Speed-consistency Based Safety Evaluation for Freeway Diverging Segments

Diverging segments are potential bottlenecks because of frequent lane change and deceleration maneuvers. Speed study has been proven to be an effective way to understand the safety performance of diverging segments. This paper addresses the safety level of diverging segments in terms of speed consistency. Speed data is extracted by Tracker based on aerial video imager collected at the diverging segment of MaQun interchange of G42 in Nanjing, China. The operating speed of vehicles is assumed to follow the Linear Regression Model with two explanatory variables—initial velocity and running distance, and the estimated operating speed is amended un der actual traffic conditions. Furthermore, average speed, speed difference and the coefficient of variation are used as safety indicators to establish the speed evaluation criteria. Last but not the least, based on vague set of material-units, the safety level of diverging segments in terms of the velocity arrives at level III, which means that consideration must be given about the safety of diverging segments. The proposed methodology can be used to estimate the safety of diverging segments.


Introduction
Freeways play a v ital ro le in serving mega-cities, which could significantly raise the speed for mid and long distance traffic.Nevertheless, the efficiency and safety of freeways has been dramatically constrained by bottlenecks.Diverging segments may easily become bottlenecks because of frequent lane change and deceleration maneuvers.Therefore, understanding the efficiency and safety of d iverging segments are important and necessary.
Freeway diverg ing segments occur primarily at offramp junctions with the freeway main line [1].Normally, there are two movements in diverging segments, na mely mainline-to-mainline and mainline-to-ramp , which can affect the operations of each other.Influence area of diverging segments is defined as the deceleration lane(s) and Lanes 1 and Lanes 2 of the freeway for a distance of 450m upstream of the diverge point [1].Figure 1 illustrates the influence area of diverging segments.Because of its importance and efficiency, diverg ing segments have already gained considerable attention from researchers.The capacity studies of diverging segments have been a focus.Researchers have analysed the capacity of diverging segments using empirical and simu lation methods [2][3].Other studies have also been conducted on level of service (LOS), traffic delay and operational characteristic [4][5][6].In addition to the studies above, there were also researches on diverging segments' safety.Some researchers explored the contributing factors to crashes at freeway diverging locations [7][8], they discovered that AADT, lane-type configuration and speed are always tend to increase the severity of crashes at freeway diverging areas.The operating speed of diverging segments were also been studied [9][10], and linear regression model were adopted to predict the speed of diverging area.Studies using speed have been proven to be an effective way to understand the safety performance of road.So me researchers identified the relationship between crashes and speed [11][12][13].Their researches demonstrated that the larger the variance of speed, the higher the crash rates.As for the speed safety of diverging segments, the linear regression model of speed was established and the safety level of speed was arrived at based on the 85th percentile individual speed difference in diverging segments [14].
Fro m what have been mentioned above, it is not hard to conclude that there were numerous studies on speed and traffic safety at diverging segments respectively.However, with respect to speed safety for diverging segments, there were not enough studies.Hence, this study conduct speed safety analysis for diverging segments.The initial speed and the travel distance are considered in the regression model.Meanwhile, volu me and weather conditions are used to revise the speed DOI: 10.1051/matecconf/201712404007 ICTTE 2017 model developed.Exp loring the connection between speed and safety would be helpful in finding hazardous diverging segments.
The sections are organized as follows.Sect ion 2 first introduces the research methodology which is used in building the model and assessing the safety level of diverging segments.Section 3 presents the statistics analysis of speed collected.Section 4 demonstrates the regression model of speed at diverging segments.The speed safety evaluation result is showed based on material-unit in section 5. Finally, Section 6 su mmarizes the findings, conclusions and limitations of the paper.

