# Exploring Traffic Paradoxes: A Study of Roundabout Corridors and Their Effects on Network Dynamics

Lorenzo Brocchini, Lorenzo Brocchini, Didier Josselin

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Lorenzo Brocchini, Lorenzo Brocchini, Didier Josselin. Exploring Traffic Paradoxes: A Study of Roundabout Corridors and Their Effects on Network Dynamics. Sustainability, 2025, 17 (22), pp.10290. 10.3390/su172210290. [hal-05377085](https://hal.science/hal-05377085v1)

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Article

# Exploring Traffic Paradoxes: A Study of Roundabout Corridors and Their Effects on Network Dynamics

Lorenzo Brocchini <fnref n="1" />,* , Antonio Pratelli <fnref n="1" /> and Didier Josselin <fnref n="2" />

## Abstract

This research is part of a broader investigation into dynamic simulation-based approaches for enhancing traffic efficiency, road safety, and sustainability in roundabout corridors and/or road corridors in general. The study emphasizes the need to analyze road intersections as interconnected systems rather than isolated components, aiming to better understand and mitigate counterintuitive phenomena known as traffic paradoxes, including the well-known Braess Paradox. The first section introduces the main traffic paradoxes, exploring their definitions, real-world implications, and reproducibility in roundabout corridors. The second section focuses on a case study of the "SS1—Via Aurelia Nord" in Pisa (Italy), where converting a traffic-light-controlled corridor into a roundabout corridor unexpectedly led to increased congestion. This paradoxical outcome is analyzed within the broader context of network dynamics and sustainable mobility planning. Dynamic simulations were performed using Aimsun software, and a novel performance index—the "Celerity Roundabout Corridors" (CRC)—was proposed to quantify and detect these paradoxical effects. The findings highlight conditions under which roundabout corridors may generate inefficiencies despite infrastructural upgrades, emphasizing the importance of systemic, simulation-based evaluations for the sustainable design and optimization of urban traffic networks.

**Keywords:** traffic paradoxes; roundabout corridors; Braess paradox; dynamic simulations; network efficiency; sustainable mobility

## 1. Introduction

Traffic networks are essential components of urban mobility systems, enabling the efficient movement of people and goods. However, their inherent complexity often gives rise to counterintuitive phenomena that challenge conventional engineering paradigms. Among these, traffic paradoxes play a key role, demonstrating that local infrastructure improvements may not always lead to global benefits.

This study focuses on roundabout corridors [1–5], defined as linear arterial roads composed of multiple interconnected roundabouts that often replace conventional signalized intersections. While individual roundabouts are typically associated with improved safety and operational performance, their network-wide impact remains uncertain.

Furthermore, in the context of sustainable mobility, understanding the systemic effects of infrastructure transformations is crucial. Enhancing traffic efficiency without compromising environmental and social objectives represents a key challenge in urban planning.

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Academic Editor: Giovanni Leonardi

Received: 18 October 2025

Revised: 10 November 2025

Accepted: 14 November 2025

Published: 17 November 2025

**Citation:** Brocchini, L.; Pratelli, A.; Josselin, D. Exploring Traffic Paradoxes: A Study of Roundabout Corridors and Their Effects on Network Dynamics. *Sustainability* **2025**, *17*, 10290. https://doi.org/10.3390/su172210290

**Copyright:** © 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

<footnote n="1">¹ Department of Civil and Industrial Engineering, University of Pisa, Largo Lucio Lazzarino 1, 56122 Pisa, Italy; antonio.pratelli@unipi.it</footnote>

<footnote n="2">² UMR 7300 ESPACE (Étude des Structures, des Processus, de l'Adaptation et des Changements de l'Espace), CNRS, Université d'Avignon, 74 Rue Louis Pasteur, 84029 Avignon, France; didier.josselin@cnrs.fr</footnote>

<footnote>* Correspondence: lorenzo.brocchini@gmail.com; Tel.: +39-333-831-3112</footnote>
Roundabout corridors and/or road corridors in general, if properly designed, can reduce vehicle idling and emissions, but when paradoxical effects emerge, they may lead to higher energy consumption and pollutant output. Therefore, studying these phenomena contributes not only to transport efficiency and safety, but also to the broader goal of sustainable network management. There are many possible counterintuitive effects that could occur, a prime example of which is the well-known Braess paradox [6–13], which suggests that adding capacity to a network can, under certain conditions, lead to increased congestion rather than improved flow. Other paradoxes, such as the Pigou-Knight-Downs Paradox [14,15], Downs-Thomson Paradox [16–18], Beckmann’s Paradox [19,20], and Induced Demand Paradox [21], similarly demonstrate that local interventions do not always translate into global benefits. These phenomena become particularly relevant when evaluating the transformation of linear arterial corridors into roundabout corridors, as they alter the systemic interactions between traffic flows.

The case study of the SS1—Via Aurelia Nord corridor in Pisa (Italy) provides an illustrative and instructive example where the conversion from a signalized arterial road to a roundabout corridor unexpectedly increased congestion in specific sections. To investigate this paradoxical behavior, the present study applies dynamic microsimulation and introduces a new performance indicator—the Celerity Roundabout Corridors (CRC) index—to quantify and interpret systemic efficiency variations between configurations. While several previous studies have assessed the operational and safety performance of individual roundabouts, there is still limited research examining the systemic effects of converting an entire arterial corridor into a continuous sequence of roundabouts. This gap represents a critical challenge for both research and practice, as such transformations can produce counterintuitive outcomes that traditional intersection-level analyses fail to capture. The general motivation behind this study is therefore to provide a comprehensive understanding of these large-scale interactions, combining dynamic simulation with a novel diagnostic metric (the CRC index) to identify, quantify, and interpret paradoxical network behaviors.

Addressing this gap, the novelty of the study lies in three main aspects: (i) adopting a systemic, corridor-wide analytical perspective that captures interdependencies between consecutive intersections; (ii) introducing the CRC index as a diagnostic metric to detect paradoxical efficiency losses at node level while preserving a network view; and (iii) providing empirical evidence of paradoxical effects observed in a real-world corridor, extending classical traffic-paradox theories to practical contexts. By combining these elements, the research contributes to sustainable and data-driven mobility planning, offering methodological and practical insights into how infrastructure design decisions influence network-wide efficiency, safety, and environmental performance. Understanding these systemic effects supports more informed infrastructure planning and contributes to the development of sustainable, evidence-based mobility policies.

The present paper is structured as follows: Section 2 reviews the theoretical background on traffic paradoxes and network efficiency; Section 3 presents the case study and methodological framework; Section 4 reports and discusses the results, including the identification of paradoxical effects through the CRC; and Section 5 concludes with policy implications and directions for future research.

## 2. Theoretical Background

This chapter explores the foundational concepts necessary to understand the dynamics of traffic paradoxes and roundabout corridors. It begins with an overview of Graph Theory, providing the mathematical basis for analyzing traffic networks. The discussion then moves to traffic paradoxes, offering a general perspective on their counterintuitive effects.
A dedicated section focuses on the Braess Paradox, highlighting its implications for network performance and transport geography. Finally, the chapter concludes with an in-depth exploration of the roundabout corridors theory, examining the conditions under which these systems may manifest paradoxical phenomena.

## 2.1. The Graph Theory

Graph theory, a branch of mathematics and computer science, studies graphs, e.g., discrete structures used to model various network and system interactions [22]. In Transport and Traffic Engineering, a transport network is represented as a graph where arcs are characterized by attributes such as capacity (physical and environmental), transport cost, and authorized traffic direction [23]. Transport cost, expressed as a scalar quantity, combines two components: one proportional to arc length and another to travel time [24]. For a generic arc i, the transport cost $c_i$ can be expressed as in Equation (1):

$$c_i = c_L \cdot L_i + VT \cdot T_i \quad (1)$$

where $T_i$ = arc travel time of arc i; $VT$ = monetary value that users assign to the unit of travel time (e.g., 0.05–0.15 €/min); $c_L$ = cost per unit of arc length (e.g., 0.15 €/km, excluding tolls); $L_i$ = length of the arc i. It must be noted that the transport cost refers to a use average cost and is considered identical for all other users of the system. The component of the transport cost that is prevalent over the others is the travel time $T_i$. The general form taken to express the travel time on the generic arc i is expressed as Equation (2).

$$T_i = T_{i,r} + T_{i,w} \quad (2)$$

where the first of the two addends of the second term relates to the arc travel time or running time (r). The second addendum refers to the waiting time (w) at the intersection located at the end of the arc itself, which becomes the connection point for the next arc. The cost function of an arc relates transport cost, typically linked to travel time, with traffic flow. Cost functions are classified as separable when dependent only on the flow through a specific arc, or non-separable when influenced by flows across the entire network.

It is also worth noting that recent developments in traffic assignment have increasingly adopted data-driven and machine learning techniques, such as end-to-end heterogeneous graph neural networks, to better capture nonlinear relationships between network structure and traffic flow dynamics [25]. Although the present study does not employ such models, it shares the same systemic perspective, focusing instead on a simulation-based diagnostic approach through a possible new index to investigate paradoxical network behaviors.

## 2.2. Traffic Paradoxes

To illustrate the point, some experiences of the Braess Paradox were related by the journal Le Monde in France [26]. The left bank route in Paris called Rive gauche of the river Seine was closed in 2013. It was expected to have more congestion in the surrounding boulevards, but this did not occur. The opposite is also true. In October 2012, the Mathilde bridge in the town of Rouen, one of the main roads crossing the Seine, caught fire following an accident involving an oil truck.

The bridge, which used to carry 80,000 vehicles a day, including lorries and cars, was closed until summer 2014 and then rebuilt identically. During this period, some vehicles switched to other bridges, while others bypassed the town. However, the global counters did not reach the figure of 80,000 daily passages. The engineers who are in charge of monitoring the Seine-Maritime road were surprised to observe that some vehicles had “disappeared”. Many similar events were noticed in different cities (Lyon, Warsaw,
Stuttgart, Seoul, etc.) [6,27,28], in one way (traffic slowed down after creating a new connected road infrastructure) or the other (stability or even a decrease in the traffic after a route or a road banning).

