Analyzing single-lane roundabout traffic and environmental impacts through cellular automaton: A focus on U-turn effects

1. Introduction

Traffic flow in cities is heavily contingent on the efficiency of intersections; however, these nodal points often become bottlenecks that impede smooth traffic flow due to issues such as delays caused by traffic lights and interference between vehicles and pedestrians, among other factors. Therefore, resolving the complexities of these issues is essential to improving intersection functionality and promoting smooth traffic. The study of intersection problems has attracted researchers from different backgrounds and from different perspectives.^1,2,3,4,5,6 The circular intersection, which has two different forms, the roundabout, and the traffic circle, is one well-known intersection design that depends on respect to priority rules. While the traffic circle seeks to speed up traffic entry, it mostly depends on drivers adhering to priority laws, specifically ceding to traffic already moving through the lanes. This reliance on user cooperation may have hazards for user safety. Roundabouts, on the other hand, are geometrically designed to intrinsically increase safety by requiring vehicles to slow down upon entry, hence reducing the danger of collision. Studies conducted in the US support the effectiveness of this design by demonstrating a significant drop in accidents following the installation of roundabouts.⁷ Many studies have examined the complex interactions between roundabout traffic systems to identify potential problems and areas for optimization. Foulaadvand et al.⁸ did a thorough investigation of this field. In one study, they used cellular automata (CA) and car-following models to analyze traffic patterns at isolated roundabouts. They found that the size of the roundabout had a significant impact on delay times, and they even identified situations in which roundabouts were the best form of traffic management. On the other hand, Foulaadvand et al.⁹ explored roundabout traffic flow using the fully asymmetric simple exclusion process (TASEP) in a different study, shedding insight on yet another aspect of roundabout dynamics. Wang and Ruskin¹⁰ took a unique approach in analyzing unsignalized multi-lane urban roundabouts, proposing a CA model known as multi-stream minimum acceptable space (MMAS). Their study underscored that the roundabout topology, turning rates and critical arrival rates are pivotal in determining traffic flow. Notably, they observed a linear increase in throughput with the arrival rate, a phenomenon sustained until an entrance road reaches saturation, delineating a clear boundary for optimal functionality. Several studies have extensively analyzed the dynamics of different circular intersection systems, providing critical insights into their functioning. Lakouari et al.¹¹ engaged in a comparative study of roundabouts and traffic circle systems, finding that larger configurations were more suited to traffic circles, while more compact designs exhibited optimal performance when implemented as roundabouts. In a different vein, Huang¹² applied a cellular automaton model to investigate the traffic patterns prevalent at roundabouts, identifying four distinguishable phases: free flow, congestion, bottleneck and gridlock, thus offering a granulated view of traffic dynamics. Nikitin et al.¹³ utilized a simulation model to assess roundabouts augmented with traffic signals, pinpointing that the proximity of crosswalks to exit roads considerably diminished traffic capacity. Belz et al.¹⁴ crafted a CA model grounded in real-world data from single-lane roundabouts, scrutinizing the behavioral patterns of moving or stopping vehicles in potential conflict scenarios across five such roundabouts. Further, Layegh et al.¹⁵ centered their study on the conflicts emerging between pedestrians and vehicles in multi-lane roundabouts, a pivotal aspect in urban planning. Taking a more holistic approach, Małecki¹⁶ introduced a CA model that accommodated various vehicle types and roundabout sizes, aiming to discern the effects of altering the island diameter on the overall roundabout capacity, thereby broadening the scope of considerations for roundabout design.

