Dynamics of connected cruise control systems considering velocity changes with memory feedback

Measurement 64 (2015) 34–48

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Dynamics of connected cruise control systems considering velocity changes with memory feedback Shaowei Yu, Zhongke Shi ⇑ Shaanxi province engineering laboratory of transportation safety supervisory control network, Northwestern Polytechnical University, Shaanxi Xi’an 710072, China

a r t i c l e

i n f o

Article history: Received 3 October 2014 Received in revised form 4 December 2014 Accepted 18 December 2014 Available online 27 December 2014 Keywords: Connected cruise control strategy Car-following model Velocity changes with memory Fuel consumptions Exhaust emissions

a b s t r a c t In this paper, a new connected cruise control strategy considering multiple preceding cars’ velocity changes with memory is designed to improve roadway traffic mobility, enhance traffic safety and reduce fuel consumptions and exhaust emissions. The linkage between multiple preceding cars’ velocity changes with memory and the following car’s acceleration or deceleration is explored by using the empirical car-following data and the gray correlation analysis method, and then an improved car-following model considering multiple preceding cars’ velocity changes with memory in the connected cruise control strategy is put forward to investigate the effects of multiple preceding cars’ velocity changes with memory on each car’s speed and acceleration, the relative distance, fuel consumptions, CO, HC and NOX emissions. The new connected cruise control strategy is designed to be able to receive signals of velocity changes with memory from multiple cars ahead through wireless vehicle-to-vehicle communication and the immediately ahead car’s relative distance and velocity difference by radar. The results of numerical simulations prove that multiple preceding cars’ velocity changes with memory have significant effects on carfollowing behaviors and that using multiple preceding cars’ velocity changes with memory feedback in designing a connected cruise control system can improve roadway traffic mobility, enhance traffic safety and reduce fuel consumptions and exhaust emissions. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Nowadays the improvement of road traffic safety and traffic efficiency are two crucial priorities for the world society. As for road traffic safety, about 1.3 million people died and fifty million people were injured each year in road crashes all over the world reported by the World Health Organization [1] and it was also estimated that the rearend collision was one of the most frequent among all the road accidents [2]. As for road traffic efficiency, congestion in the US caused around 5.5 billion hours of travel delay ⇑ Corresponding author. E-mail address: [email protected] (Z. Shi). http://dx.doi.org/10.1016/j.measurement.2014.12.036 0263-2241/Ó 2014 Elsevier Ltd. All rights reserved.

and 2.9 billion gallons of extra fuel consumption with a total cost of 121 billion dollars in 2011 [3], which has become an economically important problem affecting large and medium-sized cities. Thus, effective policies and technologies to reduce the cost of road mobility and safety by cars are of first order importance. This paper primarily focuses on the possibility of using technologies rather than policies to ease traffic congestion and enhance road traffic safety. In the past decades, researchers and manufacturers experimented several in-vehicle technologies to assist various aspects of driving, such as Advanced Driver Assistance Systems, which are supposed to improve road traffic safety as well as traffic efficiency. The adaptive cruise control

S. Yu, Z. Shi / Measurement 64 (2015) 34–48

system is one of the most famous and deployed Advanced Driver Assistance Systems. Davis [4] has shown that traffic jams can be suppressed in a mixed traffic of human-driven but the adaptive cruise control cars constituting at least 20% of the traffic flow. To overcome the limitation, integrating the adaptive cruise control system and wireless communication was experimented with the help of intervehicle communication on a closed highway in the PATH program in 1997 [5], which is often referred to as cooperative adaptive cruise control system. The SARTRE project has been experimented with car platoons since 2009 [6]. In 2011, the grand cooperative driving challenge in the Netherlands carried out the idea of feedback from the car immediately ahead and the platoon leader [7–9]. This experiment pointed out the benefits of using signals received from multiple cars farther ahead, which is in accordance with the ideas in the literatures [10–15]. Good traffic properties of the adaptive cruise control system, the cooperative adaptive cruise control system or the connected cruise control system depend on good control strategies, and good control strategies depend on the properties of individual vehicles as well as on their interactions. Many car-following models have been developed to describe interacting driver–car units on a single lane without overtaking, which include the early linear models proposed by Chandler et al. [16], the early nonlinear models presented by Pipes [17], Gazis et al. [18] and Newell [19], the recent remarkable works of Bando et al. [20], Helbing and Tilch [21] and Jiang et al. [22] and some other related car-following models in the literatures [23–40]. The optimal velocity model taking the following car’s velocity and the relative distance into account proposed by Bando et al. [20] is one of favorable car-following models, which can be used to describe many properties of the real traffic flow, such as the instability of traffic flow, the evolution of traffic congestion and the formation of stop-and-go waves. Subsequently, many efforts have been made based on the optimal velocity model by taking into account both headway and velocity difference in different ways. Helbing and Tilch [21] took the negative velocity difference into account and put forward the generalized force model. Jiang et al. [22] took both negative and positive velocity differences into account and proposed the full velocity difference model. Gong et al. [41] considered the asymmetric characteristic of the velocity differences of the vehicles in a traffic stream and presented a new car-following model. Zhu and Zhang [42] introduced a speed feedback control mechanism into the system to improve the dynamical performance of traffic flow. Cars with human drivers or autonomous controllers can receive various signals from multiple cars ahead by using vehicle-to-vehicle communication and radars. Many experts have conducted a lot of research on them. Tang et al. [10] put forward an extended car-following model considering inter-vehicle communication. Ge et al. [11] presented the two velocity difference model in the light of the optimal velocity model. Wang et al. [12] presented the multiple velocity difference model by considering multiple preceding cars’ velocity differences. Peng and Sun [13] took the effects of multiple preceding cars’

