Design and Optimization of Cluster-Based DSRC and C-V2X Hybrid Routing

Abstract

With the continuous development of connected and automated vehicles (CAVs) and Internet of Vehicle (IoV) technologies, various application scenarios have put forward higher requirements for vehicular communications. On the one hand, applications related to vehicle driving safety require lower latency and higher throughput. On the other hand, users who use cellular vehicle-to-everything (C-V2X) to transfer data will have to face high communication fees due to the increasing amount of data. Therefore, from the perspective of balancing quality of service (QoS) and user communication costs, this paper integrates dedicated short-range communication (DSRC) and C-V2X, two vehicular communication technologies with their own advantages, into a framework called cluster-based traffic differentiated hybrid routing (CTDHR), to provide services for in-vehicle communication. A vehicle clustering method based on hierarchical clustering is proposed to solve problems (e.g., the communication linking being difficult to maintain and the frequent cell handover due to high-speed movement of vehicles). The CTDHR framework is modeled on the resulting clusters and an objective equation was established. Finally, since the obtained objective equation is a nonlinear integer programming problem, we propose a heuristic algorithm to solve this optimization problem. In the simulation experiments, CTDHR shows better communication performance than the existing DSRC and C-V2X hybrid models. The experimental results show that CTDHR can reduce the communication costs of users while satisfying QoS.

1. Introduction

Automatic driving, with unparalleled advantages over traditional driving, has always been a research hotspot in academia and the industry [1]. In recent years, automatic driving technology has rapidly improved with the development of deep learning, and level 4 automatic driving has been verified in experimental scenarios [2]. Automatic driving technology can be divided into two categories: (1) a single-vehicle system; that is, relying on a single vehicle to complete automatic driving; (2) CAVs, which emphasize the sharing of information through vehicle-to-vehicle-communication (V2V), vehicle-to-infrastructure communication (V2I), and vehicle-to-person communication (V2P). The latter has lower requirements for vehicle performance, which is conducive to saving vehicle costs, and the latter has a stronger perception of the environment [3]. Due to the advantages of CAV, it has gradually become a more popular research direction in automatic driving [4]. To support CAVs, vehicular communication must still be improved in terms of transmission delay and throughput. For example, since deep learning is widely used in the field of unmanned driving, edge computing needs to be introduced to solve the problem of in-vehicle hardware capability being insufficient at supporting the operations of deep neural networks, putting forward higher requirements for in-vehicle communication [5]; in the event of an emergency, relevant information needs to be broadcast to nearby vehicles in a very short time [6]. In addition, vehicular entertainment [7], the allocation of communication resources, etc., must also be considered [8].

The DSRC based on 802.11p, proposed by the IEEE research group [9], and the C-V2X based on the cellular network proposed by 3GPP [10], have become the most likely vehicular communication technologies to be put into practical application. Studies and simulation experiments have shown that, compared with DSRC, C-V2X has better performance in terms of throughput, data transfer rate, and response time [11]. However, vehicular ad hoc networks (VANETs) based on DSRC have advantages in certain aspects. For example, the average delay of VANETs between single hops is only half of a C-V2X transmission; C-V2X needs to charge users due to the need to use the network service provider’s infrastructure, but DSRC does not charge users for direct communication between vehicles; in addition, in areas with insufficient infrastructure, DSRC can be used as an effective blindness measure [12]. Therefore, DSRC has not been abandoned in both academia and industry and is still widely used in road warning, vehicle networking, and other fields. In recent years, many scholars have combined two vehicular communication technologies into one in-vehicle communication framework for research, achieving good results [13,14,15,16,17].

Combining DSRC and C-V2X into a framework will increase latency compared to using C-V2X alone, but this is beneficial in many aspects, such as reducing the occupancy rate of cellular network communication resources, reducing energy consumption, improving throughput, reducing communication costs for users, etc. [13,14,15]. Research on hybrid applications of DSRC and C-V2X can be divided into two categories. One is the hybrid when different vehicles are equipped with different communications equipment (that is, some vehicles are only equipped with C-V2X equipment, and some vehicles are only equipped with DSRC equipment) [17]. In this scenario, the data format needs to be changed continuously during communication, and the communication management is more complicated. The other category is the hybrid implementation in the scenario where all vehicles are equipped with both communication devices [13,15,16]. Compared with the former, the latter has stronger operability, so it has received more attention from researchers. It is worth noting that due to the high mobility of vehicles, it is difficult to maintain the vehicular communications link, and frequent cell switching is required when using C-V2X [12]. To solve these problems, the cluster vehicle method is mostly introduced in the current vehicle communication. This method treats a certain number of vehicles as a cluster, and performs vehicular communication and link management in units of clusters [18,19,20,21,22].

We noticed that Qi W J et al. in [13] designed a routing mechanism named traffic differentiated clustering routing (TDCR), which integrates DSRC and C-V2X into a framework from the perspective of balancing QoS and communication costs. This routing mechanism has received much attention. However, we discovered that, to ensure the successful establishment of the communication link, TDCR uses a vehicle clustering method based on spatial sampling, and the sampling radius is too small, which leads to an excessive number of forwarding nodes in the routing path of TDCR. According to the routing method of TDCR, there is a certain probability that the routing path cannot be successfully established. As the amount of data increases, the performance of TDCR sharply deteriorates. Inspired by TDCR, we designed a new vehicle clustering method that does not rely on inter-vehicle negotiation and spatial sampling. Based on this clustering method, the number of hops in the communication link between vehicles and the roadside unit (RSU) in VANETs can be effectively reduced. Additionally, from the perspective of balancing QoS and communication costs, a hybrid routing method based on cluster and traffic differentiation was redesigned. This method is referred to as the cluster-based traffic differentiated hybrid routing (CTDHR).

The contributions of this paper are presented as follows:

• A vehicle clustering method based on the idea of hierarchical clustering is proposed. The clustering method—to ensure the stability of clusters—changes the conditions in the hierarchical clustering algorithm to measure whether two clusters can be merged, and also makes some modifications in other aspects to adapt the clustering method to the vehicle clustering scenario. The proposed clustering method not only ensures the stability of the cluster, but also reasonably controls the number of clusters, reduces the number of hops in the VANET link, and reduces the delay in transmitting the information.
• From the perspective of balancing QoS and user communication costs, the vehicular communication in the CTDHR framework is modeled, and a heuristic algorithm is proposed to solve the model. In addition, the hybrid routing of DSRC and C-V2X based on this model is completed in the heuristic algorithm.
• A simulation environment that is as close to reality as possible was designed and utilized to test the performance of CTDHR. The experimental results show that CTDHR has better performance than the existing DSRC and C-V2X hybrid frameworks.

This paper is organized as follows: We review related research work in Section 2 and describe the CTDHR framework in detail in Section 3. In Section 4, the vehicle cluster model and hybrid routing model are presented. In Section 5, a heuristic algorithm based on the routing model is designed. In Section 6, the CTDHR performance is tested in a simulation environment that is as close to reality as possible. In Section 7, we summarize our research.

2. Related Works

2.1. Research on DSRC and C-V2X

In recent years, many scholars have performed much research to improve DSRC and C-V2X. Particularly, in 2019, the IEEE research group proposed IEEE 802.11bd to update IEEE802.11p. IEEE802.bd will realize vehicular communication with a relative speed of 500 km/h, while the communication distance will be extended to 2000 m [23]. With the development of 5G, 3GPPP proposes NR-V2X on the basis of LTE-V2X so that it can use the advanced technology and spectrum resources of 5G [24].