Indeed, building on the fundamentals of graph theory, traffic engineering reveals several paradoxical phenomena that challenge traditional approaches to infrastructure improvement and traffic management. These paradoxes highlight the counter-intuitive behavior of traffic networks and the importance of a systemic approach in analyzing roundabout corridors. Below are listed some traffic engineering paradoxes, with their definitions and their relevance to roundabout corridors. They can be all considered as observations resulting from Braess paradox declinations or variations. These paradoxes are:

* Pigou-Knight-Downs Paradox [14,15]: adding a faster or higher-capacity route can unintentionally increase travel times. When drivers prioritize the quickest route, the new capacity may attract excess traffic, leading to congestion. This paradox underscores the need for network-wide considerations, particularly in roundabout corridors where isolated improvements may disrupt overall performance;

* Downs-Thomson Paradox [16–18]: Road capacity improvements without corresponding public transport enhancements can reduce system efficiency. As private car travel becomes more attractive, public transport ridership declines, potentially increasing road congestion. This paradox is especially critical in urban roundabout corridors, where balancing road and public transport efficiency is vital;

* Beckmann's Paradox [19,20]: optimizing traffic flow on individual links can worsen overall network performance. Local improvements, such as capacity expansion or route prioritization, may disrupt global traffic dynamics. For roundabout corridors, this highlights the importance of avoiding isolated optimization and considering the entire network;

* Induced Demand Paradox [21]: expanding road capacity often attracts additional traffic, negating congestion reductions. This phenomenon demonstrates the limitations of capacity expansion as a stand-alone solution. In roundabout corridors, this paradox reinforces the need of demand management strategies;

* Braess Paradox [6–13]: the most renowned and encompassing paradox in traffic engineering, extensively discussed in this study, demonstrates that adding capacity to a network can increase travel costs under certain conditions.

These paradoxes highlight the need for a systemic approach to traffic engineering, particularly in roundabout corridors, where multiple counterintuitive phenomena can interact and influence traffic dynamics. Roundabout corridors, characterized by multiple interconnected intersections, are particularly prone to these paradoxical effects when improvements fail to account for network interdependencies. A systemic, simulation-based approach is essential to anticipate and mitigate unintended consequences, ensuring that localized interventions do not undermine overall network performance.

## 2.3. *The Braess Paradox*

Building on the principles of graph theory and traffic paradoxes, it is crucial to introduce the concept of equilibrium in transport networks, formalized by John Glen Wardrop in 1952 [29,30]. Wardrop's first principle states: "*At equilibrium, all alternative routes between an origin (O) and a destination (D) used by drivers have equal cost, while unused routes have equal or greater cost*" [31]. The second principle posits: "*The users of a transport system collaborate to minimize the total cost of travel*" [32]. These principles form the foundation for understanding the Braess Paradox, which challenges the assumption that adding infrastructure always improves traffic flow.
Dietrich Braess demonstrated in 1968 that, under certain conditions, adding a new road or increasing network capacity can paradoxically raise overall travel costs [7]. This occurs because drivers, focusing on individual travel times, redistribute themselves in a way that overloads certain routes, disrupting the system's equilibrium and reducing overall efficiency. In practice, vehicles could adapt their itinerary and improve the efficiency of their journey, by sharing information on congestion, whether immediate (impending traffic jam...), local (next road on my route clogged...) or global (two hours longer than expected to return from vacation...).

Unfortunately, Homo mobilis rarely considers the holistic efficiency of the network (reducing my freeway speed by 20 km/h in the event of an ozone peak...). In game theory (of congestion), he runs the risk of paying the price of anarchy [6], leading to a degradation of the social well-being of the system due to the selfish behavior of agents.

Figure 1 illustrates this paradox. In the first configuration, drivers are seeking to minimize their individual travel times by rerouting from point A to point B, causing congestion on certain arcs (the streets) and increasing total travel costs: they are expecting using the highway will decrease their travel time. This leads to an unbalance in the flow of the network. In the second configuration, we imagine stopping the access to highway: this allows a much better flow distribution on this simpler, less connected network. This demonstrates how local changes in network topology can lead to unintended, counter-productive outcomes, especially in complex systems such as roundabout corridors. The occurrence of the Braess Paradox depends on factors like network topology [33,34], shared arcs, and the self-serving behavior of drivers who fail to consider the broader impact of their choices.

<figure><img src="image_3.png" /><figcaption>**Figure 1.** An example of the Braess Paradox. (Source: adapted by D. Josselin from https://couleur-science.eu (accessed on 30 April 2025)).</figcaption></figure>

Real-world cases (such as the closure of urban roads in Paris, Seoul, Stuttgart, and New York City) highlight how systemic effects can counteract initial expectations. These examples emphasize the importance of considering global network interactions when planning infrastructure changes. As previously said, the Braess Paradox is an important issue in transport modeling and geography. It stipulates that adding one or more roads to a network can slow down the overall traffic. Globally, as noticed by Steinberg and Zang in 1983 [35], this paradox can happen frequently (or not) in certain conditions and its occurrence still remains rather uncertain. The effect of the randomness of traffic on intersection delays was first observed and modeled by Wardrop in 1952 from a theoretical point of view, as a first principle [29]. Thence, the Braess Paradox is related to some higher theoretical framework, notably in Economics [36], e.g., via the Nash equilibrium [37] and more generally game theory [38], especially in congestion games. There are indeed many ways to study the Braess Paradox. It depends on the methodological approaches chosen but
also on numerous and various analog applications. See for instance the applications of the
Braess Paradox to power grids and generators [39], to epidemic diseases or even to chemical
reaction systems [40] or quantum physics [41]. What is common to these examples is that
they all deal with networks that can be represented by topological concrete or abstract
structures, i.e., graphs, with nodes and edges, traveled by flows. Most of the time, authors
consider a small, sometimes rather complex, network with connections and cycles. A part
of the scientific progress in comprehending the paradox is due to studying the problem
in a static approach, using descriptive mathematical models. More recently, computer
capacities enabled the process of computing micro-simulations [42] or sensitivity analysis
to find out inflection points over which the Braess Paradox appears [43]. In operation
research, Amini et al. [44] aimed at identifying the links in the Chicago-sketch network
whose closure caused the Braess Paradox, using algorithms to solve a discrete network
design problem in bi-level programming.

Bagloee et al. [45] developed a heuristic methodology (a surrogate-based algorithm) to identify roads for closure in the heart of the cities to be reclaimed for green space or pedestrian plazas in Winnipeg. In 2014, Zhao recommended adjusting the interaction between links of the network with the dynamic change in traffic to optimize a system [46]. This underlines to consider of the mobility system as a whole and to focus on its internal interactions between nodes and along edges. Since the paradox occurs in networks, the graph theory brings interesting insights. For instance, Ciardo demonstrated in 2020 [47] that graphs having a pair of twin pendent vertices are sensitive to the Braess Paradox, even if they are random graphs, especially if they are connected planar graphs. This is the case of a roundabout corridor, which is made of a series of connected roundabouts with several pendant vertices on non-oriented edges at each roundabout, where incoming and outgoing vehicle flows circulate. Since we handle pure linear networks, we can wonder if those are subject to the Braess Paradox. Under selfish routing conditions, Chen et al. [48] characterized the topologies of a type of undirected and directed “series-parallel” networks in which the Braess Paradox never occurs. In a moving context where drivers can obtain information on traffic congestion and dynamically adapt their routing, due to the re-balancing capacity of the global network traffic, appear (a little) more complex networks, all looking like linear or at least quite simple in terms of connectivity [49]. Of course, all those cases display stylized networks and do not correspond to real-world networks.

Indeed, even if we study a roundabout corridor, we know that it interacts with the
surrounding roads and that the vehicle drivers behave differently, applying a personal
decision routing process or sharing information to improve travel efficiency and to reduce
time delays (for instance using Waze). So, what we observe and simulate in our corridor is
complex and integrates the global flows in the city, although we focus on a simple linear
series of connected roundabouts. It is as if we observe the “tip of the iceberg”. In conclusion,
gaining a thorough understanding of the Braess Paradox, along with other traffic paradoxes,
is essential for accurately evaluating the dynamics of roundabout corridors. While the
Braess Paradox provides a compelling case study for understanding traffic dynamics,
the broader analysis of multiple paradoxes is essential to fully evaluate the complexity
of roundabout corridors and their impact on network dynamics. These interconnected
systems, characterized by linear sequences of roundabouts, present unique conditions
under which paradoxical effects may emerge. The next section delves into the specific
challenges and theoretical framework of roundabout corridors, providing a foundation for
their analysis within the context of traffic paradoxes.
## 2.4. The Roundabout Corridors Theory

In this final theoretical section, the "concept" of the roundabout corridor is introduced to provide a clearer understanding of how traffic paradoxes, such as those discussed in this study, may manifest in this type of infrastructure. While the Braess Paradox serves as a prominent example for interpreting counterintuitive traffic dynamics, other paradoxes, such as Pigou-Knight-Downs and Induced Demand, are also relevant in the context of roundabout corridors. Traditionally, these paradoxes have been studied at a "meso-scale," focusing on networks composed of nodes (intersections or points of attraction) and arcs (roads connecting these nodes). However, observations from the "SS1—Via Aurelia Nord" in Pisa (Tuscany, Italy) suggest that these paradoxical dynamics can also be visible at a "micro-scale."

At this scale, the network is represented by the linear road corridor, where nodes correspond to the five intersections, and arcs represent the connecting road sections, including the influence zones of roundabouts [50]. This raises a critical question: "How can the principles of graph theory and traffic paradoxes be applied to this specific scale?" A potential explanation lies in the distinctive features of the road corridor under study.