Research has also delved into the integration of circular intersections with traffic light systems. For instance, Lakouari et al.¹⁷ demonstrated that merging the two can significantly enhance throughput and reduce traffic emissions, establishing a potential avenue for optimizing traffic management. In their exploration of environmental factors, Du et al.¹⁸ utilized a CA model to analyze noise emissions at two-lane roundabouts, revealing a nonuniform distribution of noise emissions, thus shedding light on an often-overlooked aspect of traffic dynamics. Furthermore, Regragui and Moussa¹⁹ developed a CA model designed to evaluate urban traffic across multiple roundabouts, illustrating how turning movements and various geometric factors are instrumental in shaping urban traffic capacity. As illustrated by this spectrum of studies, numerous parameters come into play in determining the efficacy of a roundabout, including but not limited to driver behavior,^20,21 pedestrian movements²² and fluctuating traffic volumes.²³ Consequently, it becomes pertinent to analyze the impact of the percentage of vehicles executing full turns in a roundabout, given its potential to significantly influence the overall traffic performance in such systems. Despite this, there appears to be a gap in the literature concerning the specific impact of the proportion of vehicles making full turns within a roundabout system and how this aspect correlates with the broader traffic flow and phase dynamics. To bridge this gap, our study explores the intricate relationships between full-turn maneuvers and various metrics indicative of traffic flow and roundabout capacity. We delve into the repercussions of continuous vehicle circulation in the roundabout, taking a close look at the energy dissipation patterns arising from this phenomenon. In this pursuit, we used energy dissipation as a pivotal metric, a choice grounded in its capacity to reflect the quadratic differences between the initial and final speeds of the vehicles, thereby offering insights into the nature of vehicular interactions occurring within the roundabout. Additionally, we broaden our research to consider the effects on the environment by examining the CO₂ emissions produced by various vehicle behaviors at a roundabout intersection. By adopting this comprehensive approach, we strive to elucidate the intricate dynamics at play in roundabout traffic systems, fostering a deeper understanding and thus adding a rich layer of insight to the current body of research in this area. The remainder of this paper is structured as follows. Section 2 delineates the methodology employed in our research. Section 3 is allocated for presenting our results and facilitating discussions on them. Section 4 encapsulates our conclusions drawn from the research.

2. Methodology

2.1. Motion rules

We analyze a single-lane roundabout system characterized by four entry and exit lanes interconnected with a central circular lane. To facilitate this, we employ open boundary conditions for both the entry and exit lanes, and a periodic boundary condition is applied to the circular lane. The spatial layout is divided into distinct sites: the circulating lane comprises $L_1$ sites, while both the entry and exit lanes consist of $L_2$ sites. A given site can either be vacant or occupied by a single vehicle at any one time. The Nagel and Schreckenberg (NaSch) model is considered to mimic the motion of vehicles based on the following rules²⁴:

R1:	Acceleration: $v_j\to \mathrm{\text{min}}(v_j+1,v_{max})$,
R2:	Deceleration: $v_j\to min(v_j,d_j)$,
R3:	Randomization: $v_j\to max(v_j-1,0)$ with the braking probability $P_b$,
R4:	Movement: $x_j\to x_j+v_j$,

where $v_j$ and $x_j$ designate the speed and position of the vehicle j, respectively. $v_{\mathrm{\text{max}}}$ and $d_j$ denote the maximum velocity and the headway, respectively.

2.2. Entry/exit rules

In the roundabout system, traffic priority is granted to oncoming vehicles, that is, the vehicles already circulating within the lane. This approach substantially augments safety by reducing potential collision points between incoming vehicles and those already in the lane at the entrance points. Such priority necessitates that the aforementioned vehicles moderate their speed and ascertain the number of empty cells between them and the next vehicle in the circulating lane $g_1$ (see Fig. 1):

—	If $g_1\ge v_0+1$: the incoming vehicle can enter the circulating with speed $v_{\mathrm{\text{inc}}}=max(v_{max},v_{\mathrm{\text{inc}}}+1)$. Here, $v_{\mathrm{\text{inc}}}$ and $v_0$ designate the speed of the incoming and oncoming vehicles, respectively.
—	Otherwise, the vehicle cannot enter the circulating lane unless the oncoming vehicle uses the indicator when it approaches its required exit direction.

