Analyzing the relationship between the efficiency and safety of a turbo roundabout by the factor analysis method

Abstract

The construction of cities and economic development lead to more and more serious environmental pollution, and the concept of green and low-carbon city has been proposed. Therefore, a series of requirements have been put forward for transportation. CO and other pollutants will be produced in the exhaust of conventional fuel vehicles, which will seriously affect the urban environment, especially at intersections with large passenger and vehicle flows. When multiple roads, especially more than 4 roads, intersect on urban roads, traffic organization can usually be achieved by using a roundabout. However, due to the limited capacity of the conventional roundabout, with the rapid increase of the traffic volume, and there are many vehicles in the circle lane change and interweaving behavior. This has caused serious congestion at the roundabout, the significantly increase in pollutants emissions and the decline in air quality. As an unconventional design, the turbo roundabouts use canalized traffic to allowed drivers to select the appropriate lanes in advance depending on their destinations so that different lanes within the circle do not interfere with one another, which improves the safety of the intersection while ensuring capacity. The main purpose of this paper is to analyze the traffic efficiency and safety of the conventional roundabout scheme and turbo roundabout scheme for five-way intersections. Using VISSIM to simulate different forms of roundabout and analyzing the six selected evaluation indicators. The number of vehicles in different entrance lanes and the diameter of the circle are selected as sensitivity factors for sensitivity analysis. Finally, the factor analysis method (FAM) is used to classify the six indicators into two categories: traffic efficiency and traffic safety, so as to comprehensively evaluate the different schemes. The results show that the difference in performance between the two schemes was not significant at low traffic volumes. At high traffic volumes, the turbo roundabout was better than the conventional roundabout in terms of emissions, safety and throughput efficiency. CO emissions from vehicles on conventional roundabout are generally higher than those on turbo roundabout, up to 53.62%. Therefore, the turbo roundabout is more appropriate for heavy traffic conditions.

1. Introduction

Since the 21st century, China's economy has developed rapidly, and transportation has been vigorously developed. The number of motor vehicles has increased rapidly. However, traffic congestion and urban air quality decline also follow, and air quality has also become an important control index. With the promulgation of new energy vehicles, traffic restrictions and other relevant environmental protection policies, this measure is positive for the alleviation of air quality, but in the general trend of mainly fuel vehicles, it can't significantly improve the air quality in the short term, and it will also cause inconvenience for residents to travel. Traffic congestion as the root cause has not been solved. Urban intersections are important nodes in the urban road network, affecting the efficiency of vehicle traffic, but the current urban road intersection traffic congestion is exceptionally serious, resulting in increased vehicle emissions and greater environmental pollution. And the high pedestrian flow at intersections seriously affects the health of pedestrians. Therefore, the traffic quality at intersections is closely related to air quality.

Urban intersections, especially main road intersections, have gradually become bottlenecks in urban roads [[1], [2], [3]], which makes the urban road congestion and safety problem increasingly serious [4]. Several improvements have been proposed to increase the capacity and reduce congestion at both signal-controlled and unsignalized controlled intersections. For conventional signal intersections, left-turn traffic has been a major factor that affects the efficiency and safety of intersections [[4], [5], [6]]. Dedicated left-turn phases are often required to ensure left-turn passage, but it increases the travel time and delays [7,8]. For large intersections, the space utilization of intersections is often improved, and delays are reduced by setting up left-turn waiting areas, but it has a limited effect because intersections are still controlled by four phases [9,10]. Therefore, optimizing the signal control of intersections is a powerful method to improve the capacity of intersections through different signal optimization algorithms and coordinated signal control among multiple intersections [[11], [12], [13]]. In addition, in urban roads, especially where there are many buses, protecting the right of way for buses through signals [12,14,15] can improve the efficiency of the road network overall.

For signal-controlled intersections, some unconventional designs have been gradually proposed. The common designs include the unconventional median U-turn design (MUT), superstreet median design (SSM), bowtie design, jug handle design, quadrant roadway intersection design (QR), upstream signalized crossover intersection (USC), continuous flow intersection (CFI), and parallel flow intersection (PFI), etc. The main idea of all of these designs is to optimize the operation of left-turning traffic by changing the traffic organization of left-turning traffic and eliminating the conflict between left-turning and direct traffic to control intersections by 2-phase signals, and such unconventional designs can reduce safety risks and average delays [16].

To improve the problems of conventional roundabouts and increase capacity, the turbo roundabout solution was proposed. The most important difference between the turbo roundabout and the conventional roundabout intersection is that before the vehicles enter the circle of a turbo roundabout, the vehicles in different directions are shunted to different lanes in advance; then, the traffic heading to different directions within the circle is separated and isolated from each other. After the vehicle enters the turbo roundabout, the right-turning vehicle drives into the outer ring by the right lane and drives out of the traffic circle along the ring road. Straight vehicles, left-turning vehicles and turn-around vehicles then drive into the inner ring by the inner ring and leave the intersection at the corresponding exit. As a result, there are only merging conflicts at the turbo roundabout, thus improving the efficiency of vehicular traffic.

With the development of urbanization, more and more five-way intersections with more complex operation will appear in the road network, and the conventional roundabout can no longer adapt to the current traffic volume. However, there are few applications of turbo roundabout in China, especially for five-way intersections. And there is a lack of relevant theoretical research.

