Space-Time Resource Integrated Optimization Method for Time-of-Day Division at Intersection Based on Multidimensional Traffic Flows

Based on the change trends of trafc fow in diferent controlled directions at an intersection, the space-time resource integrated optimization method for TOD (time-of-day) division based on multidimensional trafc-fow data is proposed in this paper. By analyzing the trafc-fow data of 8, 4, 2, and 1 dimensions commonly used at the intersection, the dynamic Fisher algorithm is used to complete the time segment division of the trafc-fow sequence of diferent dimensions. On this basis, the preliminary TOD division is completed, and the phase timing and lane-use assignment corresponding to the preliminary time periods are optimized. Ten, the adjacent time periods are merged and tested to complete the fnal result of the TOD division. In order to verify the efectiveness of the proposed method, the schemes based on trafc-fow data of diferent dimensions are carried out by using the data at an actual intersection in Wuhu City, and the total and average vehicle delays of diferent schemes throughout the day are evaluated by VISSIM. Te results show that the more dimensions of trafc fow data are adopted, the more refned the TOD division scheme is, and the less the total delay and average delay at intersections throughout the day are. In particular, the TOD division scheme after further optimizing the lane-use assignment can further reduce the total and average vehicle delay throughout the day. It shows that the method using multidimensional trafc-fow data at an intersection to carry out the integrated optimization of TOD division, lane-use assignment, and phase timing has good applicability.