Meanwhile, the oncoming vehicle may exit the circulating lane to reach its intended destination (i.e. selecting one of the available exit lanes) provided the following conditions are met:

—	The first site (exit point) of the exit lane must be empty because accumulation is forbidden in our model.
—	If $g_3<v_0$ (where $g_3$ is the gap between the oncoming vehicle and its desired exit cell (see Fig. 1)).

Otherwise, if the conditions previously mentioned were not fulfilled the vehicle must slow down and wait in the exit cell until the exit point is free.

2.3. The boundaries rules

The vehicles are inserted in the entry lanes according to the mini-system method, where lane width $v_{max}+1$ is considered which represents the mini-system.²⁵ The rules of the insertion in the mini-system are as follows:

—	If the mini-system is empty, the vehicle is inserted in its first cell with probability $\alpha$ and with an initial speed of $v_{max}$.
—	Otherwise, the mini-system must be emptied first, then the vehicle is inserted with probability $\alpha$, and a speed of $v_{max}$, where the distance between the vehicle in the mini-system and that in the entry lane must be always at least equal to the maximum speed $v_{max}$.

Here, we should note that the exit lane is specified for each vehicle upon entrance to the circulating lane and it remains unchanged. In addition, in this model, we consider also a portion of vehicles that do not have any desired direction which means that vehicles can round about the central island till they define an exit lane (i.e. this rule can make vehicles turn many times about the central island).

Hence, vehicles leave the system from the exit lanes where an additional cell is added at the end of the exit lane. If the vehicle’s position is greater than the length of the exit lane $(L_2)$, the vehicle will be removed with probability $\beta$. Otherwise, the vehicle will stop at the last exit lane cell waiting to be removed with probability $1-\beta$.

2.4. Energy dissipation

In this work, we also compute energy dissipation, a metric utilized by many scholars to analyze traffic states. Zhang et al.²⁶ explored energy dissipation in the NaSch model, revealing a critical car density in deterministic cases that leads to energy loss. Conversely, in nondeterministic cases, energy dissipation occurs across all densities, uncovering the relationships between energy dissipation, braking probability and the ‘stop and go’ phenomena. Similarly, Zhu et al.²⁷ explored the interplay between energy dissipation and signal control parameters to enhance Bando’s optimal velocity model. Laarej et al.²⁸ used a two-lane cellular automaton model to examine the effects of slow vehicles on energy dissipation and satisfaction rates. We define the kinetic energy acquired by a vehicle during its movement through the following equation :

where m and v denote the mass and speed of the vehicle, respectively.

The dissipation energy is calculated based on the energy lost during deceleration. Likewise, according to the law of conservation of kinetic energy, the kinetic energy (i.e. the energy gained during acceleration) is equal to the energy dissipation (i.e. the energy that is dispersed due to the deceleration). In this model, we consider only the energy dissipation due to the deceleration and we neglect other types of energy dissipation.^29,30 We defined the dissipated energy $\mathrm{\Delta }E$ of the vehicle i between the times $t-1$ and t as follows :

Therefore, the energy dissipation rate is where N is the total number of vehicles in the system, and $t_0$ is the relaxation time, taken as a long enough time for the system to reach its steady state. T is the time period for calculating total energy dissipation.

2.5. Carbon dioxide emission model

In this study, we have employed the emission model introduced by Int Panis et al.³¹ to simulate traffic emissions. This established model calculates emissions based on a vehicles instantaneous speed and acceleration using nonlinear multivariate regression techniques. Significantly, it was calibrated utilizing data derived from real-world urban and highway driving conditions, a factor contributing to its frequent adoption by researchers, owing to its simplicity and empirically validated foundations. Building on this, Li et al.³² devised a fresh approach to analyzing varied patterns of nitrogen oxides (NO_x), carbon dioxide (CO₂), particulate matter (PM) and volatile organic compounds (VOC) emissions, leveraging GPS data from taxis in Beijing to explore the relationships between emissions and road densities. Likewise, Nyhan et al.³³ utilized GPS trajectory data from a considerable fleet of over 15 000 taxis to ascertain the requisite accelerations and speeds, forming the basis for predicting air pollution emissions including PM, CO₂, NO_x and VOC_s in Singapore. Further extending this discourse, Wang et al.³⁴ integrated a mixed NaSch traffic flow model with the empirical formula of automobile exhaust emissions to scrutinize the emissions of CO₂, PM, VOC and NO_x, considering various factors such as movement conditions, maximum velocity, vehicle lengths, and mixing ratios. For our analysis, we will rely on the Int Panis et al.³¹ model where the emission function is contingent upon the vehicle’s acceleration and instantaneous speed. This approach allows us to focus on the emissions of pollutants with significant health and economic impacts, including VOC, NO_x, PM and CO₂. We applied the general formula for pollutant emission as follows :

