The first objective of this study is to analyze a successivestage speed limit model developed for vehicles along the exit upstream ramp of directtype freeway in China. This paper (1) explains the necessity to implement speed limit to the exit ramp upstream, (2) analyzes whether speed limit is related to the length of the deceleration lane, vehicle type, saturation, and turning ratio and (3) proposes a speed prediction model and calibrates speedlimit sign validity model and establishes successivestage speed limit model.
Ramps provide the connections between freeway and roads and influence traffic efficiency and safety of the freeway and ground roads. In USA, 20% to 30% of freeway truck accidents occur at or near ramps (excluding an additional 10% to 15% that occur at weaving section and surface streets), despite the fact that weaving section account for less than 5% of all freeway lanemiles [
According to speed limit determinant factors, speed limit control methods are divided into four categories:
Road grade and geographic feature: The United States [
Driver physiological characteristics:
The comprehensive influential factors: In Australia, ARRB [
The disadvantages in above mentioned methods are:
Application scope of legal speed limit method is limited: In some sections, the actual situation on the freeway does not match the range of the legal limit speed and, therefore, legal speed limit method cannot be used under some situation.
Single speed limit is not related with the speed of change and accident data is not easy to obtain. Solomon [
Driving behavior is complex: When driver approaches the exit ramp from the main line, they need to finish a series of complex driving behaviors, such as looking for acceptance gap, slowing down, and change lanes in the slow lane. Driver’s driving habits and reflections are different in the different area or on different roads [
Consider geometry parameters only: The comprehensive influential factors method only considers geometric parameters, such as the slope and curve radius. McLean [
In this paper, the primary goal is to develop a successivestage speed limit model for vehicle speed along the exit upstream ramp of directtype freeway in China. The specific tasks of this paper can be summarized as follows:
State the necessity of operating successivestage speed limit control on the exit ramp upstream.
Analyze the relationship between operation speed and deceleration lane length on the exit ramp upstream, and prove that the speed limit should be in accordance with the deceleration lane length.
Determine whether the speed limit needs to be set for the small vehicle and large vehicles separately on the exit ramp upstream.
Analyze the main factor of the speed limit from saturation, turning ratio, and vehicle type using doublefactors curve fitting and polynomial regression.
Build speedprediction model according to the result of factor analysis.
Calibrate speedlimit sign validity model by linearization
Establish successivestage speedlimit model based on a speedprediction model and a speedlimit sign validity model.
Verify the validity of the successivestage speedlimit model by a case study.
The research is based on three hypotheses.
The speed limit for the exit ramp nose is reasonable. This research focuses on developing a successivestage speed limit model on the exit ramp upstream. The value of the speed limit of the exit ramp nose is not studied in this paper; therefore assume that the speed limit on the exit ramp nose is reasonable.
90% of rightturn drivers have finished lane change at 2/3 location of deceleration lane in China [
Except mountainous freeway, geometric line of freeway meets freeway design standard. Combining with the actual situation, as well as the result of McLean [
The type of an exit ramp has influences on the traffic flow of the exit ramp, speed distribution and driver behavior. So the exit ramp type should be determined firstly. 428 exit ramps from 11 provinces in China were observed by Google Earth. Statistically, 93.5% of the ramps fell into the above 4 categories by the change of lanes number in the main line of upstream and downstream, the setting of the deceleration lane, the number of ramp lane, and the separation situation of ramp. 55.8% of them were directtype exit ramp. Hence, directtype exit ramp is the research objective in this study. Characteristics of directtype exit ramp are as follows:
The number of lanes in the main line of upstream and downstream is constant.
The area of ramp upstream is broadened properly and has a deceleration lane.
The number of lane on the ramp is 1.
The exit ramp lanes are not separated.
Sites are selected as follows:
Safeguard facilities at the road side are in normal condition.
Has a good visual space.
Service level is A or B (to ensure that speed is not significantly affected by other vehicles in the flow).