In [25], Tang Y J et al. proposed a routing mechanism based on DSRC to improve the network response time and bandwidth utilization. In this method, a machine learning method is used to predict the future state of the vehicles to optimize the communication link to reduce the delay. Many other scholars have integrated DSRC and C-V2X, and designed a mechanism to use these two communication methods simultaneously. In [14], Ghafoor K Z et al. proposed a QoS-aware relay algorithm in a scenario where some vehicles used DSRC and some vehicles used C-V2X, which allowed vehicles using two different communication technologies to successfully network and complete information transmission. In [15], Mir Z H et al. proposed a DSRC and C-V2X hybrid vehicle network architecture and protocol stack and designed a distributed radio resource management entity that could effectively manage and coordinate radio resources in both RTAs. In [16], Heo S et al. proposed an adaptive semi-persistent C-V2X and DSRC hybrid vehicle networking model called H-V2X. In this model, when C-V2X meets the performance index, C-V2X is used for data transmission, otherwise, DSRC is used for data transmission. Qi W J et al. proposed a routing mechanism called TDCR in [13], which realizes the hybrid application of DSRC and C-V2X under consideration of the balance between the QoS requirements of different traffic and communication costs of users. In [17], Elbal BR et al. realized a hybrid framework with C-V2X as the main communication means and DSRC as a blind-compensation communication measure. In this work, V2V communication is also used to enhance cellular network base station signals. Since the two communication standards, DSRC and C-V2X, have conflicts in the 5.9GHz frequency band, how to make two different new technologies work together in the same frequency band has also become an important research topic. Ansari K. solved the problem of DSRC and C-V2X sharing in the 5.9 GHz band in [26], which enables DSRC and C-V2X to transmit data concurrently under the same framework.

In addition to making vehicular communication more efficient and reliable, how to allocate the resources of the communication system also has a crucial role in the performance of vehicular communication. In [27], Zhang J X et al. proposed an auction mechanism combined with blockchain technology, which maximizes social welfare and optimizes the allocation of communication resources on the Internet of Vehicles. In [28], Yan Y et al. proposed a multi-type and multi-resource auction mechanism, which greatly improves resource use efficiency. The mechanism has significance in promoting the progress of communication resource allocation in vehicular communication systems.

Research in the field of vehicle communication has made great progress. However, there are few considerations concerning the user level in the existing results, and the high throughput and low latency requirements for CAVs are still not fully met.

2.2. Research on Vehicle Clustering

In recent years, many scholars have proposed vehicle clustering methods for vehicle communication application scenarios:

Hang S et al. [18] proposed a multi-channel MAC protocol based on vehicle clusters and VANETs that could effectively guarantee QoS. This protocol uses different channels to transmit data within the cluster and outside the cluster, which greatly saves communication resources. In [19], Abboud K et al. introduced vehicle clustering into VANETs and achieved good results. They also employed a stochastic cluster instability model to assess the rate of change in a cluster structure with cluster membership changes and cluster overlap states. In [20], Prajapati J et al. proposed a vehicle cluster method based on vehicle location, destination, and distance. Compared with the previous vehicle cluster algorithm, this method effectively reduces the resource occupation during vehicle communication. Qi W J et al. [13] proposed a clustering method based on spatial sampling. This method ensures the stability of clusters and communication links. In [21], from the perspective of improving user experiences in high-speed mobile scenarios, Kumar D V et al. proposed a method to realize vehicle clustering using common OFDM parameters and clustering mechanisms. In this method, hybrid DSRC/WiMAX technology was utilized. The realized vehicular communication has achieved good results in various communication scenarios in the simulation experiments. In [22], Sanker S et al. proposed a vehicle clustering protocol named MADCR, which first uses Euclidean distance to obtain vehicle clusters, and then uses the mayfly optimization algorithm to select the cluster head (CH). This method not only reduces the CH selection time but also effectively reduces the end-to-end delay and increases the transmission rate.

In existing studies, clustering methods mostly rely on vehicle-to-vehicle negotiation, which increases the time overhead of clustering. This method, especially in highly delay-sensitive scenarios, such as CAVs, has difficulty meeting the requirements of a high response ratio and low delay. There is still a lack of efficient and fast clustering methods.

Table 1. Acronyms Used in Paper.

Acronyms	Definition
CAVs	connected and automated vehicles
IoV	Internet of Vehicles
DSRC	dedicated short-range communication
C-V2X	cellular vehicle-to-everything
VANETs	vehicular ad hoc networks
QoS	quality of service
CTDHR	cluster-based traffic differentiated hybrid routing
TDCR	traffic differentiated clustering routing
RSU	roadside unit
BS	base station
CH	cluster head
CM	cluster member

is the abbreviations used in this paper.

3. CTDHR Framework

In the CTDHR framework, the road is divided into segments with a fixed length, and each segment is called a service domain. There is an RSU deployed in each service domain, and the RSU participates in the transmission of data sent through VANETs. The base station (BS) is used to support the transmission of C-V2X data, and usually one BS can cover multiple service domains. As shown in Figure 1, the vehicles in the service domain are divided into several clusters (the method of cluster division will be shown in Section 4), and a cluster contains one cluster head (CH) and several cluster members (CMs). The CH is the agent for the cluster to communicate with the outside world. When a CM needs to send a data packet, it will first send the data packet to the CH, and then the CH will select DSRC or C-V2X to forward the data to the RSU/BS. In order to reduce the delay caused by intra-cluster communication as much as possible, the distance between the CM and CH in the CTDHR cluster is strictly limited within the DSRC communication radius, which enables the CM and CH to communicate directly without any relay forwarding (i.e., CM and CH are connected in one hop). It is worth noting that each CH needs to establish a VANET communication link with the RSU as much as possible. When the CH of the cluster cannot directly establish communication with the RSU, it can rely on the VANET communication link with other CHs to realize multi-hop communication with the RSU. Therefore, in CTDHR, the communication range of the RSU does not need to cover the entire service domain. In this way, even if there is no VANET link between the two clusters, VANET communication between clusters can be realized through the relay and forwarding of the RSU (of course, each CH establishes a C-V2X link with the BS, so clusters can also rely on C-V2X to achieve inter-cluster communication) [29]. In addition, this cannot only reduce the deployment density of RSUs to reduce infrastructure construction costs, but also make good use of the redundancy of other CH communication capabilities.

To complete the above data transmission process, we designed three core algorithms. As shown in Figure 2, all vehicles first report their own statuses (including driving speed, direction, and communication capability) to the edge server. After the data collection is complete, the edge server runs Algorithm 1 (see Algorithm 1 in Section 4) according to the information reported by the vehicle to assign the vehicle to different clusters, and selects the CH for each cluster. Then, according to the clustering results and the communication capabilities of the CHs, Algorithm 2 is run (see Algorithm 2 in Section 4) to obtain the VANET routing path from each CH to the RSU. Finally, the edge server distributes the clustering results and routing path information to the vehicles. At this time, the vehicles selected, such as CH, will run Algorithm 3 (see Algorithm 3 in Section 4). The main task of Algorithm 3 is to select DSRC/C-V2X according to the current perceived network state to forward the data packets to RSU/BS.

Of course, in addition to the need to complete vehicular communication, we also need to consider balancing QoS and user communication costs. In order to satisfy QoS, it is necessary to reduce the delay generated during data packet transmission as much as possible and to reduce the communication costs of users, it is necessary to transmit more data through DSRC. This is contradictory, therefore, we will model the communication process in CTDHR and balance QoS and communication costs according to the model.

4. Model

Because the vehicular communication process is the same in each service domain, in the following research, we put the view in one service domain.

4.1. Vehicle Cluster Model and Algorithm

Definition 1.

Stability of vehicle clusters. Typically, the stability of a cluster is measured by the keeping time of the cluster. The keeping time of the cluster refers to the time elapsed from the moment when the cluster is established until a CM exists in the cluster and the distance between this CM and the CH is greater than the DSRC communication radius.

