Canadian Journal of Civil Engineering
A new method for time-of-day breakpoints determination based on clustering and image processing
Journal: Canadian Journal of Civil Engineering
Manuscript ID cjce-2019-0153.R2
Manuscript Type: Article
Date Submitted by the 28-Sep-2019 Author:
Complete List of Authors: Shen, Hui; Southwest University of Science and Technology; Mianyang Polytechnic Yan, Jing; Southwest University of Science and Technology Liu, Daoguang; Southwest University of Science and Technology Liu, Zhigui;Draft Southwest University of Science and Technology; Southwest University of Science and Technology, School of computer science and technology
Keyword: signal control, clustering, image segment, TOD breakpoints
Is the invited manuscript for consideration in a Special Not applicable (regular submission) Issue? :
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A new method for time-of-day breakpoints determination based on
clustering and image segmentation
Hui Shen1,3, Jing Yan2, Daoguang Liu2, Zhigui Liu*1,2
1. School of Information Engineering, Southwest University of Science and Technology, 59, Qinglong Road, Fucheng District, Mianyang, 621000, China.
2. School of Computer Science and Technology, Southwest University of Science and Technology, 59, Qinglong Road, Fucheng District, Mianyang, 621000, China.
3. Corresponding author. Mianyang Polytechnic, 1, Xianren Road, Youxian District, Mianyang, 621000, China. Draft
Abstract: Signal control is an important part of the transportation system and it plays an important role in improving the capacity of intersections. This paper proposes a new traffic time division method for multi-period fixed-time control strategy. Firstly, we put forward a new concept-transportation overlap rate, in order to complete the clustering of daily traffic flow patterns. Then, all the daily traffic flow data belonging to the same category are composed into a matrix, which is converted into the corresponding image later with the aim of using the Fast and Robust Fuzzy C-Means Clustering (FRFCM) method to segment it. Finally, the traffic time division and breakpoints location are obtained through further analysis and processing of the segmentation results. For each period, the optimal signal cycle and green split are separately calculated by Webster’s signal timing method, in order to satisfy different traffic demands of each period and effectively improve the operation efficiency of the intersection. The simulation results at a certain intersection in Mianyang city demonstrate the effectiveness and practicability of the proposed method.
Keywords: signal control; clustering; image segment; TOD breakpoints
1. Introduction
In 1868, the first colored traffic signal light appeared in Westminster, England (Webster
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and Cobbe, 1966). Since then, signal lights at intersections have played an indispensable role in the modern traffic system, directly affecting the operation of vehicles.
According to the National Transportation Operations Coalition (NTOC, 2012), 5-10% of all traffic delays on main roads are caused by delays at signal-controlled intersections (Zhuofei Li; Lily Elefteriadou; Sanjay Ranka 2014). A reasonable signal control scheme can greatly benefit the entire transportation system by reducing or even eliminating road bottlenecks, improving transportation capacity, and relieving traffic pressure in congested areas.
During a long process of development, a lot of work has been done and many achievements have been obtained in the theoretical and experimental studies. Webster (1958) proposed an optimal method of signal timing for fixed-cycle signal system with the goal of minimizing the average vehicle delay. His method and the calculation of vehicle delay at unsaturated intersections are still in use today. However, his method is not applicable for over-saturated traffic conditions. Akcelik (1981), the pioneer of the multi-objective optimal control, improved Webster’s algorithm by combining the vehicle delay and shutdown times, and took them as the new optimization Draft objects of signal timing. But the process of solving multi-objective optimization problem is so complex that there is still no perfect solution.