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velocity differences and headways into account and proposed the multiple car-following model considering multiple preceding cars’ information. Yu and Shi [14] put forward an extended car-following model considering multiple preceding cars’ accelerations. Ge and Orosz [15] modeled the car-following dynamics of the connected cruise control vehicle with appropriately designed gains and delays by considering a platoon of cars traveling on a single lane. However, the above-mentioned car-following models [10–13,15] focus on studying the traffic phenomena from the analytical and numerical perspective, which did not use the empirical data to extract the useful information to seek the endogenous variables with higher information as the input variables of car-following model. It is necessary to test whether the results obtained by the above car-following models are quantitatively accordant with the real traffic phenomena. In essential, it needs a lot of field observations and deep data mining analysis on the real traffic flow before modeling car-following behaviors. One hand, distance, velocity, velocity difference and velocity changes with memory are easier to be obtained. Using multiple preceding cars’ velocity changes with memory information may enable the host car to better respond to the front traffic conditions. On the other hand, a driver has memory if his speed at a later time depends on his speed at a previous time. Zhang [43] developed a continuum macroscopic model arising from a car-following model with driver memory and found that driver memory in car-following behaviors can lead to viscous effects in continuum traffic flow dynamics. Tang et al. [44] proposed an extended OV model considering driver’s memory and found that driver’s memory in car-following behaviors can improve the stability of traffic flow. Under the above perspective, a new connected cruise control strategy with consideration of multiple preceding cars’ velocity changes with memory is designed, where the host car is actuated using velocity changes with memory information from other cars and local headway, velocity difference and velocity information monitored by sensors. Several numerical simulations are carried out to explore how velocity changes with memory feedback used in the connected cruise control strategy affects road driving safety, roadway traffic mobility, fuel consumptions, CO, HC and NOX emissions. 2. The related data The empirical car-following data used to analyze the linkage between multiple preceding cars’ velocity changes with memory and the following car’s acceleration or deceleration come from the survey of our Traffic Control Research Group. 2.1. The field data collection site The Jingshi Road/Shanshi East Road intersection of Jinan in China was selected for the field data collection

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S. Yu, Z. Shi / Measurement 64 (2015) 34–48 Table 2 Partial measured data with step-size memory of 2 s.

Fig. 1. The field data collection site.

(see Fig. 1). This signalized intersection is located in the downtown area and on the major arterial. It consists of one left-turn lane, three through lanes, one bus transit lane and one right-turn lane along the Jingshi Road. 2.2. Field observation and data extraction Field observation at the survey intersection was made from 9:00 AM to 10:30 AM on December 1, 2013. A total 1.5 h of video data was collected. To avoid the interference of the pedestrian flow and public transport and obtain more undisturbed empirical car-following data, the digital video camera was installed on the windowsill of a tall building adjacent to the intersection rather than on the roadside. To avoid the curbs and roadside friction, only the through lanes on the westbound approach were used for this study. To analyze the linkage between multiple preceding cars’ velocity changes with memory and the following car’s acceleration or deceleration, three successive following cars are focused on due to the constrain of the video device. It is supposed that car 1 follows car 2 and car 2 follows car 3. The field car-following data of every 1 second are extracted with the frame differential method, which contain each car’s velocity, position and acceleration, velocity difference, relative distance and multiple preceding cars’ velocity changes with memory. Partial measured car-following data with different step-size memory are listed as shown in Tables 1–3.