The equation considers $V_i(t)$, the instantaneous speed (m/s), and $a_i(t)$, the instantaneous acceleration (m/s²) of vehicle i. Additionally, constants $f_1$ to $f_6$ are unique for each type of vehicle and can be found in Table 1.

To account for the frequent fluctuations in vehicle speed in densely populated urban zones, we measure emissions in g per second per vehicle (g/s). This metric is more appropriate as it captures the real-time emission levels, which can vary considerably due to traffic congestion.

3. Results and Discussion

In our numerical simulation, we employed the following parameters: $L_1=40$, $V_{\mathrm{\text{max}}}=2$, $L_2=100$ and braking probability $P=0$. To ensure a robust dataset, the system operated over 30 000-time steps, with results derived from the final 10 000 steps to ensure stabilization of transient behaviors. This process was replicated across 100 independent simulations to enhance the robustness and statistical validity of our results. Furthermore, it was assumed that all vehicles in the simulation utilized petrol as fuel.

3.1. Effect of U-turn vehicles

Initially, our study delved into the implications of vehicles executing U-turns on the traffic dynamics across the three essential lanes in the roundabout namely, the circulating, entry, and exit lanes. As a preliminary step, we delineated the phase diagram, considering scenarios with and without vehicles completing a full rotation within the circulating lane. In the scenario absent of full-turn vehicles, every vehicle was aligned with an exit, allocated based on an equal probability distribution, thus facilitating a systematic selection of their respective destinations (refer to Fig. 1 for a detailed illustration).

From Fig. 2, we identified three distinct phases emerging in the roundabouts traffic pattern: Free flow, congestion and maximum current. In scenarios where $\alpha$ is less than $\beta$, we observe a free flow phase; in this phase, vehicles move at their preferred speeds almost without significant interruptions. Conversely, when $\alpha$ surpasses $\beta$, the system transitions into a congested phase, significantly reducing vehicle speeds due to heightened restrictions on movement. In addition, we identified a maximum current phase where traffic current remains unaffected by the $\alpha$ and $\beta$ parameters, demonstrating a stable flow. As we incorporate the behavior of vehicles completing full U-turns, constituting 40% of the traffic, the dynamics change markedly. As depicted in Fig. 2, the free flow, and congested phases contract, while the maximum current phase expands, showcasing a broader range of stable traffic conditions. This inclusion also introduces a jammed phase evident in all lanes of the roundabout. Interestingly, the circulating lane experiences a more expansive free flow phase compared to the entry and exit lanes. This phenomenon is attributed to the U-turning vehicles in the circulating lane, thereby facilitating a broader free-flow window in the circulating lane.

To gain deeper insight into the impact of vehicles making U-turns in the roundabout, we will assess how the lane capacity (i.e. the maximum current in the lane) varies with the percentage of vehicles making U-turns in the three lanes.

As depicted in Fig. 3, the capacity of the circulating lane experiences a slight increase with a higher percentage of vehicles making U-turns, while the capacity of the entry/exit lanes exhibits a consistent decrease. The capacity in the circulating lane improves slightly as the increases in the percentage of U-turning vehicles reduce incoming traffic from the other entry lanes, thereby increasing the maximum current. Moreover, the capacities in the entry and exit lanes exhibit similar patterns. This is because, as the proportion of vehicles that make full turns in the circulating lane increases, the queue of stationary vehicles in the entry lane enlarges, and the number of vehicles in the exit lane diminishes, consequently reducing the capacity of both lanes. Subsequently, we examined the energy dissipation resulting from deceleration to deepen our understanding of its impact on vehicle speed and the effects of U-turns in the circulating lane.

