Many intersections around the world are irregular crossings where the approach and exit lanes are offset or the two roads cross at oblique angles. These irregular intersections often confuse drivers and greatly affect operational efficiency. Although guideline markings are recommended in many design manuals and codes on traffic signs and markings to address these problems, the effectiveness and application conditions are ambiguous. The research goal was to analyze the impact of guideline markings on the saturation flow rate at signalized intersections. An adjustment estimation model was established based on field data collected at 33 intersections in Shanghai, China. The proposed model was validated using a before–after case study. The underlying reasons for the impact of intersection guideline markings on the saturation flow rate are discussed. The results reveal that the improvement in the saturation flow rate obtained from painting guide line markings is positively correlated with the number of traffic lanes, offset of through movement, and turning angle of left-turns. On average, improvements of 7.0% and 10.3% can be obtained for through and left-turn movements, respectively.
An intersection is a key point in addressing traffic problems in an urban road network [
Irregular intersections and guidelines.
Offset crossing
Oblique angled crossing
Guide line markings
There are two common methods to solve these problems: intersection design and standardization of cross-road intersections and traffic channelization measures such as the traffic signs and markings shown in Figure
Although intersection guideline markings are recommended in many design manuals and codes on traffic signs and markings [
The saturation flow rate is the basic metric used to determine the efficacy of intersection traffic design. It is an important input parameter, particularly with regard to signal timing and the evaluation of the operational efficiency of signalized intersections. In addition, saturation flow rate reflects the operational efficiency of vehicles and is the basis for calculating the capacity of signalized intersections.
To calculate the saturation flow rate more accurately, factors such as intersection geometry, traffic conditions, and signal control are taken into account to modify the basic saturation flow rate. Many countries formulate their Highway Capacity Manuals according to their particular circumstances, which result in different saturation flow rate adjustment factors. For example, the HCM2010 (Highway Capacity Manual 2010) [
With respect to geometric factors, Susilo et al. derived a modification of the saturation flow formula by taking into account different widths of approach lanes [
With respect to traffic factors, Washburn et al. focused on the effects of trucks on queue discharge characteristics and established passenger car equivalency values for different truck sizes [
With respect to signal control factors, Radhakrishnan et al. highlighted the effect of vehicle type, lateral position on the roadway, and green time on the discharge headway. They proposed a discharge headway model which could be used to acquire saturation flow rates and capacity at signalized intersections [
Numerous studies have been performed with the primary objective of determining the factors that influence saturation flow rates at signalized intersections. However, few previously published reports have addressed the impact of guide line markings.
The research goal was to analyze the impact of guide line markings on the saturation flow rate at signalized intersections. An adjustment estimation model was established based on field data collected at 33 intersections in Shanghai, China. The model considered the traffic flow direction, number of traffic lanes, offset of through movement, and the turning angle of the left-turns. The proposed model was validated based on a before–after case study. The reasons for the impact of intersection guideline markings on the saturation flow rate are also discussed.
To analyze the impact of intersection guideline markings on saturation flow rate, control groups were established considering traffic flow direction, number of lanes, offset for through movement, and turning angle for left-turns. Based on these control groups, 33 intersections in downtown Shanghai were surveyed.
The impact of intersection guideline markings on saturation flow rate could be affected by many factors. The following factors were considered:
(1) Traffic Flow Direction. At a signalized intersection, traffic flows in different directions have different saturation flow rates. Through movement and left-turn flows were taken into account.
(2) Number of Traffic Lanes. This study focused on three categories, namely, one, two, and three traffic lanes for through movement and left-turns.
(3) Through Movement Offset. Approach and exit lanes that are offset for through movement can make it difficult for drivers to judge the position of exit lanes. Comparing the difference in saturation flow rate between intersections with and without guideline markings under the same through movement offset is beneficial for determining the application conditions of intersection guide line markings. As shown in Figure
Through movement offset categories.