Introduction
Urban trafc signal optimization plays an important role in alleviating trafc congestion and improving the trafc capacity of road networks.Te time-of-day (TOD) division of signal control schemes is an important part of signal timing optimization and can efectively adapt signal timing schemes to changes in trafc fow [1][2][3].Research has shown that optimized TOD division and phase timing that matches the trafc fow can signifcantly improve intersection capacity and reduce vehicle delays [4][5][6][7][8][9].
TOD control involves dividing 24 h into several time periods according to changes in trafc fow at an intersection using diferent signal control schemes for diferent trafc time periods [10].In practice, trafc engineers divide a day into several time periods according to the general trends in total trafc fow at intersections, such as a peak period, fat peak period, and low peak period.However, this empirical division makes it difcult to obtain optimal solutions [11].In terms of theoretical research, most current research focuses on cluster analysis algorithms, in order to fnd optimal TOD breakpoints.For example, Wang [12] designed the TOD division method based on the C-means clustering algorithm and is verifed by actual data.Su and Dong [13] put forward the study of TOD based on Isomap and K-means clustering algorithm, the results indicated that the Isomap and K-means algorithm outperformed the traditional artifcial method.Xiu et al. [14] analyzed the macroscopic and microscopic variation of trafc fow deeply and proposed a multiperiods quadratic division based on the dynamic Fisher clustering algorithm.Guo and Zhang [15] presented an advanced cluster analysis aimed at identifying TOD breakpoints for coordinated, semiactuated modes when it is necessary for multiple intersection operations to be considered simultaneously.Although the above studies have achieved certain results by using diferent clustering algorithms in fnding TOD breakpoints, it is uncertain whether the results of TOD division are conducive to reducing trafc delays and other indicators because they have not been evaluated for trafc benefts.Since the TOD division should serve to better improve trafc beneft, in recent years, more studies have conducted in-depth research on the TOD division method with trafc beneft evaluation.For example, Park et al. [16] proposed a genetic algorithm-based clustering, which was evaluated through the performance of an actual timing plan under a microscopic simulation program, SIMTRAFFIC.Li et al. [17] proposed a TOD division method by using dynamic recurrence order clustering, the results showed that, compared with the traditional K-means method, the average delay and queue length of the intersection were reduced by the proposed method in the peak periods.Yu et al. [18] improved the traditional fuzzy c-means clustering (FCM) algorithm and proposed a new method to divide the trafc signal control periods; compared with the traditional scheme, the improved FCM algorithm can efectively reduce the average delay of vehicles.Cao et al. [19] proposed a method for the automatic division of time periods of intersection based on Fisher-ordered clustering, and the simulation results showed that the method efectively reduces the average vehicle delay.In order to improve the precision of TOD breakpoints, Bie et al. [20] proposed a method to determine the numbers of transition cycles under diferent timing plan transition conditions; the results showed that, compared with the traditional method, the proposed method produces a reasonable number of time intervals and reduces total vehicle delay by 8.9%.Ratrout [21] introduced a subtractive algorithm-based K-means technique to determine the optimum number of TODs; SimTrafc was used to evaluate the performance of the selected number of clusters with respect to total delays, total stops, fuel used, and CO emissions.Smith et al. [11] proposed the data-driven methodology for signal timing plan; the results of a case study demonstrated that, compared to currently used techniques, the methodology provided benefts when considering performance measures such as delay.Although the above studies demonstrate the efectiveness of the TOD division method through the trafc beneft evaluation, the results of TOD division are all based on the total trafc-fow data at the intersection, and the change trends of trafc fow of diferent phase are ignored, which leads to the TOD division results may not be able to meet the needs of phase timing optimization.In order to solve the above problems, some studies began to use multidimensional trafc-fow data to carry out the TOD division research.For example, Xu et al. [22] developed a doubleorder optimization model of TOD control segmented point division, the dimensions of the traditional trafc-fow data were increased, and the classic model was reconstructed in the frst-order optimization.Dai et al. [23] calculated the cycle time by considering the diference of trafc fow direction at the intersection, studied the TOD division method at the intersection, and provided a basis for a multiperiods timing scheme.Zhao et al. [24] selected the fow of each phase as the clustering data, improved the classical NJW (Ng-Jordan-Weiss) algorithm in spectral clustering, and used SimTrafc to perform simulation evaluation on the results of TOD division under diferent cluster numbers, so as to select the best number of clusters and fnally obtained the results of TOD division under the given number of clusters.Chen et al. [25] took the intersection phase fow as clustering data and fnally conducted clustering by reducing the dimension and systematically compared the infuence of K-means, hierarchical clustering, and Fisher clustering methods on TOD division.Te results show that Fisher ordinal clustering outperforms k-means and hierarchical clustering in terms of performance measures.Te above studies further verify the efectiveness of using multidimensional trafc-fow data such as phase fow to carry out TOD division.However, on the one hand, the TOD division results obtained by using trafc-fow data clustering of diferent dimensions are not compared and analyzed, and the infuence of multidimensional trafc-fow data clustering on TOD division results is not illustrated.On the other hand, TOD division is closely related to signal phase timing and lane-use assignment optimization (such as setting variable lanes at diferent time periods).In the process of TOD division, most studies have not fully considered signal phase optimization.For example, [21,22,25] all adopted Synchro software to optimize the timing scheme but did not mention the phase optimization.In addition, hardly has literature considered the lane-use assignment optimization in the process of TOD division, and the fnal TOD division result has not been further tested according to lane-use assignment, signal phase, and timing scheme.
In summary, a lot of achievements have been made in the current research on clustering algorithms for seeking TOD breakpoints.Most of the studies use the total trafc-fow data of a single dimension at the intersection to carry out the TOD division, while a few use multidimensional phase trafc-fow data to carry out the TOD division.Recent studies have adopted Synchro software to carry out signal timing optimization and adopted SimTrafc trafc simulation software for beneft evaluation to determine the optimal number of clusters in the process of TOD division.In general, the TOD division needs to serve phase timing design, and phase timing optimization is based on the trafc fow of straight and left turn at the intersection as the design basis and is closely related to the lane-use assignment of entrance lanes.Terefore, the integrated optimization of TOD division, phase timing, and lane-use assignment based on multidimensional trafc-fow data in each controlled direction at the intersection is an urgent topic to be studied, which is rarely involved at present.Terefore, based on the trafc fow of each controlled direction at the intersection, we propose a space-time resource integrated optimization method for TOD division at the intersection based on multidimensional trafc fow data.Tis method is based on the trafc-fow sequence of diferent 2 Journal of Advanced Transportation dimensions corresponding to straight-through and leftturn trafc at the intersection and uses the Fisher clustering algorithm, which has more advantages in ordering sample clustering [25], to complete the time segment division of the trafc-fow sequence of diferent dimensions.On this basis, the preliminary TOD division is completed, and then the optimized signal phases and timing schemes are completed.Furthermore, the lane-use assignment is further considered to optimize.Finally, the preliminary time periods are merged and tested to complete the fnal result of the TOD division.In order to verify the feasibility of the proposed method, the TOD division schemes based on trafc-fow data of diferent dimensions are further completed with the actual intersection data.Te vehicle delay of diferent schemes is evaluated by VISSIM trafc simulation software, and the conclusions of this paper are proposed.Tis study makes the following contributions in comparison with past work in the area: frst, an integrated optimization method of TOD division, phase timing, and lane-use assignment based on multidimensional trafcfow data is proposed, and the rationality of the fnal result of TOD division is further tested according to the lane, phase, and timing schemes.Second, the TOD division results based on trafc-fow data of diferent dimensions and the corresponding trafc beneft are compared, and the efect of multidimensional trafc-fow data clustering on the TOD division is further analyzed.Tird, in the process of signal phase timing design of the preliminary TOD division, the phase combination optimization method based on lane-use assignment optimization is further considered, and the adjacent time periods are merged and tested based on the lane-use assignment optimization results, so as to further improve the trafc beneft of the TOD division results.
Te remainder of the paper is organized as follows.Section 2 presents the methodology of TOD division of intersection based on multidimensional trafc fow.Section 3 presents the test and results of a case study at the actual intersection of Wuhu City, China.Te efectiveness of the method proposed in this paper is discussed in Section 4. Finally, Section 5 summarizes the main outcomes of this paper.

