CN107657377B

CN107657377B - Bus lane policy evaluation method based on breakpoint regression

Info

Publication number: CN107657377B
Application number: CN201710881294.7A
Authority: CN
Inventors: 钟绍鹏; 王仲; 程荣; 刘佳超; 邹延权; 李旭丰
Original assignee: Dalian University of Technology
Current assignee: Dalian University of Technology
Priority date: 2017-09-26
Filing date: 2017-09-26
Publication date: 2021-02-19
Anticipated expiration: 2037-09-26
Also published as: CN107657377A

Abstract

The invention provides a bus lane policy evaluation method based on breakpoint regression, and belongs to the technical field of bus lane policy evaluation. The method has the advantages that the actual measurement data is utilized to carry out breakpoint regression on the speeds of two different types of motor vehicles, the sudden change situation of result variables before and after a break point is analyzed by combining images, the influence of a special lane on the speeds of buses and social vehicles is quantitatively evaluated, and the urban traffic management department is assisted to make and optimize a bus special lane policy.

Description

Bus lane policy evaluation method based on breakpoint regression

Technical Field

The invention belongs to the technical field of urban traffic planning, relates to the field of public transport lane policy evaluation, and particularly relates to technical methods such as breakpoint regression and the like.

Background

Aiming at the evaluation of the effect of the bus lane, the conventional research method mainly comprises three types of practical experience summary, traffic microscopic simulation and traffic distribution theory analysis. Cox studied the application of the BUS lane in Dallas in text RESERVED BUS LANES IN DALLAS, TEXAS; thamizhaasan and P.Vedagi construct a novel microscopic simulation model HETEROSIM under a mixed Traffic Flow state in a Microsimulation Study of the Effect of Exclusive Bus Lanes on Heterogeneous Traffic Flow to simulate the behavior characteristics of a motor vehicle in a real situation, so that the Effect of a Bus lane is evaluated; shuuguang Li and YongfenggJu put forward a multi-mode dynamic traffic distribution model in Evaluation of Bus-Exclusive Lanes to evaluate the effect of the Bus lane.

The experience summarization method has stronger practicability and can be directly applied to examples; traffic microscopic simulation is close to a random test, but cannot be used as a means for evaluating a realistic effect because the actual situation cannot be reflected; the traffic distribution theory focuses more on theoretical analysis, and is difficult to apply to practical cases, and the assumed conditions of the method cannot reflect the real state of the road network. In contrast, research to evaluate the effectiveness of lane-specific policies based on empirical data is still insufficient.

The breakpoint regression provided by the invention is a statistical research method based on empirical data, can evaluate the real effect of a special road through the actual measurement data of the real road, supplements the existing research from the perspective of the actual application effect, and can verify the theoretical analysis.

Disclosure of Invention

The invention aims to provide a method for evaluating the effect of a bus lane policy based on measured data, which quantifies the influence of the bus lane on the speed of buses and social vehicles and further provides corresponding suggestions.

The technical scheme of the invention is as follows:

a bus lane policy evaluation method based on breakpoint regression comprises the following steps:

(1) variable determination and hypothesis testing

The research object is a public transport lane in peak hours, the research object is only opened for public transport vehicles in specific hours every day, break points are generated at the opening time and the ending time, and only road resource distribution changes before and after the break points;

the time t is a driving variable, the value of which directly influences the change of road resource allocation and is observable; when the time is less than the opening time, the bus lane is the same as the common lane and is used by any vehicle; when the time exceeds the opening time, the bus lane is only allowed to be used by buses, and other social vehicles are only allowed to use other common lanes;

the link average speed S is the result variable,S^bindicating the average speed, S, of the bus^cRepresenting the average speed of the taxi;

the key point of breakpoint regression is treatment effect estimation, and the treatment in the regression model is represented by introducing a binary treatment variable EBL_tThe binary variable has two values of 0 and 1. 1 represents that the bus lane is in an open period, the study object receives treatment, 0 represents that the bus lane is in a closed state, and the study object does not receive treatment;

under the actual urban traffic state, the time of the bus and the social vehicle reaching the evaluation road section has randomness, a driver cannot accurately control the reaching time to avoid or accept treatment intentionally, and the first condition that the breakpoint regression method is effective is met: the study subjects were unable to accurately control the driving variables around the discontinuity; second condition for breakpoint regression approach to be effective: other control variables influencing result variables need to be continuous at the discontinuous points, and because the continuity conditions of the variables are often not easy to directly verify, the assumption of continuity is put forward before regression, and then whether the assumption conditions are satisfied is verified through the regression results;

(2) image analysis

Before breakpoint regression, the collected data is processed, a scatter plot is plotted with speed s (m/s) as ordinate and time t (min) as abscissa, and then data points are fitted. When the global data is more and disordered, the Bin method is adopted to process the global data, the noise in the global data is removed, and the fitted curve is smoother. Performing linear or polynomial regression on the converted data points, and then preliminarily observing whether data jump exists at the breakpoint, wherein if the data jump does not exist, the subsequent regression result may be unreliable;

(3) global regression

Basic parameter regression model

S_t＝α+β₀·EBL_t+β₁t+β₂t·EBL_t+γX_t+ε_t (1)

The regression model of the basic parameters is expressed before and after the opening of the public transport laneThe average running speed of the vehicle on the target road section; wherein t represents the number of minutes from the break point, which is a driving variable, and t is 0 at the break point; dependent variable S_tIs the target link average speed in the t minute; EBL_tThe method is a binary handling variable, and comprises two values of 0 and 1, if a break point t is 0, the value is 1 when t is greater than 0, the vehicle on the road section receives the handling of lane resource allocation change, and the value is 0 when t is less than 0, the vehicle on the road section does not receive the handling of lane resource allocation; if the break point t is 0, when t is greater than 0, the time value is 0, the lane resource allocation is recovered to the normal condition, and when t is less than 0, the time value is 1, the bus lane is still in the open state. X_tVectors composed of other control variables; e is the same as_tIs white noise.