With the rise of vehicular networking technology, some researchers began to study new methods of traffic signal control for connected vehicles. Priemer and Friedrich (2009) proposed an adaptive traffic signal control algorithm by using V2I communication data to reduce the queue length, and employed complete enumeration and dynamic programming to solve the problem; Goodall et al. (2013) developed a predictive microscopic simulation algorithm (PMSA) for traffic signal control, which can predict the future traffic volume by utilizing connected vehicles data, and optimize various traffic indicators. However, the execution time of the program is too long to be suitable for real-time applications. A lot of facts demonstrate that the execution time of system program will affect the efficiency of problem solving. Therefore, scientists are considering efficient ways to improve the speed of optimization. Zhuofei Li et al. (2014) suggested a signal control optimization method that can effectively improve the capacity of the intersection and reduce vehicle delays; but this method is only applicable to connected vehicles.
The connected vehicles have not been applied widely, and it will take about twenty-five years to reach a high penetration rate (Volpe National Transportation Systems Center 2008). In the meantime, the key technologies are in the research and development stage, and the existing
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research results still need validation and support. Therefore, the current study of traffic signal timing mainly focuses on traditional vehicles, rather than intelligent vehicles.
At present, time-of-day (TOD) multi-period fixed-time control and actuated signal control at intersections are considered to be wildly used solutions. The realization of actuated signal control needs various types of sensor information, and it is necessary to take not only the cost but also the fusion of various types of data into account, all of which will result in the high initial investment and operation costs, as well as the complex control processes. By contrast, multi-period fixed-time control is simple and easy to implement. Furthermore, the sensor type used in this scheme is single and the detected data can be corrected by field investigation, so it is more suitable for traffic control at signalized intersections.
In practice, traffic engineers usually collect the counting traffic data in 1-2 days manually to plot the aggregated volumes, then divide the period of traffic time and get the TOD breakpoints according to engineering judgment (Byungkyu Park; Pinaki Santra; IlsooYun; Do-Hoon Lee 2018). However, this method is not always reliable and efficient, because it cannot automatically adjust to changes in Draftdaily traffic flow, and experts' personal judgments are often different from each other. Therefore, we propose a new time division method based on image segmentation, which can generate an intuitive and visible TOD scheme by utilizing a large amount of archived traffic data without manual counting and experts’ subjective judgments.
Normally, the amount of traffic data is normally huge and complex, so it is impractical to apply them directly. Cluster analysis is an effective approach to solve such problems, because it is good at data feature recognition and dimensionality reduction, and maintains the functional integrity of the data at the same time (Chung and Rosalion 2001). It has also been claimed that classification and clustering of the traffic data can really lead to the insight into the effectiveness of traffic strategies (Wang et al. 2006). So in this paper, the cluster analysis of traffic flow data is carried out first. In recent years, some excellent achievements have been made in the research of image segmentation, such as superpixel-based fast fuzzy C-means clustering method (Tao Lei, Xiaohong Jia; Yanning Zhang et al. 2018), automatic fuzzy clustering framework (Tao Lei; Peng Liu; Xiaohong Jia et al. 2018), etc. These researches bring new ideas and innovations to the field of image processing. We draw support from the image segmentation algorithm to complete the division of traffic time in this paper.
The next section of this paper describes the processing of traffic flow data. In section 3, we
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propose both the clustering algorithm based on overlapping rate of hourly traffic volume distribution and the traffic time division method based on image segmentation. The simulation results are described in section 4. Finally, we present our discussions and conclusions in section 5.
2. Data processing
Traffic data information should be fully utilized in the study of intersection signal control. The data used in this paper were collected at a signalized intersection in Mianyang City. The satellite image of the intersection geometry and its schematic depiction of the lane configuration are shown in Fig. 1 and Fig. 2.
The traffic flow data of every lane were measured and collected per hour by the real-time monitoring devices, which are installed on the poles above the stop lines of four entrances. The obtained data contain the traffic flow per hour from December, 2017 to July, 2018, 16 days omitted due to the Chinese statutory holidays.
The detectors collected traffic flow dataDraft per hour, so there are 24 data points per day and the flow data of each day can be described by a vector.