Dimension Analysis of Trafc Flow at Intersection Used for TOD Division.
As shown in Figure 1, it is assumed that a t (t � 1, 2, . .., 8) is the main controlled trafc fow of straight and left turn at a typical intersection.Te vehicles turning right are not controlled by the signal and yields to conficting trafc fow.q t is the trafc-fow sequence of a t in 24 h.Current methods usually take the total trafc fow at an intersection as the basis for TOD division.Tat is, the TOD division is carried out based on the trafc-fow sequence of one dimension.As mentioned above, some methods take multidimensional phase trafc-fow data to carry out TOD division, and the signal phase design at the intersection is usually a conventional four-phase scheme: the frst phase is for north-south straight-through trafc, the second phase is for north-south left-turning trafc, the third phase is for the east-west straight-through trafc, and the last phase is for east-west left-turning trafc.Twophase schemes are also common: the frst phase is for eastwest trafc and the second phase is for north-south trafc.Yet it is the combination of the controlled trafc fow of eight dimensions that determines the phase design.Tat is, except for one dimension, TOD division can be carried out based on the trafc-fow sequences of two, four, and eight dimensions at a typical intersection.Terefore, in order to analyze the impact of trafc-fow clustering of diferent dimensions on TOD division, we propose using the trafc-fow sequence of w(w � 1, 2, 4, 8) dimensions to optimize TOD division and phase timing at the intersection.Since q t is an important basis for the signal phase timing design, and TOD division and phase timing need to be carried out in an integrated manner, this paper adopts the trafc-fow sequence Q v of diferent dimensions formed by q t as the basis for TOD division.Tat is, when w � 1, Q 1 �  q t ; when w � 2, Q 1 � q 1 + q 2 + q 5 + q 6 and Q 2 � q 3 + q 4 + q 7 + q 8 ; when w � 4, Q 1 � q 1 + q 5 , Q 2 � q 2 + q 6 , Q 3 � q 3 + q 7 , and Q 4 � q 4 + q 8 ; and when w � 8,

Preliminary TOD Division Based on Trafc-Flow
Sequences of Diferent Dimensions

Principle of the Dynamic Fisher Clustering Algorithm.
Fisher clustering analysis is a statistical method specifcally designed for ordered samples.It has the advantages of multiindex clustering without destroying the original order of the samples.Te dynamic Fisher clustering algorithm is composed of the ordered sample clustering method and the dynamic clustering method.It can better determine the TOD division results according to the predetermined target [26].
Assuming that W � w 1 , w 2 , . . ., w n   is an ordered sample, the value of the sample point w i on variable V(w) is v i , and the elements similar to V(w i ) are all classifed into the same category P i , but the sample size of each category must be continuous.Tat is, Te main steps are as follows: (1) Set the preliminary segment number of the ordered sample as z and calculate all possible class diameters D(i) under the segment numbers z: where x ij is the characteristic value of the sample.(2) Calculate the objective function B(n, z): (3) Solve the optimal classifcation.Te ordered sample classifcation has the following theorem: the optimal z class segmentation must be formed by adding another class on the basis of the optimal z − 1 class segmentation, so there is the following recursive formula: (4) Change the value of z, reset the segment numbers, and calculate the class diameter until all the preset segment numbers are realized.(5) Select the appropriate segmentation result from all segment numbers, which is to draw the curve of the value of objective function B(n, z) changing with segment number z, and check the segment number z at the bend or smoothing point of the curve as the optimal segmentation result [25].

Time Segment Division of Trafc-Flow Sequence Using the Dynamic Fisher Clustering Algorithm
Step 1: Obtain the average one-day trafc-fow data of the lanes in each controlled direction at an intersection on working days and nonworking days [23].Select the statistical interval of 15 min with more stable trafcfow characteristics [24], as described in Section 2.1, form the multiple trafc-fow sequences with 96 ordered sample characteristic values corresponding to w dimensions.
Step 2: Set the segment numbers of z.Since the number of trafc time periods is generally 4 to 8 [26], in order to efectively fnd the bend point of the curve of the objective function B(n, z) and determine the optimal value of z, the value range of z can be appropriately expanded on the premise of considering the computational efciency of the computer program.Terefore, the preset value range of z in this paper is 2 to 14.
Step 3: Use equation ( 1) to calculate all possible class diameters in the case of the segment numbers of z and use equation ( 2) to calculate the objective function.
Step 4: Use equation ( 3) to fnd the optimal clustering point.
Step 5: Change the value of z and return to Step 3 until all preset segment numbers are calculated and stop.
Step 6: Draw the curve of objective function B(n, z) and take the value of z at the bend point as the optimal segmentation result of the trafc-fow sequence.
Step 7: According to the optimal segmentation results, the time segment of trafc-fow sequence of w dimensions are divided, diferent colors are used to distinguish them, and diferent boundaries are formed between diferent colors, as shown in Figure 2.

Time Segment Division of Trafc-Flow Sequence of Diferent Dimensions
Step 1: According to the multiple partition boundaries of the time segment of a trafc-fow sequence of w dimensions, the time segment of the trafc-fow sequence of diferent dimensions are divided according to the same time order.
Step 2: Processing of "outliers."Due to the extra signal transition loss, if the time segment is too short, the minimum span of the time segment is set to 30 min [22,24].However, step 1 is likely to produce 15 min time segment, called "outliers."In order to make the TOD division more practical, the outliers need to be merged [22].Te specifc processing method is as follows: defne the minimum time segment T as 30 min.Step 3: Repeat Step 2 until all the time segments are longer than or equal to T. Ten, the preliminary TOD division of the trafc-fow sequence of diferent dimensions has been completed.