Turbo roundabouts have been widely applied in Europe, and many scholars have also conducted some research on turbo roundabout intersections. Italian researcher takes a city in Italy as an example, analyzes the impact of turbo roundabout intersections on traffic flow, delay, emissions and noise, and finds that turbo roundabout intersections can significantly improve traffic efficiency and safety, reduce environmental pollution and social costs [17]; Guerrieri et al. propose a method based on the HCM 7th edition, 2022 capacity model and gap acceptance theory, which estimates the entry capacity and total capacity of basic turbo intersections under different levels of autonomous vehicle market penetration, considering the effects of pedestrian flow and lane allocation and shows the potential improvement effects of automated vehicles on the performance of turbo roundabouts through a case study [18]; Some researchers find that separated lanes for cyclists can improve safety and capacity, but also increase crossing conflicts [19]; Elhassy, Z. et al. consider the high traffic conditions and aggressive driving behavior prevalent among the Middle East countries [20]; Mądziel, M. et al. compare two types of roundabouts, multilane and turbo, in a case study of Rzeszow city in Poland. They find that turbo roundabouts can reduce emissions of CO2 and PM10, but not NOx, under certain traffic conditions [21]; Czech researcher review the regulations and procedures for designing turbo roundabouts in different European countries and compare them in terms of their effectiveness and safety. They also present the results of their field measurements and analysis of 105 turbo roundabouts in Europe. They find that the design parameters of turbo roundabouts vary significantly among countries and that some design elements can influence the speed, capacity and conflict situations of vehicles [22]; Gallelli, V. et al. use microsimulation and surrogate safety assessment models to evaluate the performance of a traditional priority junction, a conventional roundabout and a turbo roundabout in a case study in Southern Italy. They find that the turbo roundabout can improve the operational performance and reduce the queue length, travel time and delay of vehicles, but not significantly reduce the number and severity of potential conflicts [23].

The most significant motive is that roundabouts are rarely seen in China and we usually use signalized intersections. Many European researchers have studied roundabouts precisely and deeply, but the situation is totally different in China. For example, Xi'an, the city where we stayed and did research, has a population of 13 million and vehicle ownership over 5 million, but only one large roundabout exists now, which is the roundabout in this article. Many roundabouts were reconstructed into signalized intersections. We want to study the characteristics of roundabouts in China and try to find the difference from those in Europe. In addition, we are interested in the balance between traffic efficiency and safety for at-grade intersections. However, in the existing studies, no researchers have studied this balance for turbo roundabouts, which are a special type of roundabouts that have separate lanes for different directions. Moreover, the current research on turbo roundabouts mainly focuses on four-way intersections, and the advantages and disadvantages of turbo roundabouts in five-way intersections compared with traditional roundabouts in terms of safety and traffic efficiency still need to be studied. In this paper, we have selected the five-way roundabout of Qujiangchi North Road-Furong East Road-Xinkaimen South Road in Xi'an as a case study to improve its adoption of the turbo roundabout scheme. By collecting the vehicle and geometric data for this roundabout, calibration and simulation were performed using VISSIM simulation software. Finally, this paper adopts the idea of the factor analysis method to select six evaluation indices: the queue length, delay, CO emissions, TTC, PET, and CSI. We evaluate the traffic efficiency and safety of a five-way turbo roundabout under different traffic conditions, extract the common factors of all indices, analyze the relationship between traffic efficiency and safety, comprehensively assess the turbo roundabout after the factor scores and discuss the applicability of the turbo roundabout.

The organization of this paper is as follows: Section 2 reviews the relevant literature. Section 3 illustrates the actual case analysis and data collection. Section 4 presents the modeling of a conventional roundabout and turbo roundabout in VISSIM and analyzes the simulation results. Section 5 presents the sensitivity analysis of 2 schemes under different traffic scenarios. Section 6 discusses the process of the factor analysis method to analyze the traffic efficiency and analysis safety of roundabouts. The final conclusions are drawn in Section 7.

2. Literature review

2.1. Turbo roundabout

For unsignalized controlled intersections, roundabout schemes are widely used worldwide [[24], [25], [26]]. The characteristic of a roundabout is that it can be operated without signals for traffic flow organization through circle lanes, which can largely reduce road congestion and improve safety [27,28]. In terms of traffic efficiency, vehicle operations in a roundabout are related to the geometry of the circle lanes and desired speed [29]. The speed of the traffic flow at the roundabout is an important factor that affects the efficiency of the roundabout, so speed prediction at the entrance, circle lanes, and exit of the roundabout is also an important measure to study the speed distribution at the roundabout [30]. In terms of safety performance, conflicts at roundabouts are related to the geometry and proportion of left-turning traffic. In addition, conflicts more frequently occur in the merging zone inside the roundabout than inside the circle lanes [31]. For four-way intersections or more-way intersections, a roundabout is safer than a signal intersection [32]. In terms of the environment, improving the operation of right-turning traffic at roundabouts will improve the access performance and reduce emissions and fuel consumption to save energy costs [33]. Although roundabouts have better traffic efficiency and safety than conventional signal intersections, there is an interweaving behavior of traffic flow in roundabouts, the safety hazard of large roundabouts can be high, which affects traffic safety and easily causes delays, and the capacity of roundabouts is limited; when the traffic demand is high, their performance is not as good as that of signal intersections [34]. Therefore, roundabouts are used in many cases in combination with signal timing to adapt to different traffic conditions [35,36].

Due to the limitations of conventional roundabouts, alternative solutions for roundabouts are evolving today [26,37], which have advantages and disadvantages [38]. The most common alternatives are flower roundabouts and turbo roundabouts. A flower roundabout can reduce land use and make full use of the original roundabout for renovation [39].

For turbo roundabouts, actual cases in many countries [[40], [41], [42]] have proven that it is superior to the conventional scheme, and the trend of gradually replacing conventional roundabouts is rapidly rising [43,44]. Many studies on the design details and geometric layout of turbo roundabouts give clear descriptions [[45], [46], [47]].

The traffic organization of the turbo roundabout is conducive to the improvement of traffic capacity and can greatly reduce the collision of vehicles, as proven by many theoretical model analyses [[48], [49], [50]] and microscopic simulations [51,52]. In previous studies, turbo roundabouts were often considered in four-way intersections where a primary road and a secondary road intersected, and circle lanes were only considered in the form of two lanes. The capacity of the primary and secondary entrances to the traffic circle varies when the traffic volumes inside and outside the roundabout are at different levels [53], and the two-lane turbo roundabout has a high capacity [54,55] and low delay [56,57] when the traffic volumes are not very high. The overall performance of the turbo roundabout is good and contributes to the efficiency of the road network [55,58,59]. However, the capacity of a turbo roundabout with a two-lane loop is limited, so different turbo roundabout forms with multi-lane loops are constantly proposed, and this design is more suitable for intersections with high traffic demand [5,60]. In multilane circles, a combination of circles and signal control can be effective in further improving the capacity of the turbo roundabout [61]. In conclusion, the turbo roundabout has a higher capacity than the conventional scheme under most conditions [60].

