1. Introduction
Left-turning maneuvers are considered one of the most hazardous traffic maneuvers, since turning vehicles have to cross in front of the oncoming through traffic [
1,
2]. Left-turn design at intersections in urban areas has long been considered a dilemma. Providing left signal control for left-turning vehicles increases the delay [
3], while not doing so increases conflicts between the left-turning vehicles and the through traffic in the opposite direction [
4,
5]. To eliminate this problem, many alternative solutions have been proposed to improve the performance of intersections with left-turning vehicles. Examples include signal timing estimation [
6,
7], exclusive left lane design [
8] and state-of-the-art technology like pilotless automobiles [
9]. Among all these solutions, facility design remains an important approach to existing problems.
During the past few decades, various left-turn designs have been used on urban intersections to reduce problems accompanying direct left-turn (DLT) vehicles. The difficulty of completing this movement is evident in crash statistics, indicating that 45% of all crashes that occur at intersections throughout the United States involve left-turning vehicles, even though left-turning movements represent a disproportionately small percentage (10–15%) of all approaching traffic [
10,
11]. DLT vehicle movements from arterial streets or collector roads are prohibited by using non-crossing median and/or directional median openings. Left-turning vehicles will be guided to detour downstream to U-turn locations instead of a left turn. Superstreet intersections, crossover displaced left turn intersections, and upstream signalized crossover schemes are common median U-turn intersection designs [
12,
13,
14]. Left-turn vehicles also cause pedestrian-vehicle conflicts [
15]. Previous research and studies of U-turn designs have proven they have an exclusive role in reducing travel time, delay, and traffic conflicts and in improving safety at intersection areas [
16,
17,
18]. The only restriction of U-turns is the requirement for a large median width, which limits its application.
Channelization, an exclusive left-turn lane, is popularly implemented for left-turn problems. The set of left-turn lanes depends on the ratio of left-turn vehicles [
19,
20]. Displaced left-turn intersections that resolve the conflict between left-turn and opposing-through movements at the pre-signal are probably the most extensively used innovative intersection designs [
21]. Left-turn lanes appear to contribute to crashes without accounting for endogeneity [
22], and a left-turn waiting area could increase the capacity at intersections [
23].
Signalization is another popular way to reduce junction traffic conflict. A separate turn phase is often used on the approach leg to an intersections with heavy left turns [
24,
25]. The most common identified guidance for protected left-turn phases is to use a threshold based on the cross-product of left-turn volume and opposing through movement [
26]. A left-turn lane with signal control could improve the operational performance of left-turn movement at signalized intersections in China [
27,
28]. Stop-controlled intersections have a strong association between high crash risk and high traffic speed, especially for older female drivers [
29].
Some cutting-edge technologies also pay attention to left-turn problems. Augmented reality (AR) technology can offer a very realistic environment for enhancing driver reaction to different road design and traffic operations scenarios [
30]. The optic technique uses an optical combiner for combining real and virtual objects, and the video technique uses a computer or a video mixer to combine the video of the real world, from video cameras, with virtual images (computer-generated) [
31]. Head-up display (HUD) devices that are gradually being popularized in automobiles have helped drivers better process traffic information and have reduced traffic accidents in recent years [
32,
33]. Head-mounted display (HMD) devices, e.g., Microsoft Hololens, is another tool with huge potential for intelligent transportation technology for reducing traffic problems in the future [
34,
35].
In addition to turning conflicts, some researchers have also studied the relationship between vehicle emissions and traffic delay in urban areas [
36,
37]. In China, a total of 56 large and medium-sized cities, including 17 provincial capitals, have adopted vehicle restriction policies due to traffic congestion, vehicle energy conservation and emission reduction, which covers the majority of developed cities in China. In the meantime, the policies are various in restrict scopes and guidelines as in
Table 1, which not only causes inconvenience to local residents, but also causes great trouble to vehicles from other cities [
38]. Traffic delay and emissions have a strong connection, which means that reducing delay could reduce emissions [
39,
40,
41]. Different route selections and stop strategies could reduce bus emissions [
42]. Vehicle gap changes could also affect fuel and emission performance [
43].