When performing vehicle clustering, we have to consider the stability of the cluster. A stable vehicle cluster can reduce the risk of communication interruptions due to cluster dissolution. In addition, the more stable the vehicle cluster is, the longer the interval for reestablishing the cluster is required, thereby reducing the time and resource overhead (e.g., communication resources, computing device resources, etc.) required for rebuilding the cluster [18]. The number of CMs included in a cluster should also be reasonably controlled, because the communication data of the CM needs to be forwarded through the CH, and the communication capability of the CH is limited. In this paper, the number of CMs in a single cluster must not exceed N [15]. Reasonable control of the number of clusters is conducive to saving communication resources, reducing the occupation of the cellular network bandwidth, and can also affect the number of forwarding hops when CH and RSU perform multi-hop transmissions to a certain extent. Generally, as the number of clusters increases, the number of forwarding hops will also increase slightly, resulting in more delay [19].

Table 2. Notation Table.

Notation	Implication
$G\left(\mathcal{V},\mathcal{E}\right)$	Topological diagram composed of CH and RSU
$\mathcal{V}$	The set of CHs and RSU
$\mathcal{E}$	The set of edges in $G\left(\mathcal{V},\mathcal{E}\right)$
$a_i$	The $i\text{-}\mathrm{th}$ CH in the $\mathcal{V}$
$e\left(i,j\right)$	Edge between $a_i$ and $a_j$
$\mathcal{C}$	The set of clusters
$c_i$	The $i\text{-}\mathrm{th}$ cluster in the $\mathcal{C}$
R	Communication radius of DSRC
$D^{cluster}$	Merge parameter used to measure whether two clusters can be merged
$D^{vehicle}$	Used to measure whether two vehicles can establish communication
$D_{threshold}^{vehicle}$	If $D^{vehicle}\ge D_{threshold}^{vehicle}$, the two vehicles can establish stable communication
$Y_{ij}$	The remaining time that $c_i$ and $c_j$ are within the DSRC communication radius
$d^{cluster},d^{vehicle}$	The distance between the two clusters and the distance between the two vehicles
$d_{limit}$	Maximum mergeable distance
N	Maximum number of CMs that can be included in a single cluster
${\upsilon }^{min},{\upsilon }^{max}$	Maximum and minimum speed of CMs in a cluster
${\upsilon }^{vehicle}$	The speed of the vehicle
$Pat{h}_i$	VANETs communication link from $a_i$ to RSU
${\mathcal{B}}_i$	Data packet buffer of $a_i$
$b_{ik}$	$k\text{-}\mathrm{th}$ packets in ${\mathcal{B}}_i,i\in \{1,\dots ,M\}$
$S_{ik}$	Size of $b_{ik}$
$f^{CV2X},f^{DSRC}$	The transmission rates of DSRC and C-V2X, respectively
${\omega }_{ik}$	Weight of $b_{ik}$
$l_{ik}$	Maximum delay allowed for $b_{ik}$
$l^{min},l^{max}$	The upper and lower boundaries of $l_i^k$
T	The weighted delay generated in the system per unit time
p	Price per MB of cellular data
P	Communication costs incurred in the system per unit time
$q_{ik}^{CV2X}$	Sum of queuing delay and processing delay when $b_{ik}$ is sent through C-V2X
$q_{ik}^m$	The sum of queuing delay and processing delay generated when $b_{ik}$ is forwarded at $m\text{-}\mathrm{th}$ of $Pat{h}_i$
r	Vehicle’s data generation rate
$u_i^{CV2X}$	The average delay generated by the packets sent using C-V2X in $a_i$
$u_i^{DSRC}$	The average delay generated by the packets sent using VANETs in $a_i$

is the explanation of the mathematical symbols used in the paper, and these symbols will also be explained in the text when they appear.

Based on the above considerations, we were inspired by the idea of the hierarchical clustering algorithm and designed a vehicle clustering method that satisfies the above conditions. Hierarchical clustering is a bottom-up clustering method. It first initializes a class for each element. Then, we continue to merge the two closest clusters until only one class remains. Finally, the hierarchical clustering algorithm will obtain a clustering tree, and then select the appropriate number of classes from this clustering tree [30].

We first define some symbols to facilitate the following description. We use $G\left(\mathcal{V},\mathcal{E}\right)$ to denote the topological map composed of CH and RSU and use $\mathcal{V}=\left\{a_1,a_2,\dots ,a_M,RSU\right\}$ to denote the set composed of CH and RSU, where $a_i,i\in \left\{1,\dots ,M\right\}$ represents the CH of the $i\text{-}\mathrm{th}$ cluster and CH is a vehicle entity that includes attributes, such as speed, location, packet buffer, and data generation rate. $\mathcal{E}=\left\{\dots ,e(i,j),\dots ,e(k,RSU),\dots \right\}$ represents the set of edges in the topology graph, and $e\left(i,j\right)$ represents the edge from $a_i$ to $a_j$. $\mathcal{C}=\left\{c_1,c_2,\dots ,c_M\right\}$ is the set of clusters, where $c_i,i\in \left\{1,\dots ,M\right\}$ represents the $i\text{-}\mathrm{th}$ cluster.

Different from using Euclidean distance in hierarchical clustering to measure whether two clusters can be merged, in the clustering algorithm of this paper, the two clusters with the largest value of $D_{ij}^{cluster}$ will be merged. $D_{ij}^{cluster}$ is the weighted sum of $Y_{ij}$ and ${(R-d_{ij}^{cluster})}^{-1}$, $Y_{ij}$ refers to the estimated remaining time of $c_i$ and $c_j$ within the DSRC communication range, R refers to the DSRC communication radius, and $d_{ij}^{cluster}$ refers to the distance between $c_i$ and $c_j$. ${(R-d_{ij}^{cluster})}^{-1}$ can describe whether $c_i$ and $c_j$ are on the edge of each other’s DSRC communication range. The detailed definition of $D_{ij}^{cluster}$ is as follows:

$$\begin{array}{c}\hfill D_{ij}^{cluster}=\left\{\begin{array}{c}\alpha Y_{ij}+\frac{\beta }{R-d_{ij}^{cluster}},d_{ij}^c\le d_{limit}\hfill \\ 0,d_{ij}^c>d_{limit}\hfill \end{array}\right.\end{array}$$

(1)

When $c_i$ and $c_j$ are at the edge of each other’s DSRC communication range (that is, when $d_{ij}^{cluster}$ is close to R), if the speed (the speed here refers to the average speed of all vehicles in the cluster) difference between $c_i$ and $c_j$ increases, it will cause $c_i$ and $c_j$ to quickly leave the DSRC communication range. Therefore, in Equation (1), the difference between R and $d_{ij}^{cluster}$ is used to limit the merging of clusters at the edge of the DSRC communication range. $\beta$ is a negative value whose absolute value is greater than 1. When $(R-d_{ij}^{cluster})$ becomes smaller, ${(R-d_{ij}^{cluster})}^{-1}$ increases, $D_{ij}^{cluster}$ becomes smaller. $d_{limit}$ is the maximum allowed distance that clusters can merge. $\alpha$ is the weight of $Y_{ij}$, and the calculation formula of $Y_{ij}$ is:

$$\begin{array}{c}\hfill Y_{ij}=\frac{R\pm d_{ij}^{cluster}}{max\left\{\left|{\upsilon }_i^{max}-{\upsilon }_j^{min}\right|,\left|{\upsilon }_j^{max}-{\upsilon }_i^{min}\right|\right\}}\end{array}$$

