Research Article | Open Access
Li Li, Dong Zhang, Zhi-gang Xu, Ping Wang, Gui-ping Wang, "The Roles of Car Following and Lane Changing Drivers’ Anticipations during Vehicle Inserting Process: A Structural Equation Model Approach", Journal of Advanced Transportation, vol. 2018, Article ID 6372861, 19 pages, 2018. https://doi.org/10.1155/2018/6372861
The Roles of Car Following and Lane Changing Drivers’ Anticipations during Vehicle Inserting Process: A Structural Equation Model Approach
Anticipating ability is a skill that drivers count on to handle risky tasks in the traffic. This paper explores how the drivers of lane changing vehicle and its immediately car follower anticipate surrounding vehicles’ movements and adjust their manoeuvers during vehicle inserting process. The drivers’ anticipating mechanisms are modelled in the framework of structural equation model and estimated from field data. Results show that the change of lane changing type or traffic signal affects the drivers’ anticipation. Increased vehicle speed impels subject driver to anticipate driving condition in further future, but the stimulus is lower than the one coming from the kinematic comparisons of subject vehicle and other vehicles. The drivers care more about the vehicles’ interactions with which they are personally involved than the one to which they are only onlookers. The drivers’ responses to the counterpart vehicle’s movements depend on the progress of vehicle insertion and their roles in vehicle interactions.
A lane changing (LC) manoeuver is often accompanied by high collision risk, especially in congested traffic [1, 2]. The mutual misunderstanding between the drivers of LC vehicle (LCV) and surrounding car following vehicles (CFV) is a major source of the risk. However, the cases of successful LC mostly happen in real traffic, when the drivers seem to be able to predict the risk and make adjustments in advance to avoid it. Such driving skill is usually named as anticipating ability or anticipation.
Driver’s anticipation can reduce vehicle speed fluctuation and fuel consumption , but how this ability works and how to model it is still under study. Hofmann et al.  found that the anticipation gradually forms with driving experience, and some hints, such as turning light of the vehicle ahead, let the LCV driver know the counterpart’s intention. Chan et al.  reported the weaker hazard anticipation of the novice drivers from the experienced drivers. Many existing LC decision models assume that the LCV’s manoeuvre is impelled by a onetime and irrevocable decision of the vehicle driver, so the anticipation is often modelled as some predictive vehicle kinematic variables, such as vehicle gap or delay of travel time, measured at the moment of making LC decision [6, 7]. However, the assumption has been challenged by the pieces of evidence obtained from recent empirical studies [8, 9]. They found that the LCV’s inserting process could last over ten seconds, and the preparation of such insertion is even longer. Some researchers have realized the risk of ignoring the continuity of LCV manoeuvre in traffic simulation, so they modelled the LCV’s preparation movements before its insertion as a series of consecutive decisions followed by longitudinal manoeuvre adjustments [10–12]. In the models, the LCV driver’s anticipation works continuously during the process of seeking an acceptable inserting gap in LC target lane. The LCV’s longitudinal acceleration or deceleration was abstracted as the trade-off of driver’s LC desire and his/her anticipated collision risk with surrounding vehicle if conducting LC [13, 14]. It is noteworthy that most related studies are concerned with the LC preparing process on the original lane, but the anticipation should also work when the driver executes the inserting manoeuvre from the original lane to the target lane. Unfortunately, few efforts have been devoted to analyse anticipative inserting manoeuvre of the LCV driver .
More importantly, the anticipation is the behavioural basis of formulating LC model and CF model into a unified framework. Such integrated model can reduce the simulating error of many existing microscopic traffic flow models in the scenario when the LCV transits from the state of inserting preparation to the one of inserting execution [16, 17]. The modelling effort of CFV driver’s anticipation in CF scenario has lasted for decades (see Section 2), but there rarely exist studies of how the skill works in LC scenario. In fact, the absence of CFV’s anticipation could make potential conflict brought by LC manoeuver evolve to be a real collision.
To fill the existing research gaps, this study models and analyses the anticipating ability of the drivers of the LCV and its surrounding CFVs during the LCV’s inserting process. The process is divided into two consecutive periods. The working mechanisms of the drivers’ anticipation in two periods are formulated into two structural equation models (SEMs) correspondingly. A driver’s anticipation to another vehicle is abstracted as a latent variable of the SEM. Vehicle trajectories and the indicators reflecting driving environment are utilized as the observable variables of the model. The transmission path of the drivers’ anticipation on their behaviours and the influence degrees are identified based on the estimations of the SEMs.
The rest content is arranged as follows. Section 2 introduces the characteristics of driver’s anticipation. Section 3 describes the modelling effort to figure out the working mechanism of the anticipation during the LCV’s inserting process. Section 4 depicts data collection work. The model estimations are reported and discussed in Section 5. Section 6 concludes the main findings and points out the directions for future studies.