Table 1 Partial measured data with step-size memory of 1 s. a1 (m/s2)

d21 (m)

v1 (m/s)

Dv12 (m/s)

Dv2 (m/s)

Dv3 (m/s)

1.333 1.333 0.6665 0 0.6665 0.6665 1.333 0.6665 0.6665 0.6665 0.6665

13.2300 7.998 7.3315 5.0987 5.0987 4.8655 4.3323 9.7643 8.1313 6.2651 2.1995

8.6645 5.9985 4.9988 4.6655 4.3323 3.6658 2.666 3.6658 2.9993 2.3328 2.9993

2.9993 0.6665 1.333 0.9998 0.3333 0.6665 0.6665 0.9998 1.333 1.333 0

0.9998 0.9998 1.6663 0 0.9998 1.6663 0.9998 0.9998 0.9998 0.6665 0.6665

1.333 0.9998 1.6663 1.333 1.333 0.9998 0.9998 0.6665 0.3333 0.6665 0.9998

a1 (m/s2)

d21 (m)

v1 (m/s)

Dv12 (m/s)

Dv2 (m/s)

Dv3 (m/s)

0.6665 0.6665 1.333 0.6665 0.6665 0.6665 0 0.6665 0.6665 0.6665 1.333 0.6665

5.0987 4.8655 4.3323 8.1313 6.2651 4.3989 3.9324 2.7993 4.6988 4.3323 3.6991 14.0965

4.3323 3.6658 2.666 2.9993 2.3328 2.9993 2.666 2.3328 4.9988 4.3323 3.3325 4.3323

0.3333 0.6665 0.6665 1.333 1.333 0 0.6665 1.333 0.3333 0.6665 0.3333 1.6663

0.9998 2.666 2.666 1.9995 1.6663 0.6665 1.333 1.9995 1.6663 2.666 2.3328 0.6665

2.666 2.3328 1.9995 0.9998 0.9998 1.333 1.333 1.333 1.9995 1.9995 2.3328 0.9998

Table 3 Partial measured data with step-size memory of 3 s. a1 (m/s2)

d21 (m)

v1 (m/s)

Dv12 (m/s)

Dv2 (m/s)

Dv3 (m/s)

0.6665 1.333 0 0.6665 0.6665 1.333 0.6665 0.6665 0.6665 0.6665 0.6665 0.6665

4.8655 4.3323 3.9324 2.7993 4.3323 3.6991 12.0969 9.9975 5.4319 4.5655 5.9319 5.5319

3.6658 2.666 2.666 2.3328 4.3323 3.3325 3.6658 2.9993 3.6658 2.9993 4.3323 3.6658

0.6665 0.6665 0.6665 1.333 0.6665 0.3333 1.6663 1.9995 0.3333 0.9998 0.6665 0.6665

2.666 3.6658 1.6663 2.3328 3.3325 3.3325 1.333 1.6663 2.3328 2.9993 1.9995 1.9995

3.6658 3.3325 1.9995 1.9995 2.9993 3.3325 1.9995 2.666 3.3325 2.9993 1.333 1.6663

a1 is the acceleration of car 1, d21 is the relative distance between car 2 and car 1, v1 is the velocity of car 1, Dv21 is the velocity difference of car 1 and car 2, Dv2 and Dv3 are respectively the velocity changes with memory of car 2 and car 3.

2.3. Field data mining analysis To investigate the linkage between multiple preceding cars’ velocity changes with memory and the following car’s acceleration or deceleration, this paper uses the following procedure: Step 1: Use the gray correlation analysis theory to compute the relational degrees between multiple preceding cars’ velocity changes with different step-size memories and the following car’s acceleration or deceleration. Step 2: Investigate the linkage distinction with different step-size memories. Step 3: Explore the linkage difference between different number of preceding car’s velocity changes with memory and the host car’s following behaviors. The gray correlation analysis theory is considered to be an analysis of the geometric similarity between the behavior factors within a system and the car-following process can be regarded as a system. This study utilizes gray correlation analysis method to explore the linkage between two preceding cars’ velocity changes with different step-size memories and the following car’s acceleration or deceleration. The gray correlation degrees between the sub-factors

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S. Yu, Z. Shi / Measurement 64 (2015) 34–48 Table 4 Results of gray correlation analysis. lag (s)

d21(m)

v1 (m/s)

Dv12 (m/s)

Dv2 (m/s)

Dv3 (m/s)

d=1 d=2 d=3

0.8622 0.9323 0.9302

0.8916 0.9415 0.9397

0.9827 0.9887 0.9896

0.9888 0.9837 0.9671

0.9874 0.9822 0.9655

d is memory step.