Small offset
Medium offset
Large offset
(4) Left-Turn Angle. The left-turn angle size greatly affects the driver’s judgment, the vehicle’s speed, and its moving trajectory. Painting intersection guideline markings in the left-turn lane can assist drivers in quickly identifying the exit lanes and thereby eliminate hesitation time. As shown in Figure
Left-turn angle categories.
Acute angle
Right angle
Obtuse angle
Considering traffic flow direction (2 types), number of lanes (3 types), offset for through movement (3 types), and turning angle for left-turns (3 types), eighteen control groups (9 for through movement and 9 for left-turns) were established. Alternative intersections were selected to identify the most appropriate lanes for data collection. The conditions which defined an appropriate intersection are as follows. Table
Survey locations with and without guideline markings.
Through movement | ||||||
| ||||||
Number of lanes | Offset | |||||
Small | Medium | Large | ||||
Without guidelines | With guidelines | Without guidelines | With guidelines | Without guidelines | With guidelines | |
| ||||||
One | Zhoujiazui Rd - Longchang Rd | Linshan Rd - Nanyangjing Rd | Guoshun Rd - Yingkou Rd | Jinke Rd - Zuchongzhi Rd | Jungong Rd - Changyang Rd | Jiangpu Rd - Kunming Rd |
Two | Songhuajiang Rd - Yingkou Rd | Henan Rd - Beijing Rd | Changyang Rd - Linqing Rd | Jungong Rd - Changyang Rd | Zhoujiazui Rd - Huangxing Rd | Zhongshandong Rd - Yanan Rd |
Three | Guoshun Rd - Huangxing Rd | Zhoujiazui Rd - Dalian Rd | Jungong Rd - Xiangying Rd | Haining Rd - Zhoujiazui Rd | Jinhai Rd - Jinke Rd | Henan Rd - Yanan Rd |
| ||||||
Left-turn | ||||||
| ||||||
Number of lanes | Turning angle | |||||
Acute angle | Right angle | Obtuse angle | ||||
Without guidelines | With guidelines | Without guidelines | With guidelines | Without guidelines | With guidelines | |
| ||||||
One | Songhuajiang Rd - Yingkou Rd | Dongfang Rd - Lancun Rd | Jiangpu Rd - Kongjiang Rd | Huangpi Rd - Yanan Rd | Zhoujiazui Rd - Longchang Rd | Xizang Rd -Yanan Rd |
Two | Dalian Rd - Zhoujiazui Rd | Henan Rd - Fuxing Rd | Siping Rd- Zhongshanbeier Rd | Haining Rd - Wusong Rd | Wenshui Rd - Quyang Rd | Dalian Rd - Kongjiang Rd |
Three | Zhoujiazui Rd - Huangxing Rd | / | / | / | Songhu Rd - Zhayin Rd | Xujiahui Rd - Luban Rd |
/ means that this kind of intersection is not found in Shanghai, China.
(1) The volume of traffic is large enough to ensure sufficient surveyed data.
(2) The grade of approach and exit lanes is less than 2%.
(3) Near the intersection, there are no access points, such as entrances or exits of schools, parking lots, supermarkets, etc.
(4) There are no work zones near the intersection that can potentially affect the judgment of drivers.
(5) For the same control group, only one of the influence factors should be different at a time for the candidate intersection.
The saturation flow rate can be calculated by (
Surveyed data.