Optimization Method of Phase Combination.
According to Figure 1, assuming that the fow ratio corresponding to the controlled fow a t is y t , which can be calculated by (4).Without Figure 2 considering the phase sequence, a t can form 36 diferent phase schemes, and 6 phase schemes (Figure 3) can be formed in east-west and north-south directions, respectively, among which phase schemes 1 to 6 belong to the east-west direction, and phase schemes 7 to 12 belong to the north-south direction, as shown in Figure 4. Phase schemes 1 and 7 have no protected left-turn phases, which allow the trafc fow of straight and left turn in the opposite directions to be released at the same time and are suitable for the intersection with less trafc fow of left turn.Phase schemes 2 and 8 are the conventional symmetric phases, which are suitable for the intersections with more balanced trafc fow in opposite directions.Schemes 3 and 9 are phases that allow the trafc fow of straight and left turn in a single direction to be released at the same time, which are suitable for the intersections with the balanced trafc fow of straight and left turn in a single direction.Phase schemes 4, 5, 6, 10, 11, and 12 are the overlapping phases [27], which are suitable for intersections with the uneven fow in opposite directions.Te above-given phase combination can not only form a multiphase scheme but also form a two-phase or three-phase scheme according to the trafc fow.For example, phase schemes 1 and 7 can form a two-phase scheme, phase schemes 1 and 8 or phase schemes 1 and 9 can form a three-phase scheme, and phase schemes 7 and 2 or phase schemes 7 and 3 can form a threephase scheme.Te fow ratio calculation formulas and setting conditions of each phase scheme are listed in Table 1, where Y i (i � 1, 2, 3, 4, 5, 6) is the fow ratio of the 6 phase schemes in the east-west direction, and Y j (j � 7, 8, 9, 10, 11, 12) is the fow ratio of the 6 phase schemes in the northsouth direction.
where q td and S t are the lane trafc fow and saturation fow ratio of the controlled trafc fow a t , respectively, unit: PCU/ h.PHF is the peak-hour coefcient, the value of which for the main road is 0.75, the value of which for the subsidiary road and others is 0.85.Te sum of Y i and Y j is the cycle fow ratio Y u and the impact of Y u on the signal cycle time C can be analyzed with Webster's formula: where C is the signal cycle time and L is the total signal loss time.The time segment of 11:30 is less than T, b 1 =452-440=12<b 2 =491-440=51, so the time segement is merged with the previous time segement.

Journal of Advanced Transportation
As can be seen from formula (5), the larger value of Y u is, the larger value of C will be, resulting in a larger vehicle delay in the signal cycle.Terefore, the phase scheme with the least value of Y u can be selected as the preferred scheme to improve the control efciency of the signal cycle.When formula ( 5) is used to calculate the signal cycle time, Y u is required to be less than 0.9.When Y u is more than 0.9, the lane-use assignment needs to be further optimized.

Phase Combination Optimization Method for Further
considering Lane-Use Assignment.Lane-use assignment refers to the trafc direction distribution of the entrance lanes at the intersection, which is generally divided into straight, left, and right turn.At present, lane-use assignment adjustment is mainly realized through the variable lane at an intersection, which refers to the dynamic adjustment of lane-use assignment according to the change trends of trafc fow at diferent time periods of one day [28], which is an important factor to be considered in the process of TOD division, but it is less involved in the current research literature.Te lane-use assignment is closely related to the signal phase.We seek the optimal combination of lane-use assignment and signal phase mainly through the enumeration method [29].Taking the main controlled fow in Figure 1 as an example, assume that there is at least one straight lane, one left-turn lane, and one right-turn lane at each entrance of the intersection.Te specifc steps are as follows : Step  Step 2: Establish constraint conditions according to objective function variables.
where N E , N W , N S , and N N are the number of lanes at the east entrance, west entrance, south entrance, and north entrance of the intersection, respectively.q ET and q EL are the straight trafc fow and the left-turn trafc fow at the east entrance, respectively.q WT and q WL are the straight trafc fow and the left-turn trafc fow at the west entrance, respectively.q ST and q SL are the straight trafc fow and the left-turn trafc fow at the south entrance, respectively.q NT and q NL are the straight trafc fow and the left-turn trafc fow at the north entrance, respectively.S is the saturation fow ratio of the lane.Te formulas of Y i and Y j are shown in Table 1.
Step 3: Enumerate all possible allocation results of the number of straight and left-turn lanes at each entrance at intersection, list all lane-use assignment combinations that meet the constraint conditions, and calculate the value of Y u according to equation (8).
Step 4: Select N ET , N EL , N WT , N WL , N ST , N SL , N NT , N NL , i, and j corresponding to the minimum value of Y u according to the objective function (7) to determine the optimal scheme of the signal phase and lane-use assignment combination.

Signal Timing Calculation and Test
Step 1: According to the optimal phase combination, equations ( 5) and ( 9) are used to calculate the signal cycle time C and the total efective green time G E , respectively.
where g et is the efective green Table 2 time of controlled fow a t .
Step 2: Select the optimal phase combination corresponding to east-west and north-south directions in Table 2 to calculate g et .
Step 3: If g et is less than the minimum green time g min t , then multiply G E by the adjustment coefcient, which is the maximum value of g min t /g et , and return to Step 2.
Step 4: Calculate saturation x t of a t according to the following equation: where λ t is the green time ratio of a t .
Step 5: Te queue at the intersection increases rapidly when x t is more than 0.95.In order to avoid this situation, the maximum limit value of x t is set as 0.95 [30].Judge whether x t is more than 0.95.If not, go to Step 6.If so, x t � 0.95, recalculate C and g et according to equations (10) and ( 9), so that x t meets the requirements and then go to step 6.
Step 6: Calculate the display green time g t of each controlled fow a t according to the following equation: where l t is the startup loss time of a t , which is generally 3 seconds.A t is the yellow time, which is generally 3 seconds.

Journal of Advanced Transportation
Step 7: Finally, complete the calculation of all phase timing schemes of preliminary time periods.