(2)

where ${\upsilon }^{max}$ and ${\upsilon }^{min}$ represent the maximum speed and minimum speed, respectively, of the CMs in the cluster. In particular, ${\upsilon }_i^{min}$ represents the minimum velocity of the CM in cluster $c_i$. For two clusters, $c_i$ and $c_j$ within the DSRC communication range traveling in the same direction, if the average speeds of $c_i$ and $c_j$ do not change for a period of time in the future, and $d_{ij}^{cluster}$ tends to shrink (that is, $c_i$ and $c_j$ are close to each other)), then $Y_{ij}$ should be the sum of $d_{ij}^{cluster}$ and R divided by the speed difference between $c_i$ and $c_j$; that is, the numerator of Equation (2) should be added. Conversely, if $d_{ij}^{cluster}$ tends to increase (that is, $c_i$ and $c_j$ are far away from each other), then $Y_{ij}$ should be the difference between $d_{ij}^{cluster}$ and R divided by the speed difference between $c_i$ and $c_j$, and the numerator of Equation (2) should be subtracted. In addition, since the velocities between CMs within a cluster are different, we used the difference between the maximum speed of vehicles in one cluster minus the minimum speed of vehicles in the other cluster as the speed difference between the two clusters, which can make the resulting cluster more stable.

Since the number of CM members in the cluster is limited to N, even if the $D_{ij}^{cluster}$ of $c_i$ and $c_j$ is the largest, once the sum of the number of CMs of $c_i$ and $c_j$ exceeds N, ci and cj cannot be merged. The stopping condition of the clustering algorithm in this paper is until no two clusters with a distance less than $d_{limit}$ can be found. In summary, the clustering algorithm process in this paper is as follows:

• Vehicles report their current state information to the edge server;
• Initialize clusters, each cluster contains one vehicle;
• According to Equations (1) and (2), find $c_i$ and $c_j$ in all clusters, such that $D_{ij}^{cluster}$ is the largest. If the total number of CMs in $c_i$ and $c_j$ is less than N, then $c_i$ and $c_j$ are merged; otherwise, to ensure that the algorithm does not fall into an infinite loop, it is necessary to mark that $max\left\{c_i,c_j\right\}$ does not enter the next cycle.
• Repeat step 3 until no more than two clusters that meet the conditions can be identified.

The pseudocode of the clustering algorithm is shown in Algorithm 1. Lines 1 to 5 initialize variables. Lines 9 to 10 merge vehicle clusters when the conditions are met. The meaning of the 12 to 13 lines is that if the total number of CMs in the two clusters is greater than N, the larger one of the two clusters will not enter the next loop.

Algorithm 1:Vehicle Clustering. The algorithm is used to complete the vehicle clustering.

This paper uses a simple example to illustrate the clustering process of Algorithm 1. Assume that there are five vehicles $\left\{a_1,a_2,a_3,a_4,a_5\right\}$ traveling in the same direction on the current road segment. The velocity of $a_1$ is 23 and the coordinates are (1, 450); the velocity of $a_2$ is 20 and the coordinates are (6, 350); the velocity of $a_3$ is 30 and the coordinates are (3, 240); the velocity of $a_4$ is 21 and the coordinates are (5, 100); the velocity of $a_5$ is 22, and the coordinates are (2, 0). Moreover, suppose the parameters are set to: $\alpha$ = 1, $\beta$ = −200, $d_{limit}$ = −200, R = 4, $N=3$. The clustering process is shown in Figure 3. Initialize each vehicle as a cluster to obtain $\mathcal{C}=\left\{c_1,c_2,c_3,c_4,c_5\right\}$, where $c_i=\left\{a_i\right\}$. In the first round of the loop, $max\left\{D_{ij}^c\right\}=D_{4,5}^c=499.45$, $d_{4,5}^{cluster}=100.124$, $d_{4,5}^{cluster}<d_{limit}$, so merge $c_4$ and $c_5$ to $c_6$. In the second round of the loop, $max\left\{D_{ij}^c\right\}=D_{1,2}^c=99.29$, $d_{1,2}^{cluster}=110.00$, $d_{1,2}<d_{limit}$, so merge $c_1$ and $c_2$ to $c_7$. In the third round of the loop, $max\left\{D_{ij}^c\right\}=D_{3,7}^c=65.05$, $d_{3,7}^{cluster}=160.00$, $d_{4,5}^{cluster}<d_{limit}$, so merge $c_3$ and $c_7$ to $c_8$. In the fifth round of the loop, $d_{6,8}^{cluster}=263.33$, $d_{6,8}^{cluster}>d_{limit}$, at this time, $max\left\{D_{ij}^c\right\}=D_{6,8}^c=0$, the clustering process is completed. The resulting clustering result is $\mathcal{C}=\left\{c_6,c_8\right\}$, and $c_6=\left\{a_4,a_5\right\}$, $c_8=\left\{a_1,a_2,a_3\right\}$.

It is worth noting that in the above clustering process, no CH is generated. Next, we will discuss how to choose CH for each cluster. The principle is to select the vehicle in the cluster that can establish the most stable connections with other CMs as the CH. In a cluster, all CMs and CH in the cluster are connected by one hop. The parameter $D_{ij}^{vehicle}$ is introduced to evaluate the stability of the connection between the two vehicles. Different from $D_{ij}^{clucter}$, $D_{ij}^{vehicle}$ is used to directly estimate the remaining time that the vehicle is within the mutual DSRC communication range based on the current situation. $D_{ij}^{vehicle}$ does not consider whether the vehicles are on the edge of the mutual DSRC communication range, because due to the limitation of $d_{limit}$, the distance between the vehicles in a cluster and the center of the cluster is less than R, and the final selected CH will also be closer to the center of the cluster. $D_{ij}^{vehicle}$ is defined as follows:

$$\begin{array}{c}\hfill D_{ij}^{vehicle}=\left\{\begin{array}{c}\frac{R+d_{ij}^v}{\left|{\upsilon }_i^v-{\upsilon }_j^v\right|},v_i\mathrm{and}{v}_j\mathrm{close}\mathrm{to}\mathrm{each}\mathrm{other}\hfill \\ \frac{R-d_{ij}^v}{\left|{\upsilon }_i^v-{\upsilon }_j^v\right|},v_i\mathrm{and}{v}_j\mathrm{away}\mathrm{from}\mathrm{each}\mathrm{other}\hfill \end{array}\right.\end{array}$$

(3)

The symbol $d_{ij}^{vehicle}$ represents the distance between two vehicles, and ${\upsilon }^v$ represents the speed of the vehicle. When ${D_{ij}}^{vehicle}\ge D_{threshold}^{vehicle}$, then a stable connection can be established between ${\mathrm{CM}}_i$ and ${\mathrm{CM}}_j$, and $D_{threshold}^{vehicle}$ is a settable threshold. The value of $D_{threshold}^{vehicle}$ in this paper is the same as that in the TDCR model [13]. In addition, this formula is used to determine whether communication can be established between two CHs when establishing a VANET routing path in Section 5.1. We did not focus on intra-cluster communication, so intra-cluster communication will not be discussed. Notably, the algorithm works even when there are extremely sparse vehicles on the road. In the most extreme case, each cluster contains only one vehicle.

4.2. Vehicular Communication Model

The data packets of the CM must be forwarded to the CH. Then, the CH selects the communication method to send the packets according to the QoS requirements of the packets. If C-V2X is selected, the CH directly sends the data packet to the nearby cellular network base station (BS); otherwise, the packet is sent to the next node according to the VANET routing path until the packet is sent to the RSU. Last, the packet is sent to the edge server by the BS or RSU.