In terms of safety, although turbo roundabouts have fewer conflict collisions than conventional schemes overall, the speed of vehicles within the circle of turbo roundabouts is higher than that of conventional schemes [62], which may lead to more serious accidents at turbo roundabouts [60], so safety analysis of turbo roundabouts is important. In particular, the crash severity at turbo roundabouts must be discussed [63,64].

2.2. Factor analysis method

The factor analysis method is a statistical method that is often used in multicriteria decision making, and its basic purpose is to describe the relationship among multiple indices by few factors, which improves the interpretation and detects hidden structures in the data [65,66]. Factor analysis methods were first proposed in the early 20th century and mainly applied in the field of psychology [67]; currently, they have been widely used in various fields [66], including transportation [68].

In traffic safety, factor analysis is often used in combination with other algorithms and applied to traffic accident prediction models to predict the severity of road traffic accidents [69], the severity of collisions in road construction zones [70,71], and the prediction of urban rail traffic risks [72]. In addition, for environmental energy, factor analysis is used to analyze the importance of influencing factors that affects the transportation energy consumption, which helps to explain the essential reasons for transportation energy consumption to save energy and reduce consumption [73]. Factor analysis can analyze the correlation of various factors that generate risks and accidents in road safety, including human factors [74], road factors, and environmental factors, and extract the common factors among many factors for road safety assessment and prediction. The regularity derived from VISSIM simulation was found to have some correlation when the CRITIC multicriteria decision analysis was used [75]. Therefore, when using VISSIM simulation, it is necessary to consider the correlation of different indices at the turbo roundabout.

The literature review shows that most of the current studies are on four-way intersection turbo roundabout and the number of roundabout lanes is single or double lanes, and there are fewer studies on five-way intersection multi-lane roundabout. In addition, previous studies on the efficiency and safety of turbo roundabouts are often only evaluated through independent comparison and analysis of one or more indices, and the correlation between efficiency indices and safety indices is often not considered. Therefore, this study uses FAM to classify multiple indicators and considers the correlation between different indicators.

3. Problem statement and data collection

3.1. Problem statement

Xi'an is a city with a long history [76]. As of October 2021, the number of motor vehicles in Xi'an has exceeded 4 million [77]. According to AutoNavi big data [78]. In 2021, the congestion index of Xi'an ranks in the top 10 in China, which indicates that the traffic pressure of Xi'an's urban road network is very high, especially for the main road intersection in the city, and its capacity cannot satisfy the growing demand for traffic travel.

The city streets are interlaced and complex. For the case of multiple road intersections, the most common scheme is to use a roundabout for traffic organization, but the capacity of the roundabout is limited, and there is an interweaving behavior within the circle lanes, which may become a bottleneck in the urban road.

The paper takes the roundabout of Qujiangchi North Road, Furong East Road, Xiamen South Road in Xi'an City as an example, as shown in Fig. 1, which belongs to the five-way intersection, and the interweaving behavior of vehicles inside the circle lanes is more frequent.

Fig. 1.

The investigated roundabout location scheme. Coordinates: 108.99452, 34.205207.

There are more studies on various types of intersections at home and abroad, especially in Europe and the United States, where roundabouts are very common. In China, there is no mature standard practice for intersection of more than 4 roads, and the use of traffic lights, roundabouts, or other means have their own limitations. Traffic light timing schemes are extremely complex and do not point drivers in the right direction. Roundabouts do not work well in urban areas in China because Chinese drivers' skills and habits are different from those in Europe and the United States. Therefore, for five-way intersections, it is necessary to find control measures applicable to Chinese urban areas, and to study the applicability of various schemes under different traffic volume conditions. Therefore, this paper will take a five-way intersection in Xi'an city as the research object. This area is a tourist area in Xi'an city with many tourists, while the good surrounding environment attracts more and more residents to settle around it, so the motor vehicles are growing extremely fast, and the heat map of population density is shown in Fig. 2. As can be seen in Fig. 2, the five-way intersection is in the center of the whole tourist area, and its smoothness will directly affect the traffic condition of the whole area. Therefore, the findings of this study will contribute to the improvement of traffic conditions in this area and prepare control measures and reconstruction plans for the future increase of traffic volume of this five-way intersection.

Fig. 2.

Population density heat map Coordinates: 108.99452, 34.205207.

The hypothetical reconstruction of the roundabout planar intersection is shown in Fig. 3.

Fig. 3.

Turbo roundabout intersection structural diagram.

3.2. Data collection

According to AutoNavi traffic Big Data [78], the average congestion index of Xi'an city in October 2021 is shown in Fig. 4. The city's morning peak occurs between 7:00 a.m. and 9:00 a.m., with the highest peak at approximately 8:00 a.m., and the evening peak occurs between 5:00 p.m. and 7:00 p.m., with the highest at approximately 6:00 a.m. The corresponding peak periods are selected in the morning and evening for traffic data collection. Data collection should be performed to ensure that the weather road conditions are good, there are no road construction zones, and there are traffic accidents.

Fig. 4.

Average congestion index in Xi'an in October 2021. The real-time congestion index can be obtained from the Autonavi Company Webpage at https://report.amap.com/detail.do?city=610100.

The main instruments to collect the traffic volume in this paper are UAVs, as shown in Fig. 5. The statistics mainly include the total traffic volume of each entry of the intersection in the peak hour, the proportion of vehicles from each entry to different exits, and the proportion of vehicle types in each entry.

Fig. 5.

UAV photo of an actual conventional roundabout. Coordinates: 108.99452, 34.205207.

After data collection, the total morning peak traffic volume of the intersection is 3018 veh/h, and the total evening peak traffic volume of the evening intersection is 3276 veh/h. The turning ratio and vehicle group of the morning peak and evening peak are similar, so the evening peak with higher traffic volume is chosen as a representative. Table 1 shows the collected data of the evening peak period over 1 h.

Table 1.

Collected data during one peak hour (5:30 p.m. to 6:30 p.m.) on 2021.10.20.