Merging and Testing of Adjacent Periods of the Preliminary TOD Division.
Since the divided time periods need to be merged and tested [22], adjacent time periods of the preliminary TOD division need to be further merged and tested.Due to the TOD division is closely related to the lane-use assignment, phase scheme, and signal timing, and current literature about TOD division with less considering the lane-use assignment, in order to further refect the impact of lane-use assignment on TOD division, the adjacent time periods of the preliminary TOD division are merged and tested under the two conditions of whether the lane-use assignment is considered or not in this paper.
Case 1: Adjacent time periods are merged and tested without considering the lane-use assignment.
Step 1: Suppose that the two adjacent time periods are D a and D b , respectively, and the phase timing schemes calculated by the method in Sections 2.3.1 and 2.3.3 are A and B, respectively.If the phase schemes of A and B are the same, and the signal cycle time difference ΔC is not more than 15 s [20], then the adjacent time periods can be merged and go to step 2.
Step 2: Calculate the saturation x at of each controlled fow of Scheme A in time period D b and the saturation x bt of each controlled fow of Scheme B in time period D a according to equation (10).Te maximum limit value of saturation set by step 5 in Section 2.3.3 is 0.95 [30], and the time periods are merged according to the following rules.If x at ≤ 0.95 and x bt ≤ 0.95, the time periods D a and D b are merged, and the phase timing scheme with the shorter signal cycle time C in Scheme A and B is adopted.If x at ≤ 0.95 and x bt > 0.95, the time period D b is merged into the time period D a , and the phase timing Scheme A is adopted.If x at > 0.95 and x bt ≤ 0.95, the time period D a is merged into the time period D b , and the phase timing Scheme B is adopted.
If x at > 0.95 and x bt > 0.95, the time period D a and D b cannot be merged.
Step 3: Repeat the merge and test of adjacent time periods according to step 1 and step 2 until any two adjacent time periods cannot be merged, then complete the fnal result of TOD division.
Case 2: adjacent time periods are merged and tested considering lane-use assignment.
Te steps for case 2 are similar to those for case 1, the diference is that in step 1, the optimal lane-use assignment, signal phase, and timing scheme are obtained by the method described in Sections 2.3.2 and 2.3.3.If the lane-use assignment and signal phase scheme are the same in the adjacent time periods, and the signal cycle time diference ΔC is not more than 15 s [20], then the adjacent time periods can be merged, and go to Step 2. Te remaining steps are the same and are not described here.

Data Collection and Analysis.
In this paper, the trafc fow of each lane at the Jiuhua Road and Zheshan Road intersection in Wuhu City, China, is collected for one continuous week using a microwave detector.Because the TOD division and phase timing design methods for the working and nonworking days are the same, we used more representative trafc-fow data on working days for verifcation.Trough statistics, the trafc-fow data of 24 h in a working day at the intersection are obtained at 15 min intervals, as shown in Figure 5.
As shown in Figure 5, there is a large number of trafc fow at the intersection in the daytime.According to the change trends of the whole-day trafc fow of an intersection, Xu et al. [22] divided the intersection into hump type, constant-peak type, and multipeak type.And, this intersection tends to be a constant-peak type, characterized by a large number of trafc fow, mainly including shock-peak values and normal-peak values, where the low-peak values appear in a relatively short time [22].In addition, there are some diferences in the trafc fow between diferent directions of the intersection, especially between the east entrance and the west entrance.Te trafc fow of the west straight and west left-turn is much more than that of the east  6.

Design
Schemes.In order to analyze the impact of trafc-fow data clustering of diferent dimensions on the TOD division results, according to the trafc-fow data shown in Figure 5, the trafc-fow sequence of diferent dimensions are counted, as described in Section 2.1.Schemes A(w � 1), B(w � 2), C(w � 4), and D(w � 8) are adopted to carry out TOD division and phase timing design.Meanwhile, in order to further analyze the efect of lane-use assignment on TOD division results, scheme E(w � 8), considering lane-use assignment) is adopted to further carry out TOD division and phase timing design at the intersection.

Preliminary TOD Division.
Te method described in Section 2.2.2 is used to complete the preliminary TOD division of schemes A, B, C, D, and E. Since all the corresponding z value at the bend point of the objective function B(n, z) curve of the diferent trafc-fow sequence is 6 (take the objective function B(n, z) curve of the trafc-fow sequence of north left-turn as an example, as shown in Figure 7).Terefore, the optimal segmentation number of each trafc-fow sequence is 6.Te preliminary TOD division results of diferent schemes are shown in Figure 8.Since the trafc-fow dimensions adopted by schemes D and E are the same, the preliminary TOD division results of schemes D and E are the same.
It can be seen from Figure 8 that the preliminary TOD division results are determined according to the combination of the change intervals of the trafc-fow sequence of diferent dimensions.Te more dimensions, the more combinations of the change intervals, the more time periods in the preliminary TOD division, and the more it can refect the change trends of trafc fow of diferent direction.Among them, the number of time periods in the preliminary TOD division by schemes A, B, C, D, and E is 6, 8, 10, 18, and 18, respectively.Tese preliminary time periods still need to be merged and tested.E. Considering pedestrian crossings and vehicle trafc demand, the minimum green time of the straight phase and left-turn phase is 14 s and 5 s, respectively.Te fnal results of the TOD division are shown in Figure 9. Te corresponding phase timing schemes are shown in Tables 3-7.