Although through the CH, relay forwarding the packets adds extra delay, it is easier to optimize the network and reduce the overhead of communication resources [19]. If all data packets are sent through the cellular network, it will lead to a large increase in the communication cost for network users and increase the burden on the cellular network. Therefore, we combine DSRC and C-V2X communication methods in one framework and consider the balance between QoS and user communication costs in the following modeling.

First, we introduce the decision variable ${\theta }_{ik}$, its meaning is:

$$\begin{array}{c}\hfill {\theta }_{ik}=\left\{\begin{array}{c}0,\mathrm{use}\mathrm{VANETs}\mathrm{send}k\text{-}\mathrm{th}\mathrm{packet}\mathrm{of}{a}_i\hfill \\ 1,\mathrm{use}\mathrm{C}\text{-}\mathrm{V}2\mathrm{X}\mathrm{send}k\text{-}\mathrm{th}\mathrm{packet}\mathrm{of}{a}_i\hfill \end{array}\right.\end{array}$$

(4)

We use ${\mathcal{B}}_i=\{b_1,b_2,\cdots ,b_k,\cdots \}$ to represent the data packet buffer of $a_i$, where $b_k,k\in \{1,2,\cdots \}$ is the $k\text{-}\mathrm{th}$ packet in ${\mathcal{B}}_i$. In the following, we denote $b_k$ in ${\mathcal{B}}_i$ by $b_{ik}$. Moreover, ${\theta }_{ik}$ is used to represent how $b_{ik}$ is sent. When ${\theta }_{ik}$ is equal to 1, it means that VANET is used to send $b_{ik}$; when ${\theta }_{ik}$ is equal to 0, it means that C-V2X is used to send $b_{ik}$.

To balance the QoS and the user’s communication cost, we next model the total delay and total communication cost generated in the service domain per unit time. In the service domain, the delay is partly caused by packets sent via VANETs and partly by packets sent via C-V2X. Therefore, the total delay should be the sum of these two parts. No matter which part of the delay, it is composed of the following four types: processing delay, queuing delay, transmission delay, and propagation delay. As the propagation delay is extremely short, it is ignored in this paper. The transmission delay can be calculated by dividing the packet size by the data transmission rate. We used $S_{ik}$ to represent the size of $b_{ik}$, $f^{CV2X}$ to represent the data transmission rate of C-V2X, and $f^{DSRC}$ to represent the data transmission rate of VANETs. In addition, we measure the processing delay and forwarding delay with the time interval from when a data packet enters ${\mathcal{B}}_i$ to when the data packet is sent from ${\mathcal{B}}_i$, and call it forwarding delay. $q_{ik}^{CV2X}$ represents the C-V2X forwarding delay of $b_{ik}$, and $q_{ik}^m$ represents the forwarding delay generated when $b_{ik}$ is forwarded by the $m\text{-}\mathrm{th}$ node in $Pat{h}_i$. $Pat{h}_i$ represents the routing path of VANET from $a_i$ to RSU. Different packets have different QoS requirements. Packets with high QoS usually require lower transmission delays, so they should also be forwarded preferentially to reduce their forwarding delays, so we multiply the forwarding delay of each packet by a weight. $w_{ik}$ is the weight of $b_{ik}$, and its calculation formula is as follows:

$$\begin{array}{c}\hfill {\omega }_{ik}=2\times \left[1-\left(\frac{l^{max}-l_{ik}}{l^{max}-l^{min}}\right)\right]\end{array}$$

(5)

where $l_{ik}$ represents the maximum delay allowed for $b_{ik}$, which is the maximum time allowed from the start of the packet generation to the time the packet is sent to the RSU/BS. $l_{ik}$ will subtract the elapsed time in real time after the data packets are generated, which will ensure that the data packets with lower QoS requirements can also be processed in time. $\left[l^{min},l^{max}\right]$ is the value range of $l_{ik}$. The larger ${\omega }_{ik}$ is, the higher the priority of the data packet is.

Finally. We use T to represent the total delay generated in the service domain per unit time. The calculation formula of T is as follows:

$$\begin{array}{c}\hfill T\left(\mathit{\theta }\right)=\sum _{i=1}^M\sum _{b_k\in {\mathcal{B}}_i}\left[{\theta }_{ik}\left(\frac{S_{ik}}{f^{CV2X}}+{\omega }_{ik}\times q_{ik}^{CV2X}\right)+\left(1-{\theta }_{ik}\right)\left(\frac{S_{ik}}{f^{DSRC}}+{\omega }_{ik}\times q_{ik}^i\right)\right]\end{array}$$

(6)

where ${\theta }_{ik}\left(\frac{S_{ik}}{f^{CV2X}}+{\omega }_{ik}\times q_{ik}^{CV2X}\right)$ is the delay generated when the data packet is sent through C-V2X, and $\left(1-{\theta }_{ik}\right)\left(\frac{S_{ik}}{f^{DSRC}}+{\omega }_{ik}\times q_{ik}^i\right)$ is the delay generated when the data packet is sent through VANET. It should be noted that if a packet is sent through the VANET link, the packet will enter the packet buffer of each node in the link. Therefore, when a data packet is sent through VANET, it is only necessary to accumulate the delay generated at each node that the data packet passes through. This is why the superscript of $q_{ik}^i$ is i. The topology map composed of CH and RSU in the service domain is always determined, and once the topology map is determined, the optimal routing path can always be found according to algorithms such as Dijkstra. At this time, the total delay in the service domain is only related to which method is used to send the data packet. Therefore, T is a function of $\mathit{\theta }$, which is the same in the following formulas; $\mathit{\theta }$ is a vector consisting of all ${\theta }_{ik}$.

Assume that the unit price of the cellular network traffic is p dollar/MB. The total communication cost generated in the system per unit time is represented by P:

$$\begin{array}{c}\hfill P\left(\mathit{\theta }\right)=p\times \frac{{\displaystyle \sum _{i=1}^M}{\displaystyle \sum _{b_k\in \mathcal{B}}}{\theta }_{ik}\times S_{ik}}{{1024}^2}\end{array}$$

(7)

This formula is quoted from [13]. P can also reflect the level of the cellular network bandwidth consumption.

To achieve the goal of balancing the QoS of packets and user communication costs, we use the following objective function:

$$J\left(\mathit{\theta }\right)=\underset{\mathit{\theta }}{min}\left(lnT\left(\mathit{\theta }\right)+P\left(\mathit{\theta }\right)\right)$$

(8)

$$\left(1-{\theta }_{ik}\right)\times \sum _{e\left(m,n\right)\in Pat{h}_k}\left(\frac{S_{ik}}{f^{DSRC}}+q_{ik}^m\right)\le l_{ik},{\theta }_{ik}=0$$

(8a)

$$C_{e(m,n)}^{DSRC}-\sum _{b_k\in \mathcal{B}}\left(1-{\theta }_{ik}\right)\times S_{ik}\ge 0,e\left(m,n\right)\in Pat{h}_k$$

(8b)

$$C^{CV2X}-\sum _{b_k\in {\mathcal{B}}_i}{\theta }_{ik}\times Siz{e}_{ik}\ge 0$$

(8c)

$${\theta }_{ik}\in \left\{0,1\right\}$$

(8d)

where $C^{CV2X}$ represents the capacity of the link of the cellular network. $C_{e(m,n)}^{DSRC}$ represents the capacity of the VANETs link $a_m$ to $a_n$ in $Pat{h}_k$. Equation (8a) specifies that if VANETs are used to transmit $b_{ik}$, the total delay generated must be less than $l_{ik}$ for $b_{ik}$. Equations (8b) and (8c) stipulate that the capacity of the cellular network links and VANET links cannot be exceeded at any time. Equation (8d) illustrates the range of values for ${\theta }_{ik}$.