The "SS1—Via Aurelia Nord" can be classified as a roundabout corridor, a type of infrastructure that operates as a "linear system." To clarify its definition and characteristics, a roundabout corridor is defined as: "An infrastructure that includes a series of three or more roundabouts that function independently along an artery" [1]. The key characteristics that define a roundabout corridor are as follows [1,51]:

* The corridor must have from three to six roundabouts;

* Branches must be two or four lanes, mainly suburban;

* Roundabouts must have one or two lanes in the ring;

* The speed limit must be between 25 mph (~40 km/h) and 50 mph (~80 km/h);

* The total length must be between 0.5 miles (~800 m) and 4.5 miles (~7200 m);

* The distance between two consecutive roundabouts must be between 650 feet (~200 m) and 6465 feet (~1970 m);

* The characteristics of the lateral arrangements may vary (e.g., the presence or absence of sidewalks, pedestrian crossings, cycle paths, rest areas).

The road corridor selected for this research, the "SS1—Via Aurelia Nord" in Pisa (Tuscany, Italy), meets all the above-mentioned characteristics and can therefore be classified as a roundabout corridor. This classification enables the application of theoretical frameworks, including graph theory and traffic paradoxes, to understand and analyze the dynamics of such systems. The analysis in this study does not focus exclusively on the Braess Paradox but considers a range of paradoxical behaviors to provide a comprehensive assessment of traffic dynamics in roundabout corridors.

# 3. Materials and Methods

This chapter outlines the methodology used to analyze traffic dynamics and paradoxical behaviors in the "SS1—Via Aurelia Nord" corridor in Pisa (Italy). Serving as a practical application of the theoretical framework, the case study evaluates traffic paradoxes in a real-world roundabout corridor. The analysis includes an overview of the corridor's characteristics, the tools and software employed, and the data collection and processing methods. These elements aim to identify conditions under which paradoxical effects arise and assess the corridor's efficiency under varying configurations.

## 3.1. Characteristics of the Pisa Roundabout Corridor

After outlining the key theoretical considerations regarding traffic paradoxes and roundabout corridors, this section presents the case study of the roundabout corridor in
Pisa. The analysis focuses on a real-world example where a corridor previously composed of traffic-light-controlled intersections was converted into a series of roundabouts. In Pisa (Tuscany, Italy), the “SS1—Via Aurelia Nord” was originally a traditional arterial road with a sequence of intersections regulated by traffic lights. Today, this stretch has been transformed into a roundabout corridor consisting of five roundabouts. The “SS1—Via Aurelia Nord” is one of Italy’s most significant state roads, connecting Rome to the French border along the Tyrrhenian and Ligurian coasts. It passes through nine provincial capitals and several major tourist destinations. The left map in Figure 2 highlights the Tuscany region, where the case study corridor is located, while the right map shows the full alignment of the “SS1—Via Aurelia Nord” across Italy’s north-western coastal regions.

<figure><img src="image_4.png" /><figcaption>**Figure 2.** SS1—Via Aurelia in Italy. (Source: Wikipedia. Available online: https://it.wikipedia.org/wiki/Strada_statale_1_Via_Aurelia (accessed on 30 April 2025)).</figcaption></figure>

The study area is located in the western part of Pisa, extending approximately 2.5 km. It consists of a single arterial road intersected by five roundabouts as shown in Figure 3.

<figure><img src="image_5.png" /><figcaption>**Figure 3.** Roundabout corridor in Pisa, scale 1:15,000, with the numbered circles indicating the five roundabouts that compose the corridor. (Source: [52]).</figcaption></figure>
Currently, each intersection along this corridor is a roundabout, making it fully com-
pliant with the roundabout corridor classification. Previously, these intersections were
regulated by traffic lights, but over the past 15 years, they have been gradually redesigned
as roundabouts. The five intersections are:

* Intersection number 1: Via Aurelia Nord—Via delle Cascine (Figure 4);

* Intersection number 2: Via Aurelia Nord—Via Andrea Pisano (Figure 5);

* Intersection number 3: Via Aurelia Nord—Via della Fossa Ducaria (Figure 6);

* Intersection number 4: Via Aurelia Nord—Via Livornese (Figure 7);

* Intersection number 5: Via Aurelia Nord—Via Darsena (Figure 8).

<figure><img src="image_6.png" /><figcaption>**Figure 4.** Intersection number 1: (a) Previous State (2008); (b) Current State (2021). (Source: [52], adapted by authors and Google Earth Pro. Available online: https://www.google.com/earth/ (accessed on 30 April 2025)).</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Figure 5.** Intersection number 2: (a) Previous State (2008); (b) Current State (2021). (Source: [52], adapted by authors and Google Earth Pro. Available online: https://www.google.com/earth/ (accessed on 30 April 2025)).</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**Figure 6.** Intersection number 3: (a) Previous State (2008); (b) Current State (2021). (Source: [52], adapted by authors and Google Earth Pro. Available online: https://www.google.com/earth/ (accessed on 30 April 2025)).</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Figure 7.** Intersection number 4: (a) Previous State (2008); (b) Current State (2021). (Source: [52], adapted by authors and Google Earth Pro. Available online: https://www.google.com/earth/ (accessed on 30 April 2025)).</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Figure 8.** Intersection number 5: (a) Previous State (2008); (b) Current State (2021). (Source: [52], adapted by authors and Google Earth Pro. Available online: https://www.google.com/earth/ (accessed on 30 April 2025)).</figcaption></figure>
For each intersection, figures illustrate both the previous configuration (traffic-light-controlled intersection) and the current state (roundabout) where the numbering of the branches that will be used for traffic surveys is also indicated.

In the original (pre-conversion) configuration, signal timings were realistically and accurately modeled using historical traffic survey data and standard signalization principles. These traffic signals parameters, provide by AVR Group (https://avrgroup.it/) and based on the company's field surveys, formed the basis for the modeling work.

For the four-branch intersections (Intersections 1 and 2), Phase 1 served the vehicle movements along the main corridor ("SS1—Via Aurelia Nord") with a green time of 85 s and a yellow time of 4 s. Phase 2 controlled the side road approaches, with a green time of 21 s and a yellow time of 4 s. A 3 s all-red clearance interval was included between phases.

For the three-branch intersections (Intersections 3, 4, and 5), the same two-phase structure was applied. Phase 1 managed the movements along Via Aurelia Nord, with a green time of 90 s and a yellow time of 4 s. Phase 2 covered the side road inflows, with a green time of 16 s and a yellow time of 4 s. These intersections also included a 3 s all-red phase. These signal timings were implemented into the Aimsun model to ensure consistency between the simulated control strategy and real-world operational conditions.

As regards the current five roundabouts, they exhibit slight variations in their geometric characteristics, all of which were explicitly modeled in the simulation. Key parameters include the outer diameter, circulatory roadway width, number of branches, and entry lane configuration. All intersections feature multilane approaches, with two lanes per entry arm. Circulatory roadway widths range from 9 to 10 m, and one roundabout (Intersection 4) displays a non-standard elliptical geometry, as further detailed below.

Table 1 summarizes the main geometric features of each roundabout, as represented in the Aimsun microsimulation model. This table is derived from an extension of the study presented in [52], as also discussed later. It is worth noting that the "N° of Legs" refers to the "N° of Branches" of each roundabout.

<table><caption>**Table 1.** Geometric features of the five roundabouts composing the Pisa corridor [52].</caption><thead><tr><td>Node</td><td>Type</td><td>Diameter [m]</td><td>Ring Width [m]</td><td>N° of Legs</td><td>Entry Lane Configuration</td></tr></thead><tbody><tr><td>1</td><td>Conventional Roundabout</td><td>38</td><td>9</td><td>4</td><td>2 per arm (6–7 m)</td></tr><tr><td>2</td><td>Conventional Roundabout</td><td>40</td><td>9.5</td><td>4</td><td>2 per arm (6–7 m)</td></tr><tr><td>3</td><td>Conventional Roundabout</td><td>40</td><td>9.5</td><td>3</td><td>2 per arm (7 m)</td></tr><tr><td>4</td><td>Two-Geometry Roundabout</td><td>44 × 36</td><td>9–10</td><td>3</td><td>2 per arm (6.5–7.5 m)</td></tr><tr><td>5</td><td>Conventional Roundabout</td><td>37</td><td>9</td><td>3</td><td>2 per arm (7 m)</td></tr></tbody></table>

As anticipated, a noteworthy feature of this corridor is Intersection 4, which differs from conventional roundabouts. Figure 7 shows this is a Two-Geometry Roundabout [53,54], meaning it has an elliptical shape with a circular central island (Figure 9). The presence of an unconventional roundabout within a roundabout corridor represents an additional complexity in this research.
<figure><img src="image_11.png" /><figcaption>**Figure 9.** Geometry of a Two-Geometry Roundabout. (Source: [53]).</figcaption></figure>

Until now, roundabout corridors have been studied assuming they consist exclusively of conventional roundabouts. However, this variation does not affect the validity of the study, as the dynamic simulations accurately incorporate the specific geometry of each intersection, even when they deviate from standard configurations.

## 3.2. *Tools and Software Used*

To conduct a comprehensive dynamic simulation of the road corridor, Aimsun Next software, version 22.0.1, was selected as the primary software [55]. Aimsun is widely recognized for its ability to perform microscopic, mesoscopic, and hybrid traffic simulations, making it particularly well-suited for evaluating traffic behavior in roundabout corridors. Its advanced modeling capabilities allow for a detailed representation of traffic flow, congestion patterns, and vehicle interactions, which are crucial for assessing potential occurrences of traffic paradoxes.

Unlike static analytical methods, dynamic simulations provide a more realistic depiction of driver behavior, network dynamics, and the impact of infrastructure modifications over time. The use of dynamic simulations is essential in studies like this, where the interaction between consecutive intersections plays a crucial role. Traditional traffic analysis methods, such as static equilibrium models, often fail to capture nonlinear effects and the potential emergence of paradoxical situations.

Aimsun simulation environment, on the other hand, enables researchers to test different scenarios, analyze the impact of alternative road designs, and quantify the overall efficiency of the corridor. A crucial step in the simulation process is the accurate representation of the corridor's geometry. In this study, the QGIS Desktop 3.36 software was used to reconstruct the road network geometry before importing it into Aimsun. QGIS (Quantum Geographic Information System) is an open-source geographic information system that allows the visualization, editing, and analysis of geospatial data.

