALINEA delivering the most balanced results. EqALINEA reduces total delays by 45.7% (1,706 h to 927 h), achieves the highest average speed (28.3 km/h vs. NoControl’s 16.8 km/h), and maintains the highest AR (95.6%). UpALINEA also performs robustly, reducing delays by 34.1% (1,706 h to 1,123 h) and improving average speed to 24.8 km/h. ALINEA, while effective, lags behind these two strategies, underscoring its limitations in managing complex network 64 Fairness in Ramp Metering February 2025 interactions. Both models reveal increased total travel distances (TTD) under controlled strategies, which can be explained by the influence of ramp metering control. However, these increases are counterbalanced by significant gains in speed and delay reduction. For more detail information refer to Table 4 for Toy Model metrics and Table 5 for Ronda de Dalt Model results. 4.2 Fairness Evaluation 4.2.1 Gini Coefficient Analysis The Gini coefficient is used to assess inequality in delay distribution, where lower values indicate greater fairness. Table 6 presents the Gini coefficients for arrived vehicles, departed vehicles, and vehicles still in transit under each ramp metering strategy for both the Toy Model and Ronda De Dalt Model. Table 6: Gini Coefficients for Toy Model and Ronda De Dalt Model Toy Model Control Gini Arrived Gini Departed Gini on System NoControl 0.44 0.43 0.34 ALINEA 0.43 0.43 0.38 UpStreamALINEA 0.35 0.37 0.40 EqALINEA 0.41 0.40 0.35 Ronda Model Control Gini Arrived Gini Departed Gini on System NoControl 0.40 0.40 0.39 ALINEA 0.29 0.30 0.36 UpStreamALINEA 0.25 0.26 0.34 EqALINEA 0.21 0.22 0.31 65 Fairness in Ramp Metering February 2025 Fairness Trends in the Toy Model In the Toy Model, ALINEA exhibits minimal fairness improvements compared to NoControl, as the Gini coefficient for arrived vehicles remains nearly unchanged (0.43 vs. 0.44 in NoControl). However, its on-system Gini coefficient increases (0.38 vs. NoControl’s 0.34), indicating that inequality in delay accumulation worsens for vehicles still in transit. This is due to ALINEA’s focus on maximizing freeway throughput, which sacrifices fairness for on-ramp users downstream of bottlenecks (J9 and J10), where congestion propagates rapidly. As shown in Fig. 19 and Fig. 20, the ALINEA control strategy completely stops metering for ramps J9 and J10 from simulation time 1700s onward, prioritizing mainline flow but disproportionately delaying on-ramp users at these locations. Upstream ALINEA achieves a more balanced delay distribution, reducing the Gini coefficient for arrived vehicles to 0.35. This improvement occurs because metering is activated earlier, distributing delays more evenly over time as congestion forms and propagates. However, its on-system Gini coefficient remains high (0.40), suggesting that while fairness improves for completed trips, delay variability persists for vehicles still in transit. As depicted in Fig. 19 and Fig. 20, the Upstream ALINEA control strategy starts assigning more than 50% red time for ramps J9 and J10 as early as simulation time 1250s, effectively delaying congestion propagation upstream. As a result, even though Upstream ALINEA follows the same control logic as ALINEA, it avoids completely blocking access to ramps J9 and J10, ensuring more equitable on-ramp access while still managing freeway congestion. EqALINEA successfully balances efficiency and fairness, achieving the lowest on-system Gini coefficient (0.35), ensuring that waiting times are more equitably distributed across all ramps. However, the Gini coefficient for arrived (0.41) and departed vehicles (0.40) remains moderate, reflecting a deliberate trade-off between maintaining freeway efficiency and ensuring equitable ramp access. As seen in Fig. 19 and Fig. 20, EqALINEA is the only control strategy that continues assigning metering rates to on-ramp users while maintaining system efficiency, effectively mitigating extreme delays without completely restricting access. Fairness Trends in the Ronda De Dalt Model The Ronda De Dalt Model, with higher demand and a longer simulation period, shows stronger fairness improvements across all control strategies. ALINEA reduces delay inequality compared to NoControl, but on-system fairness remains a challenge, as congestion 66 Fairness in Ramp Metering February 2025 persists for vehicles still in transit. Upstream ALINEA further improves fairness, reducing the Gini coefficient to 0.25 for arrived vehicles, as ramp metering is