Entry (Drive out)	Entry (Drive in)	Flow	Car	Bus	Truck
1	2	1	336	3	2
	3	2	80	0	3
	4	3	108	4	0
	5	4	92	0	0
2	1	5	168	0	4
	3	6	36	0	0
	4	7	324	0	0
	5	8	656	6	4
3	1	9	92	0	5
	2	10	28	0	0
	4	11	8	0	4
	5	12	40	0	0
4	1	13	120	4	0
	2	14	220	0	0
	3	15	36	0	0
	5	16	72	0	0
5	1	17	152	4	5
	2	18	532	5	6
	3	19	40	3	4
	4	20	68	0	2

The collected data reveal the following characteristics.

1. The traffic volume in the east-west direction (entries No. 2 and No. 5) is larger than the traffic volume of the remaining entries.

2. For the composition of vehicles, cars account for most vehicles within the roundabout, and the proportion of buses and trucks is smaller.

3. For the roundabout geometry configuration, entry lanes No. 1, No. 3, and No. 5 have 2 basic lanes, entry No. 2 has 4 basic lanes, and entry No. 4 has 1 basic lane.

4. Establishment and simulation of the VISSIM model

4.1. Modeling in VISSIM

Based on actual collected data and UAV photos, the Qujiangchi intersection is modeled in VISSIM. The layout of this roundabout is as follows: 1–5 entries in a clockwise direction, and the diameter of the roundabout is 45 m, as shown in Fig. 6.

Fig. 6.

Geometries of conventional roundabout (A) and turbo roundabout (B) in VISSIM.

4.2. Calibration of the VISSIM model

To obtain more reasonable capacity predictions for each movement and ensure the accuracy of the model when VISSIM simulation is used for research analysis, the model must be calibrated [79]. The capacity is often used as an index for route selection in road network calibration and is highly sensitive to driving behaviors in VISSIM [80], so the capacity of the model is calibrated in this paper. The calibration process in this paper follows the calibration procedure proposed in previous studies [[81], [82], [83]]. The error in judging the capacity is mainly described using the MAPE index, which is the mean absolute percentage error and reflects the error between the collected capacity and the simulated output capacity of each traffic flow. This error is calculated according to Eq. (1).

$$MAPE=\frac{\sum _{a=1}^n{C}_v^a-\sum _{a=1}^n{C}_f^a}{\sum _{a=1}^n{C}_f^a}$$ (1)

Where a is the traffic flow, n is a total of 20 different traffic flows, $C_v^a$ is the simulated capacity of VISSIM (veh/h), and $C_f^a$ is the collected capacity (veh/h). Table 2 shows the calculated MAPE results for each traffic flow.

Table 2.

VISSIM simulation calibration results with collected data.

Entry (Drive out)	Entry (Drive in)	Flow	Investigated Capacity (veh/h)	Simulated Capacity (veh/h)	MAPE for each flow (%)	MAPE (%)
1	2	1	341	346	1.35%	0.39%
	3	2	83	94	12.77%
	4	3	112	122	9.29%
	5	4	92	94	1.74%
2	1	5	172	180	4.65%
	3	6	36	36	0.00%
	4	7	324	302	−6.67%
	5	8	666	670	0.54%
3	1	9	97	94	−3.51%
	2	10	28	29	2.86%
	4	11	12	10	−16.67%
	5	12	40	46	15.00%
4	1	13	124	108	−12.90%
	2	14	220	202	−8.36%
	3	15	36	36	0.00%
	5	16	72	72	0.00%
5	1	17	161	161	11.80%
	2	18	543	543	0.77%
	3	19	47	47	−8.09%
	4	20	70	70	13.14%

After the model calibration, the MAPE results are shown in Table 2. The calibrated model parameters are used as the basis to establish the turbo roundabout.

The calculation results show that the total error between the simulation model and reality was 0.39%, which indicates that the established VISSIM model error was within the acceptable range, and its accuracy was sufficient.

4.3. Calculation of operational measures

4.3.1. Selection of evaluation indices

Delay and queue length are the most common indices used by VISSIM to assess the traffic efficiency [84,85]. In addition, considering a more intuitive representation of the impact of traffic congestion on air quality, CO emissions were selected as an evaluation index in VISSIM. For safety performance, the surrogate safety assessment model (SSAM), a common tool, is used to identify vehicle trajectory conflicts in the TRJ file output from the simulation. The SSAM can output indices such as the number of collisions, TTC, PET, and CSI. TTC is defined as “the expected time for two vehicles to continue driving while maintaining the same speed and direction until the collision occurs at the collision point." PET is defined as the elapsed time between the departure of an encroaching vehicle and the actual arrival of a trailing vehicle at the same location’. Both TTC and PET are indices of collision propensity, and their smaller values indicate a higher probability of collisions or a higher probability of near-collision, which can reflect the number of conflicts. In addition, TTC and PET can only reflect the frequency of collisions but not the severity of conflicts. The research [60] found that turbo roundabouts were more serious collisions despite the lower probability of collisions. Therefore, the safety assessment must also introduce indicators that can reflect the severity of collisions. The CSI indices [63] can reflect the severity of potential collision conflicts based on the relationship between TTC and Maxdelta V. The larger the CSI index, the more serious the collision. The CSI is calculated according to Eq. (2). Therefore, TTC, PET, and CSI are selected as safety evaluation indices.

$$CSI=e^{-TTC}\left(\frac{1}{TTC+\frac{a}{\mathit{Max}DeltaV}}\right)$$ (2)

4.3.2. Simulation results

The collected traffic data were input into the calibrated conventional and improved models. The simulation results of the conventional five-way intersection and turbo improvement scheme are shown in Table 3.

Table 3.

Simulation results of four solutions.

	Qu(m)	Em(g)	De(s)	TTC	PET	CSI
Conventioanal roundabout	42.59	426	4.94	0.904	0.825	0.036
Turbo roundabout	41.36	368	3.6	1.055	0.998	0.023

Based on the simulation results, the turbo roundabout has less CO emissions and delays than the conventional scheme. The difference between the two schemes in terms of the queue length is not significant. However, the turbo roundabout outperforms the conventional scheme in terms of the TTC, PET, and CSI, which indicates that the probability of collision is lower and the accident severity is lower than that of the conventional scheme. Overall, under current traffic conditions, the turbo roundabout does not significantly improve the traffic efficiency, but it can effectively improve safety.