The shapefiles (ESRI vector data format for geographic features) and orthophotos of the study area were imported into QGIS, enabling the precise mapping of the road infrastructure. Once processed, the necessary outputs were extracted and transferred to Aimsun, where the road network, intersections, and traffic control elements were recreated (Figure 10).

This integration ensured a high level of accuracy in the representation of the roundabout corridor, a key factor in obtaining reliable simulation results. Furthermore, also the integration of accurate traffic data is just as crucial as the geometric reconstruction in ensuring reliable simulation results. Alongside the geometry imported from QGIS, Aimsun requires traffic demand data, which is represented through Origin/Destination (O/D) matrices. These matrices define traffic flows between different points within the network,
providing a detailed picture of movement patterns across the roundabout corridor. By incorporating O/D matrices into the simulation, it is possible to evaluate traffic distribution, congestion dynamics, and the interaction between intersections with high precision.

<figure><img src="image_12.png" /><figcaption>**Figure 10.** Map of the roundabout corridor in Pisa, showing the five consecutive roundabouts (digits 1–5) along the main alignment, reconstructed in QGIS software, scale 1:20,000. (Source: authors).</figcaption></figure>

The methodology used to collect, process, and validate the O/D matrices (which is essential for ensuring consistency between the simulation model and real-world traffic conditions) will be explored in detail in the following section, dedicated to data collection and processing.
### 3.3. *Data Collection and Processing*

As for the traffic data, some were obtained and updated from previous surveys conducted with radar instruments at intersections. For roundabouts 2 and 5, data were collected directly in the field using specialized instruments, specifically SONY DCR-SX34 digital cameras (Sony Corporation, Tokyo, Japan) as shown in Figure 11.

<figure><img src="image_13.png" /><figcaption>**Figure 11.** An example of the traffic surveys carried out on Roundabout 5 through the use of digital cameras. (Source: authors).</figcaption></figure>

The five O/D matrices for the road corridor are shown in Figure 12. As anticipated, to support the interpretation of the matrices, the numbered branches used to define traffic movements are also indicated in the current-state images of each intersection (Figures 4–8). These numbers correspond to the main arms of each roundabout and are consistent with the OD matrices and the simulation model.

Once the O/D matrices were integrated into Aimsun, the calibration process was performed to ensure the accuracy of the simulation results [56]. Calibration was conducted through a standard comparison between the real-world survey data and the outputs of the simulation model. Several discrepancy indices were computed, including R (Correlation Coefficient), U (Theil's Inequality Coefficient) [57,58], and the mean GEH statistic [59,60], by adjusting key parameters such as Simulation Step, Reaction Time at Stop, and Reaction Time at Traffic Light. The calibration process aimed to minimize discrepancies between observed and simulated traffic volumes, with the GEH statistic serving as a primary validation criterion. A simulation was generally considered acceptable when the average GEH value
was below 5 and/or when the GEH value was below 5 for approximately 80–85% of the observed data points, following standard best practices in traffic simulation.

<table><caption>**Figure 12.** O/D Matrices of the five roundabouts of the Roundabout Corridor in Pisa. Green and orange values indicate the total number of vehicles entering and exiting each intersection from the North and South along the main axis (Via Aurelia Nord), while yellow values represent the total number of vehicles per hour circulating within each intersection (Source: [52]).</caption><thead><tr><th></th><th>O/D</th><th>1</th><th>2</th><th>3</th><th>4</th><th>TOT</th></tr></thead><tbody><tr><td rowspan="4">1</td><td>1</td><td>0</td><td>30</td><td>569</td><td>110</td><td>709</td></tr><tr><td>2</td><td>102</td><td>0</td><td>73</td><td>164</td><td>339</td></tr><tr><td>3</td><td>545</td><td>79</td><td>0</td><td>268</td><td>892</td></tr><tr><td>4</td><td>26</td><td>183</td><td>173</td><td>0</td><td>382</td></tr><tr><td></td><td>TOT</td><td>673</td><td>292</td><td>815</td><td>542</td><td>2322</td></tr></tbody></table><table><thead><tr><th></th><th>O/D</th><th>1</th><th>2</th><th>3</th><th>4</th><th>TOT</th></tr></thead><tbody><tr><td rowspan="4">2</td><td>1</td><td>0</td><td>245</td><td>622</td><td>169</td><td>1036</td></tr><tr><td>2</td><td>209</td><td>0</td><td>196</td><td>54</td><td>459</td></tr><tr><td>3</td><td>761</td><td>281</td><td>0</td><td>194</td><td>1236</td></tr><tr><td>4</td><td>205</td><td>76</td><td>193</td><td>0</td><td>474</td></tr><tr><td></td><td>TOT</td><td>1175</td><td>602</td><td>1011</td><td>417</td><td>3205</td></tr></tbody></table><table><thead><tr><th></th><th>O/D</th><th>1</th><th>2</th><th>3</th><th>TOT</th></tr></thead><tbody><tr><td rowspan="4">3</td><td>1</td><td>0</td><td>33</td><td>913</td><td>946</td></tr><tr><td>2</td><td>106</td><td>0</td><td>132</td><td>238</td></tr><tr><td>3</td><td>782</td><td>75</td><td>0</td><td>857</td></tr><tr><td></td><td>TOT</td><td>888</td><td>108</td><td>1045</td><td>2041</td></tr></tbody></table><table><thead><tr><th></th><th>O/D</th><th>1</th><th>2</th><th>3</th><th>TOT</th></tr></thead><tbody><tr><td rowspan="4">4</td><td>1</td><td>0</td><td>189</td><td>892</td><td>1081</td></tr><tr><td>2</td><td>110</td><td>0</td><td>39</td><td>149</td></tr><tr><td>3</td><td>876</td><td>118</td><td>0</td><td>994</td></tr><tr><td></td><td>TOT</td><td>986</td><td>307</td><td>931</td><td>2224</td></tr></tbody></table><table><thead><tr><th></th><th>O/D</th><th>1</th><th>2</th><th>3</th><th>TOT</th></tr></thead><tbody><tr><td rowspan="4">5</td><td>1</td><td>0</td><td>25</td><td>1249</td><td>1274</td></tr><tr><td>2</td><td>32</td><td>0</td><td>43</td><td>75</td></tr><tr><td>3</td><td>1372</td><td>37</td><td>0</td><td>1409</td></tr><tr><td></td><td>TOT</td><td>1404</td><td>62</td><td>1292</td><td>2758</td></tr></tbody></table>

The calibration targets and achieved results are summarized in Table 2. In addition to the commonly used correlation coefficient (R), Theil's inequality coefficient (U), and mean GEH, the table reports the percentage of count locations with GEH < 5, allowing a direct comparison against the guideline range of 80–85%. Although this percentage is slightly below the upper limit of the range (80% vs. 85%), the model meets all other calibration benchmarks and is considered robust for comparative analysis between the two corridor configurations.
<table><caption>**Table 2.** Calibration results: observed vs. simulated flows with GEH statistics, and summary of overall calibration indices.</caption><thead><tr><th>Entry</th><th>Simulated Flow [veh/h]</th><th>Observed Flow [veh/h]</th><th>GEH</th></tr></thead><tbody><tr><td>E1 R1</td><td>706</td><td>709</td><td>0.11</td></tr><tr><td>E1 R2</td><td>972</td><td>1036</td><td>2.02</td></tr><tr><td>E1 R3</td><td>837</td><td>946</td><td>3.65</td></tr><tr><td>E1 R4</td><td>983</td><td>1081</td><td>3.05</td></tr><tr><td>E1 R5</td><td>1070</td><td>1274</td><td>5.96</td></tr><tr><td>E3 R1</td><td>669</td><td>892</td><td>7.98</td></tr><tr><td>E3 R2</td><td>799</td><td>1236</td><td>13.70</td></tr><tr><td>E3 R3</td><td>759</td><td>857</td><td>3.45</td></tr><tr><td>E3 R4</td><td>844</td><td>994</td><td>4.95</td></tr><tr><td>E3 R5</td><td>1286</td><td>1409</td><td>3.35</td></tr><tr><th colspan="4">Indices</th></tr><tr><td>R</td><td>0.830</td><td>0.8-1</td><td>yes</td></tr><tr><td>U</td><td>0.096</td><td>&lt;0.1</td><td>yes</td></tr><tr><td>Average GEH</td><td>4.822</td><td>&lt;5</td><td>yes</td></tr></tbody></table>

Once the indices reached satisfactory levels, the final calibrated parameter values were:

* Simulation Step = 0.80 s;

* Reaction Time at Stop = 1.20 s;

* Reaction Time at Traffic Light = 1.60

These values confirm a high degree of reliability in the simulated traffic model, ensuring consistency with real-world traffic conditions. It is important to note that historical traffic counts for the pre-conversion (traffic-light-controlled) configuration were not available. Therefore, the same O/D matrices collected for the current roundabout corridor configuration were also applied to the previous state in the simulations.

This approach shows that the proposed methodology can still be applied even in the presence of incomplete or unavailable O/D information, ensuring comparability between different infrastructure scenarios. The suggested formulation remains valid under such conditions, as it focuses on relative efficiency variations rather than absolute demand values. It also true that this assumption, while ensuring comparability between the two scenarios, represents a limitation of the study. In practice, traffic demand patterns may have differed between the two configurations due to network changes, user adaptation, or induced demand effects. This possibility should be considered when interpreting the results, as differences in traffic flows could influence the performance outcomes observed. That said, since the calibration process was carried out for the current roundabout corridor configuration, the obtained validated parameter values were used for its simulations. To ensure a consistent and unbiased comparison, the same calibrated values were also applied to the simulations of the previous traffic-light-controlled state. This approach guarantees that any differences in performance between the two configurations are solely due to infrastructural changes rather than variations in model parameters. Finally, as an example, Figure 13 presents an extract from the dynamic simulations carried out in Aimsun for both configurations: the traffic-light-controlled configuration and the roundabout corridor configuration.
<figure><img src="image_14.png" /><figcaption>**Figure 13.** Extract of the simulations carried out in Aimsun (Intersection number 2): (a) Traffic-light-controlled intersection; (b) Roundabout Corridor. (Source: authors).</figcaption></figure>

This comparison allows a direct evaluation of the differences in traffic behavior under
the two scenarios.