2. Characteristics of Driver’s Anticipation
Figure 1(a) shows the minimum platoon involving a LC scenario, including a LCV, its following vehicle (FV), and leading vehicle (LV) on LC target lane. The LV’s movement is assumed to affect the drivers of the LCV and the FV, but the LV driver does not suffer backward influences from the two following vehicles. The study period of this paper is the LCV’s inserting process, and its detailed definition refers to the content in Appendix. The process can be divided into two stages by the entrance moment (EM, see Figure 1(a)), when body centre of the LCV crosses lane marking line. The period before the EM is anticipating period, while the one after the EM is relaxing period. The anticipations of the LCV driver and the FV drivers begin to work at the start of the anticipating period. Three driving relationships exist in each period. The FV and the LCV involve an LC relationship in anticipating period, and the CF relationships existing in this period include the following: (1) The FV follows the LV longitudinally on the target lane, and (2) the LCV follows the LV laterally on the original lane. In the relaxing period, the FV turns to follow the LCV laterally on target lane, and the other two CF relationships continue.
Anticipating ability of the drivers in the LCV and the FV assumes working in both longitudinal and lateral directions of lane traffic. This assumption has been verified by previous studies of CF behaviour. The longitudinal anticipation is modelled as a CF driver’s estimation of one or more leaders’ movements in one or more future moments [18–20]. Lateral anticipation is presented as that a staggered leader in the same lane or the neighbouring lane of the CFV brings the driver’s lateral disturbance and triggers his or her deceleration [21, 22]. In some LC cases, the FV driver, who originally follows the LV in target lane, could anticipate adjacent LCV driver’s inserting intention and decelerate voluntarily to create a larger inserting gap for the LCV . Meanwhile, the LCV driver has a great possibility of anticipating the FV driver’s decelerating intention and take advantage of the opportunity to finish the insertion. Under similar anticipation of the two drivers working simultaneously, they can coordinate their manoeuvers to ensure the vehicle safety during the LCV’s inserting process. After the EM, the two drivers’ anticipation continues working in the relaxing period. The LCV’s relationship with the FV changes from the LC couple to a lateral CF couple, although its inserting manoeuvres continue after the EM. In this period, the two vehicles begin recovering their desired spacing with the LCV and the LV ahead, respectively [23–25]. Based on the previous findings mentioned above, the assumption of this study that the two drivers’ anticipation works during the whole LCV’s inserting process is reasonable.
Besides the nonexclusiveness and temporal continuity, other characteristics of the drivers’ anticipation should be taken into account when modelling manoeuvres of the LCV and FV during the LCV’s inserting process.
(1) Universality: driver’s anticipations exist in every LC scenario. Sometimes it can be indirectly inferred from vehicle manoeuvers, while other times it only exists in the driver’s mind. For instance, the FV driver’s conservative anticipation to the adjacent LCV in a cooperative LC scenario can be inferred from observable predeceleration of the FV before the EM . On the contrary, the FV driver who involves in a forced LC scenario has aggressive anticipation to the LCV. It induces the FV driver postponing the deceleration till or after the EM when the LCV forcibly but successfully is inserted into the target lane.
(2) Gradualness: each driver’s anticipation is gradually formed during the LCV’s inserting process as he or she continuously observes the other vehicles’ movements. It is hard to imagine that a driver can accurately recognize the other driver’s intentions by counting on the first impression only.
3.1. Structural Equation Model
The characteristics of the driver’s anticipation mentioned above belongs to the domain of human psychology. How to model and analyse the psychological influences on the manoeuvres of the LCV and the FV is the critical issue of this study.
A conceptual model is proposed under the framework of SEM to depict how the psychological traits affect the drivers’ behaviours. SEM provides an empirical approach to identify the cause-effect relationship that is formulated based on solid theories or empirical results . It can identify the effects of personal risk perception and task loads on drivers’ attitudes of driving safety . The conceptual model consists of one structural model and two measurement models. The structural model hypothesizes the influential paths of the external stimuli to the drivers’ anticipations, which could come from traffic signals, LC type, and other vehicles’ movements. The vehicle stimuli can be inferred from some observed variables that reflect vehicle kinematics at the start of a study period. This inferring system is formulated as the “measurement model 1” in Figure 2. The “measurement model 2” in the figure is another system to infer how the drivers adjust vehicle manoeuvers at the end of the period based on their anticipations.