5. Heuristic Algorithm

The objective Equation (8) is a nonlinear 01 integer programming problem, which has been proven to be NP-hard. Therefore, according to the previously established model, we designed a heuristic algorithm to approximately solve the problem. It takes more time and communication resources to make the CH aware of the global information of the network. Therefore, in practice, the network is usually not optimized as a whole, but each node is optimized according to the local information easily perceived by CH [19]. This approach is similar to that employed in the greedy algorithm; if each node can achieve the optimal result, the entire network will obtain the optimal result.

In this subsection, first, let the edge server identify the optimal VANET routing path according to the cluster results and collected vehicle information. Second, each CH selects DSRC or C-V2X to send data packets according to its own situation and the local information it can perceive.

5.1. VANET Routing Path

CH and RSU are used as nodes to establish the topology graph $G\left(\mathcal{V},\mathcal{E}\right)$. First, initialize $\mathcal{E}=⌀$. Second, establishing a communication link between CHs is similar to establishing a communication link between a CM and a CH in Section 4.1, so we also use Equation (3) to determine whether a VANET communication link can be established between the two CHs. If $D_{ij}^{vehicle}\ge D_{Threshold}^{vehicle}$, then $\mathcal{E}\bigcup \left\{e\left(i,j\right)\right\}$. We use the average of the delays generated by the past x packets transmitted through $e\left(i,j\right)$ to represent the weight $w_{ij}$ of $e\left(i,j\right)$.

After completing the establishment of $G\left(\mathcal{V},\mathcal{E}\right)$, we discuss how to establish the routing paths of VANET. First, the CHs are sorted by distance to the RSU from near to far. Second, the Dijkstra algorithm is selected to identify the shortest path from each node to the RSU. Due to the capacity limitation of the communication link, every time a path is identified, it is necessary to check whether the remaining capacity of the link in the path can accommodate the data volume of the newly added node, and if not, a new path needs to be determined.

In practice, there are cases where there is no path between the CH and the RSU in the topology graph. If there is no path between $a_i$ and RSU, then find $c_j,j\in \{j\left|d_{j,RSU}^{vehicle}\le d_{i,RSU}^{vehicle}\right\}$ closest to $c_i$. Split $max\left\{c_i,c_j\right\}$ and remove $max\left\{c_i,c_j\right\}$ from $\mathcal{C}$ and add to $\mathcal{C}$ the resulting clusters from the split. The topology map is updated, and the routing path can be identified. If the path by which the remaining capacity can meet the needs of the current cluster is not identified, then the current cluster will be set to an unreachable state, and all data for the cluster will be sent over the cellular network.

The pseudocode for the establishment of routing paths for VANETs is shown in Algorithm 2, where r represents the data transmission rate of the vehicle. The functions involving Lines 4 to 17 are to try to find the shortest paths. If the identified path is not available, mark the weight of the edge with insufficient capacity as infinite according to Line 12. If there is no path between the CH and the RSU, the processing is performed according to Lines 18–20.

Algorithm 2:Path Construction. The algorithm is used to establish VANET communication links between clusters.

Figure 4 shows the general workflow of Algorithm 2. Figure 4a is the topology diagram between CH and RSU, which includes RSU and four clusters. First, each cluster will be sorted by the distance to the RSU from near to far. Suppose the order is $\mathcal{C}=\left\{c_1,c_4,c_2,c_3\right\}$. Then, in the edge server, the Dijkstra algorithm is used to find the shortest path from $c_1$ to the RSU to obtain $Pat{h}_1=\left\{e\left(1,RSU\right)\right\}$, as shown in Figure 4b. As shown in Figure 4c,d, we successively find paths $Pat{h}_4=\left\{e\left(4,RSU\right)\right\}$ and $Pat{h}_2=\left\{e\left(2,1\right),e\left(1,RSU\right)\right\}$ for $c_4$ and $c_2$. However, when establishing the path of $c_3$, it is found that there is no path between $c_3$ and the RSU in the topology diagram. At this time, $c_2$ is the closest cluster to $c_3$ on the RSU side, and $c_2$ has more members than $c_3$, so $c_2$ is split into $c_5$ and $c_6$, as shown in Figure 4e. Insert $c_5$ and $c_6$ into the appropriate position of $\mathcal{C}$; delete $c_2$ from $\mathcal{C}$; update the topology map. Now, the vehicle cluster set is $\mathcal{C}=\left\{c_1,c_4,c_3,c_5,c_6\right\}$. As shown in Figure 4f, find the shortest path from $c_5$ to RSU to obtain $Pat{h}_5=\left\{e\left(5,4\right),e\left(4,RSU\right)\right\}$. Find the shortest path $Pat{h}_6=\left\{e(6,5),e\left(5,4\right),e\left(4,RSU\right)\right\}$ from $c_6$ to RSU, as shown in Figure 4g. When seeking the shortest path of $c_3$, $Pat{h}_3=\left\{e(3,6),e(6,5),e\left(5,4\right),e\left(4,RSU\right)\right\}$ is obtained for the first time, but the capacity of $e\left(4,RSU\right)$ cannot meet the needs of $c_3$. Therefore, we change the weight of $e\left(4,RSU\right)$ to $+\infty$, determine the shortest path of $c_3$, Obtain $Pat{h}_3=\left\{e(3,6),e(6,5),e\left(5,1\right),e\left(1,RSU\right)\right\}$, and detect that all links are available, as shown in Figure 4h. Thus far, the establishment of VANET routing paths for all clusters in Figure 4a has been completed.

5.2. Routing Policy

To facilitate the CH in evaluating the current network conditions to decide how to forward the data packets to the RSU/BS, $u_i^{CV2X}$ is used to represent the average delay of x packets transmitted from $a_i$ via C-V2X, and $u_i^{DSRC}$ is used to represent the average delay of x packets transmitted from $a_i$ via DSRC. Their calculation formulas are expressed as follows:

$$\begin{array}{c}\hfill u_i^{CV2X}=\frac{1}{x}\times \sum _{k=0}^x\left(\frac{S_{ik}}{f^{CV2X}}+q_{ik}^{CV2X}\right),{\theta }_{ik}=1\end{array}$$

(9)

$$\begin{array}{c}\hfill u_i^{DSRC}=\frac{1}{x}\times \sum _{k=0}^x\sum _{e(m,n)\in Pat{h}_k}\left(\frac{S_{ik}}{f^{DSRC}}+q_{ik}^m\right),{\theta }_{ik}=0\end{array}$$

(10)

This paper assumes that $u_i^{CV2X}\le l^{min}$ is always true [13]. When $a_i$ needs to send data, it will first select the packet with the largest weight from ${\mathcal{B}}_i$ according to Equation (5). If $u_i^{DSRC}\le l_{ik}$, $a_i$ will use VANETs to send the packet; otherwise, C-V2X will be selected to send the packet after sending a packet. Update $l_{ik},k\in \{1,2,\cdots \}$ and ${\omega }_{ik},k\in \{1,2,\cdots \}$ of all packets in the buffer, and update $u_i^{CV2X}$ or $u_i^{DSRC}$, every x packet sent via C-V2X or VANET. As long as the data packets generated by $a_i$ are sent to the BS through the C-V2X method, the cost will be paid by $a_i$.

The pseudocode of the routing policy is shown in Algorithm 3. Lines 2 to 8 are used to select the current packet that needs to be sent. Lines 9 to 13 are used to select the sending method. Line 14 is used to update the packet weight and maximum allowable delay in real-time. Line 15 is used to update the average delay according to Equations (9) and (10). After obtaining the routing paths of VANETs, each CH independently runs Algorithm 3. Combined with Equations (9) and (10), the real-time updated $u_i^{CV2X}$ and $u_i^{DSRC}$ enable the CH to grasp the current network state to a certain extent. If congestion occurs in the network, $u_i^{CV2X}$ and $u_i^{DSRC}$ obtained by feedback will inevitably increase, which will cause the CH to adjust the method employed for sending packets.