(1) xd [xd (1) xd (2) xd (24)], d 1,2,7.
d denotes Monday, Tuesday, …Sunday, xd () denotes the number of vehicles in a certain time interval. A matrix X is used to represent all the Monday’s data together . 1
1 1 1 x1 (1) x1 (2) ... x1 (24) (2) x2 (1) x2 (2) ... x2 (24) X 1 1 1 1 M M ... M xN (1) xN (2) ... xN (24) 1 1 1
N denotes the number of Mondays. Similarly, the remaining six days traffic flow matrices are available and they make up the original data set. By calculating the means of each column in matrix X d (d 1,2,7) , we get the average traffic flow for each hour in each day. The formula for calculation is shown as follows.
iNd iNd iNd 1 i i i (3) X d xd (1) xd (2) ... xd (24) , d 1,2,7. N d i1 i1 i1
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Nd denotes the number of day d in the week.
As shown in Fig. 3, during the seven days of a week, the traffic volume in different days is different. And the traffic volume changes in different time of one day are also different. The rush hour on weekend comes later than that on weekdays. In addition, the total traffic volume on workdays is less than that on weekends. By contrast, traffic conditions on Friday are also different from Monday to Thursday. After 2 p.m. on Friday, the traffic volume begins to increase perhaps because Friday is the last workday and some people will leave workplaces in advance.
The average flow of each hour in one day is an important indicator for assessing traffic conditions and the main basis for making a signal timing strategy, but it reflects poorly on the similarities of traffic conditions in different days in a week, because the average is susceptible to extreme data in the data set, and it cannot present the accurate distribution of all the data. Accordingly, we propose a new concept, overlapping rate of hourly traffic volume distribution,
which is denoted by R (m),(i, j [1,2,7]，i j;m[1,2,24]) , and it is used to describe the i j Draft similarity of traffic conditions in the same period m between dayi and dayj to a certain extent. The detailed description is as follows.
1 1 xi (m) x j (m) 2 x2 (m) x (m) (4) X (m) i X (m) j i M j M P , xQ (m) xi (m) j
P denotes the number of dayi , Q denotes the number of day j X (m) and X (m) . i min i max represent the minimum and maximum in X (m) respectively. In the same way, X (m) and i j min
X j max (m) are the minimum and maximum in X j (m). For convenience, let a X i min (m) ,
b X i max (m) , c X j min (m) , d X j max (m) , and the possible cases of overlap are illustrated in Fig. 4.
As shown in Fig. 4, there are three possible cases.
In case 1,
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b c ,a c b d (5) d a Rij (m) d a ,c a b d b c
In case 2,
d c ,a c d b (6) b a Rij (m) b a ,c a b d d c
In case 3,
c d a b a b c d (7) Rij (m) 0, c d a b a b c d
The traffic flow data are discrete values, consequently, Rij (m) may not accurately describe the cases of overlap between day i and dayDraftj in the same period m . But with the increase of the observation time, the continuity of data in Xi (m) and X j (m) will be better, so it will be used to show the similarities between X (m) and X (m) in a certain degree. The bigger the R (m) is, the i j ij more similar they are. The total similarity between day i and day j can be calculated by the following equation (8).
24 (8) Rij Rij (m) m1
After calculating , we set out to categorize the flow data by Rij (m) .
3. Methods
3.1. Clustering analysis
Clustering analysis is an important method used in analysis and data mining. I.G. Guardiola, T. Leon and F. Mallor (2014) concluded that it was the clustering analysis that performed from the perspective of the functional data, which could help to make accurate classifications of data while holding the integrity of data functions and reducing dimensions; Chung and Rosalion (2001) pointed out that Clustering analysis was a practical means of finding qualitative characteristics of data. In addition, it could help people to identify relatively homogeneous populations in data sets. So far, Clustering analysis has been applied in the field
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of transportation by many scholars. Wang et al. (2006) proposed that classification and clustering could give insight into traffic management policy and assess intelligent transportation systems’ performance; Chiou (2012) and Caceres et al. (2012) employed clustering techniques to build short-term prediction models in their studies respectively.