Final Results of TOD Division and
Among them, scheme E further optimized the laneuse assignment at the intersection; according to the method mentioned in Section 2.3.2, the optional lane-use assignment schemes in the east, west, south, and north entrances are shown in Figure 10.Selecting time period 13 as an example, the calculation results for the optimal lane and phase schemes are shown in Figure 11; the minimum value of Y i in the east-west direction is 0.41; that is, the lane-use assignment scheme E1 of east entrance and scheme W2 of west entrance are selected, and the selected phase scheme is scheme 4. Te minimum value of Y j in the north-south direction is 0.43; that is, the lane-use assignment scheme S2 of south entrance and scheme N2 of north entrance are selected, and the selected phase scheme is scheme 10.In Table 7, lane-use assignment schemes adopted in diferent time periods can be realized by variable lane facilities.For example, in the east entrance, the lane-use assignment scheme E1 is adopted in time periods of 1, 2, 12, and 13, and scheme E2 is adopted in other time periods.Te lanes marked in the red box in Figure 10 can be set as variable lanes to achieve a diferent lane-use assignment in the corresponding time periods.It can be seen from the above-given fnal results of TOD division and phase timing that, the number of fnal time periods after the merge and test of schemes A, B, C, D, and E is 6, 7, 10, 14, and 14, respectively.Among them, scheme A and scheme B both have obvious peak periods in the afternoon, which are 17:00-19:00 and 17:00-19:15, respectively.However, the period span in the morning is obviously longer, both from 07:00 to 12:15, its corresponding signal cycle time is longer, which are 186 s and 167 s, respectively, and there are fewer fat-peak periods, so the signal control efciency is not high.Scheme C has obvious peak periods in the morning and afternoon, which are 07:00-07:45 and 17: 00-18:30, respectively, and the subpeak periods in the afternoon which is 18:30-19:15.Compared with scheme A and B, the fat-peak periods are more, which are 12:15-13:30, 13: 30-15:45, and 15:45-17:00, respectively, so the signal control efciency will be improved.Scheme D has obvious peak periods and subpeak periods in the morning and afternoon.Te morning peak period is 09:00-09:45 and the subpeak period is 07:00-09:00.Te afternoon peak period is 17: 45-19:15 and the subpeak period is 17:00-17:45.And, the fat-peak periods of scheme D in the daytime are signifcantly more than those of scheme A, B, and C, which are 09: 45-10:30, 10:30-11:00, 11:30-11:30, 11:30-12:30, 12:30-13: 30, 13:30-15:45, and 15:45-17:00, respectively.Terefore, the signal control efciency will be greatly improved.Te TOD division results of scheme E and scheme D are similar.Since scheme E further optimizes the lane-use assignment, and the signal cycle time of each time periods is shorter than that of scheme D, so its signal control efciency will be further improved.In addition, the overall trend of TOD division results of various schemes is consistent, and the time nodes of TOD division of most schemes are consistent, such as 06:00, 07:00, 12:15, 15:45, 17:00, and 19:15.Except for the diferent fneness of TOD division in the daytime, the TOD division results in the evening and at night are the same.In the following, the trafc benefts of the various schemes are further evaluated and validated through trafc simulation.

Analysis of Simulation Results
. VISSIM trafc simulation software is used to simulate each time periods, phase timing, and lane-use assignment of Schemes A, B, C, D, and E, according to the actual trafc-fow data of the intersection.Te average vehicle delay of each time periods of eight controlled fows from a 1 to a 8 in Figure 2 is extracted, and the average vehicle delay data A dv , B dv , C dv , D dv , and E dv of each time periods of each scheme are calculated.Te passing vehicle data are extracted by simulation.Te total vehicle delay data A ds , B ds , C ds , D ds , and E ds for 24 hours in one day are calculated.Te results are shown in Tables 8-12.
It can be seen from Tables 8-12 that the total vehicle delay at the intersection throughout the day of schemes A, B, C, D, and E is 570.9 h, 557.8 h, 494.5 h, 465.0 h, and 364.1 h, respectively, of which scheme D is 6.0% less than scheme C, La ne sc he m e Journal of Advanced Transportation scheme C is 11.3% less than scheme B, scheme B is 2.3% less than scheme A. After the lane-use assignment is optimized in scheme E, the total vehicle delay is obviously the least, which is reduced by 21.7% compared with Scheme D. Tis indicates that the scheme with more dimensions of trafc fow will lead to less total vehicle delay at the intersection, and the reduction of total vehicle delay at the intersection is the most obvious after the lane-use assignment is further optimized.
In order to further analyze the changes of vehicle delays of each scheme, the average vehicle delay data A dv , B dv , C dv , D dv , and E dv at the intersection in each time periods with each scheme from Tables 8-12 are extracted.Te change curve of the average vehicle delay at the intersection throughout the day is drawn.In order to refect the change trends, the total trafc-fow data V of diferent controlled trafc fow at the intersection for 24 h in one day are extracted as a reference, as shown in Figure 12.
As can be seen from Figure 12, compared with schemes A, B, and C, the average vehicle delay data at the intersection of scheme D better refects the change trends of the trafc fow throughout the day.It increases with an increase in trafc fow and decreases with a decrease in trafc fow.Especially in the daytime, it refects multiple change trends with the change of trafc fow.Te change trends of the average vehicle delay data at the intersections of schemes C, B, and A decreases one by one.In particular, schemes A and B maintain a large average vehicle delay from 7:15 am to 12: 15 pm, which is obviously directly related to the TOD division and the phase timing results.Scheme E further timizes the lane-use assignment on the basis of Scheme D, and the average vehicle delay throughout the day is obviously the least.As can be seen from Figure 13, the average vehicle delay at the intersection throughout the day of schemes A, B, C, D, and E is reduced gradually, which are 33 s, 32 s, 30 s, 28 s, and 25 s, respectively.
As explained above, if a scheme with more trafc-fow dimensions is adopted, the average vehicle delay in each time periods at the intersection will be more in line with the change trends of the trafc fow, and the average vehicle delay at the intersection throughout the day will be less.Among them, scheme D is 6.7% less than scheme C, scheme C is 6.3% less than scheme B, and scheme B is 3.0% less than scheme A. After the lane-use assignment is optimized in Scheme E, the average vehicles delay throughout the day is further effectively reduced by 10.7% compared with scheme D.