The structural and measurement models are made of latent variables, observed variables, and their dependent relationships. They are illustrated as the normal rectangles, the rounded rectangles, and the directional lines in Figure 2. The dependent relationship presents as a directional line pointing from a causal variable to an affected variable. The anticipations of the LCV driver and the FV driver to future movements of surrounding vehicles are abstracted as the latent variables listed in Table 1, as they cannot always be observed from vehicle trajectories. The observed variables listed in Table 2 are defined from the view points of the LCV driver and the FV driver in specific scenarios. Their definitions will be detailed in Section 3.2.
Note: (1) : the FV’s speed; : the LCV’s speed; : the LV’s speed; : front gap for the FV or LCV driver; : lag gap for the FV driver; : lag gap for the LCV driver; : lead gap for the FV or LCV driver; : speed difference between the FV and the LV; : speed difference between the FV and the LCV; : speed difference between the LCV and the LV; : LC type; : the state of traffic signal.
(2) The variable measured at the first second, the EM, or the last instant of the LCV’s inserting process is marked by the superscript “1”, “EM”, or “n”, respectively.
3.2.1. Scenario-Dependent Variable
The LCV could be inserted into target lane in different ways , so three inserting scenarios illustrated in Figure 3 are defined in this study. In a forward inserting scenario, the LCV overtakes the FV to find opportunity of conducting the insertion. In a backward inserting scenario, the LCV lets the LV pass it and cuts in the backward gap. In a median inserting scenario, the LCV has run aside the gap between the LV and the FV for a while and finds a proper time to fill in the gap. The observed variables are measured at the start and the end of the two study periods. Their settings are defined in Table 2.
The settings of some variables at the start of the anticipating period depend on the observing point of each driver in the scenarios defined above. Here take the lag gap observed by the FV driver (), for instance. In the forward inserting scenario (see Figure 3(a)), lag gap appears in the negative direction of the FV driver while in the positive direction of the LCV driver, it sets <0 and >0. Note that the LCV driver needs to estimate the FV driver’s reaction to the LV’s movements, so the two drivers are assumed to stay in the same line when observing the front gap ( in Table 2) at the start of the anticipating period. Similarly, the FV driver is assumed to observe the lead gap ( in the table) as the LCV driver does.
3.2.2. Scenario-Independent Variable
Besides the scenario-dependent variable, the values of some variables do not relate to the scenarios defined above. Front gap always appears in the positive direction of the FV in each scenario (see Figure 2), so it holds the positive value as an input or output of drivers’ anticipations (>0 in Table 2). Speed difference is often used to measure the degree of driving safety. A driver can evaluate the collision risk to another vehicle from varying trends of their speed differences. For example, if the FV is slower than the LV (//>0 in the table), its head-end collision risk to the LV is lower, and vice versa. Hence, a positive speed difference between the two vehicles (// in the table) indicates a safer driving condition than the condition the negative difference happens. At the end of the anticipating period or in the relaxing period, the LCV enters target lane, so each vehicle’s position is fixed and the meanings of the gaps do not change for each driver (/>0, />0 and <0 in the table).
3.3. Model Definition
Two SEMs are formulated to specify the conceptual model developed in Section 3.1, and each of them consists of one structural model and two measurement models. Their definitions will be introduced in this section.
3.3.1. Definition of Structural Model
The structural model is to infer whether and how much an external stimuli could affect a driver’s anticipations of other vehicles’ future movements. The path of transmitting the effect is illustrated in Figure 4 as a directional line pointing from an exogenous observed variable to an endogenous latent variable. The former one models a stimulus while the latter one models the anticipation. Both of the LCV driver and the FV driver are involved in the driving relationships defined in Section 2 and observe the external stimuli in different ways. The two facts are the basis of structural model development.
(a) The SEM in the anticipating period
(b) The SEM in the relaxing period
The FV longitudinally follows the LV on LC target lane, and it also maintains LC relationship in the anticipating period or lateral CF relationship in the relaxing period with the LCV. The anticipations of the FV driver to the developing trends of the two relationships are abstracted as the and . The driver also predicts the relative moving trend of the LCV and the LV (). The influences of these three vehicle stimuli on the FV driver are modelled by “→” and “/ →” in Figures 4(a) and 4(b). In a similar way, the LCV driver’s anticipations of future moving trends of the FV and the LV can be modelled as “/→ ” and “→” in Figure 4(a) and → in Figure 4(b). Note that the LCV driver is assumed to be immune to the backward influences of the FV any longer in the relaxing period ( and ), as the driver has encroached into the target lane after the EM and occupied a leading position with respect to the FV. Hence, and are excluded from Figure 4(b). Besides adjacent vehicles’ movements, a drivers’ anticipation of collision risks is also related to subject vehicle speeds. A higher vehicle speed makes the driver more sensitive to an external stimulus. So speed of the LCV or the PF is assumed to affect its driver’s anticipations to other vehicles’ movements. These are modelled as “→/” and “→/” in Figure 4(a), “→/” and “→” in Figure 4(b).