In this paper, firstly we calculate Rij by equations (5)-(8), then determine the number of
clusters of the traffic condition of each day in one week by analysis ofRij . It should be noted that before clustering among the seven days of the week, the traffic condition of each day is in one category. In other words, the traffic condition on Monday is in the first category and the traffic condition on Tuesday is in the second category, and so on. Therefore, there are seven categories at the beginning, and these seven categories need to be clustered to reflect the traffic flow similarities among different days of the week. Later, we employ another clustering method, which is called the hierarchical clustering method, to cluster seven categories mentioned above.
The comparison results of two clustering methods show that the clustering method based onRij is valid and reasonable.
3.2. Traffic time division Draft
The effectiveness of multi-period fix-time control strategy for signalized intersections depends on the strict traffic time division and reasonable signal timing plans. Normally, traffic flow changes greatly in different time of one day, so multiple signal timing plans should be taken to satisfy traffic demand changes during a whole day. In general, we divide the day time into several time periods and take an appropriate signal timing plan to meet traffic demand in each period. The decision of time-of-day (TOD) breakpoints positions are crucial for multi-period fixed-time control in the intersection.
As we have mentioned above, traffic flow data can be expressed by a two-dimensional matrix and each element of it refers to a flow value, while digital image can be represented by a pixel value matrix in the same way. Therefore, a flow data matrix can be viewed as a digital image where the flow value is seen as the pixel value in some situations, so clustering algorithm used in image segmentation can be employed to the image corresponding to the traffic data matrix. Moreover, using image clustering method to segment traffic flow images is equivalent to segment traffic data matrix.
Image segmentation, which can be used to divide digital images into many disjoint areas, is the most commonly used method in image recognition and computer vision. It includes threshold segmentation, region segmentation, edge segmentation and so on. Here we divide the traffic data images by the Fast and Robust Fuzzy C-Means Clustering (FRFCM) (Tao Lei et al.
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2018), which is an excellent algorithm for region segmentation.
First and foremost, we group all the daily traffic data from the same category together to build a matrix. Then translate the traffic data matrix ‘X’ into a color image ‘A’ by functions in MATLAB, where ‘X’ refers to the traffic data matrix from the same category, and ‘A’ indicates the color image transformed from the matrix ‘X’. The image A is a rectangle, and its interior consists of many color blocks. The color of each block corresponds to each value in matrix X. The closer the flow value in the matrix X is, the more similar the pixel color in image A is. At last, Using FRFCM to cluster the different blocks of pixel colors in image A. The result of clustering will help us to find the boundaries of different color regions and determine the segmentation results. The different signal timing plans for each period will be adopted, and it can help the traffic in intersections to become more efficient and avoid the traffic congestion.
3.3. Traffic signal timing plan
In order to enhance the capacity of the intersection, different timing plans will be taken to meet the demand of each period on transportation. In rush hours, the key point focuses on maximized traffic flow, so as to evacuateDraft the queue vehicles and relieve the traffic pressure as soon as possible. In the case of off-peak period, we pay more attention to the vehicle delay. The vehicle delay refers to the loss of vehicle travelling time caused by the traffic flow interruptions due to the signal control at intersections, which includes the queue delay, stop delay and control delay. The vehicle delay is an important indicator of operating efficiency and service quality at intersections.
There is no over-saturation at the intersection researched in this paper, and our focus is mainly on the division of time periods and breakpoints determination. Therefore, we adopt the classical Webster’s timing method to calculate signal cycle and green time for each period. The specific process of signal timing can be referred to relevant literature that are readily available.
4. Results and analysis
All the methodologies introduced in Section 3 are applied in a real-world signalized intersection described in Section 2.