Discussion
Te applicability of the method proposed in this paper is discussed from two aspects: the fneness and the trafc beneft of the TOD division.
In terms of the fneness of the TOD division, an important fnding of this paper is that the more dimensions of trafc fow data adopted, the fner the TOD division result will be.According to the TOD division method proposed in this paper, the fnal time period number of TOD division obtained by schemes A(W � 1), B(W � 2), C(W � 4), D(W � 8), and E(W � 8) is 6, 7, 10, 14, and 14, respectively.Among them, scheme A(W � 1) takes the total trafc-fow data at an intersection as the basis for TOD division, and the time period number obtained is the least.Te period span in the morning is longer, and there is no obvious morning peak hours.Similar to the above situation, literature [17,18,20] used the total trafc-fow data at an intersection to carry out the optimization method research of TOD division, and the optimized time period numbers are 6, 8, and 7, respectively.Te period span in the afternoon is longer, without obvious afternoon peak periods.Literature [25] takes the two directions with a large number of trafc fow of west straight and west left-turn as representatives and adopts trafc fow data of 2 dimensions to carry out TOD division optimization.Te optimized time period number is 7, and the period span in the afternoon is also longer, without obvious afternoon peak periods.Tis is similar to the TOD division carried out in scheme B(W � 2) based on trafc-fow data of 2 dimensions of east-west and north-south directions at the intersection.Te time period number of scheme B is also 7, but the diference is that the period span in the morning is long and there is no obvious morning peak periods.Tis above situation may be related to the change of trafc fow at the intersection, but it can not be ignored that diferent optimization methods in diferent literature all have similar phenomena, which can refect that the use of trafc-fow data clustering with diferent dimensions may directly afect the fneness of TOD division results.For example, schemes D data refects the overall trafc state at the intersection, but it is too extensive for signal timing, which fails to consider the characteristics of directional trafc fow and may result in the risk of developing TOD timing plans that are not well suited for expected trafc.
In terms of the trafc benefts of TOD division, another important fnding of this paper is that the more refned the TOD division results, the less the total vehicle delay at the intersection throughout the day, the average vehicle delay in each time periods at intersection will be more in line with the change trends of the trafc fow, and the less the average vehicle delay throughout the day.After further considering the lane-use assignment optimization, the total and average vehicle delay at an intersection will be further efectively reduced.Tis paper and existing studies have reached a consensus that TOD divisions serve trafc signal control, and the two have consistent objectives.It is necessary to establish the relationship between TOD divisions and control benefts [20].Most existing studies use Synchro software to optimize signal timing and use SimTrafc software to complete the beneft evaluation while carrying out TOD divisions [2,12,14,17,20].Unlike existing studies, the proposed method integrates the TOD division, phase optimization, and timing design in the whole process, and the lane-use assignment optimization is further considered.Furthermore, the rationality of the fnal result of the TOD division is further tested according to the lane, phase, and timing schemes.Finally, the fnal result of the TOD division is evaluated by VISSIM trafc simulation.At present most studies use the index of total vehicle delay to evaluate the superiority of the optimization method [17,18,20,22,24].Firstly, the trafc beneft is evaluated by using the total vehicle delay data of 24 h in this paper.It is found that if a scheme with more trafc-fow dimensions is adopted, the total vehicle delay at the intersection throughout the day will be less.Compared with schemes A, B, and C, the total vehicle delay of scheme D is obviously the least.On the basis of scheme D, the lane-use assignment is further considered to optimize in scheme E, the signal cycle time of each period is signifcantly reduced, and the total vehicle delay of scheme D is further efectively reduced.In order to further analyze the efectiveness of this method, this paper for the frst time adopt a change curve of the average vehicle delay of the intersection throughout the day to analyze the matching degree between diferent TOD division schemes and the trafc fow of the intersection.Te scheme (e.g., scheme D) with more trafc-fow dimensions is adopted, and the average vehicle delay in each time periods of the intersection is more in line with the trends in trafc fow.Tat is the average vehicle delay increases with the increase of trafc fow and decreases with the decrease of trafc fow, refecting multiple trends, especially in the daytime.Moreover, the average vehicle delay throughout the day at the intersection is also less, and the average delay of vehicles in scheme E is also the least.References [24,25] select the optimal TOD division scheme on the premise of determining the optimal number of clusters.Te authors proposed that there should not be too many time periods for the TOD divisions.Otherwise, this will afect the trafc beneft.On the premise of determining the optimal number of clusters, the proposed