As China’s urbanization continues, vehicle ownership, including the above-mentioned restricted cities, is still growing. In addition, traffic congestion and vehicle exhaust pollution may still intensify [
44]. The restriction scope is larger and larger and more cities are joining in the vehicle restriction policy movement while the restriction policies have been proved to be ineffective for diminishing traffic problems and congestion [
45]. It is necessary to tap the potential of existing road traffic facilities and traffic management as much as possible and try to use technical methods instead of administrative polices. While numerous guidelines for the selection of left-turn phasing have been developed, there is no widely recognized guideline or criterion for the use of left-turn phasing under specific traffic conditions [
46]. In this study, an exclusive left-turn lane (ELTL) design for no-signal intersections on the way without a median is proposed to diminish left-turn conflict and delay. To reach that goal, two strategies are used. The first is channelization, an exclusive left-turn lane with stop sign control, named plan 2 in the following. The second is signalization, an exclusive left-turn lane with signal light control, named plan 3 in the following. The present situation, without an exclusive left-turn lane, named plan 1, was also evaluated for comparison. It could be easily predicted that both methods could reduce delay and emissions, but how to select a proper method for a certain intersection remains a problem.
The primary objective of this study is evaluation of the entropy evaluation method (EEM) based on selection of the three situations, for which it is very easy to determine the priority level and reconstruction method for large scale intersections, and making the traffic flow more smoothly to achieve vehicle energy conservation and emissions reduction, and to use the restriction policy instead. The travel time, delay, number of stops, number of vehicles, CO emissions, and fuel consumption are evaluated for various traffic situations. The EEM is widely used in evaluating and calculating plans of multiple elements, such as physics [
47], information [
48], medical science [
49,
50], business [
51], environment [
52], statistics [
53], finance [
54] and other interdisciplinary subjects [
55,
56]. This is the first time to introduce EEM into transportation evaluation, which could judge the plans synthetically instead of several indexes separately. The rest of this article is organized as follows:
Section 2 contains a problem statement and
Section 3 details the design schemes.
Section 3 includes data collection, VISSIM simulation calibration, and sensitivity analysis. In
Section 4, we discuss the EEM method calculation process and verify the validity of the EEM. Conclusions are drawn in
Section 5, see
Figure 1.
4. Results
Under every arterial and collector volume combination, every index result in the VISSIM simulation was separately with six flows individually. In addition, the six flow results are taken together to obtain the node result corresponding to the volume combination. The calculation is as follows:
where
X denotes the following six indexes: travel time, delay, number of stops, number of vehicles, CO emissions, and fuel consumption.
means that both plans 2 and 3 could improve the operating situation, but the improvement ratio has a difference. How to choose a suitable plan for many intersections on road S107 mentioned earlier remains a problem. The EEM was used to calculate the different weights of the six indexes and obtain the final result matrix of plan selection under different traffic volume combinations.
Each plan has six indexes and each index has 45 values. First, we convert the plan-3 result into one matrix. For example,
is a 45*1 column vector and represents the travel time of plan 1.
T is a 45*3 matrix as follows:
The remaining five indexes underwent the same process:
where
denote the sum of the results of all three plans.
, etc. denotes the simulation result of each plan.
Second, from each 45*3 matrix, we select the minimum value of each row and output the column number of the minimum value of each row; forty-five column numbers can be obtained and a new matrix named
generated.
denotes which plan has the best performance under the same traffic volume combination:
All six matrixes of Equation (
11) should be calculated as
where
denotes the minimum value of each row of travel time. The remaining five parameters denote the same.
The third step is to calculate the weight of the six indexes and put all six indexes into a single matrix
Y:
Calculating the weight of six indexes is the fourth step, so that one obtains a scientific method to choose a suitable plan from the three plans.
In information theory, entropy is a measure of uncertainty. The more information there is, the less uncertainty and less entropy there is. According to the characteristics of entropy, we can judge the randomness and disorder degree of a scheme by calculating the entropy value, and we can also judge the dispersion degree of an index by using the entropy value. The greater the dispersion degree of the index, the greater the influence of the index on the comprehensive evaluation. Therefore, the weight of each index can be calculated according to the variation degree of each index by using the tool of information entropy, which provides a basis for the comprehensive evaluation of multiple indexes.
The EEM is an objective weighting method that determines the weight of indicators according to the information provided by the observed values of various indicators. In this article, the data matrix Equation (
14) is
. For an index
, the greater the gap between the index
, the greater the role of the index in the comprehensive evaluation. If all the index values of an index are equal, the index has no effect in the comprehensive evaluation.
Normalization of indicators: heterogeneous indicators are homogeneous. Since the measurement units of various indicators are not uniform, they should be standardized before the comprehensive indicators are calculated with them; that is, the absolute value of the indicators is converted into a relative value, and
, so as to solve the problem of homogenization of different qualitative indicators. Moreover, due to the different meanings represented by positive and negative index values (the higher the positive index value is, the better; the lower the negative index value is, the better), we use different algorithms for data standardization processing for high and low indexes. The specific methods are as follows:
Calculate the weight of index
j of plan
i:
Calculate the entropy value of the index
j:
where
and satisfies
.