and main-factor of the following car’s acceleration or deceleration are computed and listed respectively as shown in Table 4. From the second row of Table 4, it can be obviously found that the most similar sub-array with the following car’s acceleration or deceleration is velocity changes with memory of car 2, that velocity changes with memory of car 3 and the velocity difference between car 1 and car 2 are more similar with the following car’s acceleration or deceleration than the following car’s velocity and headway, and that the similarities of the velocity difference between car 1 and car 2, velocity changes with memory of car 2 and velocity changes with memory of car 3 with the following car’s acceleration or deceleration are much the same. From the third row of Table 4, it can be obviously found that the most similar sub-array with the following car’s acceleration or deceleration is the velocity difference between car 1 and car 2, that velocity changes with memory of car 2 and velocity changes with memory of car 3 are more similar with the following car’s acceleration or deceleration than the following car’s velocity and headway, and that the similarities of the velocity difference between car 1 and car 2, velocity changes with memory of car 2 and the velocity changes with memory of car 3 with the following car’s acceleration or deceleration are much the same. From the fourth row of Table 4, we can find the same conclusions as those in the third row. Now, we try to find the differences of the effects of velocity changes with different step-size memories and the impacts of different number of preceding car’s velocity changes with memory on car-following behaviors by averaging the above results of gray correlation analysis, which are listed as shown in Table.5. By vertical comparison of the fifth and the sixth columns of Table 5, it can be obviously found that the similarities of velocity changes with memory of car 2 and velocity changes with memory of car 3 with the following car’s acceleration or deceleration gradually decrease with the increase of the value of the parameter d but they are much the same, which is similar with the results in the Table 4. By horizontal comparison of the fifth and the sixth columns of Table 5, it can be obviously found that the similarities of velocity changes with memory of car 2 with the Table 5 Averaged results of gray correlation analysis. lag (s)

d21 (m)

v1 (m/s)

Dv12 (m/s)

Dv2 (m/s)

Dv3 (m/s)

d=1 d=2 d=3

0.1829 0.1931 0.1941

0.1892 0.1949 0.1961

0.2085 0.2048 0.2065

0.2098 0.2037 0.2018

0.2095 0.2034 0.2015

following car’s acceleration or deceleration are more similar than those of the third car’s velocity changes with memory, that is to say, the impacts of different number of preceding car’s velocity changes with memory on the host car’s following behaviors gradually decrease with the increase of the number of the considered preceding cars, which is in accordance with the conclusions in the Table 4. It can be concluded that two preceding cars’ velocity changes with different step-size memories have significant effects on car-following behaviors, that the effects of multiple preceding car’s velocity changes with memory gradually decrease with the increase of memory step, and that the impacts of different number of preceding car’s velocity changes with memory on the host car’s following behaviors gradually decrease with the increase of the number of the considered preceding cars. These conclusions should be taken into account in car-following modeling and parameters setting process. 3. Model The existing car-following models can be formulated as below [45]:

€xn ðtÞ ¼ f ½Dxn ðtÞ; v n ðtÞ; Dv n ðtÞ; . . .;

ð1Þ

where xn ðtÞ is the nth car’s position at the time t, v n ðtÞ is the nth car’s velocity at the time t,Dxn ðtÞ and Dv n ðtÞ are respectively the relative distance and the velocity difference between car n and car (n + 1). The above data mining analysis shows that multiple preceding cars’ velocity changes with different step-size memories have significant effects on car-following behaviors, but Eq. (1) and its extensions cannot be directly employed to explore the impacts of velocity changes with memory on car-following behaviors, so it is necessary to develop a new car-following model on the basis of the existing car-following models. Here, we consider a platoon of n + m cars running on a signal lane as shown in Fig. 2. All cars are supposed to be equipped with the connected cruise control system and the improved car-following model considering multiple preceding cars’ velocity changes with memory based on the full velocity difference model is constructed, which can be formulated as follows:

€xn ðtÞ ¼ j½VðDxn ðtÞÞ  v n ðtÞ þ kDv n ðtÞ þ

m X 

cj v nþj ðtÞ  v nþj ðt  dÞ



ð2Þ

j¼1

where xn ðtÞ is the position of car n at the time t; VðÞ is the optimal velocity function; Dxn ðtÞ and Dv n ðtÞ are the headway and the velocity difference between car n and car   n + 1 at the time t; v nþj ðtÞ  v nþj ðt  dÞ is velocity changes

Fig. 2. A vehicle platoon of n + m cars running on a signal lane.