Movement | Number of lanes | Offset/Turning angle | Guidelines | Surveyed hours | Useful cycles | Useful vehicles |
---|---|---|---|---|---|---|
Through | One | Small offset | Without | 1 | 11 | 214 |
Through | One | Small offset | With | 1 | 11 | 214 |
Through | One | Medium offset | Without | 1 | 11 | 282 |
Through | One | Medium offset | With | 1 | 18 | 177 |
Through | One | Large offset | Without | 1 | 11 | 114 |
Through | One | Large offset | With | 1 | 18 | 177 |
Through | Two | Small offset | Without | 1 | 24 | 633 |
Through | Two | Small offset | With | 1 | 9 | 161 |
Through | Two | Medium offset | Without | 1 | 9 | 232 |
Through | Two | Medium offset | With | 1 | 10 | 91 |
Through | Two | Large offset | Without | 1 | 13 | 364 |
Through | Two | Large offset | With | 1 | 8 | 217 |
Through | Three | Small offset | Without | 1 | 8 | 659 |
Through | Three | Small offset | With | 1 | 7 | 378 |
Through | Three | Medium offset | Without | 1 | 11 | 296 |
Through | Three | Medium offset | With | 1 | 8 | 458 |
Through | Three | Large offset | Without | 1 | 7 | 195 |
Through | Three | Large offset | With | 1 | 8 | 400 |
Left-turn | One | Acute angle | Without | 1 | 19 | 133 |
Left-turn | One | Acute angle | With | 1 | 16 | 83 |
Left-turn | One | Right angle | Without | 1 | 13 | 252 |
Left-turn | One | Right angle | With | 1 | 7 | 94 |
Left-turn | One | Obtuse angle | Without | 1 | 8 | 76 |
Left-turn | One | Obtuse angle | With | 1 | 16 | 180 |
Left-turn | Two | Acute angle | Without | 1 | 13 | 240 |
Left-turn | Two | Acute angle | With | 1 | 8 | 158 |
Left-turn | Two | Right angle | Without | 1 | 10 | 206 |
Left-turn | Two | Right angle | With | 1 | 7 | 251 |
Left-turn | Two | Obtuse angle | Without | 1 | 15 | 163 |
Left-turn | Two | Obtuse angle | With | 1 | 12 | 569 |
Left-turn | Three | Acute angle | Without | 1 | 10 | 479 |
Left-turn | Three | Obtuse angle | Without | 1 | 15 | 671 |
Left-turn | Three | Obtuse angle | With | 1 | 7 | 233 |
Sum | 33 | 378 | 9050 |
Data collection.
Aerial view of intersection using UAV
Image capturing of vehicle trajectory
In this section, the saturation flow rate of through movement and left-turns is studied based on the collected data and control groups. Firstly, the distribution of saturation headways is investigated. Subsequently, the adjustment factor model is established for quantitative analysis of the effect of guideline markings.
By separating through movement and left-turns, the headway of each cycle under different conditions is calculated, and the distribution histogram of the headways is obtained. The corresponding trend line is then fitted for a comparison between the intersections in the control groups. In the comparison graphs, the further the curve is to the left, the smaller the saturation headway and the higher the saturation flow rate are.
The results of the comparison of through movement saturation headways are shown in Figure
Comparison of through movement headways with and without guideline markings.
(1) In every control group, the saturation headway of an intersection with guideline markings is smaller compared to intersections without guide line markings.
(2) Apart from the control group with a single lane and small offset, there is a noticeable difference in saturation headways between intersections with and without guideline markings.
(3) The greater the offset, the more pronounced the effect of the guide line markings on the saturation flow rate.
(4) The larger the number of lanes, the more pronounced the effect of the guide line markings on the saturation flow rate.
The method of analysis for left-turn traffic is the same as that for through movement. However, for left-turns, the trend of the difference in the saturation flow rate is investigated by controlling the left-turn angle or number of traffic lanes. The results of the comparison are shown in Figure
Comparison of left-turn headways with and without guideline markings.
(1) Setting guideline markings can improve the saturation flow rate irrespective of the turning angle.
(2) The greater the number of left-turn traffic lanes, the more pronounced the effect of the guide line markings on the saturation flow rate.
(3) The smaller the left-turn angle, the more pronounced the effect of the guideline markings on the saturation flow rate.
Referring to the adjusted saturation flow rate model of HCM 2010 [
Small, medium, and large offsets are defined as offset 1, 2, and 3, respectively. As shown in Figure
Comparison of saturation headways for through movement.