Table 1. The results of Rij
Table 1 gives the numerical value of overlap rate for two days, and the value is obtained by
(4)-(8). As it can be seen, R16 1.46 is the minimized value in this table, which means that the similarity of Thursday and Saturday is the smallest, in other words, the difference of traffic
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condition between Thursday and Saturday is the greatest. By the idea of GDS, we categorize the traffic patterns into three groups, Monday, Tuesday, Wednesday and Thursday are in the same group, because the overlapping rates of hourly traffic volume distribution between them are higher. By the same analytical method, Saturday and Sunday are grouped together and Friday forms a group of itself.
In comparison, we cluster the average daily traffic flow with the hierarchical clustering method (Johnson S C, 1967). The process of hierarchical clustering method is as follows: at the very beginning, each object to be clustered is regarded as one category. Based on the iterative computation, the closet two categories will be combined and this process will be finished until there is only one category. In each phase, the distances between clusters are recomputed by update formula according to the particular clustering method.
Fig. 5 presents the result of hierarchical clustering. The cluster centers of data set from Monday to Thursday are closer, and their longitudinal distance correspondingly is closer than other three days, which indicates the similarity of daily flow in Monday, Tuesday, Wednesday and Thursday is closer. Weekends (SaturdayDraft and Sunday) flow changes are more consistent, so they are classified in one category. Though Friday’s data are placed in the same category with the former four days in Fig. 5, the distance between them is more distant, so it is categorized separately at last. The result of hierarchical clustering is consistent with the clustering result
based on Rij , which suggests that it is reasonable to determine the traffic flow categories by overlapping rate of hourly traffic volume distribution.
Concerning the problem of clustering algorithms of the seven days of one week, I. G. Guardiola (2014) used the method based on the functional principal component analysis and divided the seven days into two categories: weekdays and weekends; the relevant source, by Rui (2005), has investigated the method which is used to determine the most suitable for the number clustering. However, they pointed out that in general occasions, there is no other clustering method with optimized standard. Therefore, it is still a problem to figure out the most suitable clustering number, which relies on the existed data to a large degree. The clustering result based
on the analysis of Rij is justified , and it is reasonable to divide the traffic situation of seven days of one week into three categories.
Fig. 6 shows the corresponding traffic data images of each group (category). There is a corresponding relationship between the color of each pixel and traffic flow data of each group. The closer the values are, the more similar the colors are. It can be seen clearly from the images that the depth of color blocks and the boundaries of color transition regions are different in each
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group, but they are practically identical to those in the same group.
The results of FRFCM used for three images are shown separately in Fig. 7, Fig. 8 and Fig. 9. Here we set up three different cluster numbers cn , andcn 3,4,5 , to get different image segmentation results.
It can be seen that after the image clustering, some boundaries between different colors blocks are disordered, because of the randomness and fluctuation of the traffic flow. In terms of areas where color blocks are mixed, or in other words, vertical dividing lines in the image are discontinuous, we will take some treatments. The processed images are shown in Fig. 10, Fig. 11 and Fig. 12. From these images, the results of time interval division are clear at a glance.
According to the clustering and segmentation of traffic flow data images, when the number of classification is 3 (cn 3 ), 0-7 is the first period, 7-8 is the second period, 8-23 is the third period and 23-0 is the fourth period. Among these four periods, the second period and the fourth period correspond to the same block color (white), which means that there is a little discrepancy between the traffic volumes in 0-7 and 23-0, and the same signal timing plan can be used in these two periods. When cn 4Draft , time division is more detailed. On the basis of the former, 12-13 is divided into a period, and it’s the same with 22-23. In this case, period 7-8 and 22-23 have the same color (yellow). When cn 5 , 0-1 becomes an independent period. As the number of cluster increases, the same situation occurs in Fig. 11 and Fig. 12. Because the more number of cluster we set, the more precisely the image is segmented, and the more time periods we get.