Methodology
This study built a mult ivariab le linear regression model to estimate the speed of vehicles at freeway diverg ing segments according to the statistics analysis of speed data collected.Linear regression allows multi-variables to be properly calibrated, and outputs are relatively easy to interpret.What is more important is that the assumptions of linear regression models are often suitably satisfied in practical applications [15].
In this study, vehicles are classified into heavy (wheel base is larger than 7m o r power density is small or equal to 15kw/t) and s mall ones (the others).The operating speed model are established for heavy and small vehicles individually, the operating speed of vehicles at diverging segments is then arrived at according to the ratio of the speed for heavy vehicles and the s mall vehicles estimated.
The research assumes that the operating speed are jointly influenced by init ial speed, travel distance, volume and weather factors.To be mo re specific, initia l speed 0 v and travel distance L are put in the regression model, the others are used to revise the estimated model.Speed can be expressed as (1): where fo llo w a normal d istribution with mean and standard deviation equal to 0 and , respectively.0 1 and 2 are estimated constants.Linearity, homoscedastic disturbances and normally distributed disturbances should be checked to make sure that linear regression is appropriate.
In our study, speed 0 v , speed difference d and coefficient of variation for speed cv are calculated according to the speed regression model bu ilt, wh ich are assumed to be the indicators related to speed safety of diverging segments.Vague sets [16] surpass fuzzy sets when deal with uncertain information [17].Thus vague sets are applied in this study to estimate the safety level of speed at diverging segments.Co mpared with traditional mult i-object ive decision methods, vague sets can effectively deal with uncertainty conditions.The comprehensive material-element can be calculated as (2): where ij v is the vague value of object i with indicator j , ij t represents for the true membership function and ij f denotes the false membership function.In our study, all the indicators are supposed to be as smaller as they can, thus ij t and ij f are calculated as ( 3) and ( 4), respectively. where x denotes the value of object i with indicator j , is the min imu m value of indicator j of all objects.The essence of this process is normalization.
The weights of indicators are calcu lated by means of AHP.And similarit ies between the matter-element under test and the indicator of standard are computed as (5): where x represents for the indicator value for the matter- element under test, j y is the indicator value for different levels.The comprehensive similarity is computed as (6):

The statistic characteristics
The research study the diverging segment of MaQun interchange of G42 in Nanjing, Ch ina.The speed data was extracted by Tracker based on aerial video imager collected.Three cross-sections (the diverge point C, the midpoint B and terminal point A) of datasets were screened from data extracted at the influence area of diverging segment.In this research, the segment is set as straight line for convenience, and the speeds are analysed and modelled for heavy vehicle and small vehicles(the others ), respectively.Descriptive statistics are useful way to understand the primary characteristics of speed.Take heavy vehicles as ICTTE 2017 example, Tab le 1 prov ides speed informat ion about the basic statistics for heavy vehicles.The statistics indicate that the speed of each cross section follows normal distribution.There seems little difference among the statistics for section A, B and C, which means central tendency of heavy vehicles' speed.The curves of speed with heavy vehicles and s mall vehicles are illustrated by Figure 2. The characters of the speed curve are as fo llows.First, it is obvious that the vehicle will decelerate when reaching the diverge point.Second, there appears dissimilarity in terms of speed range with heavy and small vehicles.Furthermore, it can be easily seen from Figure 2 that the speeds present a decreasing trend for all the vehic les.What is more important is that deceleration of different vehicles demonstrate different and that the deceleration d istance are longer for the heavy vehicles in co mparison to small vehicles.A multivariable linear regression model is built to estimate the speed for heavy and small vehicles at diverging segment.Table 2 shows the parameter estimates of the regression estimated on the collected data for heavy vehicles.
It can be easily seen from Table 2 that this model contains a constant and two exp lanatory variables -the init ial speed and travel distance.The signs of the estimated parameters are in line with expectation.Travel distance is with a negative coefficient, indicat ing that long distance might decreases the speed of heavy vehicles, which is easy to be understood.Meanwhile, long distance (L) also indicates of worse travel conditions, and then results in low speed of heavy vehicles.Initial speed 0 v is with positive coefficient which determines the operating speed.The two independent variables are statistically significant with the value of 1.96 t ³ under level of significance 5%.The value of 2 R adj is 0.7325, which indicates that 73.25 percent of total variance can be explained by independent variables.*Variable significant at 95% interval.
Linearity, homoscedastic disturbances and normally distributed disturbances are checked to make sure that linear regression is appropriate.Thus the regression model of speed can be expressed as (7): The regression models of small vehicles can be expressed as ( 8) by the same method.
where s v represents for the operating speed for small vehicles.The exp lanatory variab les are of the same meaning as noted before.

Model calibration
Vo lu me and weather factors are found to have significant impact on the actual operating speed of vehicles.Vo lu me is with negative impact, indicating that high volume might decrease the speed of vehicles.Wet road surface condition reduces the speed of vehicles.It leads to smaller friction and results in longer braking distances.Meanwhile, vehicles are mo re likely to lose control under wet road condition, thus the driver tends to decelerate for safety consideration.
The speed model can be rewritten as ( 9) with consideration of volume and weather conditions: DOI: 10.1051/matecconf/201712404007 where v represents for the actual operating speed of vehicles, and 0 v is the estimated speed by regression model, v v denotes the speed reduction because of high volume and f denotes the coefficients of speed reduction due to road surface conditions.
The speed reductions for freeways with volu me and weather condition are shown as Table 3 to Tab le 4, respectively.