activated earlier, preventing extreme bottlenecks at individual ramps. However, EqALINEA delivers the most equitable results, with Gini values of 0.21 for arrived vehicles and 0.22 for departed vehicles, demonstrating its effectiveness in distributing delays fairly across all users. A notable trend in the Ronda De Dalt Model is that on-system Gini coefficients remain high across all strategies (0.31–0.39). This occurs because the simulation extends beyond peak hours (1000s to 10800s), allowing long-distance travelers to experience reduced delays, which influences the fairness assessment. Future evaluations could benefit from dynamically analyzing on-system fairness relative to traffic intensity to better capture time-dependent equity variations. 4.2.2 On-Ramp User Experience Analysis The evaluation of ramp metering strategies focuses on their ability to balance efficiency and equity across on-ramps. Key metrics—maximum waiting times, merging rates, red time distribution, and successful freeway entries—highlight the trade-offs between benchmark control methods (ALINEA, UpALINEA) and the fairness-oriented EqALINEA algorithm. In the following analysis, key metrics will be examined to illustrate the the impact of different ramp metering strategies on user experience at individual ramps. •Waiting Time Distribution: Both average and maximum waiting times (Tables 7 and 8) reveal EqALINEA’s ability to mitigate extreme delays while balancing average congestion. In the Toy Model, EqALINEA reduces average waiting times by 53% for J9 (210.23 s vs. ALINEA’s 455.73 s) and 47% for J10 (216.63 s vs. ALINEA’s 411.77 s), despite J11’s higher maximum wait (183 s vs. ALINEA’s 33 s). This trade-off reflects a deliberate redistribution: J11’s maximum wait remains 44% lower than under UpALINEA (380 s), while its average wait decreases by 39% (194.11 s vs. 322.99 s), demonstrating prioritized fairness over localized optimization. 67 Fairness in Ramp Metering February 2025 In the Ronda Model, EqALINEA narrows disparities between ramps. While E3 and E5 experience increased average waits (203.12 s and 186.82 s) compared to ALINEA (105.70 s and 103.78 s), their maximum waits remain controlled (281 s and 250 s vs. ALINEA’s 95 s and 88 s). Conversely, high-congestion ramps like E2 and E4b see reduced average waits (213.52 s and 175.98 s) under EqALINEA compared to ALINEA (223.84 s and 188.16 s)but E4 faces a increment from 175.83 s to 191.12 and the maximum waits for E2 and E4 decreasing by 56% and 50%, respectively. This equilibrium prevents systemic bottlenecks, as no ramp exceeds 280 s in maximum delay -although, in theory, the delay should not surpass 240s (4 minutes), which requires further investigation- (Table 8). Table 7: Average Waiting Time per On-Ramp [s] Toy Model Metric NoControl ALINEA UpALINEA EqALINEA J9 122.96 455.73 469.71 210.23 J10 152.34 411.77 482.18 216.63 J11 93.64 101.46 270.30 155.46 Average 122.98 322.99 407.4 194.11 Ronda De Dalt Model Metric NoControl ALINEA UpALINEA EqALINEA E2 140.41 223.84 257.91 213.52 E3 71.77 105.70 147.25 203.12 E4 108.49 175.83 222.09 191.12 E4b 108.88 188.16 148.66 175.98 E5 60.85 103.78 149.55 186.82 Average 98.08 159.46 185.09 194.11 68 Fairness in Ramp Metering February 2025 Table 8: Maximum Waiting Time per On-Ramp [s] Toy Model Ramp NoControl ALINEA UpALINEA EqALINEA J9 400 1312 1337 308 J10 314 1224 1147 252 J11 12 33 380 183 Max 400 1312 1337 308 Ronda De Dalt Model Ramp NoControl ALINEA UpALINEA EqALINEA E2 195 620 607 274 E3 20 95 202 281 E4 158 524 409 261 E4b 82 267 377 264 E5 14 88 183 250 Max 195 620 607 281 69 Fairness in Ramp Metering February 2025 •Merging Rate per On-Ramp [veh/cycle]: While NoControl achieves the highest merging rates (e.g., 10.86 veh/cycle at J9 in the Toy Model; Table 9), it lacks regulation, leading to unstablesaturation traffic flow. ALINEA and UpALINEA suppress merging rates significantly (e.g., 2.7 veh/cycle at J9 for ALINEA), prioritizing freeway throughput over ramp accessibility. EqALINEA strikes a middle ground, improving merging rates compared to UpALINEA (5.19 veh/cycle vs. 2.58 veh/cycle at J9) while ensuring no single ramp dominates access. This balance is particularly evident in the Ronda Model, where EqALINEA narrows the gap between ramps (3.36–4.07 veh/cycle) compared to ALINEA’s wider disparity (3.15–5.64 veh/cycle). Table 9: Merging Rate per On-Ramp [veh/cycle] Toy Model Ramp NoControl ALINEA UpALINEA EqALINEA J9 10.44 2.7 2.58 5.19 J10 10.14 2.82 