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S. Yu, Z. Shi / Measurement 64 (2015) 34–48

with memory of car n + j; m is the number of the considered preceding cars; j, k and cj are sensitivity parameters. The nth car’s optimal velocity function is adopted as follows:

VðDxn ðtÞÞ ¼ V 1 þ V 2 tan hðC 1 Dxn ðtÞ  C 2 Þ

ð3Þ

Comparing with the existing car-following models, the new proposed car-following model may better describe the impacts of velocity changes with memory on driving behaviors since velocity changes with memory are explicitly taken into account in the modeling process. 4. Numerical simulations In this section, several numerical simulations are carried out by employing the above-proposed car-following model to explore how multiple preceding cars’ velocity changes with different step-size memories affect the host car’s velocity, acceleration, headway, fuel consumption, CO, HC and NOX emissions on a signal-lane roadway. The full velocity difference model is used for comparative analysis. When cj ¼ 0, the new proposed car-following model can be reduced to the full velocity difference model. Moreover, we consider that all cars are identical and have the same range policy, headway gain, velocity difference gain and velocity changes gain. 4.1. Simulation for the hard braking process Here, we consider the traffic flow of a signal-lane roadway with one traffic light and study how multiple preceding cars’ velocity changes with different step-size memories affect the host car’s driving behaviors during the red phase period. Numerical simulations for the arrival traffic flow at a signalized intersection are conducted and two preceding cars’ velocity changes with memory are taken into account here. The initial conditions are supposed as follows: the traffic signal is green and 10 cars are running with an uniform velocity of 4.6647 m/s; the 10th car is at the origin; the distance between the platoon leader car and the stop line is 5 m; the relative distance between two successive cars are all 10 m; when the time step t = 0, the traffic light turns red, and then the platoon leader car immediately begins to slow down, the other cars will gradually slow down and follow the leading cars, all cars will finally stop in a column behind the stop line. The parameters are adopted as follows: j = 0.41 s1, k ¼ 0:5, c1 = 0.1, c2 = 0.05, V1 = 6.75 m/s, V2 = 7.91 m/s, d = 2, C1 = 0.13 m1, C2 = 1.57, l = 5 m. First, we explore the impacts of two preceding cars’ velocity changes with memory step of 2 s on the following cars’ velocities, accelerations and headways. Fig. 3(a) and (b) respectively illustrate velocities’ evolutions of 10 cars simulated by the new proposed car-following model and the full velocity difference model. From Fig. 3, it can be found that the following cars can basically duplicate the leading cars’ velocities but with some delay time and eventually stop behind the stop line in a column, that the delay time simulated by the new proposed car-following model is shorter than that simulated

Fig. 3. Velocities of 10 cars simulated by: (a) the new proposed model, (b) full velocity difference model.

by the full velocity difference model, and that there are no negative velocities existing from car 2 to car 10 in Fig. 3 (a) while there exist in Fig. 3(b). It can be concluded that the new proposed car-following model considering multiple preceding cars’ velocity changes with memory can solve the problem of negative velocities existing in the full velocity difference model to a certain extent, and that two preceding cars’ velocity changes with memory has very obvious impacts on each car’s motion, which is in accordance with the results of the above data mining analysis. In order to explore how two preceding cars’ velocity changes with memory affect the following cars’ velocities, accelerations and headways more clearly, we select car 4, car 6, car 8, and car 10 to carry out comparative analysis. Figs. 4–6 respectively depict velocities’, accelerations’ and vehicular gaps’ evolutions of car 4, car 6, car 8 and car 10 simulated by the new proposed car-following model and the full velocity difference model. The black curves stand for velocities, accelerations and vehicular gaps simulated by the new proposed car-following model and the

S. Yu, Z. Shi / Measurement 64 (2015) 34–48

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Fig. 4. Velocities of car 4, car 6, car 8 and car 10 simulated by different car-following models.

green ones stand for those simulated by the full velocity difference model. From Fig. 4, it can be found that velocity curves can be divided into two steps. In the first step, the following cars simulated by the new proposed car-following model decelerate more quickly than those simulated by the full velocity difference model. In the second step, the following cars simulated by the full velocity difference model decelerate more quickly than those simulated by the new proposed car-following model. These results indicate that the following cars simulated by the new car-following model can decelerate in advance due to considering the effects of two preceding cars’ velocity changes with memory and unhurriedly slow down until they come to a complete stop but those cars simulated by the full velocity difference

model cannot. In addition, it can be also found that the effects of two preceding cars’ velocity changes with memory on the following cars’ motions increase with the increase of the number of the considered preceding cars. From Fig. 5, it can be found that all the acceleration curves can be also divided into two steps. In the first step, the following cars simulated by the new proposed car-following model decelerate much harder than those simulated by the full velocity difference model. In the second step, the following cars simulated by the full velocity difference model decelerate much harder than those simulated by the new proposed car-following model. It can be concluded that the harder decelerations enable the following cars to slow down unhurriedly and not to result in negative velocities in the new proposed car-following model,

