The impact of vehicle lane-changing on the speed and delay of vehicles in the target lane based on the GMM-HMM

Abstract

Lane-changing maneuvers are pervasive in urban traffic scenarios, significantly impacting the operational dynamics of vehicles in the target lane, particularly under conditions of high traffic density (0.80 ≤ V/C ≤ 0.90). This study employs a Gaussian Mixture Model Hidden Markov Model (GMM-HMM) to quantitatively analyze the influence of lead vehicle lane-changes on the speed and delay of subsequent vehicles in the target lane. Our methodology involves a detailed examination of the transitive effects of these maneuvers across various states, revealing that lane-changes by the lead vehicle result in deceleration of following vehicles in the target lane with a frequency of 81.2% for the first vehicle, 66.71% for the second, 52.24% for the third, 27.36% for the fourth, and 10.95% for the fifth. The study underscores that the lane-changing actions of the lead vehicle have a substantial impact on the deceleration times of the first three following vehicles, with a diminishing effect on the fourth and fifth vehicles. These findings provide critical insights for urban traffic management, suggesting that under high-density traffic conditions, lane changes significantly disrupt the flow of traffic, contributing to congestion. Our results offer a basis for developing strategies aimed at mitigating traffic congestion and enhancing traffic flow efficiency.

Introduction

Lane-changing behavior among vehicles is a ubiquitous aspect of traffic dynamics, intricately influenced by a multitude of factors including traffic environmental conditions and driver personality traits¹. The motivations for lane changes are twofold: to enhance the operational velocity of the vehicle or to alter the direction of travel. Both motivations have profound implications for the operational dynamics of vehicles following in the target lane. Empirical studies have demonstrated that while lane changes may augment the flow rate in the target lane, they can significantly impair traffic flow efficiency and diminish the downstream passage capacity². Inadequate lane-changing practices have been identified as precursors to vehicle collisions and subsequent traffic congestion³. Statistically, accidents attributed to longitudinal lane changes constitute 5–10% of total traffic accidents, with 1171 collision incidents in Australia alone in 2017 due to lane changes^4,5. Furthermore, it has been noted that approximately 6.0% of all accidents are directly caused by lane changes, contributing to over 10.0% of the total delay time from traffic accidents⁶. The execution of lane changes has also been scrutinized for its impact on traffic delays and vehicle queuing⁷, with models constructed to assess the influence of lane changes on traffic flow operation speed based on empirical data⁸. Fuzzy control theory has been employed to dissect vehicle lane-changing models, providing a quantitative analysis of the impact of the frequency of lane changes on traffic flow⁹.

The ramifications of vehicle lane changes on the operation of subsequent vehicles in the target lane are inextricably linked to traffic flow characteristics, which are contingent upon vehicle speed and density^{10,11,12,13,14,15}. Under low traffic volume conditions, the substantial distance between vehicles and the relatively short lane-changing distance required by the target vehicle result in minimal impact on following vehicles^{16,17,18,19,20}. In the research of vehicle trajectory, Chen^21,22 systematically analyzed the differences in highway lane-changing behavior under different scenarios based on vehicle trajectory data, using statistical significance tests and heatmaps. The Criteria Importance Through Intercriteria Correlation (CRITIC) method was employed to determine the weights of various indicators, and a comprehensive measurement model for driving behavior risk was constructed. Sun²³ collected traffic data of target vehicles through devices such as lidar and GPS, and used convolutional neural networks to predict vehicle lane-changing trajectories, which improved the accuracy of lane-changing prediction. Conversely, high traffic volumes narrow the inter-vehicle distances, necessitating a longer lane-changing distance that often compels following vehicles to decelerate or halt. In accordance with the “Beijing Urban Road Traffic Operation Evaluation Index System” (DB11/T785-2011) and the linear regression analysis of average vehicle speeds at varying saturation levels^24,25,26, a vehicle speed range of 19.0–22.0 km/h corresponds to a road saturation level of 0.80 to 0.90. Considering the “Urban Comprehensive Traffic System Planning Standard” (GB/T51328-2018), expressway traffic is subject to fewer external perturbations. Synthesizing the speed data from the South Second Ring Expressway in Xi’an during peak hours, the traffic speed varies from 12.9 to 19.4 km/h. Thus, this study concentrates on the impact of lane changes by vehicles on expressway sections with a traffic load degree between 0.80 and 0.90, providing a focused analysis of the operational consequences within this critical traffic density range. The innovative contributions of this study are threefold:

• (1) Methodological Advancement: We introduce the GMM-HMM, a robust statistical framework, to model the complex interactions and sequential dependencies in traffic flow affected by lane-changing behaviors. This approach allows for a more nuanced understanding of the probabilistic patterns in traffic dynamics.