The freeways selected in this study should include two lanes, three lanes, and four lanes in one direction in the main line.
The range of deceleration lane length is 150–250 m.
The values of the speed limit on the main line are 100 km/h and 120 km/h; the values of the speed limit on exit ramp are 40 km/h and 60 km/h, respectively.
No congested traffic phenomenon.
As a result, seven exit ramps in Nanjing, China were chosen as candidate sites.
The exit ramp impact area is within 500 meters upstream of nose, according to HCM, as length 500 m from the nose [
Speed profile of the exiting flow.
Data in this study includes geometric parameters, trafficflow parameters and trafficcontrol parameters.
Geometric parameters include alignment elements and lane number in the main lanes and deceleration lane length. It is known that the alignment is not considered in above studies. Therefore, geometric parameters refer to the lanes number in the main lanes and deceleration lane length. The main traffic control parameter is main lane speed limit and exit ramp speed limit. Deceleration behavior on the main line mainly happens on the outside lane. Trafficflow parameter includes traffic volume and point speed of the outside lane.
Traffic flow parameters are collected during the peak hour from 8 to 11 a.m or 2 to 5 p.m on a clear, well visibility, and regulartemperature day.
The procedures of data collection are designed as follows:
The radargun holder is in charge of shooting speed, reading the last three digits of the plate number, and informing the recorder of the information.
Observers are hidden from traffic to minimize the effect of their presence on passing vehicles.
The data collected from the camera were sorted into smallvehicle and largevehicle categories. The small vehicle has less than 20 seats for passenger vehicles or less than 2 tons in weights for freight vehicles.
It was found that
Discard nonnormal data that does not conform to normal distribution using statistic software SPSS [
Fitzpatrick [
10 km/h <
It is worth noticing that the accident rate of observations with
In Figure
Through the above analysis, we can conclude that it is necessary to operate successivestagespeed limit control on the exit ramp upstream.
The
There are threespeed curves in Figure
It is not needed to design different speed limits for small vehicles and large vehicles, respectively, on the exit ramp upstream, as the speed limit control pattern on the main line.
According to hypothesis 3, the only difference of the seven sites in terms of geometric aspect is the deceleration lane length. Speeddecelerationlanelength curve is used to judge whether the speed limit needs to be determined according to deceleration lane length.
The range of deceleration lane length used in this paper is 150–250 m. The range almost covers all decelerationlanelength of freeway in China. If there are different trends in speeddeceleration lane length curves in Sites 1, 2, 3, 4, 5, 6, and 7, the speed limit should be determined due to the differences of the deceleration lane length.
Figure
In segments 1–4, curves of all 7 sites are nearly flat. In segments 4–6, however, there are two opposite trends. The curves of Sites 1, 2, 3, and 7 rise in segments 45, and then drop in segments 56. The trends of the curve 4, 5, 6 are opposite. The common characteristics of 1, 2, 3, and 7 is that their deceleration lane length are more than 200 m. The lengths of the deceleration lane of 4, 5, and 6 are less than 200 m.
Hence, deceleration lane length is related to
In order to analyze whether the number of lanes of main line affect speed, speedlane number curve is displayed in this section. The numbers of lanes in the main line for one direction are 2, 3, 4 in this study.
Speedlane number curves are shown in Figure
Speedlane number curves.
In segment 1 to segment 4, the curves are similar to each other. The difference of the curve is manifested in 4–6. The highest speed level appears in four lanes, and then in three lanes and two lanes. The trend of the curve is similar with the curve in Figure
We can deduce that the lane number in the main line does not relate to speed, and lane number in the main line has not been considered when we determine the speed limit.
Many drivers become irritated by frequency of slow speed. Considering the maneuverability of the speed limit sign, the number of successivestage speed limit should not be more than two stages.