**4. Results and Discussion**

This chapter presents the results of the dynamic simulations conducted on the "SS1—Via Aurelia Nord" corridor in Pisa, evaluating the impact of its conversion from a traffic-light-controlled system to a roundabout corridor. The analysis compares the performance of both configurations, introduces the novel Celerity Roundabout Corridors (CRC) index to assess efficiency, examines the presence of paradoxical traffic effects, and discusses the broader implications of the findings for traffic engineering and infrastructure planning.

4.1. *Performance Comparison Between Configurations*

A series of dynamic simulations were conducted using Aimsun software to model both the current state of the roundabout corridor and its previous state, which consists of five traditional traffic-light-controlled intersections. The results were evaluated against conventional performance indicators such as delay, speed, and Level of Service (LoS), which also served as baseline metrics to validate the outcomes of the novel performance index introduced. The analysis revealed significant inefficiencies in the current configuration and confirmed the persistence of congestion throughout the corridor. This outcome highlights a broader issue in evaluating such transformations, particularly when focusing on isolated intersections rather than analyzing their systemic interactions within a network. Despite substantial investments aimed at replacing traffic-light intersections with roundabouts to enhance traffic efficiency and safety, the overall system failed to deliver the anticipated benefits. Typically, the approval of such projects requires demonstrating improvements in efficiency and safety at individual intersections.

However, when assessed as part of an interconnected system, the results diverge,
revealing inefficiencies that were not evident to detect in isolated studies. The outputs
of the simulations provide clear evidence of the inefficiency in the current configuration.
Specifically, Figure 14 illustrates two key performance metrics. The top graph shows the
average delay time, which stands at 72 s per kilometer, while the bottom graph indicates an
average speed of 36 km/h. These values are aggregated over the entire corridor and derived
from the time series data produced by the simulation. The performance indicators were
monitored at 10 min intervals between 17:00 and 18:00, reflecting the dynamic evolution of
congestion and traffic flow conditions.
<figure><img src="image_15.png" /><figcaption>(a)</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>(b)</figcaption></figure>

<caption>**Figure 14.** Estimation of the congestion from the dynamic simulation: (a) delay time [s/km] as a function of time (1 h); (b) speed [km/h] as a function of time (1 h). (Source: authors).</caption>

To improve the interpretability of the results, each figure includes a horizontal line indicating the average value, as well as a summary box in the top-right corner displaying key statistics extracted from the simulation output. According to the HCM-Highway Capacity Manual [61–63], these values correspond to a Level of Service (LoS) classification of F, indicating severe congestion. The Level of Service (LoS) is a qualitative measure that describes the operational conditions of a road or intersection, ranging from A (free-flow conditions with minimal delays) to F (forced or breakdown flow with excessive delays). The LoS classification F for this corridor reflects conditions where the traffic demand exceeds capacity, leading to significant delays and low travel speeds.
In conclusion, these findings emphasize the necessity of adopting a systemic approach in traffic studies. While the conversion of individual intersections into roundabouts may have enhanced their localized performance, the overall efficiency of the network was not improved. The “linear system” nature of the roundabout corridor appears to amplify the likelihood of paradoxical effects, where localized improvements fail to translate into global benefits. This underscores the critical importance of evaluating traffic systems globally to avoid unintended consequences.

## 4.2. Introduction of the Novel Performance Index CRC

The definition of the Celerity Roundabout Corridors (CRC) index originates from the empirical evidence observed during the dynamic simulations. Despite the general expectation that roundabout corridors would enhance traffic flow, some sections of the studied corridor performed better in the previous, signalized configuration. This counterintuitive outcome raised a methodological question: how can the occurrence of paradoxical effects be systematically identified within a road corridor undergoing functional transformation—such as from a signalized to a roundabout-based configuration?

Traditional performance measures, such as delay or average speed, were not fully adequate for this purpose, as they neglect the magnitude and distribution of traffic flows among different approaches. In particular, comparing intersection delays alone could obscure inefficiencies along the main arterial direction, where traffic volumes are typically higher. While a global delay reduction may suggest an overall improvement, vehicles traveling along the primary flow could actually experience increased delays due to the loss of hierarchical priority introduced by roundabouts.

To capture these effects, the CRC was developed as a diagnostic indicator that combines delay and traffic flow along the corridor’s main direction. This integration allows both the severity of congestion (through delay) and the extent of its impact (through flow) to be assessed simultaneously, highlighting where efficiency deteriorates despite infrasstructural upgrades. Accordingly, the CRC was designed to evaluate and compare the efficiency of a road corridor in two configurations: the previous state (a corridor with five traffic-light-controlled intersections) and the current state (a roundabout corridor).

More in depth, the CRC focuses on the main direction of the corridor, providing a comprehensive assessment of traffic flow efficiency based on delay, a fundamental parameter in traffic engineering. Dynamic simulations conducted using Aimsun software allowed for the calculation of delays for individual road sections within the corridor for both configurations. By keeping the vehicular flow constant across scenarios, the CRC was computed using Equation (3):

$$CRC = \frac{delay_{currentstate} \cdot Q_{currentstate}}{delay_{previousstate} \cdot Q_{previousstate}} \quad (3)$$

where $delay_{currentstate}$ and $delay_{previousstate}$ represent the delays measured for the current and previous states, respectively; $Q_{currentstate}$ and $Q_{previousstate}$ represent the vehicular flow rates for the current and previous states, respectively. A CRC value greater than 1 indicates that the current state (roundabout corridor) performs worse than the previous state (traffic-light-controlled intersections), due to longer delays. Conversely, a CRC value less than 1 signifies that the current state is more efficient.

The CRC must be intended as a first, simple, and flexible diagnostic tool rather than a universal or prescriptive index. Its formulation—based on the product of delay and flow—captures both the duration of congestion and the number of vehicles affected. This provides a more systemic representation of corridor efficiency than delay alone, as it reflects both the severity and spatial extent of congestion.
Furthermore, while this study applies the CRC to a linear corridor and its main travel direction, its formulation can be extended to multi-directional or nonlinear corridors. Separate CRC values may be computed for each major branch, preserving its diagnostic role while capturing variations across multiple flows. For more complex geometries, the index can be combined with network-partitioning techniques to assess performance at the sub-network level, ensuring its applicability to diverse real-world contexts.

Although a formal sensitivity analysis was not included, the CRC was qualitatively cross-validated against conventional performance indicators (delay, speed, and Level of Service), showing consistent trends across intersections. These comparisons confirm that the CRC reliably reflects efficiency variations detected by standard metrics while offering additional diagnostic insight into corridor-scale interactions. Future research will focus on quantitative validation under varying traffic conditions and on testing the CRC's robustness across different corridor typologies.

That said, Table 3 presents the results of the CRC calculations for the main direction of the corridor (branches 1 and 3 of each roundabout), specifically focusing on "SS1—Via Aurelia Nord." Intersections where the CRC exceeds 1 are highlighted, indicating worse performance in the roundabout corridor configuration.

<table><caption>**Table 3.** Calculation of CRC index for the five intersections of the corridor.</caption><thead><tr><th></th><th>Intersection 1</th><th>Intersection 2</th><th>Intersection 3</th><th>Intersection 4</th><th>Intersection 5</th></tr></thead><tbody><tr><td>delay current state branch 1 [s]</td><td>2.25</td><td>0.84</td><td>0.26</td><td>0.58</td><td>0.31</td></tr><tr><td>delay previous state branch 1 [s]</td><td>3.82</td><td>3.14</td><td>3.58</td><td>297</td><td>1.83</td></tr><tr><td>Q branch 1 [veh/h]</td><td>709</td><td>1036</td><td>946</td><td>1081</td><td>1274</td></tr><tr><td>delay current state branch 3 [s]</td><td>2.48</td><td>9.93</td><td>4.93</td><td>7.72</td><td>1.56</td></tr><tr><td>delay previous state branch 3 [s]</td><td>4.26</td><td>4.58</td><td>3.68</td><td>4.20</td><td>1.92</td></tr><tr><td>Q branch 3 [veh/h]</td><td>892</td><td>1236</td><td>857</td><td>994</td><td>1409</td></tr><tr><td>CRC</td><td>0.59</td><td>1.47</td><td>0.68</td><td>1.12</td><td>0.51</td></tr></tbody></table>

This is a critical issue, as some intersections, such as Intersection 2 and Intersection 4, exhibit CRC values greater than 1, indicating increased congestion rather than the expected improvement. This finding is particularly alarming because it suggests that the implemented modifications, rather than optimizing traffic flow, have led to a degradation in performance at these points. Conversely, other intersections display CRC values below 1, reflecting localized efficiency gains. Although a global CRC value could in principle be calculated by aggregating delays and flows across all intersections, we chose to focus on local CRC values.

This approach allows for the detection of paradoxical effects at specific nodes, which might be masked by a single aggregate figure. The aim of the CRC framework is therefore to support detailed diagnostic analysis, rather than to provide a single corridor-wide performance score. Furthermore, it is worth emphasizing that in the study case, the vehicular flow (Q) was kept constant between the two scenarios due to the unavailability of traffic flow data for the previous state. However, the formula used for calculating CRC is flexible and capable of accounting for differences in vehicular flow between the two situations if such data were available.

Such assumption can also be supported in light of two of the cited paradoxes—the Pigou-Knight-Downs [16–18] and Beckmann [19,20] paradoxes—according to which local improvements that increase the capacity of an intersection may attract additional traffic, altering the previous network equilibrium and leading to higher overall demand. In this sense, the use of identical O/D matrices in the present simulations represents a conservative assumption, as the real post-conversion scenario would likely exhibit higher total traffic
volumes. Consequently, the CRC values reported here may underestimate the magnitude of paradoxical effects, reinforcing the diagnostic relevance of the index for identifying such behaviors.