The coefficient of each variable in the regression model reflects the influence degree of each variable on the result variable; wherein the most important target parameter for regression is beta₀The value of which directly reflects the magnitude of the treatment effect at the discontinuity. Beta is a₁And beta₂Is the regression coefficient of the driving variable t, the size of which determines the overall variation trend of the result variable (speed) with the driving variable (time) before and after the discontinuity. Gamma is a vector formed by regression coefficients of other control variables, reflects the influence degree of the other control variables on the result variable, and although the vector is not a main object of research, the change of the value and the change in the robustness test can verify the hypothesis of breakpoint regression and verify whether the other control variables are related to treatment effects.

Separating a taxi from a bus, respectively calculating the average speed of the taxi and the bus, and distinguishing models applied in regression mainly on selection of other control variables; for taxis, the taxi has two states of passenger carrying and no-load during operation, and theoretically, the speed is high in the passenger carrying state, so that the passenger carrying ratio is taken as one of other control variables; on an urban road, when a bus lane is not opened, buses and social vehicles are mixed, the buses influence taxis, if the number of the buses on a road section is too large, the relative speed of the buses is low, the phenomena of lane changing for entering and leaving and waiting for passengers exist, the operation of the taxis is influenced, and the number ratio of the buses to the taxis is used as a control variable; in addition, the quantity of taxis and floating buses on the road section in unit time is also used as a control variable; the linear regression model for the taxi was:

in the formula:

P，γ_P-taxi passenger ratio and its regression coefficient in unit time;

C，γ_Cthe number of the taxi floating cars in unit time and the regression coefficient thereof;

B，γ_B-the number of floating buses and their regression coefficients in unit time;

R，γ_R-the number ratio of buses to taxis and their regression coefficients in a unit time.

For the regression of the bus, other control variables are the number of the floating buses, the number of the taxi floating buses and the number ratio of the number of the taxi floating buses to the number of the taxi floating buses, so that the regression model of the bus is as follows:

in the formula:

C，γ_Cthe number of the taxi floating cars and the regression coefficient thereof in unit time;

R，γ_R-the ratio of the number of taxis to buses in a unit time and the regression coefficient thereof.

Obtaining regression coefficients of all variables and corresponding standard errors from the regression results, and evaluating the treatment effect by comparing the regression coefficients with the standard errors; the positive and negative values and the relative size of the regression coefficients reflect the influence degree of the corresponding variables on the result variables, and when the regression coefficients are small or stable within a certain range, the control variables are considered to have no relation to the treatment effect size in the selected data range, so that the reliability of the breakpoint regression estimation result is proved;

after global linear regression, polynomial regression is usually performed by adding multiple terms in order to better fit the time-dependent variation of the resulting variables, and also as part of the robustness test. The high-order term of the time t can be added directly on the basis of a linear regression model during regression. The global nth polynomial regression expression of the bus is (4), and the global nth polynomial regression expression of the taxi is (5):

(4) local linear regression

Let t₀And selecting data points with the width h on both sides of the break point for regression, wherein the data points which are smaller than the break point are used as control groups, and the data points which are larger than the break point are used as treatment groups. Assuming the regression function for the treatment group (right side of discontinuity) is linear:

S_i＝α_r+β_r·t_i+ε_i (6)

the regression aims to obtain values of the break points through data values on the right side of the break points, different weights need to be given to the data points as the distances from the different data points to the break points are different and the influence on the estimated point values is larger as the distances are closer, the weights are larger as the distances are closer to the break points, otherwise, the weights are smaller, and the weight distribution is realized through a specific kernel function K. Final selection (. alpha.)_r，β_r) The values are such that the data to the right of the break point is given the smallest sum of the local weighted squares, i.e.

Thus, the point estimate of the treatment group at the discontinuity is

S_r(t₀)＝α_r+β_r·(t₀-t₀)＝α_r (8)

The regression coefficient can also be obtained by the control group in the same way

Thereby obtaining an estimate of the control group at the discontinuity point as

S_l(t₀)＝α_l+β_l·(t₀-t₀)＝α_l (10)

The final treatment effect estimate is

τ＝α_r-α_l (11)

(5) Robustness testing of estimates

When breakpoint regression is carried out, robustness test is carried out to test that the estimated value of the treatment effect has certain stability and reliability; robustness tests are mainly divided into two main categories:

1) robustness testing for global polynomial regression

The robustness test aiming at the global polynomial regression is mainly realized by changing the polynomial degree and changing the data range;

global polynomial regression estimates values using data far from the breakpoint, and thus is greatly affected by data far from the breakpoint, and in order to check reliability of the estimated value of the treatment effect, it is necessary to continuously reduce the window width around the breakpoint as a center, so that the used data range is reduced to a sufficiently small width around the breakpoint. The treatment effect estimated values in different data ranges and different polynomial times are compared, if the data ranges and the polynomial times are changed, the treatment effect estimated values can be maintained in a certain range, the fluctuation is not large, and the estimated values have certain reliability;

2) robustness testing for local linear regression

The robustness test aiming at the local linear regression is mainly realized by changing the kernel function type and the bandwidth size;

the type of the kernel function determines the weight value of data around the evaluation point, and the method mainly adopts a rectangular kernel function, a triangular kernel function and a leaf-Pinicukov kernel function to carry out robustness test; the bandwidth is selected to balance accuracy and variance. Comparing treatment effect estimated values under different kernel function types and different bandwidths, wherein if the kernel function types and the bandwidths are changed, the treatment effect estimated values can be maintained within a certain range, and the fluctuation is not large, so that the estimated values have certain reliability;

in addition, the lane-only policy driving variable studied by the present invention is time, and it is difficult for policy enforcers and traffic drivers to unify the time, that is, the time when the treatment occurs is not necessarily exactly at the fixed open time, which causes a certain deviation in the estimation of the treatment effect. Therefore, when the robustness is tested, the breakpoint position needs to be adjusted back and forth to perform regression estimation, and the change situation of the estimation value is examined to determine the real position of the breakpoint.