Multifactor analysis of variance was performed to investigate whether the guideline markings, number of traffic lanes, offset and the interaction of these factors have a significant influence on the saturation flow rate. The results are shown in Table
Multifactor analysis of variance for through movement.
Source | Sum of Squares | df | Mean Square | F | Sig. |
---|---|---|---|---|---|
Offset | 0.394 | 2 | 0.197 | 87.166 | 0.000 |
Number of traffic lanes | 0.582 | 2 | 0.291 | 128.841 | 0.000 |
Intersection guideline markings | 0.387 | 1 | 0.387 | 171.280 | 0.000 |
Offset | 0.170 | 12 | 0.014 | 6.275 | 0.000 |
Calculated values of the adjustment factor for guideline markings under different conditions are listed in Table
Adjustment factor values of guideline markings for through movement.
Number of traffic lanes | Offset | ||
---|---|---|---|
Small | Medium | Large | |
1 | 1.014292 | 1.020304 | 1.027451 |
2 | 1.038911 | 1.063478 | 1.079167 |
3 | 1.118143 | 1.130612 | 1.136235 |
The effect of guideline markings on the saturation flow rate for left-turns is quantitatively analyzed in the same manner as for through movement. The acute, right, and obtuse angles are defined as angle 1, 2, and 3, respectively. As shown in Figure
Multifactor analysis of variance for left-turns.
Source | Sum of Squares | df | Mean Square | F | sig |
---|---|---|---|---|---|
Turning angle | 0.098 | 2 | 0.049 | 391.781 | 0.000 |
Number of traffic lanes | 0.225 | 2 | 0.112 | 902.585 | 0.000 |
Intersection guideline markings | 1.054 | 1 | 1.054 | 8467.279 | 0.000 |
Offset | 0.093 | 9 | 0.010 | 83.036 | 0.000 |
Comparison of saturation headways for left-turns.
Calculated values of the adjustment factor for guideline markings under different condition are listed in Table
Adjustment factor values of guideline markings for left-turns.
Number of traffic lanes | Turning angle | ||
---|---|---|---|
Acute angle | Right angle | Obtuse angle | |
1 | 1.145957 | 1.105042 | 1.081278 |
2 | 1.212121 | 1.139738 | 1.110612 |
3 | / | / | 1.135758 |
/ means that the value is unavailable owing to lack of surveyed data.
The proposed model was further validated based on a before–after comparative analysis. The intersection of Mingsheng Rd. and Lingshan Rd. in Shanghai, China, was used, as shown in Figures
Mingsheng Rd. and Lingshan Rd. intersection.
Before (no guideline markings)
After (with guideline markings)
Comparison of saturation headways with and without guideline markings
To verify the accuracy of the adjustment factor model, the difference between the calculated and measured saturation flow rates of each cycle was analyzed using the Mann-Whitney nonparametric test for two independent samples. As shown in Table
Result of significant difference (Mann-Whitney test).
Indicator | Value |
---|---|
Mann-Whitney U | 7.000 |
Wilcoxon W | 8.000 |
Z | -0.498 |
Asymptotic significance (2-sided) | 0.619 |
Precision significance (2-sided) | 0.762 |
An irregular intersection could cause difficulty for a driver to identify appropriate exit lanes. Therefore, a vehicle may interfere with other lanes, leading to a decrease in saturation flow rate. The relationship between the adjustment factor for guide line markings and the ratio of the degree of interference at intersections with guideline markings to those without guideline markings is analyzed in this section.
The degree of interference is defined as the ratio of the number of vehicles which do not enter the corresponding exit lanes to the number of all vehicles in that direction. As shown in Figure
Interference vehicles.
Calculated values for the degree of interference at different intersections for through movement and left-turns are listed in Tables
Degree of interference for through movement.