Evaluation criteria
Transportation is a co mplex, diverse and stochastic system involving people, vehicles, roads and traffic management.And operating speed of vehicles is influenced by all these factors.Research shows that average speed ( v ), speed difference ( d ) and the coefficient of variat ion ( cv ) are assumed to have straightforward influence on speed safety of vehicles [18].Speed difference is the difference between the average speed and the design speed.The coefficient of variation is the ratio of the standard deviation and the average speed.In this paper, three indicators are used to evaluate the safety level for vehicles according to Specifications for Highway safety audit [19] and the speed safety criteria of highway [20], the criteria of vehicles developed with the consideration of traffic circu mstances, which is shown as Table 5.

Safety evaluation
In our study, vague sets are applied to estimate the safety level of speed for vehicles.There are several steps to follow to arrive at the safety level of vehicles speed.First, the comprehensive material-element can be calculated by (2).Second, the weights of indicators are calculated by means of AHP.Furthermore, similarities between the matter-element under test and the indicator of standard are co mputed by (5).Finally, the co mprehensive similarity is co mputed by ( 6) and the safety level of speed is confirmed.

Vague sets
The research studies the speed safety level of the diverging segment of MaQun interchange of G42 in Nanjing, China.The diverging seg ment is of three lanes and one auxiliary lane with mainline design speed 60 km/h.
According to the regression model and speed reductions, the average operating speed is calculated at 20.0175km/h (the ration of heavy vehicles and small ones is calculated at 17.1372%), the speed difference is 39.9825 km/h and the coefficient of variation is 14.1745%.The co mprehensive material-units and the vague sets are calculated by (2), as is shown in Table 6 and Table 7, respectively.

The weights of indicators
The weights of indicators are calculated by means of AHP, which is presented as Table 8.

The similarities
The similarit ies between the matter-element under test and the indicator of standard are computed by (5).The results are presented as Table 9.It is obvious that a larger similarity value ind icates the safety level of speed.The safety levels of average speed, speed difference and the coefficient of variation are Level II, Level III and Level I, respectively.

The safety level
Table 10 provides informat ion about the comprehensive similarity co mputed by (6).The similarity is 0.8150, 0.7847 and 0.8266 for Level I, Level II and Level III, respectively.Which indicates the speed safety level of diverging segment is level III.Hence, the result found in this study is that the safety level of diverging segment in terms of speed is not the optimal.And measures like speed limit should be taken to manage the speed of diverging segments.

Conclusion
Freeways diverging segments may easily become bottlenecks for traffic safety.One effective way to improve the safety of diverg ing segments is to study the speed safety with the objective of identifying the hazardous diverging segments and reducing the risk of diverging segments by traffic control and management.
In order to provide effective predictors for diverging segments' speed, this research study the diverging segment of MaQun interchange of G42 in Nanjing, China.The speed data was extracted by Tracker based on aerial video imager co llected.The regression linear model shows that initial speed and travel distance are important factors with negative and positive coefficient, respectively.Besides the two factors, volume and weather factors are used to calibrate the operating speed.Based on the proposed model, the safety level of diverging segments can be identified using vague sets.The results show that the safety level of diverg ing segments in terms of speed is not the optimal, and measures like speed limit should be taken to manage the speed safety of diverging segments.
There are limitations of this study.The regression model considered only two variables regardless of significant GOF.The studied segments are straight lines, other geometric designs do not vary too much.More geometric designs can be explored in the future.

Figure 1 .
Figure 1.Influence area of diverging segment maximu m value of indicator j of all objects, and min j x

d
is used to illustrates the similarity between the indicator under test and the standard value, j w is the weight for indicator j , between the matter-element under test and the indicator of standard.It is obvious that a larger similarity value indicates the safety level of speed.

Figure 2 .
Figure 2. The speed curve of vehicles

v
denotes the operating speed of heavy vehicles, 0 v and L are of the same meaning defined before.

Table 1 .
The summary statistics of speed for heavy vehicles

Table 2 .
The linear regression parameters of heavy vehicles

Table 3 .
The speed reduction of different LOS

Table 4 .
The speed reduction of weather condition

Table 5 .
The criteria for speed safety

Table 6 .
The comprehensive material-units

Table 7 .
The comprehensive vague sets of material-units

Table 8 .
The indicators weights

Table 9 .
The indicators similarity

Table 10 .
The comprehensive similarity for different speed safety levels