• (2) Empirical Data Analysis: Our research utilizes real-world traffic data collected under high-density conditions, providing a comprehensive analysis of how lane changes influence the speed and delay of following vehicles. This empirical approach offers a practical perspective on traffic flow management.

• (3) Impact Assessment: By quantifying the deceleration times and delays caused by lane changes, we provide actionable insights into the operational disruptions caused by these maneuvers. This quantification enables traffic managers to develop targeted strategies to mitigate the negative impacts of lane changes on traffic flow.

Methodology

Data collection method

The data collection involves gathering information on lane-changing vehicles and vehicles located behind the target vehicle in the target lane on the South Second Ring Expressway in Xi’an, including vehicle speed and location coordinates. For capturing lane-changing scenarios, a drone is used to take vertical shots of vehicles operating on the expressway at a fixed altitude and position. The drone is flown at an altitude of approximately 120 m; exceeding this altitude would result in air traffic control restrictions. Figure 1 illustrates the lane-changing scenario captured by the drone.

Fig. 1

Vehicles on the road section captured by the drone.

Data processing method

The operational characteristics data of vehicles are extracted using Tracker Video Analysis Tool (Version 6.1.6, available at: https://www.vicon.com/software/tracker/), as it can track the lane-changing process of the target vehicle and the operational status of the following vehicles in the target lane in real-time. Figure 2 shows the information of lane-changing vehicles extracted by Tracker software, where the red circle represents the lane-changing process of a vehicle, and the data on the right side of the image are the vehicle speed, position coordinates, and other information extracted by the Tracker software.

Fig. 2

Vehicle information extracted by tracker software.

When Tracker software extracts some vehicle data, there may be missing or abrupt changes in the values. To overcome missing or abrupt data, interpolation methods are used for data processing to ensure that the survey data is continuous and smooth. Interpolation methods estimate the value of unknown points using nearby numerical points²⁷. This method does not require a large amount of historical data and is computationally efficient, but the error increases when there are many consecutive missing values^28,29,30,31. Let $\left({x}_{1},f({x}_{1})\right)$ and $\left({x}_{2},f({x}_{2})\right)$ be known points, and $\left({x}_{1}\ne {x}_{2}\right)$, then $f(x)$ is estimated using linear interpolation.

$$f(x) = f(\mathop x\nolimits_{1} )\frac{{\mathop x\nolimits_{2} - x}}{{\mathop x\nolimits_{2} - \mathop x\nolimits_{1} }} + f(\mathop x\nolimits_{2} )\frac{{x - \mathop x\nolimits_{1} }}{{\mathop x\nolimits_{2} - \mathop x\nolimits_{1} }}$$

(1)

When extracting vehicle speed over a continuous period, since speed is continuous and unbroken, if there is a jump in the speed extracted at moment $i$, it indicates that the speed at that moment may be problematic. To eliminate abnormal data, the average of the speeds at the preceding and following moments $i-1$ and $i+1$ is used as the speed value for the current moment $i$.

When there is an outlier: ${v}_{i}=\frac{{v}_{i-1}+{v}_{i+1}}{2}$.

When there are m consecutive odd-numbered outliers, define the middle outlier as ${v}_{i}$: ${v}_{i}=\frac{{v}_{i-\frac{m+1}{2}}+{v}_{i+\frac{m+1}{2}}}{2}$; since $\frac{m-1}{2}$ is an even number, a virtual intermediate quantity j needs to be introduced between $\frac{m-1}{2}$, with the speed of the intermediate quantity j being ${v}_{j}=\frac{{v}_{i-\frac{m+1}{2}}+{v}_{i}}{2}$;and so on, from which ${v}_{i-1}$, ${v}_{i+1}$, … ${v}_{i-\frac{m-1}{2}}$, ${v}_{i+\frac{m+1}{2}}$ can be calculated.

When there are m consecutive even-numbered outliers, a virtual intermediate variable j needs to be introduced, and the calculation of the data is the same as the calculation process for consecutive odd-numbered outliers.

Figure 3a shows the original vehicle speeds extracted by Tracker software, from which it can be seen that there are abrupt anomalies in the extracted data. After processing with interpolation methods, the survey data clearly no longer contains abrupt data. To further smooth the survey data, LOWESS smoothing method is used for processing. Figure 3b is the vehicle speed after smoothing.