In Algorithms 2 and 3, all constraints of Equation (8) are satisfied. By optimizing the VANET link, the delay of transmitting data packets through VANETs is reduced as much as possible, enabling as few packets as possible to be transmitted through C-V2X, reducing the communication costs of users. This approach achieves the goal of balancing QoS and communication costs.

Algorithm 3:Routing Policy. The algorithm used to choose which way (DSRC or C-V2X) to send the packet.

6. Results

This paper compares the CTDHR framework with the TDCR framework. First, the three parameters $\alpha$, $\beta$, and $d_{limit}$ of Equation (1) are selected. Second, the clustering results and communication performance of CTDHR and TDCR are compared. In the experiment, we still do not care about the communication within the cluster, and only consider the communication between the clusters.

6.1. Experimental Setting

• The establishment of the simulation experiment environment. Before the experiment started, we used Python3.8 to build a simulation environment for vehicle communication scenarios. First of all, we observed the changes in the traffic flows at ten highway intersections in reality at 7:00 a.m.–9:00 a.m. and 3:00 p.m.–5:00 p.m. through video tapes, and obtained the speed characteristics and the interval distributions of vehicles entering the intersection. According to the observation results, the vehicle speeds obeyed normal distributions with a mean of 23 m/s and a variance of 6; the interval between two vehicles on the same lane entering the intersection obeyed a normal distribution with a mean of 3.7 s and a variance of 1.2. We then simulated a two-way six-lane highway with a length of 2000 m and generated vehicles with different speeds and directions at the beginning of the lanes based on the survey results. In addition, each vehicle had a different data generation rate. In this way, after a period of simulation, the road was filled with a certain number of vehicles. At this time, the possible collision of the vehicle must be considered. In the simulation environment of this paper, when two vehicles might have collided, the rear vehicle may have taken measures to change lanes and brake to avoid the collision. The speed of the vehicle also had a probability to change. Another important point is that the RSU was located in the middle of the road in the experiment. In addition, in the simulation program, the position of the vehicle was updated every 0.1 s. In previous vehicular communication simulations, there were insufficient numbers of vehicles [16,17,19,20], or insufficient mobility of vehicles (vehicles either did not move [16] or moved at a constant speed [21]). In this paper, the driving conditions of the vehicle in the real environment were fully imitated in the simulation environment to reflect the real performance of the vehicle communication method.
• Experimental parameter settings. To verify the applicability of CTDHR under the high-speed movement of the vehicle, the speed range of the vehicle was 18 to 28 m/s. Moreover, the number of vehicles in the experimental scene obeyed the normal distribution of $\mathcal{N}\left(130,5\right)$. Although the communication radius was extended to 2000 m in IEEE802.11bd, the road was usually curved, and there were obstacles between two vehicles to block the transmission of signals, so the communication radius of DSRC was set to 400 m in this paper. $l_{ik}$ obeys the normal distribution of $\mathcal{N}\left(17,8\right)$ in milliseconds, but its value is still limited to $\left[l^{min},l^{max}\right]$. Since it is difficult to obtain the accurate data transmission rate of DSRC in the current research, according to the spectrum resources and sub-carrier spacing of 802.11bd [31], the data transmission rate of DSRC was estimated to be 200 Mbps using the Nyquist criterion and Shannon formula. Refer to

  Table 3. Experimental parameter settings.

  Parameter	Value
  Parameter $\alpha$ of Equation (1)	0.1
  Parameter $\beta$ of Equation (1)	−150
  Maximum allowable distance that two clusters can be merged $d_{limit}$(meter)	170
  Threshold for establishing a robust communication link $D_{threshold}^{vehicle}$	6
  Length of road (meter)	2000
  Number of vehicles	$\mathcal{N}\left(130,5\right)$
  Communication radius of DSRC R (meter)	400
  DSRC sub-carrier spacing (KHz)	156.25
  Speed of vehicle $\upsilon$ (meters per second)	$\left[18,28\right]$
  Data transfer rate of DSRC $f^{DSRC}$ (Mbps)	200
  Data packet $Size$ (Byte)	$\left[200,1800\right]$
  Maximum delay allowed $l_{ik}$ for $b_{ik}$ (ms)	$\mathcal{N}\left(17,8\right)$
  Vehicle’s data generation rate r (Mbps)	$\left[0.4,8\right]$
  The unit price of C-V2X traffic charges p (per MB)	0.1
  Upper limit of vehicles in a cluster N	15

  for other parameter settings.
• To facilitate the comparison of the CTDHR and TDCR clustering algorithms, this paper uses cluster stability and the number of clusters to measure the quality of cluster results. The stability of a cluster is measured by the cluster hold time, which refers to the time from when the cluster is established to when the distance between any CM and CH in the cluster exceeds the DSRC communication radius. In addition, the number of clusters in the system should be kept in an appropriate range because a smaller number of clusters can reduce the number of hops on the VANET link, thereby reducing the delay of packet transmission. However, if the number of clusters is too small, the interval between two clusters will be too large to establish a communication link, or congestion may easily occur during communication.
• Both CTDHR and TDCR were tested in the same simulation environment.
• We implemented CTDHR and TDCR using Python 3.8. The hardware configuration of the experimental platform is detailed as follows: the processor is an Intel(R) Core(TM) i5-10400F CPU with 8 GB of memory and a 256 GB SSD.

6.2. Experimental Results

6.2.1. Parameter Selection

Choosing a good value for $\alpha ,\beta ,d_{limit}$ can enhance the stability of the cluster and control the number of clusters. In the experiment, we used the dichotomy method to roughly determine the value of $\alpha$ in $\left[0,2.0\right]$, the value of $\beta$ in $\left[-50,-200\right]$, and the value of $d_{limit}$ in $\left[100,300\right]$. After determining the value range, each different parameter combination was tested in 20 different road simulation environments, and the clustered results were obtained. Figure 5 is a box plot obtained in the test of the effect of different values of $\alpha ,\beta ,d_{limit}$ on the number of clusters and cluster stability.

According to Equation (1), $\alpha$ is the weight of $Y_{ij}$, but $Y_{ij}$ is only affected by the current state of the vehicle, and the vehicle state may change at any time. Thus, reducing the influence of $Y_{ij}$ on $D_{ij}^{clusterr}$ can increase the stability of the cluster. With a continuous decrease in $\alpha$, the stability of the cluster shows an increasing trend and the outliers gradually decrease. So, the value of $\alpha$ is 0.1. If two clusters of $c_i$ and $c_j$ at the edge of each other’s DSRC communication range are merged, the resulting cluster may be very unstable. By increasing $\beta$, the $D_{ij}^{clusterr}$ value of the two clusters can be reduced, thereby limiting the merging of these two clusters. However, as shown in Figure 5b,e, when $\beta$ is greater than −160, the beta has less effect on cluster stability and the number of clusters. This is because the D-limit limits the maximum distance that clusters are allowed to merge, which makes it less likely that clusters at the edge of mutual DSRC communication can merge. At $\beta =-160$, the mean of the number of clusters increases, and in some cases the number of clusters starts to increase. So we take the value of BETA as −150. As shown in Figure 5e,f, $d_{limit}$ has an important impact on the number and stability of clusters. The larger the $d_{limit}$ is, the more distant the clusters can be merged. When $d_{limit}$ is 170, a reasonable number of clusters can be obtained while maintaining good stability. At this time, the number of clusters will be reduced, and the clusters containing more CMs will be less stable. Therefore, as increases, both the stability of the cluster and the number of clusters tend to decrease. The final values of the three parameters are 0.1, −150, and 170.