In any case, the adaptability of the CRC formulation ensures that the index can accu-
rately represent efficiency changes even when variations in traffic demand are considered.
In particular, if the actual traffic demand in the pre-conversion scenario had been lower
than in the current configuration—as suggested by empirical evidence on user attraction
to roundabouts—CRC values for certain intersections might have been even higher than
those reported. This would further strengthen the indication of paradoxical effects, as
the performance gap between the two configurations could be underestimated under the
equal-flow assumption adopted in this study.

In conclusion, the CRC framework supports the identification of critical nodes within complex infrastructures such as road corridors, where paradoxical effects are most evident, while preserving a broader perspective on overall network performance. Further refinement and validation of the CRC across different corridor typologies are encouraged as part of future research. These findings reinforce the importance of evaluating traffic networks at a systemic level, as localized improvements at individual intersections may not necessarily result in global network efficiency.

Finally, it should also be noted that the model implicitly accounts for variability in geometric and operational conditions, as the analyzed corridor includes intersections with different sizes, layouts, and control characteristics. These variations provide an initial robustness check for the proposed approach. Moreover, the CRC formulation is designed to remain applicable to corridors with different link lengths, capacities, or control strategies, supporting its generalization to broader traffic contexts.

4.3. *Identification of Paradoxical Effects*

The results obtained from the dynamic simulations provide strong indications of paradoxical traffic effects within the roundabout corridor. The performance comparison between the two configurations (traffic-light-controlled intersections versus the roundabout corridor) revealed unexpected inefficiencies in the current system, despite the infrastructural improvements. These inefficiencies align with several well-documented traffic paradoxes, which challenge conventional assumptions in transport planning. The CRC analysis presented in Table 3 further supports the presence of paradoxical behaviors. Specifically, intersections 2 and 4 show CRC values greater than 1, indicating that despite the replacement of traffic lights with roundabouts, travel delays have increased. This suggests that local improvements at individual intersections did not translate into better performance for the entire corridor, a key characteristic of traffic paradoxes.

The observed inefficiencies can be interpreted through multiple paradoxical frameworks:

*   **Braess Paradox:** The transformation of the corridor into a roundabout corridor introduced new paths and altered the distribution of traffic flows, but instead of improving travel times, it resulted in higher delays for certain movements.

*   **Pigou-Knight-Downs Paradox:** The increased capacity at roundabout intersections may have unintentionally attracted additional traffic, raising congestion and reducing expected benefits.

*   Induced Demand Paradox: The infrastructural upgrade may have encouraged higher traffic volumes, leading to congestion levels that offset the anticipated efficiency gains.

*   Beckmann's Paradox: The focus on optimizing individual intersections rather than the entire system contributed to inefficiencies in the overall traffic flow.

The presence of these paradoxical effects highlights the complexity of traffic networks
and the risks of evaluating infrastructure improvements in isolation. The findings from
this case study suggest that while roundabouts are generally perceived as efficient solutions for intersection management, their benefits can be limited when implemented in a corridor without considering the broader network dynamics. These results emphasize the importance of evaluating traffic systems as interconnected structures rather than as a series of independent elements when planning road infrastructure projects.

In addition to identifying where paradoxical effects occur, the analysis also provides insight into their underlying causes. In particular, the less favorable performance of two intersections can be explained by both geometric and operational conditions. Intersection 4, characterized by an elliptical two-geometry design, presents limited circulating space and higher conflict density, which reduce discharge capacity along the main direction. Intersection 2, instead, is strongly affected by upstream interactions and queue spillback from adjacent nodes, leading to congestion propagation and local performance deterioration. These findings highlight how geometric constraints and dynamic interdependencies between intersections can trigger paradoxical behaviors within a linear corridor.

More generally, the replacement of coordinated signal control with roundabouts eliminates the progression benefits that previously favored the main arterial stream. The redistribution of right-of-way among approaches alters delay patterns, penalizing through movements with higher volumes while benefiting minor approaches. This loss of hierarchical priority—together with the increased flow variability induced by continuous operation—explains why local improvements at specific intersections may not translate into global efficiency gains. From a design perspective, these insights reinforce the importance of assessing geometric feasibility, intersection spacing, and flow balance before implementing corridor-wide conversions, using diagnostic tools such as the CRC to anticipate potential paradoxical outcomes.

### 4.4. Discussion of Findings

The findings presented in this study require careful analysis to derive meaningful conclusions regarding the impact of converting traffic-light-controlled intersections into roundabouts within the studied corridor. As previously discussed, not all intersections along the corridor exhibit a CRC > 1; this indicates that, in some cases, the conversion from traffic lights to roundabouts has led to improved traffic efficiency. However, certain intersections, particularly those along the main direction, show a CRC > 1. This suggests that while efficiency may have increased at specific locations—likely due to reduced delays on secondary roads—the primary traffic flow has suffered. The transition from traffic signals to roundabouts eliminates hierarchical flow priority, potentially leading to increased delays on major routes. Therefore, transforming an entire arterial road into a roundabout corridor may not always be the most beneficial or necessary approach from a network-wide perspective. Instead, selectively converting only specific intersections may provide a more balanced outcome, mitigate paradoxical effects while also reducing economic costs. In this regard, some preliminary qualitative considerations can help identify intersections that are more suitable for conversion to roundabouts.

Factors such as the balance of traffic volumes between approaches, the geometric feasibility of accommodating a standard roundabout design, pedestrian and cyclist crossing demand, and the potential for upstream-downstream interactions should be assessed in combination with CRC-based analysis. This integrated evaluation can support more informed engineering decisions and reduce the likelihood of corridor-wide inefficiencies. Recent studies have further explored this topic by jointly analyzing efficiency and safety across different corridor configurations, demonstrating how mixed layouts of roundabouts and traffic signals can, in certain cases, outperform full conversions in terms of overall network performance [52]. Such considerations can also be complemented by possible
practical decision rules emerging from the CRC framework. One example is to use the CRC index as a preliminary diagnostic tool for identifying intersections within a corridor that may warrant further investigation. Intersections with relatively higher CRC values can be flagged as potentially critical nodes, where the conversion to a roundabout might not yield the desired network-wide benefits. Once such locations are identified, more detailed analyses—covering aspects such as safety performance, environmental impacts, cost-benefit considerations, and stakeholder needs—should be conducted before making any final design or policy decisions. In this way, the CRC serves not as a stand-alone determinant, but as an evidence-based screening method to prioritize resources and focus subsequent in-depth studies on the most critical points of the network. In any case, in the present study, while these considerations provide a useful framework for identifying potentially “safe” candidates for conversion, the quantitative evaluation of each scenario was ultimately based on the CRC index, which explicitly incorporates the Q parameter, representing vehicle flow.

At this stage of research, it is important to clarify that the Qcurrent state and the Qprevious state are assumed to be equal, leading them to cancel out in Equation (3). This assumption arises from the use of identical O/D matrix values for both traffic configurations due to the unavailability of historical traffic data for the previous state. Nevertheless, empirical observations indicate that roundabouts have attracted higher traffic volumes compared to their previous traffic-light-controlled counterparts. Road users often perceive roundabouts as more attractive due to their continuous flow dynamics, a tendency consistent with recent studies that have demonstrated the capacity of roundabouts to attract additional traffic and influence driver behavior under varying geometric and control conditions [64–66]. This observation implies that if lower values of traffic flow Q had been considered for the previous state, the CRC values might have been even higher, further emphasizing the paradoxical effects observed. While this remains a theoretical conjecture, it is supported by the experimental findings that initiated this research. Beyond its theoretical implications, the findings of this study offer several practical insights for transport policy and planning.

The proposed framework can serve as a diagnostic tool for corridor-level decision-making, helping planners identify where roundabout conversions may produce paradoxical effects. In this sense, the results highlight the importance of integrating simulation-based analysis with policy instruments such as adaptive signal design, selective roundabout conversion, and demand-management strategies (e.g., route guidance or modal shift incentives). Linking corridor efficiency evaluation with these planning measures can therefore support evidence-based strategies aimed at minimizing systemic inefficiencies and enhancing sustainable network performance at the urban scale. In this sense, the prevention of traffic paradoxes also directly aligns with sustainability objectives, as avoiding inefficient network configurations helps reduce fuel consumption, greenhouse gas emissions, and the overall environmental footprint of mobility systems. This approach supports the transition toward low-carbon, adaptive, and resource-efficient urban transport infrastructures. All these insights highlight the necessity of a systemic approach to intersection planning and network design. Future research should explore strategies to optimize intersection selection for conversion and investigate adaptive solutions that balance local improvements with global traffic efficiency. Given these findings, the study also underscores the necessity of dynamic simulation tools in traffic engineering.

Traditional static models may fail to capture the emergence of paradoxical effects, whereas microscopic simulations, such as those conducted in Aimsun, provide a more accurate representation of real-world traffic conditions. The ability to model network-
wide interactions dynamically is essential for anticipating unintended consequences and designing more effective traffic systems.

# 5. Conclusions

This study examined the systemic effects of converting a signalized arterial corridor into a sequence of roundabouts, focusing on both local and corridor-wide dynamics. The analysis was applied to the SS1—Via Aurelia Nord corridor in Pisa (Italy) through dynamic microsimulation, introducing the Celerity Roundabout Corridors (CRC) index as a diagnostic metric for efficiency assessment. The results revealed that, while some intersections experienced performance gains after conversion, others—particularly along the main direction—recorded CRC values greater than 1, indicating paradoxical effects with increased congestion. These findings confirm that full corridor conversion to roundabouts does not necessarily guarantee improved global performance and that selective interventions may yield more balanced outcomes.

The main novelty of this research lies in three main aspects explained in the introduction section: (i) it adopts a systemic, corridor-wide analytical perspective to capture interdependencies among consecutive intersections rather than evaluating them in isolation; (ii) it introduces the CRC index as a first, simple, and flexible diagnostic tool, intended as a starting point for detecting paradoxical efficiency losses while maintaining a network-level viewpoint; (iii) it provides empirical evidence of paradoxical behaviors observed in a real-world infrastructure, extending classical traffic-paradox theories to practical contexts. By combining these elements, the study advances both the methodological and applied understanding of corridor-scale dynamics in sustainable traffic engineering.