Fig. 3

Comparison of sample data correction.

Construction of GMM-HMM

On expressway sections with a traffic load degree of 0.80–0.90, it is assumed that vehicles in operation follow the vehicle-following characteristics, and the operation state of the following vehicle can only be determined by the operation state of the preceding vehicle. The target vehicle’s lane change will affect the 1st vehicle following it in the target lane, and the 2nd vehicle following will be affected by the 1st vehicle following, with this influence being transmitted sequentially, and the operation characteristics of the n-th vehicle following will be affected by the (n-1)-th vehicle following. Figure 4 illustrates the “state” transition process during the vehicle’s lane change process, where the symbols represent: TLB1V is the 1st vehicle ${x}_{1}$ following the target vehicle in the target lane, TLB2V is the 2nd vehicle ${x}_{2}$ following the target vehicle in the target lane, and so on for the other letters.

Fig. 4

Markov transition process.

The Hidden Markov Model (HMM) can be represented by the parameter λ, generally denoted as $\lambda =\left[N,M,A,B,\prod \right]$, where each parameter has the following meaning:

• N represents the set of all possible values for the hidden states, $N=\{{q}_{1},{q}_{2},\dots ,{q}_{n}\}$, where ${q}_{1}$ indicates a decrease in speed, ${q}_{2}$ indicates no change in speed, and ${q}_{3}$ indicates an increase in speed.

• M represents the set of all possible values for the observed states, $M=\{{v}_{1},{v}_{2},\dots ,{v}_{m}\}$. Since the investigated speeds are continuous, they need to be discretized. The intervals for ${v}_{1}$ through ${v}_{7}$ are as follows: $v_{1} \varepsilon (0,1.5)$, $v_{2} \varepsilon \left[ {1.5,2.5} \right)$, $v_{3} \varepsilon \left[ {1.5,2.5} \right)$, $v_{4} \varepsilon \left[ {2.5,3.5} \right)$, $v_{5} \varepsilon \left[ {3.5,4.5} \right)$, $v_{6} \varepsilon \left[ {4.5,5.5} \right)$, $v_{7} \varepsilon \left[ {5.5, + \infty } \right)$

• $\prod$ represents the initial probability distribution of the hidden states, $\prod ={[{\pi }_{i}]}_{N\times 1}$, where ${\pi }_{i}=P\left({i}_{1}={q}_{i}\right)$).

• A represents the state transition matrix, $A={[{a}_{ij}]}_{N\times N}$, where ${a}_{ij}=P({i}_{t+1}={q}_{j}|{i}_{t}={q}_{i}$), indicating the probability that the hidden state at time t + 1 is ${q}_{i}$ given that the hidden state at time t is ${q}_{i}$.

• B represents the observation state generation matrix, $B={[{b}_{j}(k)]}_{N\times M}$, where ${b}_{j}\left(k\right)=P({o}_{t}={v}_{k}|{i}_{t}={q}_{j}$), indicating the probability that the observation state at time t is ${v}_{k}$ given that the hidden state at time t is ${q}_{j}$.

Given the model $\lambda =\left[N,M,A,B,\prod \right]$ and the observation sequence $O=\{{o}_{1},{o}_{2},\dots ,{o}_{T}\}$, calculate the probability of the observation sequence occurring under this model, $P(O|\lambda )$. This type of problem is suitable for selecting the model with the highest output probability when there are multiple models, i.e., the model that best fits this observation sequence.

The solution to this problem can be approached using the forward–backward algorithm. First, define the forward variables: the probability that the observation sequence up to time t is ${o}_{1},{o}_{2},\dots ,{o}_{t}$ and the hidden state at time t is ${q}_{i}$, given the model λ. This is represented by the Eq. (2):

$${a}_{t}(i)=P({o}_{1},{o}_{2},\dots ,{o}_{t},{i}_{t}={q}_{i}|\lambda )$$

(2)

By definition, it is known that:

$${a}_{1}(i)= {\pi }_{i}{b}_{i}\left({o}_{1}\right)$$

(3)

Recursively, for $t=\text{1,2},\dots ,T-1$

$${a}_{t+1}(i)= \left[\sum_{j=1}^{N}{\alpha }_{t}\left(j\right){a}_{ij}\right]{b}_{i}\left({o}_{t+1}\right)$$

(4)

$$P\left(O|\lambda \right)=\sum_{i=1}^{N}{\alpha }_{T}\left(i\right)$$

(5)