In order to evaluate the effectiveness of different divisions and determine the most reasonable breakpoints, we use microscopic traffic simulation software VISSIM for simulation results and analysis. Its inputs are average traffic volume per period, and the signal timing plan is made according to the classical Webster’s timing method. Here we focus on three indicators of traffic, Q represents the number of vehicles actually passing the intersection , D represents the average vehicle delay and S represents the average stops. Q0 denotes the number of vehicles entering the intersection. The simulation results are shown in Table 2, Table 3 and Table 4, and all the results are the average value after many simulations.
Table 2. Table of the simulation results for group 1
Table 3. Table of the simulation results for group 2
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Table 4. Table of the simulation results for group 3
As is shown in the Table 2, Table 3 and Table 4, the longer the span of the time period is, the worse the traffic index turns out to be. Taking the second group as an example, during the period from 0 to 7, the three indexes are worse than that from the other two periods: 0-1 and 1-7. However, the slight differences can be ignored. The same case happens in the following periods: 8-23, 8-12, 12-13, 13-22 and 22-23. The indicators of traffic operation in period 8-23 are the worst, because the time span is larger than other periods. Therefore, if the same signal timing plan was adopted in this period, it would be difficult to meet the different traffic demands at each stage of this period. In comparison, The indicators of traffic operation in the periods 8-12, 12-13, 13-22 and 22-23 are better, because their time span is smaller. Considering the similarity of indicators between 12-13 and 13-22, these two periods can be combined into one. With the same analysis and processing method, we get the final time division results for each group in Fig. 13.
In order to achieve a better traffic control effect, the suitable signal timing scheme based on the traffic demand is carried out in each period. Draft
5. Discussion and conclusion
In this paper, we proposed a new method for time-of-day breakpoints determination based on clustering and image segmentation. The whole process of the traffic data processing and clustering for a signalized intersection are presented in detail. In the meantime, the processing of image segmentation results and the final determination of time division scheme are also introduced.
It is inspiring to find that the proposed method can contribute to operation efficiency of the intersection, which means that it can be readily used in practice. The outstanding performances of this new method are concluded as follows:
1. It is more intuitive and straightforward to display the traffic time division results based on image segmentation.
2. The proposed method is simple and easy to implement. The computational complexity of FRFCM algorithm is O(n w2 qct) , where N is the number of pixels of an image, c is the number of clustering prototype, t is the iteration number, w is the size of the filtering window, and q is the number of gray levels in the image. The average time needed for the whole process is only 0.52541 seconds, which can fully satisfy the application requirements.
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3. Traffic time division based on clustering and image segmentation is the basis of multi-period fix-time control strategy, and it is more conducive to improving intersection performance.
Applying image processing method to traffic time division is an innovation in the application. It is an effective way to find TOD breakpoints and achieve the most suitable traffic indicators for each time period. It also provides a practical method for the multi-period traffic control. The proposed method is simpler and faster, and the final result indicates that it is feasible and effective in solving practical problems. The output images are more intuitive and clear for us to analyze, estimate and research the intersection signal control scheme. Moreover, the paper also makes contributions to the research of the city traffic state pattern recognition.
It should be noted that each TOD breakpoint in this paper is located in the integral point, because the traffic flow data is collected every hour. If the time interval of data collecting were decreased, the results of the time division would be more accurate, and the traffic control effect of the intersection would be better. We leave this topic for the future research.
Acknowledgements Draft
All the traffic data in this paper was provided by Traffic Police Detachment of Mianyang City, and this research was sponsored by Intelligent Traffic Command Center (ITCC) at Traffic Police Detachment of Mianyang City. The authors wish to express their gratitude to Section Chief Zhang and his staff at ITCC for the support and assistance.
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Fig. 1. The satellite image of the intersection geometry
Fig. 2. Schematic depiction of the lane configuration
This intersection has four entrances from the north, south, east and west. It is located on the main road with a circular pedestrian overpass, so there is no need to consider pedestrian crossing. Draft
Fig. 3. The average daily traffic flow of the intersection
Fig. 3 shows the average daily traffic flow at the intersection from Monday to Sunday. The value of each time point is calculated by formula (3).