The invention has the beneficial effects that: the method is based on breakpoint regression of empirical data, the actual effect of the special lane is evaluated by utilizing the actual measurement data of the actual road, the urban traffic management department can be assisted to make and optimize the bus special lane policy, the cost of the method is low, the obtained conclusion is direct and effective, and the method has certain popularization value.

Drawings

FIG. 1 is a schematic diagram of a breakpoint regression application.

Fig. 2 is an electronic map of a target link.

Fig. 3(a) is a bus breakpoint fitting image at the opening time of the bus lane, the width of the box body is 1, and the fitting polynomial degree is 1.

Fig. 3(b) is a bus breakpoint fitting image at the opening time of the bus lane, the width of the box body is 1, and the fitting polynomial degree is 2.

Fig. 3(c) is a bus breakpoint fitting image at the opening time of the bus lane, the width of the box body is 1, and the fitting polynomial degree is 3.

Fig. 3(d) is a bus breakpoint fitting image at the opening time of the bus lane, the width of the box body is 2, and the fitting polynomial degree is 1.

Fig. 3(e) is a bus breakpoint fitting image at the opening time of the bus lane, the width of the box body is 2, and the fitting polynomial degree is 2.

Fig. 3(f) is a bus breakpoint fitting image at the opening time of the bus lane, the width of the box body is 2, and the fitting polynomial degree is 3.

Fig. 3(g) is a bus breakpoint fitting image at the opening time of the bus lane, the width of the box body is 3, and the fitting polynomial degree is 1.

Fig. 3(h) is a bus breakpoint fitting image at the opening time of the bus lane, the width of the box body is 3, and the fitting polynomial degree is 2.

Fig. 3(i) is a bus breakpoint fitting image at the opening time of the bus lane, the width of the box body is 3, and the fitting polynomial degree is 3.

Note: in fig. 3(a) -3(i), t-0 is discontinuity 7:30AM, t-1 is 7:31AM, t-1 is 7:29AM, and so on.

Fig. 4(a) is a bus breakpoint fitting image obtained by advancing the breakpoint from 7:30AM by 1 min.

And (b) in fig. 4 is a bus breakpoint fitting image obtained by advancing the breakpoint from 7:30AM by 5 min.

Fig. 4(c) is a bus breakpoint fitting image obtained 7min in advance of the breakpoint from 7:30 AM.

FIG. 4(d) is a bus breakpoint fitting image obtained by advancing the breakpoint from 7:30AM by 10 min.

Fig. 5(a) is a bus breakpoint fitting image at the closing time of the bus lane, the width of the box body is 1, and the fitting polynomial degree is 1.

Fig. 5(b) is a bus breakpoint fitting image at the closing time of the bus lane, the width of the box body is 1, and the fitting polynomial degree is 2.

Fig. 5(c) is a bus breakpoint fitting image at the closing time of the bus lane, the width of the box body is 1, and the fitting polynomial degree is 3.

Fig. 5(d) is a bus breakpoint fitting image at the closing time of the bus lane, the width of the box body is 2, and the fitting polynomial degree is 1.

Fig. 5(e) is a bus breakpoint fitting image at the closing time of the bus lane, the width of the box body is 2, and the fitting polynomial degree is 2.

Fig. 5(f) is a bus breakpoint fitting image at the closing time of the bus lane, the width of the box body is 2, and the fitting polynomial degree is 3.

Fig. 5(g) is a bus breakpoint fitting image at the closing time of the bus lane, the width of the box body is 3, and the fitting polynomial degree is 1.

Fig. 5(h) is a bus breakpoint fitting image at the closing time of the bus lane, the width of the box body is 3, and the fitting polynomial degree is 2.

Fig. 5(i) is a bus breakpoint fitting image at the closing time of the bus lane, the width of the box body is 3, and the number of times of the fitting polynomial is 3.

Note: in fig. 5(a) -5(i), t-0 is discontinuity 9:30AM, t-1 is 9:31AM, t-1 is 9:29AM, and so on.

Fig. 6(a) is a breakpoint fitting image of a taxi at the opening time of a bus lane, where the width of the box is 1 and the number of times of the fitting polynomial is 1.

Fig. 6(b) is a breakpoint fitting image of the taxi at the opening time of the bus lane, where the width of the box is 1 and the number of fitting polynomials is 2.

Fig. 6(c) is a breakpoint fitting image of the taxi at the opening time of the bus lane, where the width of the box is 1 and the number of fitting polynomials is 3.

Fig. 6(d) is a breakpoint fitting image of the taxi at the opening time of the bus lane, where the width of the box is 2 and the number of fitting polynomials is 1.

Fig. 6(e) is a break-point fitting image of the taxi at the opening time of the bus lane, the width of the box body is 2, and the fitting polynomial degree is 2.

Fig. 6(f) is a breakpoint fitting image of the taxi at the opening time of the bus lane, where the width of the box is 2 and the fitting polynomial degree is 3.

Fig. 6(g) is a breakpoint fitting image of the taxi at the opening time of the bus lane, where the width of the box is 3 and the number of fitting polynomials is 1.

Fig. 6(h) is a breakpoint fitting image of the taxi at the opening time of the bus lane, where the width of the box is 3 and the number of fitting polynomials is 2.

Fig. 6(i) is a breakpoint fitting image of a taxi at the opening time of a bus lane, where the width of the box is 3 and the number of times of the fitting polynomial is 3.

Note: in fig. 6(a) -6(i), t-0 is discontinuity 7:30AM, t-1 is 7:31AM, t-1 is 7:29AM, and so on.