Similarly, the backward variable is defined as:

$${\beta }_{t}(i)=P({o}_{t+1},{o}_{t+2},\dots ,{o}_{T}|{i}_{t}={q}_{i},\lambda )$$

(6)

By definition, it is known that:

$${\beta }_{T}(i)=1$$

(7)

Recursively, for $t=T-1,T-2,\dots ,T$

$${\beta }_{t}\left(i\right)={\sum_{j=1}^{N}{a}_{ij}b}_{j}\left({o}_{t+1}\right){\beta }_{t+1}(j)$$

(8)

$$P\left(O|\lambda \right)=\sum_{i=1}^{N}{\pi }_{i}{b}_{i}\left({o}_{1}\right){\beta }_{1}(i)$$

(9)

The so-called forward–backward algorithm is to split an observation sequence of length 1-T into two segments, 1-t and t-T. The probability of the entire observation sequence O can be expressed as:

$$P\left(O|\lambda \right)=\sum_{i=1}^{N}{\alpha }_{t}\left(i\right){\beta }_{t}\left(i\right)$$

(10)

Suppose there is a random variable x, then the GMM can be represented by Eq. (11):

$$GMM\left(x;\Theta \right)=\sum_{k=1}^{K}{w}_{k}N(x;{m}_{k},{\Sigma }_{k})$$

(11)

where $N(x;{m}_{k},{\Sigma }_{k})$ is called the k-th component of the GMM, and the expression is as follows:

$$N\left(x;m,\Sigma \right)=\frac{1}{{(2\pi )}^\frac{D}{2}{|\Sigma |}^\frac{1}{2}}{e}^{\frac{1}{2}(x-m){\Sigma }^{-1}{(x-m)}^{T}}$$

(12)

${w}_{k}$ is the mixing coefficient, that is, the weight of the k-th component, and it satisfies the following Eq. (13):

$$\sum_{k=1}^{K}{w}_{k}=1,0\le {w}_{k}\le 1$$

(13)

At this time, the observation state generation matrix in the GMM-HMM is no longer a discrete matrix but a set of Gaussian mixture functions $B=\{{b}_{1}\left(O\right),{b}_{2}\left(O\right),\dots ,{b}_{N}\left(O\right)\}$, and the observation value probability density function is given by Eq. (14):

$${b}_{i}\left(O\right)=\sum_{k=1}^{K}{w}_{ik}N(O;{m}_{ik},{\Sigma }_{ik})$$

(14)

In the Equation, O represents the observation sequence, ${w}_{k}$ is the mixing coefficient, N is the Gaussian function, ${m}_{k}$ and ${\Sigma }_{k}$ are the mean and covariance matrix of the k-th Gaussian component when the hidden state is ${q}_{i}$. Thus, the GMM-HMM can be represented as $\lambda =\left[\prod ,A,{w}_{ik},{m}_{ik},{\Sigma }_{ik}\right]$ The update Equation for the initial probability matrix and the state transition matrix are the same as those for the discrete HMM. The update Equation for the other parameters require the introduction of a new variable ${\gamma }_{t}(i,m)$, which is defined as the probability that the observation sample ${o}_{t}$ at time t belongs to the m-th Gaussian component of the hidden state ${q}_{i}$, given the entire observation sequence O. The expression is as follows(15) : The update Equation for the other parameters are as follows (Eqs. 16–18):

$${\gamma }_{t}\left(i,m\right)=P\left({i}_{t}={q}_{i}|O,\lambda \right)P\left(gauss=m|{o}_{t}\right)=\frac{{\alpha }_{t}\left(i\right){\beta }_{t}\left(i\right)}{\sum_{j=1}^{N}{\alpha }_{t}\left(j\right){\beta }_{t}\left(j\right)}\times \frac{{w}_{m}{N}_{m}\left({o}_{t}\right)}{\sum_{k=1}^{K}{w}_{k}{N}_{k}\left({o}_{t}\right)}$$

(15)

$$\overline{{w }_{ik}}=\frac{\sum_{t=1}^{T}{\gamma }_{t}\left(i,k\right)}{T}$$

(16)

$$\overline{{m_{ik} }} = \frac{{\mathop \sum \nolimits_{t = 1}^{T} \gamma_{t} \left( {i,k} \right) \times o_{t} }}{{\mathop \sum \nolimits_{t = 1}^{T} \gamma_{t} \left( {i,k} \right)}}$$