5. Sensitivity analysis based on VISSIM under different traffic scenarios

5.1. Determination of the sensitivity factors and establishment of different traffic scenarios

The congestion at intersections is mainly influenced by the traffic volume, while the actual data collected only consider the situation at conventional roundabouts during peak hours and do not reflect other traffic conditions. When the traffic volume increases, more vehicles approach the inner lane of the circle. For conventional roundabout intersections, the interweaving behavior of vehicles inside the circle lane increases, and the diverging and merging behavior increases; for turbo roundabout intersections, more vehicles are waiting to enter the inner ring before entering the ring, and the queues may become longer, which leads to more conflicts. In addition, the vehicle operation in a roundabout is mainly controlled by the circle lanes, and the diameter of the circle will affect the safety of the traffic. Therefore, traffic volume and circle diameter need to be selected as sensitivity factors to study the performance of roundabouts under different conditions.

Considering the limited capacity of the roundabout, according to the collected traffic data and capacity manual [86], when the design speed is 50 km/h, the corresponding maximum service traffic volume is taken as 500 veh/h/ln as the model input traffic volume. The traffic volume and circle diameter are taken as shown in Table 4.

Table 4.

VISSIM volume in the sensitivity analysis.

Item	Value
Volume (veh/h/ln)	100/150/200/250/300/350/400/450/500
Diameter(m)	40/45/50/55/60

In this paper, k is the kth group of traffic conditions, which takes values of 1–45. For example, k = 1 denotes 100 veh/h/ln × diameter of 40 m, k = 2 denotes100 veh/h/ln × diameter of 45 m, etc., up to k = 45, which denotes 500 veh/h/ln × diameter of 60 m.

5.2. Sensitivity analysis

The sensitivity analysis results of the six indices for different traffic volumes and circle diameters in Fig. 5 show the degree of improvement of each index for the turbo scheme compared to the conventional roundabout, where positive indicates improvement and negative indicates negative improvement.

Fig. 7(A) shows the degree of improvement in the maximum queue length of the turbo compared to the conventional scheme. When the traffic volume is high and the diameter is large, the turbo has a shorter maximum queue length than the conventional scheme, with a maximum improvement of 48.67%, due to the traffic organization of the turbo roundabout. The turbo roundabout requires vehicles with different turns to move ahead in the corresponding lanes, so certain lanes will have longer queue lengths due to the early queuing of vehicles.

Fig. 7.

Improvement ratio of USC compared with conventional solution: (A) Queue Length; (B)CO emissions; (C) Delay; (D) TTC; (E) PET; and (F) CSI.

Fig. 7(B) compares the turbo roundabout and conventional scheme in terms of the CO emissions. There are less CO emissions at the turbo roundabout than the conventional scheme in most cases, which indicates that vehicles stop less at the turbo roundabout and has a higher throughput than the conventional scheme in most cases.

Fig. 7(C) compares the delay indices. In most cases, the improvement of the turbo roundabout is better. When the traffic volume is small, the improvement of the turbo roundabout is not obvious, and there is even some negative improvement, reaching a minimum of −5.86%; however, when the traffic volume increases, the turbo roundabout significantly improves in the upper reaches of the delay and can reach a maximum of 85.06%.

Fig. 7(D) and (E) show the degree of improvement of the turbo roundabout for the TTC and PET indices. Overall, the turbo roundabout shows improvement for both indices: the TTC and PET index shows a greater improvement in most cases. However, when the diameter and traffic volume are small, the improvement is not significant, and even there is a negative improvement. In summary, the improvement in both TTC and PET of the turbo roundabout indicates that the turbo roundabout has lower probability of collision loading than the conventional roundabout, which proves that the turbo roundabout can reduce the safety risk.

Fig. 7(F) shows the degree of improvement in CSI index of the turbo compared to the conventional scheme. When the traffic volume and the diameter is large, the improvement of the turbo is higher, reaching a maximum of 57.33%; when the traffic volume and the diameter decreases, the turbo roundabout CSI gradually shows negative improvement, with a minimum of −23.61%.

However, in general, the improvement of the turbo roundabout CSI is better, and the negative improvement occurs in only a few cases. In summary, the turbo roundabout has lower crash severity than the conventional scheme in most cases, and the turbo roundabout may have higher crash severity than the conventional scheme when the diameter is smaller.

In terms of traffic efficiency, when traffic volumes are low and traffic circle diameters are small, turbo roundabouts produce longer queue lengths than the conventional scheme. But in most cases, the turbo roundabouts have more significant improvements in CO emissions and delays, especially when traffic pressure is high. For safety, turbo roundabouts have significant improvements in TTC and PET, which indicates that turbo roundabouts have a lower probability of accidents, while turbo roundabout improvements in CSI indices compared to the conventional scheme are both positive and negative, which indicates that under certain conditions, turbo roundabouts have higher accident severity than the conventional scheme, as shown in Table 5.

Table 5.

Improvement of the turbo roundabout compared with the conventional roundabout.

Indices	Minimum	Maximum	Average
Qu	−84.7%	48.67%	−0.087%
Em	−5.22%	53.62%	19.00%
De	−5.86%	85.06%	40.57%
TTC	2.32%	85.21%	29.03%
PET	10.15%	230.92%	33.99%
CSI	−15.66%	85.58%	37.93%

6. Traffic efficiency and analysis safety based on the factor analysis method

6.1. Simulation data processing

In the sensitivity analysis, the turbo roundabout and conventional scheme were analyzed in 45 traffic conditions, and six indices were selected. Here, the impacts on the traffic efficiency and safety performance of the turbo roundabout and conventional scheme under different traffic conditions with certain diameter conditions were analyzed.