Fig. 7(a) is a breakpoint fitting image of a taxi at the closing time of a bus lane, where the width of the box is 1 and the number of times of the fitting polynomial is 1.

Fig. 7(b) is a breakpoint fitting image of the taxi at the closing time of the bus lane, where the width of the box is 1 and the number of times of the fitting polynomial is 2.

Fig. 7(c) is a breakpoint fitting image of the taxi at the closing time of the bus lane, where the width of the box is 1 and the number of fitting polynomials is 3.

Fig. 7(d) is a breakpoint fitting image of the taxi at the closing time of the bus lane, where the width of the box is 2 and the number of fitting polynomials is 1.

Fig. 7(e) is a breakpoint fitting image of the taxi at the closing time of the bus lane, where the width of the box is 2 and the number of times of the fitting polynomial is 2.

Fig. 7(f) is a breakpoint fitting image of the taxi at the closing time of the bus lane, where the width of the box is 2 and the fitting polynomial degree is 3.

Fig. 7(g) is a breakpoint fitting image of the taxi at the closing time of the bus lane, where the width of the box is 3 and the number of fitting polynomials is 1.

Fig. 7(h) is a breakpoint fitting image of the taxi at the closing time of the bus lane, where the width of the box is 3 and the number of times of the fitting polynomial is 2.

Fig. 7(i) is a breakpoint fitting image of a taxi at the closing time of a bus lane, where the width of the box is 3 and the number of times of the fitting polynomial is 3.

Note: in fig. 7(a) -7(i), t-0 is discontinuity 9:30AM, t-1 is 9:31AM, t-1 is 9:29AM, and so on.

FIG. 8 is a general flow diagram of a breakpoint regression method.

FIG. 9 is a regression data processing flow chart.

Detailed Description

The following describes embodiments of the present invention in conjunction with technical solutions, and simulates the implementation effects of the present invention.

1. Selection of target road section and preparation of regression data

Selecting the southeast road in the Rohu region of Shenzhen city as a target road section, wherein the bus lane is arranged on the outermost side of the road, and the open time is 7: 30-9: 30 and 17: 30-19: 30, which are large in traffic volume each day. The number of the bus lines passing through the road section is 16, and two roadside type stop stations are provided. Fig. 2 is an electronic map of a target link.

And extracting data points of taxis and buses in the southeast road of the deep south within five hours from 6:00 to 11:00 of five days from 6, 9 days to 13 days in 2014 as regression basic data, and calculating the average speed in SPSS software. According to the floating car calculation model, selecting a unit time interval of 1min, calculating the average speed of the bus and the taxi in each minute within 5 hours, and counting the number of the buses and the taxies in each minute and the passenger carrying rate of the taxies.

And (4) performing breakpoint regression analysis by taking the opening time and the ending time of the bus lane as breakpoints respectively, wherein the width of the global data is 1.5h before and after the breakpoints respectively. The breakpoint is 7:30, the data range is 6:00 to 9:00, and the time before and after the breakpoint is 90min respectively. Tables 1 to 4 show the comparison between before and after the break point of the regression data of the taxi and the bus.

TABLE 1 taxi regression data breakpoint front and back comparison (7:30 as breakpoint)

TABLE 2 taxi regression data breakpoint front-back comparison (breakpoint 9: 30)

TABLE 3 bus regression data breakpoint front and back comparison (with 7:30 as breakpoint)

TABLE 4 bus regression data breakpoint front and back comparison (with 9:30 as breakpoint)

2. Breakpoint regression analysis

(1) Bus regression result analysis

In order to graphically observe the appearance of breakpoints, an image of global data was rendered prior to regression, and data points were fitted. Fig. 3(a) -3(i) show the variation of the average speed of the road section with time under the conditions of different box numbers and different fitting polynomial times, respectively, each point in the graph represents the average speed of the bus corresponding to the number of minutes, and the line in the graph is a fitted time trend line. The number of the cases in FIGS. 3(a), 3(b), and 3(c) is 90, and the width of the case is 1 min; the number of the boxes in FIGS. 3(d), 3(e) and 3(f) is 45, and the width of the boxes is 2 min; the number of cases in FIGS. 3(g), 3(h), and 3(i) was 30, and the case width was 3 min. The degree of the fitting polynomial of FIGS. 3(a), 3(d), and 3(g) is 1; the fitting polynomial degree of fig. 3(b), 3(e), 3(h) is 2; the fitting polynomial degree of fig. 3(c), 3(f), and 3(i) is 3. Through these nine images, it can be seen very intuitively: in addition to the three graphs of the linear fit (fig. 3(a), 3(d), 3(g)), the other quadratic and cubic polynomial fit graphs all show that at the bus lane opening time (7:30AM), the average speed of the bus undergoes a boost, with a magnitude of about 0.5-0.8 m/s.

We find that the scatter data is closer to the curve of the polynomial regression as the number of bins decreases (i.e. bin width increases). Without introducing other control variables, as the degree of polynomial used for fitting increases (from 1 to 3), the break point of the upward mutation becomes gradually obvious, which indicates that the change of the average speed of the target link with time is not linear when the other control variables are not taken into consideration. Fitting with a polynomial of more than a second degree may result in obvious breakpoints, but the existence of the breakpoints cannot be fully described only by the image, because the higher the degree of the polynomial used for fitting, the more likely the data is overfit. There is also a possibility that the breakpoint does not appear on time at 7:30AM, and social vehicles may avoid driving into the bus lane before the policy regulation start time for avoiding penalties, so that the breakpoint appears in advance, but the advance time is not too long. Fig. 4(a), 4(b), 4(c), and 4(d) are linear fitting images obtained after the initial breakpoint 7:30AM is advanced by 1min, 5min, 7min, and 10min, respectively, and it is found that there is no obvious change (unstable small downward mutation occurs) compared with the previous one, which may indicate that the possibility that the linear fitting mutation is not obvious due to the advance of the breakpoint is very low and is not considered.