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Fig. 5. Accelerations of car 4, car 6, car 8 and car 10 simulated by different car-following models.

and that the new proposed car- following model can solve the problem of negative velocities existing in the full velocity difference model indeed, which is in accordance with the results of the above velocity analysis. These conclusions can also be obtained in Fig. 6. From Fig. 6, it can be found that all vehicular gap curves can be divided into two steps. In the first step, vehicular gaps of the following cars simulated by the new car-following model change much slowly than those simulated by the full velocity difference model. In the second step, vehicular gaps of the following cars simulated by the full velocity difference model change much slowly than those simulated by the new car-following model. It can be also found that vehicular gaps of the following cars simulated by the new proposed car-following model change gradually decrease to the a fixed minimum, that vehicular gaps

of the following cars simulated by the full velocity difference model first decrease to the minimum and then gradually increase to a fixed value, which means there exists car-backing problem in the full velocity difference model. Next, we carry out a numerical simulation to explore the impacts of different memory steps on the following cars’ velocities and accelerations. The memory step is set as 1 and 3 respectively and the other parameters are adopted as above. When d = 0 or cj = 0, the new car-following model can be reduced to the full velocity difference model. The velocities’ and accelerations’ evolutions of the selected cars simulated by different models are respectively illustrated in Figs. 7 and 8. From Fig. 7, we can learn that different memory steps have different effects on the following cars’ motions, that with the increase of the value of the parameter d, that

S. Yu, Z. Shi / Measurement 64 (2015) 34–48

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Fig. 6. Vehicular gaps of car 4, car 6, car 8 and car 10 simulated by different car-following models.

the problem of negative velocities existing in the full velocity difference model can be solved to a certain extent, and that the following cars simulated by the new car-following model decelerate more quickly than those simulated by the full velocity difference model with the increase of memory step. In addition, velocity curves can be divided into two steps. In the first step, the following cars simulated by the new proposed car-following model decelerate more quickly than those simulated by the full velocity difference model. In the second step, the following cars simulated by the full velocity difference model decelerate more quickly than those simulated by the new car-following model. These conclusions can be also obtained from Fig. 8. It can be concluded that two preceding cars’ velocity changes with different step-size memories have obviously different impacts on the following cars’ velocities and accelerations and that the new proposed car-following model can be employed to explore the impacts of multiple

preceding cars’ velocity changes with memory on the following cars’ driving behaviors. 4.2. Simulation for the traffic flow evolution with a small disturbance Here, the above-proposed car-following model is employed to conduct numerical simulations under the periodic boundary condition to explore how multiple preceding cars’ velocity changes with memory affect the traffic flow evolution with an initial small perturbation and each car’s velocity, acceleration, headway, fuel consumptions, CO, HC and NOX emissions, where the initial conditions are supposed as follows: 50 cars uniformly distribute on the ring road with the length L = 750 m. The initial small perturbation is 5 m and the parameters are adopted as above. First, we explore the impacts of multiple preceding cars’ velocity changes with memory on the traffic flow evolution

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Fig. 7. Velocities of car 4, car 6, car 8 and car 10 simulated by different car-following models.

with an initial small initial perturbation and can obtain each car’s velocity, acceleration and headway. Fig. 9 depicts velocity distributions obtained at the time steps of t = 50 s, t = 100 s, t = 300 s, t = 1000 s, t = 3000 s and t = 5000 s, where the black curves stand for velocities of 50 cars simulated by the new proposed car-following model and the green ones stand for those simulated by the full velocity difference model. From Fig. 9, it can be found that multiple preceding cars’ velocity changes with memory have great impacts on the traffic flow with a small initial perturbation, that velocities of all cars fluctuate around the initial velocity v0 = 4.6647 m/s between the minimum and maximum caused by the initial disturbance, that the fluctuation of the new proposed car-following model is much smaller than that of the full velocity difference model. Therefore, it is not difficult to understand why it is easier for the new proposed car-following model to get stable than the full velocity difference model. The motion of cars can organize a ‘‘hysteresis loop’’ after sufficient time steps. Here, we selected the 25th car as the

target car to further investigate the phase diagram for more differences and advantages. The ‘‘hysteresis loop’’ is illustrated as shown in Fig. 10. As can be seen from Fig. 10, the hysteresis loop obtained from the new proposed car-following model is significantly different from that from the full velocity difference model. Since the new proposed car-following model takes multiple preceding cars’ velocity changes with memory into account, the velocity’s fluctuation simulated by the new proposed car-following model is much smaller than that simulated by the full velocity difference model, which indicates that the stability of the traffic flow simulated by the new proposed car-following model is superior to that simulated by the full velocity difference model. The analysis of the above stop-and-go charts and hysteresis loops prove that the stability of the new proposed car-following model considering multiple preceding cars’ velocity changes with memory is superior to that of the full velocity difference model and that the new proposed carfollowing model considering multiple preceding cars’ velocity changes with memory can describe the traffic flow