The simulation results of the indices for 2 schemes under 5 diameters for all traffic conditions are summarized in A₁-A₅. For example, see Eq. (3).

$$A_k={\left[Q{u}_k,E{m}_k,D{e}_k,TT{C}_k,PE{T}_k,CS{I}_k\right]}^T$$ (3)

Among them, where matrix A_k is as shown in Eq. (4).

$$Q{u}_k=\left[Q{u}_1,Q{u}_2,Q{u}_j,\cdots ,Q{u}_{45}\right]$$ (4)

In the formula, k denotes 5 types of circle diameters, j denotes 45 types of traffic conditions, Qu is the queue length, Em is the CO emissions, De is the delay, and TTC, PET and CSI are the safety indices in the SSAM.

Denote all elements in A₁ by the matrix Y as shown in Eq. (5).

$$Y={\left[y_1,y_2,\cdots ,y_i,\cdots ,y_6\right]}^T$$ (5)

Where matrix y_i is as shown in Eq. (6)

$$y_i=\left[y_{i1},y_{i2},y_{i3},\cdots ,y_{i46}\right]$$ (6)

Here, i is the index serial number.

6.2. Factor analysis

Step 1

Data normalization process to ensure the uniformity of the indices, the indices must be normalized.

• (1)For the selected 6 indices, Qu, Em, De, TTC, PET, and CSI are numbered 1–6. Among these indices, larger vehicle number TTC and PET indices are better, and smaller Em, Qu, De, and CSI are better, so Qu, De, and CSI should be forwarded to the larger the better. The specific methods are as shown in Eq. (7).

$$y_{ij}^{\prime }=\max \left\{y_j\right\}-y_{ij},j=1,3,6$$ (7)

$${y_{ij}}^{″}=\frac{{y_{ij}}^{\prime }-\min \left\{{y_{1j}}^{\prime },\cdots ,{y_{4j}}^{\prime }\right\}}{\max \left\{{y_{1j}}^{\prime },\cdots ,{y_{4j}}^{\prime }\right\}-\min \left\{{y_{1j}}^{\prime },\cdots ,{y_{ij}}^{\prime }\right\}},i=1\text{to}6,j=1\text{to}45$$ (8)

Finally, we obtain ${y_{ij}}^{″}$.

Step 2

Prerequisite test. Before adopting factor analysis, it is necessary to verify whether the original variables are strongly correlated; if there is no strong correlation between the variables, the common factors cannot be reflected.

• 1)KMO test and Bartlett's sphericity test the main purpose of the KMO test is to test whether there is a strong correlation between indices. The test value is in [0,1]; a closer value to 1 indicates that there are more common factors between the variables and they are more suitable for the factor analysis. A value greater than 0.7 is generally considered suitable; when the test value is less than 0.5, it is not suitable for the factor analysis.
• (2)Different indices have different dimensions, and they must be converted into a uniform dimension to be compared. The absolute indices are converted into relative indices, so normalization is required. For ${\gamma }^{\prime }$, each element of which is represented by ${y_{ij}}^{\prime }$, each individual result ${y_{ij}}^{\prime }$ is normalized using Eq (8).

Bartlett's sphericity test is used to test whether the correlation matrix of indices is the unit matrix, i.e., to test whether the indices are independent of one another; a higher correlation between the indices is more suitable for the factor analysis.

Bartlett's spherical test is used to test whether the correlation between the variables in the correlation matrix is a unit matrix to test whether each variable is independent of each other. If the variables are independent of one another, the common factor cannot be extracted from them, and the factor analysis cannot be applied. Bartlett's spherical test determines that if the correlation matrix is a unit matrix, then the variables are independent and the factor analysis is invalid. When significance <0.05, the variables are correlated, and the factor analysis is valid.

The results of the KMO test and Bartlett's sphericity test for the 2 schemes at 5 diameters are shown in Table 6.

Table 6.

Results of the KMO and Bartlett's sphericity test.

	Diameter of circle	D = 40 m	D = 45 m	D = 50 m	D = 55 m	D = 60 m
KMO test	Value	0.578	0.569	0.634	0.577	0.642
Bartlett's sphericity test	Approximate ${\chi }^2$	137.561	146.58	128.242	115.785	112.839
	Degree of freedom	15	15	15	15	15
	Significance	0.00	0.00	0.00	0.00	0.00

Based on the test results, the 6 indices can be used for the factor analysis.

Step 3

Factor extraction and factor loading solving.

The factors were extracted, and the factor loadings were solved according to the principal component analysis. The cumulative variance contributions of the factors and the gravel plot were obtained as shown in Table 7, Table 8, Table 9, Table 10, Table 11.

Table 7.

Results of the KMO and Bartlett's sphericity test (D = 40 m).

Explanation of the total variance (D = 40 m)
	Initial Eigenvalue			Extraction of the sum of squares of loads			Sum of squared rotating loads
Ingred-ients	Total	Percentage of variance	Cumulative	Total	Percentage of variance	Cumulative	Total	Percentage of variance	Cumulative
1	3.44	57.332	57.332	3.44	57.332	57.332	3.083	51.386	51.386
2	1.966	32.772	90.104	1.966	32.772	90.104	2.323	38.718	90.104
3	0.369	6.146	96.251
4	0.191	3.176	99.427
5	0.03	0.503	99.929
6	0.004	0.071	100

Table 8.

Results of the KMO and Bartlett's sphericity test (D = 45 m).

Explanation of the total variance (D = 45 m)
	Initial Eigenvalue			Extraction of the sum of squares of loads			Sum of squared rotating loads
Ingred-ients	Total	Percentage of variance	Cumulative	Total	Percentage of variance	Cumulative	Total	Percentage of variance	Cumulative
1	3.871	55.294	55.294	3.871	55.294	55.294	3.108	44.405	44.405
2	2.103	30.039	85.333	2.103	30.039	85.333	2.865	40.928	85.333
3	0.572	8.173	93.506
4	0.235	3.359	96.864
5	0.182	2.603	99.467
6	0.004	0.053	100

Table 9.

Results of the KMO and Bartlett's sphericity test (D = 50 m).

Explanation of the total variance (D = 50 m)
	Initial Eigenvalue			Extraction of the sum of squares of loads			Sum of squared rotating loads
Ingred-ients	Total	Percentage of variance	Cumulative	Total	Percentage of variance	Cumulative	Total	Percentage of variance	Cumulative
1	3.177	52.956	52.956	3.177	52.956	52.956	2.891	48.187	48.187
2	2.247	37.445	90.401	2.247	37.445	90.401	2.533	42.214	90.401
3	0.306	5.105	95.506
4	0.228	3.793	99.299
5	0.035	0.590	99.889
6	0.007	0.111	100

Table 10.