Beyond its theoretical implications, the findings highlight the importance of integrating simulation-based diagnostics into urban mobility planning. Identifying where paradoxical effects occur can support more informed design choices, balancing local improvements with overall network efficiency. Understanding these systemic effects also contributes to the broader goals of sustainability by reducing unnecessary energy consumption, travel delays, and emissions. In fact, by integrating these systemic and diagnostic approaches within sustainable mobility planning, the study provides a possible methodological foundation for designing transport networks that are both efficient and environmentally sustainable.

## *Study Limitations and Future Research Works*

Future research should validate the CRC across different corridor typologies and traffic contexts and explore integrated evaluations of efficiency and safety to further strengthen the robustness and practical value of the proposed framework. The assumption of identical Origin-Destination (O/D) matrices across the two simulated scenarios represents a methodological limitation of the study. This simplification was necessary due to the lack of historical traffic data for the pre-conversion state and was explicitly acknowledged in Section 4.2. Nevertheless, this assumption may influence the magnitude of the observed performance differences since infrastructure changes can alter route choice and induce additional demand. As previously stated, such variations may affect the magnitude of performance differences, as infrastructure modifications can influence route choice and potentially induce extra demand. However, in line with the Pigou-Knight-Downs and Beckmann paradoxes, local capacity improvements can attract additional traffic, modifying the network balance and potentially reinforcing—rather than mitigating—these paradoxical effects. Consequently, the adopted approach should be interpreted as conservative, providing a cautious yet reliable comparison framework that can be applied in similar case studies. In any case, future studies should integrate elastic demand and feedback models to account for all possible dynamic variations in travel behavior, drawing on previous
findings on flow control strategies and metering approaches [67–70]. Addressing these
aspects will further consolidate the robustness and general applicability of the proposed
CRC framework.

**Author Contributions:** Conceptualization, L.B., A.P. and D.J.; methodology, L.B.; software, L.B.; validation, L.B., A.P. and D.J.; formal analysis, L.B. and D.J.; investigation, L.B.; resources, A.P. and D.J.; data curation, L.B. and A.P.; writing—original draft preparation, L.B.; writing—review and editing, A.P. and D.J.; visualization, L.B.; supervision, A.P. and D.J.; project administration, A.P. and D.J.; funding acquisition, A.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the
corresponding author.

**Conflicts of Interest:** The authors declare no conflicts of interest.

## References

1. Bugg, H.D.; Hummer, J.E.; Schroeder, B.J. Methodology to Compute Travel Time of a Roundabout Corridor. *Transp. Res. Rec. J. Transp. Res. Board* **2015**, *2483*, 20–29. [CrossRef]

2. Fernandes, P.; Fontes, T.; Pereira, S.R.; Rouphail, N.M.; Coelho, M.C. Multicriteria Assessment of Crosswalk Location in Urban Roundabout Corridors. *Transp. Res. Rec. J. Transp. Res. Board* **2015**, *2517*, 37–47. [CrossRef]

3. Fernandes, P.; Guarnaccia, C.; Teixeira, J.; Sousa, A.; Coelho, M.C. Multi-Criteria Assessment of Crosswalk Location on a Corridor with Roundabouts: Incorporating a Noise Related Criterion. *Transp. Res. Procedia* **2017**, *27*, 460–467. [CrossRef]

4. Fernandes, P.; Salamati, K.; Rouphail, N.M.; Coelho, M.C. The effect of a roundabout corridor's design on selecting the optimal crosswalk location: A multi-objective impact analysis. *Int. J. Sustain. Transp.* **2016**, *11*, 206–220. [CrossRef]

5. Fernandes, P.; Rouphail, N.M.; Coelho, M.C. Turboroundabouts Along Corridors: Analysis of Operational and Environmental Impacts. *Transp. Res. Rec. J. Transp. Res. Board* **2017**, *2627*, 45–56. [CrossRef]

6. Bagloee, S.; Ceder, A.; Tavana, M.; Bozic, C. A heuristic methodology to tackle the Braess Paradox detecting problem tailored for real road networks. *Transp. A Transp. Sci.* **2014**, *10*, 437–456. [CrossRef]

7. Braess, D. Über ein Paradoxon aus der Verkehrsplanung. *Unternehmensforschung Oper. Res.* **1968**, *12*, 258–268. [CrossRef]

8. Pas, E.I.; Principio, S.L. Braess' paradox: Some new insights. *Transp. Res. Part B Methodol.* **1997**, *31*, 265–276. [CrossRef]

9. Nagurney, A.; Ladimer, S.N. The Braess Paradox. *Int. Encycl. Transp.* **2021**, *601–607*. [CrossRef]

10. Nikolova, N.D.; Armenski, I.S.; Tenekedjieva, L.T.K.; Mednikarov, B. Domains and Solutions of the Braess Paradox. *J. Appl. Comput. Sci. Methods* **2011**, *3*, 17–43. Available online: https://bibliotekanauki.pl/articles/108705 (accessed on 30 April 2025).

11. Sousa, A.A.; Chaves, A.; Farias, G.A.; Peeters, F.M. Braess paradox at the mesoscopic scale. *Phys. Rev. B* **2013**, *88*, 245417. [CrossRef]

12. Zverovich, V.; Avineri, E. Braess' Paradox in a Generalised Traffic Network. *J. Adv. Transp.* **2015**, *49*, 114–138. [CrossRef]

13. Coletta, T.; Philippe, J. Linear Stability and the Braess Paradox in Coupled Oscillators Networks and Electric Power Grids. *Phys. Rev. E* **2016**, *93*, 032222. [CrossRef] [PubMed]

14. Morgan, J.; Orzen, H.; Sefton, M. Network architecture and traffic flows: Experiments on the Pigou–Knight–Downs and Braess Paradoxes. *Games Econ. Behav.* **2009**, *66*, 348–372. [CrossRef]

15. Ding, C.; Song, S. Traffic Paradoxes and Economic Solutions. *J. Urban Manag.* **2012**, *1*, 63–76. [CrossRef]

16. Dechenaux, E.; Mago, S.D.; Razzolini, L. Traffic congestion: An experimental study of the Downs-Thomson paradox. *Exp. Econ.* **2014**, *17*, 461–487. [CrossRef]

17. Afimeimounga, H.; Solomon, W.; Ziedins, I. The Downs-Thomson Paradox: Existence, Uniqueness and Stability of User Equilibria. *Queueing Syst.* **2005**, *49*, 321–334. [CrossRef]

18. Zhang, F.; Yang, H.; Liu, W. The Downs–Thomson Paradox with responsive transit service. *Transp. Res. Part A Policy Pract.* **2014**, *70*, 244–263. [CrossRef]

19. Boyce, D.E.; Mahmassani, H.S.; Nagurney, A. A Retrospective on Beckmann, McGuire and Winsten's Studies in the Economics of Transportation. In *Papers in Regional Science*; Wiley: Hoboken, NJ, USA, 2005; Volume 84, pp. 85–103. [CrossRef]
20. Boyce, D.E. Beckmann's transportation network equilibrium model: Its history and relationship to the Kuhn-Tucker conditions. *Econ. Transp.* **2013**, *2*, 47–52. [CrossRef]

21. Hymel, K. If you build it, they will drive: Measuring induced demand for vehicle travel in urban areas. *Transp. Policy* **2019**, *76*, 57–66. [CrossRef]

22. Grinberg, D. An introduction to graph theory. *arXiv* **2023**, arXiv:2308.04512. [CrossRef]

23. Gowda, D.V.; Shashidhara, K.S.; Ramesha, M.; Sridhara, S.B.; Manoj Kumar, S.B. Recent Advances in Graph Theory and its Applications. *Adv. Math. Sci. J.* **2021**, *10*, 1407–1412. [CrossRef]

24. Cirilovic, J.; Vajdic, N.; Mladenovic, G.; Queiroz, C. Developing Cost Estimation Models for Road Rehabilitation and Reconstruction: Case Study of Projects in Europe and Central Asia. *J. Constr. Eng. Manag.* **2014**, *140*, 04013065. [CrossRef]

25. Liu, T.; Meidani, H. End-to-end heterogeneous graph neural networks for traffic assignment. *Transp. Res. Part C Emerg. Technol.* **2024**, *165*, 104695. [CrossRef]

26. Razemon, O. Quand les voitures s'évaporent. *Le Monde*, 23 August 2016. Available online: https://www.lemonde.fr/blog/transports/2016/08/23/voitures-evaporees/ (accessed on 30 April 2025).

27. Rapoport, A.; Kugler, T.; Dugar, S.; Gisches, E.J. Choice of routes in congested traffic networks: Experimental tests of the Braess Paradox. *Games Econ. Behav.* **2009**, *65*, 538–571. [CrossRef]

28. Bazzan, A.L.C.; Klügl, F. Case studies on the Braess Paradox: Simulating route recommendation and learning in abstract and microscopic models. *Transp. Res. Part C Emerg. Technol.* **2005**, *13*, 299–319. [CrossRef]

29. Wardrop, J. Some Theoretical Aspects of Road Traffic Research. *Proc. Inst. Civ. Eng. Part II* **1952**, *1*, 325–378. [CrossRef]

30. Correa, J.R.; Stier-Moses, N.E. Wardrop Equilibria. In *Wiley Encyclopedia of Operations Research and Management Science*; Wiley: Hoboken, NJ, USA, 2011. [CrossRef]

31. Aashtiani, H.Z.; Poorzahedy, H.; Nourinejad, M. Wardrop's first principle: Extension for capacitated networks. *Sci. Iran.* **2021**, *28*, 175–191. [CrossRef]

32. Kuang, Z.; Mazalov, V.V.; Tang, X.; Zheng, J. Transportation network with externalities. *J. Comput. Appl. Math.* **2021**, *382*, 113091. [CrossRef]

33. Wang, A.; Tang, Y.; Mohamand, Y.T.; Xu, P. Modifying link capacity to avoid Braess Paradox considering elastic demand. *Phys. A Stat. Mech. Its Appl.* **2022**, *605*, 127951. [CrossRef]

34. Monks, K.M. Braess' Paradox in City Planning: An Application of Multivariable Optimization. Calculus. 2019. Available online: https://digitalcommons.ursinus.edu (accessed on 30 April 2025).