Fig. 4. Cases of overlap between day i and day j in the same period m
There are three possible cases. If a≤c X j (m) have an overlapping area, and the overlapping rate of hourly traffic volume distribution Ri j (m) can be calculated by (5). If a≤c Fig. 5. The result of hierarchical clustering It is obvious that Monday and Tuesday are clustered together at the start, because the distance (value in ordinate) of traffic data sets of these two days is the closest. After that Wednesday and Thursday successively join the first cluster for the same reason, so the first category contains Monday, Tuesday, Wednesday and Thursday. The distance between https://mc06.manuscriptcentral.com/cjce-pubs Saturday and Sunday’ data sets is closer by comparison and they are clustered together. Page 15 of 33 Canadian Journal of Civil Engineering Friday’s data set is far away from the previous two categories so Friday is a cluster of its own. Fig. 6. Traffic data images The image generation method refers to 3.2, and the clustering results refer to the analysis of R in Section 4. Group 1 contains the traffic flow data of Monday, Tuesday, ij Wednesday and Thursday, and the image of group 1 contains more pixels. Group 2 only contains Friday’s traffic flow data and group 3 contains the traffic flow data of Saturday and Sunday, but the corresponding image contains less pixels. The abscissa represents 24 hours in a day, and the ordinate is the number of days. Fig. 7. TheDraft clustering result of group 1 Fig. 8. The clustering result of group 2 Fig. 9. The clustering result of group 3 We can obviously see the clustering and segmentation of each image. As is shown in the Fig. 7, the first image is obtained when cn 3 , the second image is obtained when cn 4 and the third one is got when cn 5 . Fig. 8 and Fig. 9 are also laid in this way. Fig. 10. The proposed images of group 1 Fig. 11. The proposed images of group 2 Fig. 12. The proposed images of group 3 Fig. 10, Fig. 11 and Fig. 12 show the time division separately after the processing of Fig. 7, Fig. 8 and Fig. 9. The treatments are taken as follows: If there are two or more different color blocks in the same rectangular area corresponding to each hour, and the area of one color is much larger than that of the other colors, the largest color block will be chosen to represent the color of this rectangular. If color blocks in the same rectangular area corresponding to one hour period have no outstanding proportion, we will cover this area in a brand new color (pink). https://mc06.manuscriptcentral.com/cjce-pubs Canadian Journal of Civil Engineering Page 16 of 33 Fig. 13. TOD breakpoints for each group As shown in Fig. 13, traffic hours in group 1, which includes the traffic data from Monday to Thursday, are divided into three periods, 0-7, 7-21, and 21-0. While the traffic hours in group 2 (only includes Friday) are divided into six periods, 0-7, 7-8, 8-12, 12-22, 22-23, and 23-0. Traffic hours in group 3 (includes Saturday and Sunday) are divided into 5 periods, 0-7, 7-9, 9-19, 19-22, and 22-0. Draft https://mc06.manuscriptcentral.com/cjce-pubs Page 17 of 33 Canadian Journal of Civil Engineering Fig.1. The satellite image of the intersection geometry Draft https://mc06.manuscriptcentral.com/cjce-pubs Canadian Journal