Calculate the entropy redundancy:
Calculate the weight of each index:
The weights of the six indexes are shown in
Table 6.
The matrix
Y denotes the plan number corresponding to the optimal value of each index under every traffic volume combination. A matrix
is generated as
where
represents weight in
Table 6. In matrix
Y (Equation (
14)), every row is the different plan numbers of six indexes under every volume combination. For example, the first row of matrix
Y is
From Equation (
21), it is shown that the first row of matrix
Y only has the option of plans 2 and 1. Plan 3 did not obtain the best value under this situation. Multiplying the corresponding terms in Equation (
21) and
Table 6, the weight of plan 2 in
is
The weight of plan 1 in
is
The first row of matrix
A is
In matrix A, each column represents plans 1, 2, and 3. The results in every row of matrix A denote the different weights of plans under corresponding volume combinations. Because , plan 1 is the final choice of the first row in matrix Y, which is the first volume combination, i.e., arterial volume 686 veh/h and collector volume 100 veh/h.
Based on Equations (
20)–(
24), we generate a matrix
T to save the final selected plan number of each row:
Matrix
T contains 45 plan numbers, which are the final choices of all volume combinations. Transposing matrix
T into a
matrix, we obtain the results plotted in
Figure 9.
Figure 9 shows the final plan choice under all 45 volume combinations. Plan 1 appeared on both sides when the arterial volume ranged from 686–1026 veh/h to 2401–3430 veh/h on the horizontal axis. When arterial volumes were 686 and 3430 veh/h, plan 1 occupied three blocks; when the arterial volumes were 2401 and 3087 veh/h, plan 1 occupied two blocks; and when the arterial volumes were 1026 and 2744 veh/h, plan 1 only showed in one block. From the vertical axis (the collector volume), plan 1 appeared three times when the collector volumes were 100, 300, and 400 veh/h, and twice and once when the collector volumes were 200 and 500 veh/h, respectively.
Plan 2 in
Figure 9 was distributed mainly in left and central parts. Plans 2 and 1 were interspersed in the columns of arterial volumes of 686 and 1026 veh/h. All 15 blocks between 1372 and 2058 veh/h shown in blue represent that plan 2 is the best choice in this large range. Plan 2 was distributed sporadically when arterial volumes were larger than 2401 veh/h. Plan 2 could be mainly used under 2058 veh/h, and especially between 1372–2058 veh/h.
Plan 3 in
Figure 9 appeared centrally and only occupied eight blocks in the entire scale. When arterial volumes were less than 2058 veh/h, plans 2 and 1 performed better than plan 3. Plan 3, signal control, could be useful when both arterial and collector volumes are large.
Collector street volume also has some influence on plan performance, especially arterial volumes larger than 2401 veh/h. This means that the plan choice was based mainly on arterial street volume, but, when arterial volumes were larger than 2401 veh/h, the plan choice depends on collector street volume.
Based on
Figure 9, we selected the corresponding index values and compared the improvement ratio with the present situation (plan 1), and the results are shown in
Figure 10.
Figure 10a denotes travel time based on
Figure 9. Travel time was reduced obviously over the entire range, except for an arterial volume of 3430 veh/h. In the range of arterial volumes 1372–2744 veh/h, travel time was generally reduced by 25% and reached a peak value of 45% at 2744 veh/h. Compared to
Figure 7a and
Figure 8a,
Figure 10a has two peak values that combine two advanced parts.
Figure 10b shows delay based on
Figure 9. This figure avoids the negative change of
Figure 8a when arterial volume was less than 1372 veh/h, from almost −300% increased to −25% at most, which is a great improvement.
Number of stops is shown in
Figure 10c, and
Figure 10b avoided the negative change of
Figure 7c and
Figure 8c. The majority situations of the entire scale improved, except for an arterial volume of 3430 veh/h and a collector volume of 200 veh/h.
Number of vehicles has a strong decreasing trend over the entire range in
Figure 7d and
Figure 8d. With the EEM calculation, the strong trend has a more significant change than before. The original reduced area has four peak values, which is significant progress.
Figure 10e,f denote CO emissions and fuel consumption, and they exhibit the same trend. Both indexes were reduced by up to 20% when arterial volumes was less than 2058 veh/h, and then increased after that. The increase of CO emissions and fuel consumption could not be avoided because of the large volume of vehicles. When the main indexes of travel time and delay increased, CO emissions and fuel consumption also increased.