Number of lanes | Offset | Guidelines | Degree of interference | Ratio of interference |
---|---|---|---|---|
2 | Small | With | 0.208 | 0.506 |
Without | 0.411 | |||
3 | Small | With | 0.271 | 0.536 |
Without | 0.506 | |||
2 | Medium | With | 0.236 | 0.518 |
Without | 0.456 | |||
3 | Medium | With | 0.31 | 0.585 |
Without | 0.53 | |||
2 | Large | With | 0.28 | 0.526 |
Without | 0.532 | |||
3 | Large | With | 0.342 | 0.605 |
Without | 0.565 |
Degree of interference for left-turns.
Number of lanes | Turning angle | Guidelines | Degree of interference | Ratio of interference |
---|---|---|---|---|
2 | Acute angle | With | 0.24 | 0.549 |
without | 0.439 | |||
| ||||
3 | Acute angle | With | / | / |
without | 0.389 | |||
| ||||
2 | Right angle | With | 0.174 | 0.511 |
without | 0.341 | |||
| ||||
3 | Right angle | With | / | / |
without | / | |||
| ||||
2 | Obtuse angle | With | 0.153 | 0.484 |
without | 0.316 | |||
| ||||
3 | Obtuse angle | With | 0.24 | 0.504 |
without | 0.476 |
/ means that the value is unavailable owing to the lack of surveyed data.
The correlation between the adjustment factor for guideline markings and the ratio of the degree of interference at intersections with and without guideline markings was analyzed using the Pearson correlation test (see Table
Correlation analysis.
Movement | Adjustment factor | Ratio of interference | ||
---|---|---|---|---|
Through movement | Adjustment factor | Pearson correlation | 1 | 0.891 |
sig.(2-tailed) | 0.017 | |||
N | 6 | 6 | ||
Ratio of interference | Pearson correlation | 0.891 | 1 | |
sig.(2-tailed) | 0.017 | |||
N | 6 | 6 | ||
Left-turn | Adjustment factor | Pearson correlation | 1 | 0.990 |
sig.(2-tailed) | 0.01 | |||
N | 4 | 4 | ||
Ratio of interference | Pearson correlation | 0.990 | 1 | |
sig.(2-tailed) | 0.01 | |||
N | 4 | 4 |
Painting guideline markings have become an important way to deal with traffic problems caused by intersection geometries where the approach and exit lanes are offset or cross at oblique angles. This study investigated the influence of guideline markings on the saturation flow rate at signalized intersections. An adjustment estimation model was developed based on field data collected at 33 intersections in Shanghai, China. From the analysis, the following conclusions can be drawn.
(1) Painting guideline markings can improve the saturation flow rate at signalized intersections. The improvement has a positive correlation with the number of traffic lanes, offset of through movement, and turning angle of left-turns. On average, improvements of 7.0% and 10.3% can be obtained for through and left-turn movements, respectively.
(2) The proposed model was validated on the basis of a before–after case study. Nonparametric test results show that no statistically significant difference exists between the results estimated by the proposed model and those obtained from the field survey, which confirms the accuracy of the proposed model.
(3) There is a positive correlation between the adjustment factor for guideline markings and the ratio of the degree of interference at the intersection with and without guideline markings, which explains why guideline markings can minimize the interference at irregular intersections. On average, 45.4% and 49.6% of the interference between the lanes at the same approach can be eliminated for through and left-turn movements, respectively.
This investigation only focused on the influence of guide line markings. In a future study, other traffic channelization measures such as the influence of traffic islands on the saturation flow rate may be investigated. Moreover, considering the impact of pedestrians and bicycles, the effectiveness of guideline markings to separate vehicles into different lanes and for separating vehicles and bicycles should be analyzed simultaneously.
The saturation headway data used to support the findings of this study are included within the supplementary information file(s) available
The authors declare that they have no conflicts of interest.
The research is supported by the National Natural Science Foundation of China under grant No. 51608324.
The supplementary materials are the original data of the saturation headways for left-turn and through movement at each surveyed intersection.