Figure 4 illustrates the energy dissipation as a function of injection $\alpha$ and extraction $\beta$ rates, including scenarios where vehicles complete a full U-turn in the circulating lane. In the circulating lane, depicted in Fig. 4(a), both the free flow ($\alpha <\beta$) and the congestion ($\alpha >\beta$) phases show reduced energy dissipation. This trend is attributed to the uniform speed maintained by vehicles during the free-flow phase and the near-standstill conditions observed in the extreme jam phase. However, we noticed a gradual increase in energy dissipation as both $\alpha$ and $\beta$ increased, culminating in a plateau region where the peak energy dissipation reached $E_d∕m=0.4$. This pattern is shown in the entry lane, as illustrated in Fig. 4(b), although the peak energy dissipation here is slightly lower at $E_d∕m=0.15$. Contrarily, the plateau region is absent in the exit lane (see Fig. 4(c)), a phenomenon attributed to the exclusion probability $\beta$, which induces the formation of a queue near the last cell in the exit lane where the maximum of energy dissipation is reduced $E_d∕m=0.10$. Hence, the introduction of U-turning vehicles into the system yields notable variations in energy dissipation across different lanes, as seen in Figs. 4(d)–4(f). Specifically, while the energy largely remains stable in the circulating lane at about $E_d∕m=0.4$, a substantial reduction is observed in both the entry lane ($E_d∕m=0.10$) and the exit lane ($E_d∕m=0.06$). This phenomenon can be attributed to the saturation of the circulating lane with U-turning vehicles, which naturally decreases the influx of vehicles in this lane, consequently diminishing the outflow into the exit lane and thereby reducing overall energy dissipation in both lanes (i.e. entry and exit). After analyzing energy dissipation, we turn our focus to the environmental implications, particularly in terms of carbon dioxide CO₂ emissions.

Figure 5 shows the peak CO₂ emissions observed for all combinations of $\alpha$ and $\beta$, as a function of the percentage of vehicles making U-turns in the three lanes. We note a slight increase in the maximum CO₂ emissions corresponding to the rise in the percentage of vehicles making U-turns in the circulating lane. This trend can be attributed to the saturation of the circulating lane with U-turning vehicles, which naturally reduces the influx of vehicles into this lane, thereby causing a minor alteration in CO₂ emissions. Compared to the entry lane, the diminished influx into the circulating lane results in the formation of queues in the entry lanes, subsequently increasing CO₂ emissions. As regards the exit lane, as the journey of vehicles in the circulating lane increases with the number of U-turning vehicles, the outflow into the exit lane decreases, leading to a reduction in CO₂ emissions.

3.2. Effect of the influx of directionless vehicles in circulating lanes

In this subsection, we study the effect of the rate of entering vehicles without direction (i.e. vehicles that keep turning in the circulating lane) on the traffic flow in the roundabout. The probability ($P_{\mathrm{\text{ext}}}$) of choosing the nearest exit point to leave the circulating lane is fixed at $P_{\mathrm{\text{ext}}}=0.01$. As illustrated in Fig. 6, we have constructed a phase diagram, considering situations both with and without vehicles that keep turning in the circulating lane. The situation where the vehicles are assigned an exit with equal probability is studied in the first section of the paper. As the result shows, when the percentage of vehicles that keep turning in the circulating lane increases, the free flow and the congestion phases are reduced while the maximum current phase expands in the three lanes of the roundabout.