To further determine whether the treatment effect exists at the breakpoint, four times of OLS (ordinary least squares) regression experiments of the global data were performed in sequence, and the regression results are shown in table 5. The OLS (1) is a common least square normal linear regression, only a binary disposal variable and a time driving variable are introduced, the obtained disposal effect value is 0.006, the improvement of 0.006m/s of the road section average speed of the bus after the breakpoint is shown, the value is close to zero, and the true existence of the disposal effect cannot be proved. The OLS (2) regression introduces three variables of the number of buses and taxis floating cars per minute of a target road section and the ratio of the buses and the taxis floating cars on the basis of the OLS (1), and the obtained treatment effect result is-0.03, which shows that after other control variables are considered, the treatment effect is negative, but the value is too small, the existence of the treatment effect cannot be proved, but the result of image analysis is proved: a linear regression fit fails to observe a significant breakpoint. In the OLS (3) regression, a quadratic term of time t is introduced on the basis of the OLS (2), and the obtained regression result is shown in the column (3) in the table, where the treatment effect is 0.34, which is significantly improved compared with the previous linear regression, and the R-square value (0.363) of the overall regression is increased, which shows that the regression of the quadratic polynomial is better than the fitting effect of the linear regression for the global data. The OLS (4) regression increases the polynomial with respect to time t to 3 degrees, and the resulting result is comparable to the quadratic polynomial regression (0.212), and it can be assumed that the estimates of treatment effects have stabilized.

TABLE 5 bus data Global regression results (with 7:30AM as breakpoint)

In addition, the regression coefficients of other variables in the global regression in combination with the image can reflect some information. The time variable regression coefficients obtained by the four times of OLS global regression are all negative values, which indicates that the running speed of the bus is gradually reduced along with the increase of time before the breakpoint, and indicates that the traffic of the target road section gradually enters the early peak of commuting and the traffic condition begins to deteriorate. The image also confirms this, and the trend of the fitted trend line before the breakpoint is continuously reduced. The variable of "time × handling variable" can represent the change situation of the speed trend along with the time after the break point, and the estimated values obtained by the linear regression of the first two times are negative values, which indicates that the speed is accelerated to decrease along with the time after the bus lane is opened, and the traffic condition is deteriorated, as shown in fig. 3(a), 3(d) and 3(g), the slope of the straight line after the break point is reduced; the polynomial regression results of the last two times show that the speed is reduced along with the time after the breakpoint, the traffic is improved, but the overall descending trend is not changed, and the graph reflects similar conditions. However, in terms of numerical values, the coefficient values of the two variables of the time and the time multiplied by the handling variable are very small, and even if the two variables have a certain increasing or decreasing change trend, the two variables are very weak, which can show that the bus lane has some effects on improving the bus running speed, but the effects are not large, and simultaneously shows that the change trend of the result variable along with the driving variable does not change obviously in the cell before and after the breakpoint, the traffic condition reflected by the speed does not change greatly, but only the whole body deviates downwards to a certain degree after the breakpoint, and the side surface reflects that the handling effect is only caused by the change of a single factor of the establishment of the lane.

The regression coefficient values of the two variables of the number of taxis per minute and the number of buses per minute are positive, which indicates that the speed of the buses and the number of the buses and the taxis have positive correlation, but the influence of the number of the floating buses on the running speed of the buses in a research period can be considered to be small due to small numerical values. The regression coefficient of the quantity ratio variable of the two motor vehicles is also a positive value and is approximately equal to 0.04, the running speed of the bus is in positive correlation with the relative quantity ratio of the two motor vehicles, but the influence is weak because the numerical value is not large. These results all show that the operation of the bus is not much affected by the taxi within 1.5h around the time when the bus lane is opened. Meanwhile, in the global data range, the influence of other control variables introduced by regression on result variables is weak, which has a certain reason to explain that the treatment effect is caused by the change of the single factor of opening the public transport lane.

To further test the robustness of the treatment effect estimates, we performed regression experiments of first and second degree polynomials for different data ranges. The regression results are shown in Table 6. By comparing the treatment effect results under different regression conditions, the difference between the treatment effect estimated values obtained by the times of the two regression equations is the minimum when the data range is 60min before and after the breakpoint, which shows that the treatment effect size is not influenced by the regression times when the data bandwidth is 60 min; however, when the data bandwidth becomes larger or smaller, the results obtained by linear regression are smaller than the results of quadratic regression, and the results of quadratic regression are closer to the results under the bandwidth of 60min, which again shows that when performing OLS regression, the results obtained by selecting the higher-order polynomial are better than the results obtained by linear regression, the reliability is higher, and the regression estimation value hardly changes with the change of the data range, so that the regression estimation value can be considered to be robust and reliable. The finding of a larger estimate of treatment effect in a small data range compared to the results of global regression (table 5) is not unexpected because the estimate obtained using polynomial regression is more affected by the distance from the breakpoint, and a more true treatment effect value can only be obtained by continuously narrowing the data range to a certain interval around the breakpoint.

TABLE 6 comparison of regression results for bus data at different data ranges (7:30AM as breakpoint)

TABLE 7 treatment effect estimation of local regression (bus breakpoint 7:30AM)

After performing the traditional OLS parameter regression, we also performed local linear regression under different conditions (different kernel functions, different bandwidths), and the target value of the regression is the treatment effect. The regression results are shown in Table 7. Comparing the differences in treatment effect under different conditions in the table, it can be found that: when the bandwidth is too large, the obtained treatment effect estimation value is small, and the treatment effect can be almost considered to be absent; when the bandwidth is gradually reduced, the estimation value begins to increase, can be stabilized in the range of 0.55 to 0.7, and is close to the previous OLS regression result, which indicates that the results obtained by the parametric regression and the nonparametric regression have similarity, so that the reliability is certain.