(17)

$$\overline{{\Sigma }_{ik}}=\frac{\sum_{t=1}^{T}{\gamma }_{t}\left(i,k\right){(o}_{t}-{m}_{ik}){{(o}_{t}-{m}_{ik})}^{T}}{\sum_{t=1}^{T}{\gamma }_{t}\left(i,k\right)}$$

(18)

Based on the aforementioned Eq. (15), (16), (17), and (18), it can be seen that as long as the number and dimension of the Gaussian components in the Gaussian Mixture Model, the number of hidden states, the observation sequence, and appropriate initial parameter values are given, a well-trained model $\lambda =\left[\prod ,A,{w}_{ik},{m}_{ik},{\Sigma }_{ik}\right]$ can be obtained.

Results

After constructing the GMM-HMM, during the process from the target vehicle’s lane change initiation to completion, there are three changes in the speed of the following vehicle in the target lane, which are speed increase, speed decrease, and speed unchanged, respectively. It is assumed that the corresponding speed changes are represented by a speed increase Δv > 0, a speed decrease Δv < 0, and a speed unchanged Δv = 0. When the GMM-HMM outputs speed changes, it assigns a speed decrease value output as ${A}_{1}=-1$, a speed increase value output as ${A}_{2}=1$, and a speed unchanged value output as ${A}_{0}=0$. The statistical of the following vehicle’s speed change is shown in Fig. 5. Figure 6 shows the predicted results of the following vehicle speed in the target lane.

Fig. 5

Statistical process of deceleration time of the following vehicle.

Fig. 6

GMM-HMM prediction the speed of the following vehicle in the target lane.

Table 1 shows the statistical distribution of deceleration time for the following vehicles in the target lane. It can be observed that within the lane change time ${t}_{c}$, the 1st vehicle behind the target vehicle decelerates for 81.2% of the time, the 2nd vehicle behind the target vehicle decelerates for 66.71% of the time, the 3rd vehicle behind the target vehicle decelerates for 52.24% of the time, the 4th vehicle behind the target vehicle decelerates for 27.36% of the time, and the 5th vehicle behind the target vehicle decelerates for 10.95% of the time. The lane change of the vehicle has a significant impact on the deceleration time of 1st vehicle behind, 2nd vehicle behind, and 3rd vehicle behind respectively, but a smaller impact on the deceleration time of 4th vehicle behind, 5th vehicle behind. Therefore, when conducting statistical analysis of vehicle lane change and its consequences, only the operational speed, position coordinates, and other information of the five following vehicles in the target lane are analyzed.

Table 1 Prediction of the impact of the lane change of the target vehicle on the speed of the following vehicle in the target lane.

After the GMM-HMM predicts the operational delay of the following vehicles, it is necessary to compare the predicted delay values with the actual delay values to determine the accuracy of the model’s predictions. To determine the accuracy of the predicted values, it is first necessary to clarify the theoretical travel distance of 1st vehicle behind the target vehicle Assuming that the vehicle immediately behind travels at a constant speed before the lane change, the theoretical distance traveled by 1st vehicle behind the target vehicle during the lane change time ${t}_{c}$ is ${S}_{l}$; during the process of the target vehicle’s insertion into the target lane, the distance traveled by 1st vehicle behind the target vehicle within the lane change time ${t}_{c}$ is ${S}_{b}$. The difference between the theoretical distance and the actual distance is the delay distance.

$$S_{b} = \mathop \int \limits_{0}^{T} v_{b} dt \approx x_{Tb} - x_{0b}$$

(19)

In the Equation: ${x}_{Tb}$ represents the x-coordinate of the 1st vehicle behind the target vehicle at the moment the target vehicle completes its lane change, ${x}_{0b}$ represents the x-coordinate of the 1st vehicle behind the target vehicle at the initial moment of the target vehicle’s lane change.

Within the same travel distance, because the target vehicle’s insertion into the target lane will cause a reduction in the speed of the 1st vehicle behind the target vehicle, the delay time ${t}_{by}$ for the 1st vehicle behind the target vehicle to travel the same distance is considered. The total delay time ${t}_{y}$ for all vehicles behind in the target lane during the target vehicle’s lane insertion process is also considered.

$${t}_{by}=\frac{{v}_{b0}\times {t}_{c}-{s}_{b}}{{v}_{b0}}$$

(20)

$${t}_{y}=\sum_{i=1}^{n}{t}_{iy}$$

(21)

In the Equation: ${t}_{iy}$ represents the delay time of the i-th vehicle behind the target vehicle in the target lane, in seconds (s). $n$ represents the number of delayed vehicles behind the target vehicle in the target lane. From the previous analysis, it is known that the target vehicle has a significant impact on the 1st to 5th vehicles immediately behind it, and a relatively smaller impact on vehicles after the 5th. Therefore, $n$ is taken to be within 5.