To delve deeper into the impact of such vehicles, Fig. 7 illustrates the capacity by showcasing the peaks of traffic in the three lanes as a function of varying percentages of vehicles without a set direction. We observe that the capacity in the circulating lane is higher, primarily because this lane becomes saturated with vehicles that continue to circle around the central island of the roundabout. This saturation diminishes the opportunities for vehicles in the entry lanes to find a safe gap to merge into the circulating lane, thereby increasing the capacity of the circulating lane at the expense of the other lanes (i.e. exit and entry lanes). Regarding the entry lanes, the queue of stopped vehicles increases, which reduces the capacity. For the exit lanes, the decrease in vehicles that get out from the circulating lane results in a reduction of capacity in these lanes.

As we saw, the vehicles that keep turning can affect the flow in all lanes, influencing the speed of vehicles. One effective metric for studying the heterogeneity in vehicle speeds is the dissipation energy resulting from vehicle deceleration.

Figure 8 shows the dissipation energy as a function of the injection $\alpha$ and extraction $\beta$ rates, for different percentages of the vehicles that keep turning in the circulating lane. First, we take 10% of the vehicles that keep turning in the circulating lane. The circulating lane (see Fig. 8(a)) shows a decrease in dissipated energy for the totally free-flow phase ($\alpha <\beta$). For the congestion phase ($\alpha >\beta$), the number of stopped vehicles in the system increases, leading to a reduction in energy dissipation. It can be observed that the energy dissipation is lower where the traffic is either free-flowing or extremely congested. The metric of energy dissipation can be useful in determining whether the emergence of local interaction is observed or not. Specifically, as free space increases, the emerging phenomenon is free-flowing traffic, whereas global congestion corresponds to the alternative emergent phenomenon (i.e. when the free space between vehicles is extremely reduced). In cases between these phases, the traffic flow comprises a mixture of stopped and moving vehicles, which increase the dissipation of energy, here the formation of the plateau is due to the saturation where the dissipation energy becomes decoupled from the variation of $\alpha$ and $\beta$. The pick of the energy dissipation observed in the circulating lane is $E_d∕m=0.4$. For the entry lane (see Fig. 8(b)), the maximum dissipated energy is reduced to $E_d∕m=0.08$, we can explain this by an increasing queue of stopped vehicles in this lane. For the exit lane (see Fig. 8(c)), the maximum dissipated energy, $E_d∕m=0.08$, is reached when ($\alpha >\beta$). As the extraction rate $\beta$ increases, the dissipation energy decreases, consequently improving the traffic quality in the exit lane.

To understand the impact of vehicles that persist in circulating within the lane on energy dissipation, we increased the percentage of these vehicles to 35%. Both the circulating lanes depicted in Fig. 8(a) and the circulating lane in Fig. 8(d) exhibit almost similar patterns, achieving the same maximum value of dissipated energy. However, the plateau region representing the maximum of the dissipated energy in Fig. 8(d) is more extensive than the one observed in Fig. 8(a). This occurs as the increased number of vehicles continuously circulating around the roundabout’s island reduces the flow in the circulating lane’s dependence on $\alpha$ and $\beta$, thereby expanding the plateau region. It should be noted that approaching the boundaries between different traffic phases can either worsen or improve traffic conditions. Specifically, as one approaches the boundary leading to the free-flow phase from the maximum current, traffic conditions ameliorate, resulting in a decrease in energy dissipation. Conversely, when nearing the boundary transitioning from maximum current to the congestion phase, traffic conditions deteriorate, leading to a noticeable reduction in energy dissipation. For the entry lanes, the influx of vehicles persistently circulating results in a decrease in vehicle speed, subsequently diminishing energy dissipation. Here, the peak energy dissipation shifts from $E_d∕m=0.08$ to $E_d∕m=0.04$ (see Figs. 8(b)–8(e)). Regarding the exit lanes, increasing the percentage of vehicles persistently circulating to 35% decreases the number of vehicles exiting the circulating lane. Consequently, the maximum energy dissipation at the exit lane in Fig. 8(f) is reduced in comparison to that in Fig. 8(c).