The same image analysis and regression analysis was then performed for the bus lane closing time 9:30 AM. The existence of the breakpoint can be clearly found in fig. 5(a) -5(i), and even if the polynomial degree and the number of boxes are changed, the abrupt change at the breakpoint is stable. The linear fitting image intuitively shows the slope change of the trend line before and after the breakpoint, the speed before the breakpoint is continuously improved, and the speed after the breakpoint tends to be stable; the second and third order fit images all showed an upward trend in velocity before the breakpoint, while a slight decrease in velocity after the breakpoint occurred.

The regression results (tables 8, 9, 10) also demonstrate that there is a breakpoint, with the average velocity around the breakpoint reduced by about 0.6m/s, and that the treatment effect obtained with data near the breakpoint has a maximum value of about-0.8, which is similar to the previous results with a 7:30AM breakpoint. Compared with the starting time of the bus lane, the treatment effect of the ending time is relatively large, which shows that the effect of the bus lane is more obvious in the period around the ending time.

TABLE 8 Global regression result of average speed of bus (9:30AM) bandwidth:180min

And comparing the regression results of the two breakpoints, and analyzing the influence of the special road of the target road section on the bus. The average running speed of the bus at the target road section is increased to a certain extent before and after the opening time of the bus lane, and the overall average increasing amplitude is about 8.2% compared with the average speed before the breakpoint; before and after the closing time of the special road, the average running speed of the bus on the target road section is reduced to some extent, and compared with the average speed before the breakpoint, the total reduction range is 9.9%. In contrast, the speed of the bus at the opening time is increased by a smaller amount than the speed at the closing time, that is, the effect at the opening time is not as significant as the effect at the closing time. The reason why this result occurred was analyzed: at the opening moment, the traffic volume of a target road section just begins to increase, but the target road section does not enter the peak time period, at the moment, the opening of a bus lane is prepared in advance for coping with the sharp increase of the traffic demand at the peak time period, and the regression coefficient of the variable of the number ratio of buses to taxis per minute is not large, so that the mutual interference between the taxis and the buses is not large, and the speed increasing effect of the bus lane on the buses is not obvious because the overall traffic operation of the road section is smooth and the mutual influence between social vehicles and the buses is small; secondly, no signal priority rule of the bus is set at the upstream and downstream intersections of the target road section, delay of the intersections can also be one of the reasons causing unobvious effects, and the time of the bus passing through the road section is not shortened too much due to the influence of the delay of the intersections; in addition, the passenger flow of the buses is increased in the process of entering the peak time period, the parking time of each bus is also increased, and the reason that the speed is not obviously improved is probably the same. And then, the change of the closing time of the private road is analyzed, the peak time period may not be passed at this time, the traffic volume is maintained at a high level, but at this time, a plurality of social vehicles may be required to occupy the public transportation private road for driving, and particularly social vehicles for getting on and off taxis, temporarily parking other private vehicles and entering a target road section by turning right at an upstream intersection. This forces the bus to use other lanes to mix with other social vehicles, thereby reducing traffic speed. In addition, as the lane used by the bus is no longer the outermost lane, more lanes need to be crossed when the bus enters and exits, and traffic conflicts with other lanes, the time for entering and exiting the bus is increased to some extent, so that the running speed of the road section is reduced, at this moment, the bus lane is closed suddenly, and the running speed of the bus is reduced more obviously.

TABLE 9 regression comparison of bus data under different data ranges (breakpoint 9:30AM)

TABLE 10 treatment effect estimation of local regression (bus breakpoint 9:30AM)

(2) Taxi regression result analysis

Although the public transportation lane is convenient to set up, adverse effects may be caused to social vehicles, so the effects of the public transportation lane need to be considered when evaluating the effects of the public transportation lane. A taxi is used for representing a social vehicle, and the influence of a bus lane on the social vehicle is analyzed. The same steps as the steps for analyzing the bus result are carried out, and before data regression is carried out, the condition of the breakpoint is observed through an image. The width of the box body of FIGS. 6(a), 6(b) and 6(c) is 1 min; the width of the box body of FIGS. 6(d), 6(e) and 6(f) is 2 min; the case width of FIGS. 6(g), 6(h), and 6(i) was 3 min. The degree of the fitting polynomial of fig. 6(a), 6(d), 6(g) is 1; the fitting polynomial degree of fig. 6(b), 6(e), 6(h) is 2; the fitting polynomial degree of fig. 6(c), 6(f), and 6(i) is 3. The results of the image fitting are different from the results of the previous buses, and we find that the size of the abrupt change at the breakpoint gradually decreases as the number of times of fitting gradually increases.

The results of the global data regression (table 11) also demonstrate the features reflected by the images: as the polynomial degree increases, the value of the treatment effect decreases. The OLS (1) and the OLS (2) are both linear regression, other variables are not introduced into the former, and four other control variables of passenger carrying ratio, taxi quantity, bus quantity and the ratio of the passenger carrying ratio to the taxi quantity to the bus quantity are introduced into the latter, but the treatment effect estimated values obtained by two times of regression are quite close to each other, namely-1.045 and-0.969 respectively, and standard errors are very small, which indicates that in the linear regression, the influence of other control variables on the treatment effect estimated values is very weak, namely the influence of other variables on the average speed of the taxi is very small. However, when the number of regression was increased to 2 times, the treatment effect value decreased nearly in half, only to-0.493, and when the number was increased to 3 times, the treatment effect value increased to-0.627. Although the R-squared values of the 2 and 3 regressions are higher than those of the two previous linear regressions, the obtained estimation criteria are too wrong, and the obtained treatment effect estimation does not have certain confidence.