According to Eq. (20) and (21), the delay values for the 2nd, 3rd, 4th, and 5th vehicles behind the target vehicle during its lane change process can be calculated. The figure shows a comparison between the predicted delay values and the calculated delay values for the vehicles behind in the target lane during the target vehicle’s lane change process.

From Figs. 7 and 8, it can be seen that the absolute error of the model’s predicted delays is primarily concentrated below 30%, and the average absolute error of the model’s predictions is 12.81%, which indicates that the model has a good prediction accuracy.

Fig. 7

Vehicle delay comparison.

Fig. 8

Absolute error of predicted delay values.

Discussion and conclusion

The results of this study align with previous research indicating that lane changes can significantly disrupt traffic flow^2,3. However, our findings provide a more granular understanding of the impact on specific vehicles following the lane change, quantifying the deceleration effects and associated delays. The significant deceleration observed for the first three vehicles following the target vehicle in the lane change suggests that these vehicles are most vulnerable to disruptions, potentially due to their proximity and the sudden nature of the maneuver.

The operational delay findings are consistent with the literature highlighting the negative impact of lane changes on traffic flow^6,7. The delay values calculated in this study offer empirical evidence that can be used to develop predictive models for traffic management systems, enhancing their ability to anticipate and mitigate congestion.

The implications of our findings are twofold. Firstly, from a traffic management perspective, there is a clear need for strategies that discourage unnecessary lane changes, particularly during peak hours when the impact on traffic flow is most pronounced. Secondly, from a driver behavior standpoint, our results emphasize the importance of educating drivers about the potential downstream effects of their lane-changing decisions.

The present study, leveraging the Gaussian Mixture Model Hidden Markov Model (GMM-HMM), has provided a detailed analysis of the impact of vehicle lane changes on the speed and delay of vehicles in the target lane under high-density traffic conditions. Our findings offer valuable insights into the operational disruptions caused by lane-changing maneuvers and contribute to the broader understanding of traffic flow dynamics. After studying the lane-changing behavior of vehicles under high-density conditions on expressways, the following conclusions are drawn:

• 1. Under high-density conditions, lane changes by vehicles can affect the operation of the following vehicles in the target lane. During the lane-changing process, it can cause the following effects: the 1st vehicle behind the target vehicle decelerates for 81.2% of the time, the 2nd vehicle behind the target vehicle decelerates for 66.71% of the time, the 3rd vehicle behind the target vehicle decelerates for 52.24% of the time, the 4th vehicle behind the target vehicle decelerates for 27.36% of the time, and the 5th vehicle behind the target vehicle decelerates for 10.95% of the time. It is illustrated that in an operational environment with high road traffic load, vehicle lane changes are highly likely to affect the operation of following vehicles in the target lane.

• 2. By analyzing the delay of following vehicles during the lane-changing process, the operational delay of following vehicles is basically below 20.0 s. Approximately 50% of the vehicles cause an overall operational delay for following vehicles between 5.0 and 10.0 s during the lane change; about 28% of the vehicles cause an overall operational delay for following vehicles of more than 10.0 s during the lane change; and about 22% of the vehicles cause an operational delay for following vehicles of less than 5.0 s during the lane change. It is explained that in an operational environment with high road traffic load, vehicle lane changes are highly likely to increase delays for multiple following vehicles in the target lane, leading to an increase in their operation time.

• 3. Under conditions of high road traffic load, lane changes by vehicles on urban expressways will affect the operation of following vehicles in the target lane. Therefore, during the morning and evening peak hours in cities, vehicle lane-changing behaviors should be reduced. At the same time, corresponding control strategies should be formulated to regulate the occurrence of vehicle lane changes, thereby improving the overall operational efficiency of the road.

While this study provides a robust analysis of the immediate impact of lane changes on traffic flow, future research could benefit from exploring long-term traffic flow patterns following repeated lane changes and the development of adaptive traffic management systems that respond to real-time data on lane-changing behaviors.

In conclusion, our study underscores the significant influence of vehicle lane changes on traffic dynamics, particularly under high-density conditions. The insights gained from this research can inform the development of traffic management strategies aimed at optimizing traffic flow and reducing congestion, ultimately enhancing road safety and efficiency.