35. Steinberg, R.; Zangwill, W.I. The Prevalence of Braess' Paradox. *Transp. Sci.* **1983**, *17*, 301–318. [CrossRef]

36. Alperovich, G. An Economic Interpretation of Braess' Paradox. *Int. J. Transp. Econ.* **1997**, *24*, 145–155. Available online: http://www.jstor.org/stable/42747285 (accessed on 30 April 2025).

37. Eriksson, K.; Eliasson, J. The Chicken Braess Paradox. *Math. Mag.* **2019**, *92*, 213–221. [CrossRef]

38. Passacantando, M.; Gnecco, G.; Hadas, Y.; Sanguineti, M. Braess' paradox: A cooperative game-theoretic point of view. *Networks* **2021**, *78*, 264–283. [CrossRef]

39. Schäfer, B.; Pesch, T.; Manik, D.; Gollenstede, J.; Lin, G.; Beck, H.P.; Witthaut, D.; Timme, M. Understanding Braess' Paradox in power grids. *Nat. Commun.* **2022**, *13*, 5396. [CrossRef]

40. Lepore, D.M.; Barratt, C.; Schwartz, P.M. Computational Models of Chemical Systems Inspired by Braess' Paradox. *J. Math. Chem.* **2011**, *49*, 356–370. [CrossRef]

41. Pala, M.G.; Baltazar, S.; Liu, P.; Sellier, H.; Hackens, B.; Martins, F.; Bayot, V.; Wallart, X.; Desplanque, L.; Huant, S. Transport Inefficiency in Branched-Out Mesoscopic Networks: An Analog of the Braess Paradox. *Phys. Rev. Lett.* **2012**, *108*, 076802. [CrossRef]

42. Bittihn, S.; Schadschneider, A. The Effect of Modern Traffic Information on Braess' Paradox. *Phys. A Stat. Mech. Appl.* **2021**, *571*, 125829. [CrossRef]

43. Zhuang, D.; Huang, Y.; Jayawardana, V.; Zhao, J.; Suo, D.; Wu, C. The Braess's Paradox in Dynamic Traffic. In Proceedings of the 25th IEEE International Conference on Intelligent Transportation Systems (ITSC) 2022, Macau, China, 8–12 October 2022. [CrossRef]

44. Amini, A.; Ameli, M.; Winzenrieth, B.; Busch, F.; Bogenberger, K.; Leclercq, L. A Braess Paradox Exploitation Framework for Optimal Traffic Banning Strategy. In Proceedings of the Transportation Research Board 101st Annual Meeting 2022, Washington, DC, USA, 9–13 January 2022. Available online: https://hal.science/hal-03680834 (accessed on 30 April 2025).

45. Bagloee, S.A.; Cederc, A.A.; Sarvi, M.; Asadi, M. Is it time to go for no-car zone policies? Braess Paradox Detection. *Transp. Res. Part A* **2019**, *121*, 251–264. [CrossRef]

46. Zhao, C. Dynamic Traffic Network Model and Time-Dependent Braess' Paradox. In *Discrete Dynamics in Nature and Society*; Wiley: Hoboken, NJ, USA, 2014. [CrossRef]

47. Ciardo, L. The Braess' Paradox for Pendent Twins. In *Linear Algebra and Its Applications*; Elsevier: Amsterdam, The Netherlands, 2020; Volume 590, pp. 304–316. [CrossRef]
48. Chen, X.; Diao, Z.; Hu, X. Network Characterizations for Excluding Braess's Paradox. *Theory Comput. Syst.* **2016**, *59*, 747–780.
[CrossRef]

49. Acemoglu, D.; Makhdoumi, A.; Malekian, A.; Ozdaglar, A. Informational Braess' Paradox: The Effect of Information on Traffic Congestion. *Oper. Res.* **2018**, *66*, 893–917. [CrossRef]

50. Raza, S.; Al-Kaisy, A.; Washburn, S. Investigation of Roundabouts Influence Areas Along Rural and Suburban Corridors. *Adv. Transp. Stud.* **2022**, *58*, 21–38. Available online: https://www.atsinternationaljournal.com/2022-issues/investigation-of-roundabout-influence-areas-along-rural-and-suburban-corridors/ (accessed on 30 April 2025).

51. National Cooperative Highway Research Program (NCHRP). *Report 772: Evaluating the Performance of Corridors with Roundabouts*; Transportation Research Board: Washington, DC, USA, 2014. [CrossRef]

52. Brocchini, L.; Pratelli, A.; Josselin, D.; Losa, M. A Microsimulation-Based Methodology for Evaluating Efficiency and Safety in Roundabout Corridors: Case Studies of Pisa (Italy) and Avignon (France). *Infrastructures* **2025**, *10*, 186. [CrossRef]

53. Pratelli, A.; Souleyrette, R.R.; Brocchini, L. Two-Geometry Roundabouts: Design Principles. *Transp. Res. Procedia* **2022**, *64*, 299–307.
[CrossRef]

54. Pratelli, A.; Brocchini, L. Two-Geometry Roundabouts: Estimation of Capacity. *Transp. Res. Procedia* **2022**, *64*, 232–239. [CrossRef]

55. Campo, A.; D'Autilia, R. Simulation tools to compare and optimize mobility plans. In Proceedings of the 5th IEEE International Conference on Models and Technologies for Intelligent Transportation Systems (MT-ITS) 2017, Naples, Italy, 26–28 June 2017. [CrossRef]

56. Mahut, M.; Florian, M.; Tremblay, N.; Campbell, M.; Patman, D.; Krnic McDaniel, Z. Calibration and Application of a Simulation-Based Dynamic Traffic Assignment Model. *Transp. Res. Rec. J. Transp. Res. Board* **2004**, *1876*, 101–111. [CrossRef]

57. Theil, H. *Applied Economic Forecasting*; North-Holland Publishing Company: Amsterdam, The Netherlands, 1966.

58. Tratar, L.F.; Strmčnik, E. Forecasting methods in engineering. *IOP Conf. Ser. Mater. Sci. Eng.* **2019**, *657*, 012027. [CrossRef]

59. Feldman, O. The GEH Measure and Quality of the Highway Assignment Models. Association for European Transport and Contributors. 2012. Available online: https://trid.trb.org/view/1324899 (accessed on 30 April 2025).

60. Xiao-Yun, L.; Lee, J.; Chen, D.; Bared, J.; Dailey, D.J.; Shladover, S.E. Freeway Micro-Simulation Calibration: Case Study Using Aimsun and VISSIM with Detailed Field Data. In Proceedings of the 93rd TRB Annual Meeting, Washington, DC, USA, 12–16 January 2014. Available online: https://www.academia.edu/25092992/Freeway_Micro_simulation_Calibration_Case_Study_Using_Aimsun_and_VISSIM_with_Detailed_Field_Data (accessed on 30 April 2025).

61. National Academies of Sciences, Engineering, and Medicine. *Highway Capacity Manual*, 6th ed.; The National Academies Press: Washington, DC, USA, 2016. Available online: https://nap.nationalacademies.org/catalog/24798/highway-capacity-manual (accessed on 30 April 2025).

62. National Academies of Sciences, Engineering, and Medicine. *Highway Capacity Manual*, 7th ed.; The National Academies Press: Washington, DC, USA, 2022. Available online: https://nap.nationalacademies.org/catalog/26432/highway-capacity-manual (accessed on 30 April 2025).

63. National Cooperative Highway Research Program (NCHRP). *Report 672: Roundabouts: An Informational Guide—Second Edition*; Transportation Research Board: Washington, DC, USA, 2010. [CrossRef]

64. Guerrieri, M.; Khanmohamadi, M. COM-Roundabout: The first smart commutable and self-regulating roundabout for HDVs and CAVs. *Int. J. Transp. Sci. Technol.* **2025**, in press. [CrossRef]

65. Boulagouas, W.; Catalina, O.C.A.; Mariscal, M.A.; Herrera, S.; García-Herrero, S. Effects of mobile phone-related distraction on driving performance at roundabouts: Eye movements tracking perspective. *Heliyon* **2024**, *10*, e29456. [CrossRef]

66. Shatnawi, A.; Drine, A.; Al-Zinati, M.; Althebyan, Q. Simulation Study of Speed Control at Congested Arms of Roundabouts. In Proceedings of the 22nd International Arab Conference on Information Technology (ACIT), Muscat, Oman, 21–23 December 2021. [CrossRef]

67. Lebacque, J.P.; Haj-Salem, H. Ramp Metering, Speed Management and Braess-like Paradoxes. In Proceedings of the TRISTAN V: The Fifth Triennial Symposium on Transportation Analysis, Le Gosier, Guadeloupe, France, 13–18 June 2004. Available online: https://tristanconference.org/system/tristan-v/website/pdf/abstract_00153.pdf (accessed on 30 April 2025).

68. Akçelik, R. Roundabout Metering Signals: Capacity, Performance and Timing. *Procedia Soc. Behav. Sci.* **2011**, *16*, 686–696. [CrossRef]

69. Trubia, S.; Curto, S.; Barberi, S.; Severino, A.; Arena, F.; Pau, G. Analysis and Evaluation of Ramp Metering: From Historical Evolution to the Application of New Algorithms and Engineering Principles. *Sustainability* **2021**, *13*, 850. [CrossRef]

70. Brocchini, L.; Pratelli, A. Exploring the Potential Application of Ramp Metering Systems to Improve the Performances of Roundabout Corridors. In Proceedings of the ITFT 2024: International Conference on Intelligent Transport Systems, Helsinki, Finland, 19–21 October 2024; Springer: Cham, Switzerland, 2025; pp. 260–270. [CrossRef]

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