6.2.2. Comparison of Clustering Methods

After completing the selection of parameters, Algorithm 1 was tested in 100 different simulation environments.

Table 4. Statistics on the stability of clusters and the number of clusters for CTDHR and TDCR.

	Framework	Average Value	Max Value	Min Value	Median Value
Cluster Keep Time	CTDHR	35.07	50.00	24.00	34.50
	TDCR	38.48	51.00	28.00	38.00
Number of Clusters	CTDHR	13.90	16.00	11.00	14.00
	TDCR	20.00	20.00	20.00	20.00

shows the comparison between Algorithm 1 and the TDCR clustering algorithm in 100 tests.

In TDCR, the method of spatial sampling is used to cluster vehicles, and the sampling radius is half of the DSRC communication radius (when R is 400 m, the sampling radius is 200 m), so the number of clusters in TDCR is constant, 20. In the clustering method of CTDHR, the parameter $d_{limit}$ is used to control the size of the cluster, so the coverage of the cluster is not fixed. When $d_{limit}$ is determined to be 170, the theoretical maximum coverage of the cluster is 340 m. Therefore, the clustering method of CTDHR can obtain fewer clusters. Moreover, in the clustering method of this paper, the one-hop connection between the CM and the CH is also realized. The small number of clusters means that the number of hops in the VANET link can be reduced as much as possible. When there is no congestion in the network, fewer hops make each packet forward as few times as possible, thereby reducing the total delay in the network. Moreover, fewer clusters mean fewer communication resources of the cellular network are required. Fewer clusters also facilitate cluster management and reduce the consumption of communication resources.

Due to the speed difference between vehicles, the vehicle may change its current state at any time. Therefore, the more vehicles in the cluster, the worse the stability of the cluster. When the number of vehicles on the road is the same, the smaller the number of clusters, the higher the average number of vehicles in the cluster. Therefore, the cluster stability of CTDHR is slightly worse than that of TDCR. In Equation (1), $Y_{ij}$ considers merging clusters that can stay connected longer, while ${(R-d_{ij})}^{-1}$ restricts the merging of clusters at the edge of the mutual DSRC communication radius. Therefore, the stability of CTDHR is also fully guaranteed, and the loss of various statistical features is within an acceptable range compared with TDCR. In addition, the number of vehicles in a single CTDHR cluster will not exceed N, which avoids the situation that the number of CMs in a single cluster is too much to exceed the communication capability of the CH. However, this situation may appear in TDCR.

6.2.3. Comparison of VANET Communication Link

After completing the establishment of the cluster and the election of the CH, the communication link is established on the cluster obtained in Section 5.1 using Algorithm 2. For comparison, the VANET link of TDCR was also established.

Table 5. Statistics on the stability of clusters and the number of clusters for CTDHR and TDCR.

	Framework	Average Value	Max Value	Min Value	Median Value
Total number of hops in a single test	CTDHR	30.75	40.00	23.00	30.00
	TDCR	47.88	61.00	40.00	47.00
Maximum number of hops in a single test	CTDHR	3.80	5.00	3.00	4.00
	TDCR	4.36	6.00	3.00	4.00
Average number of hops in a single test	CTDHR	2.21	2.92	1.87	2.17
	TDCR	1.54	2.00	1.15	1.50

shows a comparison of 100 groups of data obtained by the test.

Notes: In each test, each CH generates a VANET communication link to the RSU. The total number of hops in a single test is the sum of the hops of all links in a single test. The maximum number of hops in a single test refers to the number of hops of the longest link in a single test. The average number of hops in a single test is the total number of hops in a single test divided by the number of CHs.

Since the number of clusters in CTDHR is smaller than TDCR, its total hop count is also smaller than TDCR in the test. In Algorithm 2, when the VANET link capacity cannot meet the node’s demand, the node will look for other VANET paths. The newly identified path is no longer the shortest, so CTDHR is larger than TDCR in terms of the average hop count. However, due to the small number of clusters in CTDHR, the maximum number of hops of a single link in CTDHR is still smaller than that in TDCR. Thus, the maximum number of ’forwarding’ in CTDHR is less than TDHR for packets sent via VANETs when another condition is the same. Therefore, CTDHR generates less forwarding delay and can better satisfy the QoS of data packets.

6.2.4. Vehicle Communication Performance Test

After completing the link construction, the performances of CTDHR and TDCR were compared in the test, where the data generation rate of the vehicles gradually increased from 0.4 to 8 Mbps in steps of 0.4. At each data generation rate, tests were performed in 100 different simulation environments and the test results were averaged. The duration of a single test was 1 s. Figure 6 shows the results of the objective equations, total delay, and cellular network bandwidth consumption obtained from the CTDHR and TDCR comparison experiments.

The overall latency of CTDHR is less due to the smaller number of clusters and shorter VANET link for CTDHR at the same vehicle density. Moreover, the routing policy of CTDHR uses VANET to transmit data packets as much as possible, so the cellular network bandwidth consumption of CTDHR is also smaller than that of TDCR. As shown in Figure 6b, when the data generation rate of the vehicle is greater than 4.4 Mbps, the delay of TDCR suddenly increases, indicating that congestion occurs in the network at this time. However, CTDHR does not experience congestion until the data generation rate is greater than 5.2 Mbps. CTDHR reduces the time delay and cellular network bandwidth consumption generated in the system as much as possible, so the result of its objective equation is also smaller than that of TDCR.

In addition to cellular network bandwidth consumption and delay, we also compared the QoS satisfaction rate and packet loss rate of the two methods. In the experiment, if the real delay from the generation of $b_{ik}$ to the transmission to the RSU/BS was less than $l_{ik}$, the QoS requirements were considered as met.

As shown in Figure 7, CTDHR has better performance in terms of both packet loss rate and QoS satisfaction rate. CTDHR can effectively address the situation in which the remaining capacity of the link is less than the data generation rate of the newly added node when generating the routing path. Therefore, CTDHR avoids the situation where traffic is concentrated on one node, which effectively relieves the pressure on each forwarding node in the topology and is less likely to cause congestion than TDCR. The final performance is that with an increase in the vehicle data generation rate, the packet loss rate of CTDHR is much smaller than that of TDCR. In addition, the CTDHR routing policy is more flexible. According to the QoS of each packet, the appropriate transmission methods are selected, which also makes CTDHR satisfy the QoS of the packet at a higher rate.

7. Conclusions

This paper redesigns the vehicle cluster method, communication link establishment method, and routing policy based on the TDCR idea. In the vehicle clustering method, we no longer adopt the spatial sampling method of TDCR; we redesigned a clustering method that is suitable for vehicle clustering based on the idea of hierarchical clustering. In CTDHR, a new cluster model was designed, and the parameters in Equation (1), which reduce the number of clusters while ensuring the stability of clusters, were carefully selected. The link capacity was fully considered when establishing the communication link so that the network obtained a greater throughput. The flexible routing strategy enables data packets to choose the appropriate transmission method according to the environmental conditions.

Through the above improvements, CTDHR reduces the packets sent through the cellular network while ensuring QoS, so that more packets are sent through VANETs, which reduces the communication costs of the user. In the comparative experiment with TDCR, CTDHR achieves superiority in the following aspects: the number of clusters, the maximum number of hops of the VANET communication link, and the communication performance. Although CTDHR is slightly inferior to TDCR in terms of cluster stability and maximum hop count of VANET links, this is within the acceptable range. It can be seen that even with the above optimizations, the throughput of CTDHR is still low. In future research, we will attempt to (1) introduce deep learning methods to solve the problem of link generation in VANETs, and (2) use reinforcement learning to obtain better routing strategies.