TABLE 11 taxi average speed Global regression results ((7: 30AM breakpoint) bandwidth:180min

To test the robustness of the estimates, we performed OLS regression of different data ranges for comparison, see table 12. As a result, it was found that: the data bandwidth is 60min and 120min, the treatment effect estimated values are basically the same, and the estimated values of regression coefficients of other control variables are also very similar, which indicates that the regression results obtained under the two bandwidth conditions are relatively stable; when the data bandwidth is 30min, the treatment effect value is obviously reduced, and the regression coefficient of the variable of the taxi passenger ratio becomes a negative value, and the result seems to be contrary to the fact, because the passenger ratio reflects the ratio of the number of passenger taxis passing through the road section and the total number of the taxis in unit time, empirically, the speed of the taxi when carrying passengers is larger than the speed when the taxi is unloaded, so that the larger the passenger ratio is, the larger the average speed of the road section is, the positive correlation is formed between the passenger ratio and the road section, but the regression result is opposite to the experience. This may occur because the bandwidth is selected to be too small and the amount of data contained may not reflect the general trend.

TABLE 12 taxi data regression comparisons at different bandwidths (breakpoint 7:30AM)

The results of the local linear regression also reflect the same problem, see table 13. The effect estimate obtained at 30min bandwidth is significantly smaller than that obtained at other bandwidths, but the values obtained for the rectangular kernel function are still relatively close to-1.07. Results at other bandwidths fluctuate between-0.868 and-1.235 with standard errors in results within acceptable ranges.

TABLE 13 treatment Effect estimation of local regression (taxi 7:30AM breakpoint)

The same breakpoint analysis is also performed for the closing time of the dedicated track. The images in fig. 7(a) -7(i) under different conditions all reflect a positive abrupt change in velocity at the breakpoint, and the abrupt value of the linear fit is significantly greater than the results of the quadratic and cubic fits.

From the regression results of the global data (table 14), whether introducing other control variables has little effect on the linear OLS regression results, the first two treatment effects estimate very closely, 2.039 and 2.161, respectively, while the results of quadratic and cubic polynomial regression are relatively small, 1.249 and 1.571, respectively. The data range was narrowed (table 15) and the treatment effect estimate was found to increase gradually from 1.353 to 2.218. The parametric regression at this time cannot obtain a stable effect estimation value, and the results of the non-parametric regression are also needed to be compared. The results of the non-parametric local linear regression (table 16) show that: besides the relatively small estimate at the 90min bandwidth, the estimate under other conditions can be maintained in the range of 1.8 to 2.2, similar to the linear regression results at the previous global OLS (1), OLS (2), 30min and 60min bandwidths, so to speak, the treatment effect is in the range of 1.8 to 2.2.

TABLE 14 taxi average speed Global regression results (breakpoint 9:30AM) bandwidth 180min

Comprehensively analyzing the influence of the establishment of the bus lane on social vehicles represented by taxis. The average speed of the taxi on the target road section is reduced by about 10.0% before and after the opening time of the bus lane, so that the taxi is really influenced by the opening of the bus lane. At the closing time of the special lane, the average speed is increased, the increasing amplitude is about 25.9 percent and is more than 2 times of the decreasing amplitude of the opening time, which shows that the special bus lane has great influence on the taxi in the time interval of the closing time, and the reason that the taxi has great demand on the lane where the special bus lane is located in the time interval around the closing time (9:00-10:00AM) can be probably because passengers getting on and off the taxi need to utilize the outermost lane. On the contrary, the speed is not greatly reduced in the beginning time period (7:00-8:00AM), probably because the demand of residents on the taxi is not large at the moment, the traffic operation in the time period is overall fast, and the influence of the taxi on the bus is not obvious. The regression coefficient of the passenger variable in the regression result also corroborates this result, the value of this coefficient is about 0.8 in the breakpoint analysis at the starting time, and the value rises to near 2 even to exceed 3 in the breakpoint analysis at the ending time, which shows that the number of passengers has a great influence on the speed of the taxi in the period after the peak period, so that if the exclusive lane is closed to make the taxi freely use the outside lane, the number of passengers can be greatly increased, thereby increasing the average running speed.

TABLE 15 taxi data regression comparisons at different data ranges (breakpoint 9:30AM)

TABLE 16 treatment Effect estimation of local regression (taxi breakpoint 9:30AM)

3. Policy evaluation and optimization suggestions

The regression results in the foregoing are summarized to obtain a table 17, and due to the influence of the policy of the bus lane, after the bus lane is opened, the average speed of the bus in the target road section is improved by 8.2%, and the average speed of the taxi is reduced by 9.9%; after the special lane is closed, the speed of the bus is reduced by 10.0 percent, and the speed of the taxi is improved by 25.9 percent.

Table 17 summary table of effect of special channel

The result shows that setting up of bus lane has obvious promotion effect to the bus, but the difference of open period, and the influence effect can have certain difference, compares in open period, and the influence degree of bus is bigger at closing the time lane, and the analysis result reachs the optimization suggestion: the opening end time of the target-section-dedicated road should be appropriately delayed.

The bus lane also has certain influence on social vehicles represented by the taxi, but the influence is related to the requirements of passengers getting on and off the taxi by parking on the roadside, and the speed of the taxi is greatly improved at the end moment because the parking requirements of the passengers getting on and off the taxi are increased after 9:00 AM. The side also shows that the taxi has certain use requirements on the bus lane, and in order to not influence the passing of the bus and ensure the implementation of the bus priority policy, social vehicles such as the taxi and the like should be correspondingly limited, such as a centralized docking station is set; meanwhile, matched priority facilities such as signal priority and the like are set for the bus, and the bus is matched with a special lane to ensure smooth and convenient bus passage.