Results of the KMO and Bartlett's sphericity test (D = 55 m).

Explanation of the total variance (D = 55 m)
	Initial Eigenvalue			Extraction of the sum of squares of loads			Sum of squared rotating loads
Ingred-ients	Total	Percentage of variance	Cumulative	Total	Percentage of variance	Cumulative	Total	Percentage of variance	Cumulative
1	3.892	64.866	64.866	3.892	64.866	64.866	2.630	43.831	43.831
2	1.243	20.713	85.579	1.243	20.713	85.579	2.505	41.748	85.579
3	0.499	8.316	93.895
4	0.303	5.054	98.949
5	0.056	0.937	99.886
6	0.007	0.114	100

Table 11.

Results of the KMO and Bartlett's sphericity test (D = 60 m).

Explanation of the total variance (D = 60 m)
	Initial Eigenvalue			Extraction of the sum of squares of loads			Sum of squared rotating loads
Ingred-ients	Total	Percentage of variance	Cumulative	Total	Percentage of variance	Cumulative	Total	Percentage of variance	Cumulative
1	3.786	63.097	63.097	3.786	63.097	63.097	2.699	44.981	44.981
2	1.489	24.809	87.906	1.489	24.809	87.906	2.575	42.925	87.906
3	0.421	7.016	94.922
4	0.245	4.078	99
5	0.047	0.79	99.79
6	0.013	0.21	100

Based on the contribution of the factors to the explanation of the variables and the factor loading plots, among the 5 diameters, 2 common factors can explain 85–90% of the information of the 6 indices; in other words, the 6 indices can be simply grouped into 2 categories.

Step 4

Factor Rotation. When the common factors among the indices are identified, the elements of each row of the factor loading matrix are not large (because the sum of squares is less than 1) but are generally balanced and difficult to interpret; to make the factors more interpretable, they must be rotated, and the initial factors are linearly combined.

In this paper, we use the maximum variance method for factor rotation.

Therefore, the component matrix after factor rotation is shown in Table 12.

Table 12.

Component matrix after the rotation.

Component matrix after the rotation
Diameter	D = 40 m		D = 45 m		D = 50 m		D = 55 m		D = 60 m
Ingredients	1	2	1	2	1	2	1	2	1	2
Qu	−0.091	0.935	−0.126	0.918	−0.059	0.905	−0.122	0.911	−0.514	0.78
Em	0.084	0.906	0.065	0.902	0.055	0.902	−0.203	0.871	−0.153	0.979
De	−0.529	0.719	−0.291	0.914	−0.214	0.914	−0.451	0.82	0.066	0.902
TTC	0.97	−0.234	0.818	−0.508	0.958	−0.246	0.838	−0.435	0.909	−0.145
PET	0.976	−0.173	0.985	−0.054	0.992	−0.043	0.978	−0.166	0.917	−0.053
CSI	0.946	−0.163	0.898	−0.155	0.968	−0.051	0.843	0.163	0.86	−0.414

After performing the factor rotation, when the diameter of the loop is certain, the 6 indices can be represented by 2 common factors. Factor 1 contains TTC, PET, and CSI, and factor 2 contains queue length, delay, and the CO emissions. The 2 factors represent the traffic safety performance and efficiency of a roundabout, respectively, which indicates a certain correlation among the three traffic efficiency indices of the queue, delay and CO emissions and among the three safety indices of TTC, PET, and CSI. While the two categories of traffic efficiency indices and safety performance indices have a different correlation with each other, the six indices can be grouped into two categories by analyzing the laws of simulation results through objective data.

Step 5

Factor score. After the factor rotation, the factor scores were calculated using regression methods by Eq. (9).

$$S={\alpha }^{\prime }{R}^{-1}{Y}^{″}$$ (9)

Component conversion matrices and total factor scores of the 2 scenarios for each traffic condition at 5 circle diameters are shown in Fig. 8, Fig. 9.

Fig. 8.

Factor score between efficiency and safety in the conventional roundabout: (A) D = 40 m; (B) D = 45 m; (C) D = 50 m; (D) D = 55 m; and (E) D = 60 m.

Fig. 9.

Factor score between efficiency and safety in the turbo roundabout: (A) D = 40 m; (B) D = 45 m; (C) D = 50 m; (D) D = 55 m; and (E) D = 60 m.

From Fig. 8, Fig. 9, with the traffic volume increasing from low to high, the importance of the traffic efficiency of each scheme gradually changes from low to high, the trend of the safety performance changes from high to low, and the two categories of indices have opposite trends. It shows that.

• 1.When the traffic volume is low, most of the vehicles are in the free flow state, the vehicle speed is fast, the vehicle interference is small, and the difference in traffic efficiency among different programs is not significant, so the relative influence of safety performance has a greater proportion.
• 2.When the traffic volume is high, most of the vehicles are in the free flow state to the congested flow state or even the saturated flow state, and the improvement of the efficiency of the scheme is more important to improve the performance of the scheme.
• 3.When the two curves of traffic efficiency and safety intersect, i.e., balance is reached, the scheme is more balanced at this time. Fig. 9 shows that the turbo roundabout corresponds to a larger traffic volume at the balance point compared with the conventional scheme, which implies that the turbo roundabout has a greater capacity to ensure the balance of scheme efficiency and safety, which indicates the advantages of the turbo roundabout.

6.3. Comprehensive evaluation of the scheme

According to the process of factor analysis in the previous section, to intuitively obtain the combined performance of the conventional scenario and turbo roundabout under each traffic condition, the comprehensive score for each scheme is obtained using the factor scores and sum of squared rotated loadings based on the factor analysis, as shown in Eq. (10).

$$S_{scheme}=\sum _i^l\sum _i{S}_i{V}_i$$ (10)

l is the number of common factors, and i is the ith factor.

The scheme scores of the conventional roundabout and turbo scheme in each case are shown in Fig. 10.

Fig. 10.