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Fig. 8. Accelerations of car 4, car 6, car 8 and car 10 simulated by different car-following models.

evolution with a small perturbation well, improve the stability of traffic flow and suppress the appearance of traffic jams. The above numerical simulations have investigated the impacts of multiple preceding cars’ velocity changes with memory on each car’s driving behaviors. Recently driving behaviors have been seen to offer considerable potential method for reducing fuel consumptions and exhaust emissions [46]. The existing studies indicate that driving behaviors can affect drivers’ fuel consumptions and exhaust emissions [47–56]. Wu et al. [46] developed and validated a new fuel-economy optimization system to help drivers, especially new drivers learn how to manipulate pedals according to traffic and environmental situations and eventually form an eco-driving style. Tang et al. [47] use Ahn’s model to explore the vehicle’s fuel consumptions of car-following models. Rakha et al. [48] incorporated Ahn’s model into the simulation tool INTEGRATION to explore the effects of traffic light on the vehicle’s fuel consumptions and emissions. Shi et al. [51] studied the relation between the fuel consumptions and the stability of traffic flow simulated by several typical car-following models

and found that minimizing the energy consumptions will depend crucially on the stability of the traffic flow simulated by the corresponding car-following model. Tang et al. [54] incorporated the theories of the literature [50] into a car-following with consideration of real-time road conditions to study the impacts of the car-following behaviors considering real-time road conditions on fuel consumptions, CO, HC and NOX emissions and found that fuel consumptions and exhaust emissions are related to the stability of traffic flow. Therefore, it is very necessary to explore the impacts of multiple preceding cars’ velocity changes with memory in the connected cruise control strategy on each car’s fuel consumptions, CO, HC and NOX emissions under the traffic flow with a small initial perturbation. We use the VT-Micro model proposed by Ahn [50] to explore the impacts of multiple preceding cars’ velocity changes with memory on the car’s cumulative fuel consumptions, which can be expressed as:

lnðMOEe Þ ¼

3 X 3 X i¼0 j¼0

K ei;j  v i 



dv dt

j ! ð4Þ

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Fig. 9. Velocities of all cars simulated by different car-following models at different time steps.

where MOEe is car’s fuel consumption rate or exhaust emission rate, K ei;j is the model regression coefficient for MOE ‘‘e’’ at speed power ‘‘i’’ and acceleration power ‘‘j’’ for negative accelerations, v is the instantaneous speed, dv/dt is the instantaneous acceleration. The model regression coefficients are obtained from the literature [46], where the curves at t = 300 s denote each car’s cumulative fuel consumptions during the time period from 0 to 300 s and the initial conditions are adopted as the same as above. Fig. 11 depicts each car’s cumulative fuel consumptions simulated by different car-following models during the time periods of t = 300 s, t = 800 s and t = 1500 s, where the black curves stand for the cumulative fuel consumptions of 50 cars simulated by the full velocity difference model and the green ones stand for those simulated by the new proposed car-following model. From Fig. 11, we can obtain:

(a) Each car’s cumulative fuel consumptions simulated by the new proposed car-following model are lower than those simulated by the full velocity difference model at different time. (b) Each car’s cumulative fuel consumptions produce oscillating phenomena. The fluctuation of cumulative fuel consumptions simulated by the new proposed car-following model is much smaller than that simulated by the full velocity difference model, which is in accordance with the velocity fluctuation. (c) The fluctuation range of the 49th car’s cumulative fuel consumptions simulated by the new proposed car-following model is higher than the other 49 cars due to the initial small perturbation. (d) The fluctuation amplitude of the 49th car’s cumulative fuel consumptions simulated by the new proposed car-following model gradually decreases with the increase of the simulation time because

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Fig. 10. Hysteresis loops obtained from: (a) the full velocity difference model, (b) the new proposed car-following model.