The speed limit has a certain impact on operational speed, but not all vehicles travel under the speed limit. In 1986, Anders and Arne [
Equation (
It is can be found that
It is widely believed that influence factors of speed include geometric parameters, trafficflow parameters, and traffic control parameters. Trafficflow parameters include traffic volume, speed, density, average time headway, average space headway, turning ratio and vehicle type, and so forth. Traffic flow parameters comprise density, average time headway, and average space headway. Therefore, traffic volume, turning ratio and vehicle type are chosen in this paper. To increase the universality of the model, traffic volume is converted to saturation.
Doublefactor curve fitting is used to analyze the correlation between various factors and speed by
A twofactor multinomial model is developed to compare how saturation and percentage of large vehicles affects operational speed. Independent variables are selected by the stepwise regression method. Every variable selected by the stepwise regression method is tested. Percentage of large vehicles is eliminated in SPSS.
Saturation is selected as the main factor affecting operational speed. Step length needs to be decreased to increase model fit. The Adjusted region of saturation is
Hypothesis tests are carried out in SPSS. Outputs are
It can be concluded that the variation of deceleration is more significant than speed difference and speed. The research scope is divided into three sections according to the variation of the deceleration. The entire exiting process is divided into three sections below, as shown in Figure
Segments of research scope divided by deceleration.
In Figure
Average deceleration in each section.
Deceleration lane length (m) 




<200 m  0.15  1.30  0.73 
>200 m  0.31  1.09 
Denote
In
Combine (
Define
At present, the placement of the speedlimit sign is determined by the basis of the psychical process of drivers perceiving and reacting to signs. The determinant of the perceptionreaction process is the placement of the danger point. Thus, the paper is focused on a danger point to confirm the placement of successivestage speed limit in this section.
By analyzing deceleration characteristics curves, we found drivers began to slow down in segment 1. Between segment 1 and segment 2, curves decreased smoothly and steadily. A significant change in deceleration happened in segment 2–4. According to
The placement and clear height of successivestage speed limit sign are determined according to
After investigation, we got the information about
Using successivestage speed limit model, the value of successivestage speed limit can be gained.
The previous studies show when the curve radius is greater than 1000 m, 85% of the desired speed is not affected by horizontal alignment. JTG/T B052004 [
In segments 4–6, the
Curves of the small vehicle and large vehicle have a similar trend. Meanwhile, difference of
In segments 4–6, deceleration curves show two opposite trends. The curve of Sites 1, 2, 3, and 7 rise in segments 45, and then drop in segments 56. The trend of the curve of 4, 5, and 6 is opposite. The common characteristic of 1, 2, 3, and 7 is that their deceleration lane length is more than 200 m. The length of the deceleration lane about 4, 5, and 6 is less than 200 m. Hence, deceleration lane length is related with
Speedlane number curves in the main line are similar with deceleration curves. The similarity suggests that the difference of speedlane number curves is caused by different deceleration lane length. We can deduce that lane number in the main line does not relate with speed and the lane number of the main line has not been considered when determine the speed limit.
Doublefactor curve fitting is used to analyze the correlation between saturation, turning ratio, and large vehicles rate and speed. Based on test results of models, saturation is selected as the main factor of operational speed. As a result, the paper built speedsaturation prediction model.
The research scope is divided into three sections according to the variation of the deceleration. Based on field investigation speed or speedsaturation prediction model and the speedlimit sign validity model, the value of successivestage speed limit is deduced according to kinematic principles.
The conclusions are summarized as follows:
It is necessary to set successivestage speed limit control on the exit ramp upstream.The successivestage speed limit is not needed to be developed for small vehicles and large vehicles, respectively, on the exit ramp upstream.
Geometry parameters are not considered in building successivestage speed limit model.
Deceleration lane length is related to
Lane number in the main line does not relate to speed and cannot be considered when determining the speed limit.
Saturation is the main factor affecting speed, and the paper built a speedsaturation prediction model.
This work was supported by the National Natural Science Foundation (51078232), Jiangsu Provincial Communications Department Science Foundation (2010Y17), Hebei Provincial Communications Department Science Foundation (Y2010016).