Plan score between the conventional roundabout and turbo roundabout: (A) D = 40 m; (B) D = 45 m; (C) D = 50 m; (D) D = 55 m; and (E) D = 60 m.

From Fig. 10, the turbo roundabout has a higher overall score than the conventional intersection under all traffic conditions for all five diameters, which indicates that the turbo roundabout performs better than the conventional scheme overall when considering the traffic efficiency and safety of the scheme.

7. Discussion

The original hypothesis of this study is that turbo roundabouts are superior to conventional roundabouts in terms of operational efficiency and safety, and that factor analysis method can effectively simplify and reflect the relationship among multiple evaluation indicators.

In this section, we will further explain and infer the results of the applicability and superiority of the turbo roundabout planar intersection strategy at a five-leg intersection, and the comprehensive evaluation of the two schemes using factor analysis method, and compare or criticize them with relevant literature or theory. We will also explain the scope and limitations of this study, and use them to define and emphasize the scope of application of this study's findings. Finally, we will discuss the applicability of this study's results in a larger field, and the suggestions for future research and practical application.

We found that turbo roundabouts have no advantages compared with conventional scheme at low traffic flows, while under high traffic flow, turbo roundabouts' operational efficiency is significantly improved. This result is similar to the results of the Italian researchers [17] and other literature, that is, in five-leg intersections, turbo roundabouts are still not very suitable for low traffic flow, as in four-leg intersections. This may be because under low traffic flow, conventional roundabouts can provide more lane choices and larger capacity, while turbo roundabouts limit the vehicle's travel path and speed. This also shows that the turbo roundabout planar intersection strategy is not a universal solution, but needs to be selected or optimized according to the actual situation.

Then we found that in terms of safety, turbo roundabouts are superior to conventional roundabouts in indicators such as TTC, PET, etc., and the number of conflict points is significantly reduced. This result is consistent with an Italian study [17] and other literature, confirming the safety advantages of turbo roundabouts. This is mainly due to the design features of turbo roundabouts, that is, by setting mandatory lane change lines and islands, reducing lane changes and conflict points, reducing vehicle interference and collision risk.

This also shows that the turbo roundabout planar intersection strategy can effectively improve traffic safety and reduce traffic accidents. This is consistent with the safety principles of the turbo roundabout planar intersection strategy proposed by Fortuijn, L.G [87]. They pointed out that the turbo roundabout planar intersection strategy can significantly improve vehicle safety by separating traffic flow, simplifying process, reducing speed, increasing visibility and other ways. Finally, we used factor analysis method to extract two common factors representing traffic efficiency and safety respectively, and calculated the comprehensive evaluation scores of the two schemes under different scenarios. The results show that under different traffic scenarios, turbo roundabouts have higher comprehensive evaluation scores than conventional roundabouts. And compared with the traditional scheme, the turbo roundabout has a larger traffic volume corresponding to the balance point, which means that the turbo roundabout has a larger capacity to ensure the balance of scheme efficiency and safety. This result also supports our hypothesis and answers our question about the applicability and superiority of turbo roundabouts at five-leg intersections.

Next we will explain the scope and limitations of this study and use them to define and emphasize the scope of application of this study's findings. The scope and limitations of this study mainly include the following points.

• 1.This study only selected one typical five-leg intersection as a case study which may not represent all characteristics and situations of five-leg intersections. Therefore, there may be some limitations to this study's results which cannot be directly generalized to other types or sizes of intersections.
• 2.This study only considered two schemes' operational efficiency and safety under different traffic flows and ring diameters without considering other factors that may affect intersection performance such as vehicle composition driving behavior signal control etc. Therefore, there may be some biases in this study's results which may not fully reflect reality.
• 3.This study used VISSIM software for simulation analysis although it has been calibrated and validated there are still some errors and uncertainties. Therefore, there may be some error ranges in this study's results which cannot be completely equivalent to actual data.

8. Conclusion

This paper uses the turbo roundabout to improve the conventional scheme. And factor analysis method (FAM) is used to explore the influence relationship between two types of indicators, efficiency and safety of the roundabout. The principal component extraction method is used to extract the common factors of six indicators; then the factors are rotated to make them more expressive and the final factor scores and scheme scores are calculated. The results show that.

• 1.As the traffic volume increases, the trend of the degree of influence of efficiency changes in the opposite direction to that of safety. The turbo roundabouts generally perform better than conventional roundabouts under most traffic volume conditions, especially in high traffic situations, which can effectively improve traffic efficiency and safety performance.
• 2.The turbo roundabout in the equilibrium state can satisfy the higher traffic, which indicates that the turbo roundabout has a higher capacity than the conventional scheme.
• 3.The calculated scores of the schemes using the factor scores show that the turbo roundabout has higher comprehensive scores than the conventional scheme under each traffic condition, which indicates the better overall suitability of the turbo roundabout.
• 4.The results of this study confirm the applicability of the turbo-roundabout planar intersection strategy in five-way intersections. This strategy can provide better operational efficiency and safety for complex five-way intersections with high traffic volume, high speed, multi-lane, and multi-direction, thus improving the smoothness and reliability of urban traffic.
• 5.The results of this study validate the effectiveness of factor analysis method in the design and optimization of the turbo roundabout. Through this method, the balance point between traffic efficiency and safety of roundabout intersections can be found, which can guide the design and optimization of roundabout intersections.

Funding

This work was supported by Natural Science Basic Research Program of Shaanxi (Program No. 2023-JC-QN-0560), Scientific Research Program Funded by Shaanxi Provincial Education Department (Program No. 21JK0908).

Data availability statement

Data included in article/supp. material/referenced in article.

CRediT authorship contribution statement

Qinghua He: Conceptualization, Formal analysis, Investigation, Methodology, Visualization, Writing – original draft, Writing – review & editing. Yuanying Meng: Formal analysis, Methodology, Writing – review & editing. Wang Tan: Formal analysis, Methodology. Xin Tian: Conceptualization, Formal analysis, Software, Writing – review & editing. Shangru Liu: Conceptualization, Investigation, Software, Visualization, Writing – review & editing. Hang Yang: Investigation, Software. Yang Shao: Project administration. Binghong Pan: Conceptualization, Funding acquisition.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.