In general, with the EEM calculation, the final plan choice could make the traffic operation smoother and maximize traffic capacity, thus avoiding the single reconstruction plan disadvantages and showing an easy number matrix for traffic management departments to choose a suitable plan for different intersections. With the EEM, travel time, delay and number of stops could reduce obviously 70% at most, CO emissions and fuel consumption are also reduced up to 20%, which is a great improvement with traffic volume reduced gently.
The length of the simulation road in VISSIM is 630 m. The total length of the real road in
Figure 2 is 84.3 km with 87 uncontrolled T-intersections. If all 87 T-intersections will be reconstructed by EEM, the optimized segment length will reach 630 × 87 = 54,810 m = 54.8 km, which accounts for 65% of the whole road. The improvement of six indexes for one single T-intersection with EEM is shown in
Figure 9. For the whole road, the maximum optimization of six indexes, travel time, delay, number of stops, number of vehicles, CO emissions and fuel consumption could reach 29%, 45%, 45%, 26%, 13% and 13%, respectively. This degree of optimization is significant, and, even if the optimization method in this paper only works in half of the cases, the reduction is still huge. This is a great optimization result. In comparison, the automatic start-stop technology popularized by vehicles in recent years can save fuel by 3–10% [
82,
83]. The research method in this paper can achieve the same fuel saving level as automatic start-stop, which is very significant for the whole society to save energy and reduce emissions.
Verifying the Validity of the EEM
The collected data could be used to verify the validity of the EEM. The collected real traffic data are presented in
Table 4, showing that the arterial volume is 2040 veh/h in two directions and the collector street volume is 200 veh/h. From the matrix in
Figure 9, the EEM result shows that plan 2 is the best choice under this volume combination. The three plans are compared below.
The comparison of the three plans with the collected data from
Table 4 are shown in
Figure 11. Plans 2 and 3 had an obviously better performance than plan 1 on travel time, delay, and number of stops. In addition, plans 2 and 3 were very similar and without obvious differences in these three indexes. For number of vehicles, plan 2 > plan 3 > plan 1. For CO emissions and fuel consumption, they had that same relation, namely that plan 3 > plan 1 > plan 2. Therefore, it is very easy to find that plan 2 was the best option of the three plans with collected data and exhibited the same result shown in
Figure 9, which verifies that the plan choice made using the EEM is reliable.
5. Conclusions
China is in the rapid development stage of urbanization, with the rapid increase of urban population and continuous growth of vehicles, traffic congestion and air pollution becoming increasingly serious. The main measurement is vehicle restriction policy, forbidden nonlocal vehicles and restricted use of local vehicles, for the majority of Chinese cities to reduce traffic congestion and emissions. The administrative rule is simple and crude, which will have a negative impact on citizens’ travel and regional economic development. Tapping the potential of the existing road network, especially the low-cost reconstruction method of existing roads, is essential to improve traffic condition, and reduce congestion and air pollution.
At present, having no median strip or waiting area at intersections has a strong negative effect on, and poses a safety hazard for, passing traffic flows. In this study, two improved schemes, channelization and signalization, were both compared with the present situation. A VISSIM simulation model was developed and calibrated to evaluate the present features, and the channelization and signalization were also evaluated for comparison. Six indexes—travel time, delay, number of stops, number of vehicles, CO emissions, and fuel consumption—were used to evaluate the three plans.
The results show that the three plans have the best performance under different situations on T-intersections. Plan 1, the present situation, could be used for low arterial volumes, e.g., 686 veh/h. Plan 2, channelization, could be mainly used when arterial volumes are between 1372 and 2058 veh/h. Plan 3, signalization, only appeared in the area when arterial volumes were larger than 2401 veh/h, but all three plans were mixed in this section. All three plans could not solve the traffic problem when the arterial volume was 3430 veh/h, which corresponds to service level E in [
59], as all six indexes were seriously deteriorated.
The calculation in this paper is only for one intersection, if a city as large as Xi’an could use this method in the whole city. It will be significant to reduce the driving interference of vehicles at intersections, acceleration and deceleration distance, number of stops and exhaust emissions. The EEM method in this study is simple and clear for engineers to learn and apply. These findings can be utilized as a guideline for traffic police departments and road designers to determine when, where, and how the different plans should be used, and which intersection has the priority in reconstruction. This is also an attempt to use a technical method instead of administrative vehicle restriction policy for reducing traffic congestion and emissions. Before the method is used in the future, some issues should be studied first. First, an exclusive right-turn lane can also be designed for the two right-turning flows to isolate the influence of the other flows. Second, this study only covers a three-direction T-junction, so how the EEM should be used and implemented for a four-direction junction also needs further study. The authors recommend that future studies focus on these issues.