2.43 5.13 J11 10.86 7.8 4.23 6.39 Average 10.48 4.44 3.08 5.57 Ronda de Dalt Model Ramp NoControl ALINEA UpALINEA EqALINEA E2 8.03 3.78 3.37 3.90 E3 8.87 5.52 4.45 3.47 E4 7.40 3.15 3.86 3.36 E4b 8.52 4.34 3.61 4.07 E5 9.43 5.64 4.44 3.77 Average 8.45 4.49 3.95 3.71 •Number of Vehicles Joined to Highway (veh): The number of vehicles successfully merging onto the highway reflects the balance between congestion control and equitable access (Table 10). In the Toy Model, EqALINEA allows a more consistent entry rate across ramps (197–236 veh/ST), significantly improving upon UpALINEA (115–177 veh/ST) and ALINEA (130–274 veh/ST), which restrict access at certain ramps. While ALINEA achieves slightly higher throughput at J11, it does so at the expense of J9 and J10, which experience substantial reductions in merging rates. 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Yu (2011) Dhp method for ramp metering of freeway traffic, IEEE Transactions on Intelligent Transportation Systems,12 (4) 990–999. 80 Fairness in Ramp Metering February 2025 A Appendix & Additional Data Table 12: Presence of Ramp Metering Worldwide State Country City Year Citation North America US Illinois 1963 Mizuta et al. (2014a) Europe UK Birmingham 1986 Agency (2010) Sweden Stockholm 2003 Trafikverket (2019) Netherlands Amsterdam 1989 Taale et al. (1994) Germany Duisburg, Rhine-Ruhr region 1996 Universität Duisburg-Essen (n.d.) France Paris 1996 Haj-Salem et al. (2001) Switzerland Zurich 2022 Switzerland (2022) Turkey Istanbul 2016 Municipality (n.d.) Oceania Australia Melbourne 1971 Johnson and Bajenov (2018) New Zealand Auckland 1983 Transport (n.d.) Asia Israel Tel Aviv Commission (n.d.) China Suzhou 2022 ThePaper (2022) Taiwan 1982 Institute of Transportation, MOTC (2023) Africa South Africa Johannesburg and Ekurhuleni 2006-2009 Freeway (2015) Table 13: Exit Interval Average Flow (veh/h) Control JE2 JE3 JE4 JE4b JE5 NoControl 1385 1106 1878 1411 1445 ALINEA 1181 1161 1559 1345 1422 UpStreamALINEA 1125 1167 1538 1292 1388 EqALINEA 1093 1125 1028 1058 1351 Average 1096 1140 1501 1277 1401 81 Fairness in Ramp Metering February 2025 Table 14: Comparison of Ramp Metering Algorithms Types of Algorithms Parameters Site of Detector Strengths Limitation Demand Capacity D-C occupancy Upstream Downstream Measured from upstream flow and downstream occupancy The minimum metering rate is used when downstream occupancy exceeds a critical value (Ocr) Demand Capacity INRETS capacity Downstream Multi-detectors = 3 Measured from upstream flow and downstream occupancy For free-flowing conditions and heavy congestion ALINEA algorithm occupancy Downstream Measured from downstream occupancy Critical occupancy is more reliable than relying only on capacity value RWS algorithm occupancy Upstream Measured from upstream flow Similar to the D-C algorithm Percent occupancy algorithm D-C capacity Upstream Measured from upstream flow and occupancy Acquired from the demand capacity (D-C) algorithm MALINEA occupancy Downstream Measured from occupancy upstream and downstream In the upstream merge section, ALINEA was unable to reduce congestion. Choosing the optimum position for the downstream detectors’ station is difficult FL-ALINEA occupancy Downstream Measured from downstream flow and occupancy Choosing the optimal position for the downstream detectors’ station is difficult Speed-Occupancy algorithm occupancy and speed Upstream Measured from speed and occupancy for upstream Traffic conditions could be reflected by both speed and occupancy parameters ANCONA algorithm speed Downstream Measured from speed for upstream Unable to detect congestion when located downstream from an active bottleneck Local ALENA occupancy Downstream = 2 Measured occupancy from downstream Maximizes mainline throughput by maintaining desired occupancy Hero ALENA occupancy Upstream Downstream Measured occupancy from upstream and downstream Difficult to estimate downstream detector flow drop when the mainline is close to capacity 82 Fairness in Ramp Metering February 2025 Figure 19: Toy model Occupancy Variation J9. Source: Own source 83 Fairness in Ramp Metering February 2025 Figure 20: Toy model Occupancy Variation J10. Source: Own source 84 Fairness in Ramp Metering February 2025 Figure 21: Toy model Occupancy Variation J11. Source: Own source 85 Fairness in Ramp Metering February 2025 Figure 22: Toy model Average Speeds J9. Source: Own source Figure 23: Toy model Average Speeds J10. Source: Own source 86