Moreover, LC type () can reflect the influence of LC intention degree on a driver’s behaviour. With respect to a discretionary LC, a mandatory LC usually arouses the LCV driver’s stronger LC intention and inserting manoeuvers of the LCV could be more aggressive. Its impact on the FV could be harder too. Such influence is modelled as “→/” in Figure 4(a). is excluded from Figure 4(b), as the LCV has entered the target lane after the EM and the variance of LC type should be ineffective for the drivers. In addition, the influence of traffic signals () on a driver’s decision at urban arterial cannot be ignored. This factor is assumed to affect the drivers’ anticipations at the anticipating and relaxing periods. It is modelled as “→///” in Figure 4(a) and “→//” in Figure 4(b).
3.3.2. Definition of Measurement Model
There exist two measurement models in Figures 4(a) and 4(b). One measurement model is used to infer the stimulus of surrounding vehicle perceived by a driver at the start of the anticipating or relaxing period. The stimulus is assumed to derive from vehicle spacing and speed difference, which is modelled as “/→/”, “→/”, “/→/”, and “→/ ” in Figure 4(a) and “→/”, “→/”, and “/→/” in Figure 4(b). Another measurement model is to identify how the two drivers adjust vehicle spacing and speed difference at the end of a period based on their anticipations of other vehicles’ future movements. The FV driver can control its spacing and speed difference to the LV, while the LCV driver can control the ones to the LV. These are modelled as “→/” and “→/ ” in Figure 4(a) and “→/” and “→/” in Figure 4(b). The drivers of the LCV and the FV jointly control lag gap and the speed difference between them in the anticipating period, so it can be modelled as “→”, “→”, and “/→” in Figure 4(a). In the relaxing period, only the FV driver hold the controls, while the LCV driver is assumed to not care the FV’s movements any more after the EM. It can be reflected as “→/ ” in Figure 4(b).
3.3.3. Correlated Variables
Correlation test is made to the observed variables, and test results are listed in Tables 3 and 4. The bolded coefficients indicate the pairs of the variable whose correlations are modelled in the SEMs, which are illustrated in Figure 4 as the normal rectangles connected by curved lines. The correlations are set based on the logic of driving behaviour. Since the anticipations of the LCV driver and the FV driver are assumed to work simultaneously after the start of anticipating period, the exogenous variables in Figure 4(a) are set to be uncorrelated. At the end of the anticipating and relaxing period, it assumes that the kinematical indicators whose values are determined by the same driver are set to be correlated.
Note: (1) a/b: a is coefficient of variable correlation in the anticipating period, and b is the one in the relaxing period. (2) : the coefficient is significant at 95% confidence level.
Note: (1) “a/b”: “a” is coefficient of variable correlation in the anticipating period, and “b” is the one in the relaxing period. (2) : the coefficient is significant at 95% confidence level.
4. Data Collection
An arterial link in Shanghai with 200 m length is selected as the study site. Traffic video was captured at a roadside building in the height of 70 m to cover the whole link (see Figure 5). The trajectories of 250 group vehicles were extracted from the video by self-developed software  in 10 hz and calibrated to real-world coordinate using the method in . The trajectory recording points locate at the head or rear bumper of a vehicle, where the subject vehicle collides with other vehicles most possibly. The noise in the raw trajectories was filtered referring to the method in . The speed of some vehicles was calculated from the calibrated trajectories and compared with the values measured by three radar guns located at the cross-sections marked in the figure. The error of the speed calculated from the trajectories was found to be limited in 0.1 m/s. The vehicle kinematical indicators in Table 2 were calculated from the trajectories and used to estimate the SEMs proposed before. The information of traffic signal and LC type was recorded from a pedestrian overpass at upstream intersection. The LCV’s inserting manoeuvre is a discretionary LC if LC original and target lanes serve the same direction traffic; otherwise, it is a mandatory LC.
5. Results Interpretation and Discussion
The statistical software Stata is applied to formulate and estimated the two SEMs. The models are estimated at a 95% confidence level, and the goodness-of-fit measures show they fit the data well: Cronbach alpha value = 0.81/0.83; root-mean-square-error of approximation (RMSEA) = 0.08/0.04; comparative fit index (CFI) = 0.90/0.93; standardized root mean squared residual (SRMR) = 0.07/0.05. Tables 5 and 6 list the estimated unstandardized and standardized coefficients. The former ones will be interpreted in Section 5.1, while the latter ones are used to calculate the indirect path effects listed in Table 7, which will be interpreted in Section 5.2.
Note: (1) C.: coefficient, S.C.: standard coefficient, S.E.: standard error.
(2) “”: the coefficient is significant at 95% confidence level.
(3) “←”: the path direction shown in Figure 4(a).