of Civil Engineering Page 18 of 33 Fig.2. Schematic depiction of the lane configuration Draft https://mc06.manuscriptcentral.com/cjce-pubs Page 19 of 33 Canadian Journal of Civil Engineering Fig.3. The average daily traffic flow of the intersection Draft https://mc06.manuscriptcentral.com/cjce-pubs Canadian Journal of Civil Engineering Page 20 of 33 Fig.4. Cases of overlap between day i and day j in the same period m Draft https://mc06.manuscriptcentral.com/cjce-pubs Page 21 of 33 Canadian Journal of Civil Engineering Fig. 5. The result of hierarchical clustering Draft https://mc06.manuscriptcentral.com/cjce-pubs Canadian Journal of Civil Engineering Page 22 of 33 Fig. 6. Traffic data images Draft https://mc06.manuscriptcentral.com/cjce-pubs Page 23 of 33 Canadian Journal of Civil Engineering Fig.7. The clustering result of group 1 Draft https://mc06.manuscriptcentral.com/cjce-pubs Canadian Journal of Civil Engineering Page 24 of 33 Fig.8. The clustering result of group 2 Draft https://mc06.manuscriptcentral.com/cjce-pubs Page 25 of 33 Canadian Journal of Civil Engineering Fig.9. The clustering result of group 3 Draft https://mc06.manuscriptcentral.com/cjce-pubs Canadian Journal of Civil Engineering Page 26 of 33 Fig. 10. The proposed images of group 1 Draft https://mc06.manuscriptcentral.com/cjce-pubs Page 27 of 33 Canadian Journal of Civil Engineering Fig. 11. The proposed images of group 2 Draft https://mc06.manuscriptcentral.com/cjce-pubs Canadian Journal of Civil Engineering Page 28 of 33 Fig. 12. The proposed images of group 3 Draft https://mc06.manuscriptcentral.com/cjce-pubs Page 29 of 33 Canadian Journal of Civil Engineering Fig. 13. TOD breakpoints for each group Draft https://mc06.manuscriptcentral.com/cjce-pubs Canadian Journal of Civil Engineering Page 30 of 33 Table 1 The result of Rij 1 2 3 4 5 6 7 1 0 7.68 8.69 4.83 7.46 1.46 4.54 2 7.68 0 7.13 10.17 5.73 1.83 3.4 3 8.69 8.69 0 8.94 5.5 2.72 4.31 4 4.83 10.17 8.94 0 4.26 2.98 1.85 5 7.46 5.73 5.5 4.26 0 3.05 4.63 6 1.46 1.83 2.72 2.98 3.05 0 7.49 7 4.54 3.4 4.31 1.85 4.63 7.49 0 Draft https://mc06.manuscriptcentral.com/cjce-pubs Page 31 of 33 Canadian Journal of Civil Engineering Table 2 Table of the simulation results for group 1 Q0 Q D S 0-2 1210 1201 5.01 0.3 2-7 960 955 4.31 0.25 0-7 1100 1091 6.05 0.35 7-21 3850 3777 29.36 1.12 21-0 2000 1984 9.53 0.58 21-23 2500 2483 9.08 0.53 23-0 1700 1703 8.33 0.45 Draft https://mc06.manuscriptcentral.com/cjce-pubs Canadian Journal of Civil Engineering Page 32 of 33 Table 3 Table of the simulation results for group 2 Q0 Q D S 0-1 950 940 4.37 0.25 0-7 850 849 5.71 0.43 1-7 760 756 5.37 0.34 7-8 3300 3274 17.87 0.76 8-12 3900 3882 27.88 1.04 8-23 3800 3733 43.71 2.67 12-13 3850 3820 25.8 1.02 13-22 3700 3648 26.14 1.06 22-23 3000 2987 16.08 0.72 23-0 2200 2182 8.93 0.43 Draft https://mc06.manuscriptcentral.com/cjce-pubs Page 33 of 33 Canadian Journal of Civil Engineering Table 4 Table of the simulation results for group 3 Q0 Q D S 0-7 850 823 5.9 0.37 7-9 2800 2758 14.06 0.64 9-19 4000 3795 33.1 1.29 9-21 3800 3739 52.35 1.93 19-22 3700 3691 25.13 0.98 21-22 3700 3653 26.16 1.02 21-23 3100 3071 16.6 0.71 22-23 2600 2573 13.36 0.61 22-0 2450 2413 12.42 0.59 23-0 2200 2192 10.29 0.5 Draft https://mc06.manuscriptcentral.com/cjce-pubs