the unstable traffic flow resulted from the initial small perturbation gradually changes into the stable status. Finally, we explore each car’s cumulative exhaust emissions under the traffic flow with a small initial perturbation and the model regression coefficient is obtained from the Ref. [46], where the curve at t = 500 s is each car’s cumulative exhaust emissions during the period from 0 s to 500 s. Figs. 12–14 respectively depict each car’s cumulative CO, HC and NOX emissions simulated by different car-following models, where the black curves stand for the cumulative exhaust emissions of 50 cars simulated by the full velocity difference model and the green ones stand for those simulated by the new proposed car-following model. From Fig. 12, we can obtain: (a) Each car’s cumulative CO emissions simulated by the new proposed car-following model are lower than those simulated by the full velocity difference model at different time. (b) Each car’s cumulative CO emissions produce oscillating phenomena. The fluctuation of cumulative CO emissions simulated by the new proposed car-following model is much smaller than that simulated by the full velocity difference model, which is in accordance with the velocity fluctuation. (c) The fluctuation range of the 49th car’s cumulative CO emissions simulated by the new proposed

Fig. 11. The cumulative fuel consumptions of 50 cars simulated by different car-following models.

car-following model is higher than the other 49 cars due to the initial small perturbation. (d) The fluctuation amplitude of the 49th car’s cumulative CO emissions simulated by the new proposed car-following model gradually decreases with the increase of the simulation time because the unstable traffic flow resulted from the initial small perturbation gradually changes into the stable status. From Fig. 13, we can obtain: (a) Each car’s cumulative HC emissions simulated by the new proposed car-following model are lower than those simulated by the full velocity difference model at different time.

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Fig. 12. The cumulative CO consumptions of 50 cars simulated by different car-following models.

(b) Each car’s cumulative HC emissions produce oscillating phenomena. The fluctuation of cumulative HC emissions simulated by the new proposed carfollowing model is much smaller than that simulated by the full velocity difference model, which is in accordance with the velocity fluctuation. (c) The fluctuation range of the 49th car’s cumulative HC emissions simulated by the new proposed carfollowing model is higher than the other 49 cars due to the initial small perturbation. (d) The fluctuation amplitude of the 49th car’s cumulative HC emissions simulated by the new proposed car-following model gradually decreases with the increase of the simulation time because the unstable traffic flow resulted from the initial small perturbation gradually changes into the stable status.

Fig. 13. The cumulative HC consumptions of 50 cars simulated by different car-following models.

From Fig. 14, we can obtain: (a) Each car’s cumulative NOX emissions simulated by the new proposed car-following model are lower than those simulated by the full velocity difference model at different time. (b) Each car’s cumulative NOX emissions produce oscillating phenomena. The fluctuation of cumulative NOX emissions simulated by the new proposed carfollowing model is smaller than that simulated by the full velocity difference model, which is in accordance with the velocity fluctuation.

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It can be concluded that taking multiple preceding cars’ velocity changes with memory in designing the connected cruise control strategy can reduce fuel consumptions, CO, HC and NOX emissions. 5. Conclusions The data mining analysis shows that multiple preceding cars’ velocity changes with different step-size memories have significant effects on car-following behaviors. The numerical results indicate that taking multiple preceding cars’ velocity changes with memory in designing the control strategy for the connected cruise control system can enhance traffic safety, improve the stability of traffic flow and reduce fuel consumptions, CO, HC and NOX emissions. However, there are some limitations in this paper as follows: (1) We only obtain three successive cars’ car-following behaviors with memory step of 3 s for the time being, due to the limitation of visual angle. (2) The communication delay and the time delay in the controller of the connected cruise control system are not considered explicitly for the present. We will employ the technologies on image fusion for the empirical data of more successive cars’ car-following behaviors with more memory steps and consider communication delay and the time delay in the controller to develop an actual car-following model to investigate the impacts of multiple preceding cars’ velocity changes with different step-size memories on car-following behaviors, fuel consumptions and exhaust emissions. Acknowledgments This study has been supported by National Natural Science Foundation (Grant No. 61134004) and Shaanxi Provincial Science Foundation (Grant No. 2013JQ7014). The authors would like to thank the anonymous reviewers for their helpful comments and valuable suggestions which could refine this paper. References Fig. 14. The cumulative NOX consumptions of 50 cars simulated by different car-following models.

(c) The fluctuation range of the 49th car’s cumulative NOX emissions simulated by the new proposed carfollowing model is higher than the other 49 cars due to the initial small perturbation. (d) The fluctuation amplitude of the 49th car’s cumulative NOX emissions simulated by the new proposed car-following model gradually decreases with the increase of the simulation time because the unstable traffic flow resulted from the initial small perturbation gradually changes into the stable status.

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