Claims

1. A bus lane policy evaluation method based on breakpoint regression is characterized by comprising the following steps:

(1) variable determination and hypothesis testing

the average speed S of the link is the resulting variable, S^bIndicating the average speed, S, of the bus^cRepresenting the average speed of the taxi;

the key point of breakpoint regression is treatment effect estimation, and the treatment in the regression model is represented by introducing a binary treatment variable EBL_tThe binary variable has two values of 0 and 1; 1 represents that the bus lane is in an open period, the study object receives treatment, 0 represents that the bus lane is in a closed state, and the study object does not receive treatment;

(2) image analysis

Before breakpoint regression, processing collected data, drawing a scatter diagram with speed s (m/s) as a vertical coordinate and time t (min) as a horizontal coordinate, and fitting data points; when the global data is more and disordered, processing the global data by adopting a Bin method, removing noise in the global data and enabling a fitted curve to be smoother; performing linear or polynomial regression on the converted data points, and then preliminarily observing whether data jump exists at the breakpoint, wherein if the data jump does not exist, the subsequent regression result may be unreliable;

(3) global regression

Basic parameter regression model

S_t＝α+β₀·EBL_t+β₁t+β₂t·EBL_t+γX_t+ε_t (1)

The basic parameter regression model represents the average running speed of the vehicles on the target road section before and after the bus lane is opened; wherein t represents the number of minutes from the break point, which is a driving variable, and t is 0 at the break point; dependent variable S_tIs the target link average speed in the t minute; EBL_tIs a binary disposal variable, has two values of 0 and 1, if the break point t is 0, then when t is the open time of the special channel>The value of 0 is 1, which indicates that the vehicle on the road section receives the treatment of the change of the lane resource allocation, when t<The value of 0 is 0, which indicates that the vehicle on the road section does not accept the treatment of lane resource allocation; if the break point t is 0, then when t is the closing time of the special track>The value of 0 is 0, which indicates that the lane resource allocation is recovered to the normal condition, when t<The time value of 0 is 1, which indicates that the bus way is still in an open state; x_tVectors composed of other control variables; epsilon_tIs white noise;

the coefficient of each variable in the regression model reflects the influence degree of each variable on the result variable; wherein the most important target parameter for regression is beta₀The value of which directly reflects the magnitude of the treatment effect at the discontinuity; beta is a₁And beta₂The regression coefficient of the driving variable t determines the overall variation trend of the result variables before and after the break point along with the driving variable; gamma is a vector composed of regression coefficients of other control variables, reflecting other controlsAlthough the influence degree of the system variable on the result variable is not a main object of research, the value of the system variable and the change in the robustness test can verify the hypothesis of breakpoint regression and verify whether other control variables are related to treatment effects;

in the formula:

P，γ_P-taxi passenger ratio and its regression coefficient in unit time;

R，γ_R-the number ratio of buses to taxis and their regression coefficients in a unit time;

in the formula:

R，γ_R-the ratio of the number of taxis to buses in a unit time and the regression coefficients thereof;

obtaining regression coefficients of all variables and corresponding standard errors from the regression results, and evaluating the treatment effect by comparing the regression coefficients with the standard errors; the positive and negative and relative sizes of the regression coefficients reflect the influence degree of the corresponding variables on the result variables, and when the regression coefficients are small or stable within a certain range, the control variables are considered to have no influence on the treatment effect size within the selected data range, so that the reliability of the breakpoint regression estimation result is proved;

after global linear regression, polynomial regression is generally performed by adding multiple terms in order to better fit the time-dependent variation curve of the resulting variable, and also as part of the robustness test; during regression, a high-order term of time t can be directly added on the basis of a linear regression model; the global nth polynomial regression expression of the bus is (4), and the global nth polynomial regression expression of the taxi is (5):

(4) local linear regression

Let t₀Selecting data points with width h on both sides of the discontinuity point for regression, and controlling the points smaller than the discontinuity pointGroups, larger than the discontinuity are treatment groups; assuming the regression function to the right of the treatment group, i.e. the discontinuity, is linear:

S_i＝α_r+β_r·t_i+ε_i (6)

the regression aims to obtain values of the break points through data values on the right side of the break points, different weights need to be given to the data points as the distances from the different data points to the break points are different and the influence on the estimated point values is larger as the distances are closer, the weights are larger as the distances are closer to the break points, otherwise, the weights are smaller, and the weight distribution is realized through a specific kernel function K; final selection (. alpha.)_r,β_r) The values are such that the locally weighted sum of squares of the data to the right of the break point is minimized, i.e.

Thus, the point estimate of the treatment group at the discontinuity is

S_r(t₀)＝α_r+β_r·(t₀-t₀)＝α_r (8)

S_l(t₀)＝α_l+β_l·(t₀-t₀)＝α_l (10)

The final treatment effect estimate is

τ＝α_r-α_l (11)

(5) Robustness testing of estimates

1) robustness testing for global polynomial regression

global polynomial regression estimates values by using data far away from the breakpoint, so that the global polynomial regression is greatly influenced by the data far away from the breakpoint, and in order to check the reliability of the estimated value of the treatment effect, the window width needs to be continuously reduced by taking the breakpoint as a center, so that the used data range is reduced to be small enough around the breakpoint; the treatment effect estimated values in different data ranges and different polynomial times are compared, if the data ranges and the polynomial times are changed, the treatment effect estimated values can be maintained in a certain range, the fluctuation is not large, and the estimated values have certain reliability;

2) robustness testing for local linear regression

the type of the kernel function determines the weight value of data around the evaluation point, and the method mainly adopts a rectangular kernel function, a triangular kernel function and a leaf-Pinicukov kernel function to carry out robustness test; the bandwidth selection needs to achieve a balance between accuracy and bias; the treatment effect estimated values under different kernel function types and different bandwidths are compared, and if the kernel function types and the bandwidths are changed, the treatment effect estimated values can be maintained within a certain range and have small fluctuation, which indicates that the estimated values have certain reliability.