16
Journal of Advanced Transportation method carries out the time segments division in a singledimension trafc-fow sequence, and further uses multidimensional trafc-fow sequences to complete the fnal results of TOD division.According to the VISSIM simulation evaluation, the scheme with more time periods is formed, and the vehicle delay is the lowest (e.g., scheme E).Tis shows that the number of time periods is not the main factor afecting the trafc benefts.Te key is to see whether the corresponding lane, phase, and timing schemes of each time periods adapt to the changes in trafc fow.Te method proposed in this paper uses multidimensional trafc-fow sequences to carry out the integrated design and inspection of TOD division, phase timing, and lane-use assignment.Tis may be more suitable for the trends in trafc fow.Terefore, the benefts to trafc are ensured.In addition, the method proposed in reference [22] is not applicable to intersections of the constant-peak type, and its vehicle delay is larger than the traditional total trafc-fow segmentation model.Te tested intersection in this paper tends to be the constant-peak type, and scheme A is similar to the scheme for traditional total trafc-fow segmentation models, the vehicle delay of which is the largest, this indirectly shows that the proposed method in this paper has better applicability.

Conclusion
Based on the change trends of trafc fow in each controlled direction at the intersection, we carry out a study on spacetime resource integrated optimization method for TOD division at the intersection based on multidimensional trafc fow.First of all, the trafc fow of diferent dimensions for TOD division are analyzed, and the dynamic Fisher algorithm is used to complete the time segment division of the trafc-fow sequence of diferent dimensions.On this basis, the preliminary TOD division is completed.Ten, the signal phases and timing schemes are completed.Furthermore, the lane-use assignment is further considered to optimize.Finally, the adjacent time periods are merged and tested to form the fnal result of the TOD division.In order to verify the efectiveness of the proposed method, the TOD division schemes based on trafc-fow data of diferent dimensions is further completed with the actual intersection data.Te vehicle delay of diferent schemes are evaluated by VISSIM trafc simulation software.Te results show that adopting trafc-fow data clustering of 8 dimensions (8 controlled trafc fow) to carry out TOD division at the intersection, the TOD division results are the most refned, and the total and average vehicle delay throughout the day are superior to other TOD division schemes of using trafc-fow data clustering of fewer dimensions.On this basis, after further considering the lane-use assignment optimization, the total and average vehicle delay throughout the day at the intersection are further efectively reduced, which indicates that the integration optimization method of TOD division, phase timing, and lane-use assignment based on multidimension trafc-fow data clustering is feasible and has good reference signifcance in the study of TOD division at an intersection.
Due to limitations with data collection, we only used trafc-fow data from a single intersection during a sample of one week.Te results are thus defcient in some ways.Trafc-fow data need to be collected from multiple types of intersections over a longer time to verify the applicability of the proposed method.In addition, in future research, we will use big data and vehicle-road cooperation technology to study TOD divisions for continuous multicoordinated controlled intersections.
If the divided time segment in step 1 is less than T, calculate b 1 and b 2 , where b 1 is the diference of trafc fow between the time segment and the previous time segment, and b 2 is the diference of trafc fow between the time segment and later time segment.If b 1 ≤ b 2 , the time segment is merged with the previous time segment; If b 1 > b 2 , the time segment is merged with the later time segment.Te divided result of the 15 min time segment (11:30) in the trafc-fow sequences of 8 dimensions is shown in Figure 3.

N a 7 a 8 a 4 a 3 a 6 a 5 a 1 a 2 Figure 1 :
Figure 1: Main controlled trafc fow at a typical intersection.

Figure 2 :
Figure 2: Time segment division results of trafc-fow sequence using the dynamic Fisher clustering algorithm.

Figure 3 :
Figure 3: Example of the outlier processing of time segment division of trafc-fow sequence of 8 dimensions.

5 Figure 4 :
Figure 4: Phase schemes corresponding to the controlled trafc fow at intersection.

Figure 5 :Figure 6 :Figure 7 :
Figure 5: Trafc-fow data of 24 h in a working day at Jiuhua road and Zheshan road intersection.

Figure 9 :
Figure 9: Final results of TOD division of Jiuhua road and Zheshan road intersection.(a) Scheme A. (b) Scheme B. (c) Scheme C. (d) Scheme D (E).

Figure 10 :
Figure 10: Optional lane-use assignment schemes in the east, west, south, and north entrances.

Figure 11 :
Figure 11: Calculation results of optimal lane and phase schemes in time period 13.(a) E-W.(b) S-N.

Figure 12 :Figure 13 :
Figure 12: Change curve of the average vehicle delay at the Jiuhua road and Zheshan road intersection in each time periods of one day.

Table 3 :
Phase timing results of time periods of scheme A. C a 1 a 2 a 3 a 4 a 5 a 6 a 7 a 8

Table 4 :
Phase timing results of time periods of scheme B.

Table 5 :
Phase timing results of time periods of scheme C.

Table 6 :
Phase timing results of time periods of scheme D. C a 1 a 2 a 3 a 4 a 5 a 6 a 7 a 8

Table 7 :
Lane-use assignment and phase timing results of time periods of scheme E.

Table 8 :
Analysis results of the average vehicle delay in scheme A.