Subsequently, we illustrated how the maximum CO₂ emissions vary with the percentage of directionless vehicles. From Fig. 9, it is observed that the maximum CO₂ emissions remain stable despite the increase in the percentage of vehicles persistently circulating. This stability is attributed to most vehicles in the circulating lane maintaining a higher speed, with the heterogeneity of speed originating from the entry point. In the case of the entry lanes, the scenario differs. Initially, the increase in the percentage of vehicles persistently circulating in the circulating lane leads to an enhancement in speed heterogeneities within this lane, subsequently elevating CO₂ emissions. However, as the number of persistently circulating vehicles continues to rise, CO₂ emissions are reduced. This drop is due to the deterioration of traffic flow and the formation of persistent queues of stopped vehicles, minimizing acceleration and deceleration events essentially, most vehicles are in a standstill situation, which sharply reduces CO₂ emissions. As for the exit lanes, the number of vehicles exiting the circulating lane decreases as the percentage of persistently circulating vehicles in this lane increases. This development improves the traffic flow in the exit lanes and, consequently, results in a reduction of CO₂ emissions.

4. Conclusion

Roundabouts are pivotal intersections that facilitate the reduction of conflicts between vehicles without the necessity for traffic lights and have been adopted widely across the world. However, the efficiency of the roundabout system can be influenced by several factors. One such underexplored aspect is the impact of vehicles that remain in the circulating lane for extended durations, and their consequential effect on other lanes. These vehicles can broadly fall into two categories: those making a full turn, and those without a predetermined exit, who continue to circulate until they decide to exit the roundabout. In this study, we examine the effects of U-turns on the traffic flow within the roundabout, establishing that such maneuvers tend to augment congestion in the entry lane due to the established priority rules. Consequently, incoming vehicles are compelled to wait until an adequate gap is available, resulting in the emergence of waiting queues at the entry lane and an increase in CO₂ emissions in the entry lane. Our results suggest that an uptick in the number of such vehicles diminishes the free flow and congestion phases while enlarging the maximum current phase. This also gives rise to a jammed phase within the circulating lane. The increase in the percentage of vehicles persistently circulating in the circulating lane has multifaceted effects on both energy dissipation and CO₂ emissions across all lanes. When examining energy dissipation, an increase in such vehicles leads to a marked reduction in dissipated energy during the free-flow and congestion phases. In these extremes, traffic is either fluid or in a state of congestion, resulting in lower energy dissipation, indicative of the emergence of local interaction. The analysis of CO₂ emissions demonstrates that an increase in the number of vehicles without a predetermined exit stabilizes maximum emissions in the circulating lane due to maintaining speed heterogeneity. Conversely, the entry lanes experience a rise in CO₂ emissions initially due to increased speed heterogeneities, which eventually decline as persistent queues form and traffic flow deteriorates, leading to reduced acceleration and deceleration events. Improved traffic flow in the exit lanes, is due to the reduction of the number of vehicles in this lane, subsequently resulting in decreased CO₂ emissions. In summary, the presence of persistently circulating vehicles influences traffic dynamics, energy dissipation and CO₂ emissions in varying degrees across different lanes. These observations are instrumental in comprehending the interplay between traffic flow, energy consumption and environmental impact in the context of vehicle circulation within roundabouts. To ameliorate the roundabout system’s functionality, we propose the introduction of traffic lights to lessen vehicle interactions, or the designation of exclusive lanes for vehicles engaged in full turns. This study serves as a critical resource for understanding the subtle effects of U-turns and indecisive driving on roundabout traffic flows and offers a foundation for further scholarly exploration into vehicle interactions in multi-lane roundabouts and their correlation with the environment.

ORCID

A. Ez-Zahar  https://orcid.org/0000-0003-4587-3203

N. Lakouari  https://orcid.org/0000-0002-7180-1038

O. Oubram  https://orcid.org/0000-0003-2783-7364

R. Marzoug  https://orcid.org/0000-0002-6578-696X

H. Ez-Zahraouy  https://orcid.org/0000-0001-5615-8614