Improving Transmission in Integrated Unmanned Aerial Vehicle–Intelligent Connected Vehicle Networks with Selfish Nodes Using Opportunistic Approaches

Abstract

The integration of unmanned aerial vehicles (UAVs) into vehicular networks offers numerous advantages in enhancing communication and coverage performance. With the ability to move flexibly in three-dimensional space, UAVs can effectively bridge the communication gap between intelligent connected vehicles (ICVs) and infrastructure. However, the rapid movement of UAVs and ICVs poses significant challenges to the stability and reliability of communication links. Motivated by these challenges, integrated UAV–ICV networks can be viewed as vehicular delay-tolerant networks (VDTNs), where data delivery is accomplished through the “store-carry-forward” transmission mechanism. Since VDTNs exhibit social attributes, this paper first investigates the opportunistic transmission problem in the presence of selfish nodes. Then, by enabling node cooperation, this paper proposes an opportunistic transmission scheme for integrated UAV–ICV networks. To address the issue of node selfishness in practical scenarios, the proposed scheme classifies the degree of cooperation and analyzes the encounter probability between nodes. Based on this, information is initially flooded, and the UAV is selected for data distribution by jointly considering the node centrality, energy consumption, and cache size. Finally, simulation results demonstrate that the proposed scheme can effectively improve the delivery ratio and reduce the average delivery delay compared to state-of-the-art schemes.

1. Introduction

1.1. Background and Motivations

The vehicular delay-tolerant network (VDTN) is a novel transmission architecture designed to address issues, such as the potential unavailability of an end-to-end path between the source and destination in vehicular communication environments [1,2,3,4]. In VDTNs, intelligent connected vehicles (ICVs) can store, carry, and forward data asynchronously [5]. Communication is possible even when there is no continuous network connection. This transmission architecture is particularly suitable for scenarios where infrastructure is inadequate, such as highways or remote areas [6]. In this situation, by adopting “store-carry-forward” mechanisms, vehicular networks can effectively reduce link interruptions, thereby enhancing the efficiency of information exchange between ICVs [7,8,9].

The application domains of VDTNs are diverse, including autonomous driving, geographic information retrieval, and emergency response services. In VDTNs, road side units (RSUs) typically serve as local central nodes, responsible for data forwarding and information caching [10]. However, because the RSUs are fixed, they will face serious challenges in actual vehicular networks. Especially in environments with high mobility, fixed RSUs can lead to reduced delivery ratio and increased delivery delay. Additionally, in rural road scenarios, the coverage of fixed RSUs is limited, which affects transmission performance [11,12,13].

Facing the above challenges, the introduction of unmanned aerial vehicles (UAVs) as replacements for traditional RSUs has emerged as a potential solution [14,15,16]. UAVs are highly mobile and can be deployed flexibly, enabling them to cover areas that are difficult for fixed RSUs to reach. Therefore, the limitations of RSUs can be addressed to provide wider network coverage. In addition, the coverage of blind spots can be reduced. In this situation, UAVs not only enhance network flexibility but also facilitate rapid deployment in emergency scenarios, positioning them as a critical technique for optimizing the performance of VDTNs [17,18,19]. Furthermore, using UAVs in VDTNs can promote vehicular applications in complex scenarios and provide feasible ideas and technical support for the development of future intelligent transportation systems.

1.2. Related Works

Due to their highly flexible mobility, UAVs have attracted significant research interest in the field of VDTNs. There are numerous works that combine UAVs with different techniques to improve the quality of service (QoS) of vehicular applications. The authors in [20] addressed the challenge of the low transmission efficiency in DTNs by proposing a social-based mechanism that utilizes community and centrality information to enhance the delivery rate. In this mechanism, a collaborative multiagent reinforcement learning algorithm is introduced, which can enable distributed nodes to learn effective collaboration strategies for relay selection. In [21], the authors investigated the feasibility of deploying the epidemic routing protocol in VDTNs. The study demonstrates that maintaining an appropriate time-to-live (TTL) value in the epidemic routing protocol ensures high packet delivery and low packet loss rates, even in large-scale VDTNs. Additionally, the authors in [22] proposed a novel service discovery algorithm based on Markov models to address the challenges of high mobility in VDTNs. Building upon the BUBBLE Rap forwarding protocol, two relay selection approaches were designed in [23], aiming to improve delivery delay.

Moreover, UAVs have garnered significant interest in supporting VDTNs due to their cost-effectiveness, high maneuverability, and flexible deployment. Inspired by these, the authors in [24] presented an optimal deployment strategy for relaying UAVs in vehicular networks. The proposed strategy can improve the system capacity by maximizing user rates and reducing outage probabilities. To deal with the problem of the uneven distribution of on-board tasks, a mobility-aware service offloading scheme is proposed for UAV-assisted vehicular networks [25]. This scheme effectively minimizes task processing delays while attaining near-optimal performance in service offloading and migration costs. Furthermore, efforts [26,27,28] have been made to explore the use of both cooperative and non-cooperative UAVs in vehicular networks.

The above works promote the application of UAVs into VDTNs to support opportunistic transmissions. Nevertheless, there are still some problems remained to be further investigated.

• First, the authors in [20,21,22,23] have explored the application of opportunistic transmission in VDTNs. However, these studies primarily focused on leveraging the mobility of ICVs or temporary caching at roadside RSUs to facilitate data distribution. While these studies effectively improve the transmission performance of vehicular communications, they ignore the potential benefits of integrating UAVs into VDTNs. Therefore, additional research is essential to investigate the integration of UAVs in opportunistic transmission strategies and to assess their effects on delivery ratios and latency.
• Second, although the authors in [24,25,26,27,28] have investigated the deployment of relaying UAVs in vehicular networks, these works have primarily focused on end-to-end delay-sensitive transmissions and optimized network resources (such as spectrum, power, and trajectory) to enhance network performance. However, they did not address the transmission problem in scenarios where direct communication links are not available within vehicular networks.
• Finally, most of the aforementioned studies assumed that all communication nodes in vehicular networks are cooperative. The existence of selfish nodes that can negatively affect transmission performance was not taken into account. It is noted that, in vehicular networks characterized by social attributes, selfish nodes may exhibit non-cooperative behavior by refusing to forward data or by consuming excessive resources, resulting in lower overall efficiency.

1.3. Contributions

Motivated by the above, this paper proposes an integrated UAV–ICV networking framework to explore the potential for air-to-ground node collaboration. The contributions of this paper are summarized as follows:

• First, this paper investigates the application of opportunistic transmission in integrated UAV–ICV networks, where the “store-carry-forward” mechanisms are adopted. Then, considering the selfish behavior of communication nodes due to factors such as energy, cache, and other practical constraints, this paper defines the types of node cooperation and analyzes the probability of encounters between nodes.
• Second, an opportunistic transmission scheme for integrated UAV–ICV networks, enabled by node cooperation, is proposed. By evaluating the forwarding capabilities of each relay node, this paper initially floods the information to be transmitted. On this basis, this paper uses UAVs to assist with delivery.
• Finally, to demonstrate the advantages of the designed scheme, this paper compares it with the state-of-the-art schemes [21,22,23] via simulations. Real map data are used for the simulations. The simulation results indicate that the designed scheme outperforms the state-of-the-art schemes in terms of the delivery ratio and average delivery delay. Furthermore, the effect of the proportion of selfish nodes and the cooperation threshold on the performance of integrated UAV–ICV networks is fully discussed.

1.4. Organization

The remainder of this paper is organized as follows: Section 2 introduces the considered system model, which includes the opportunistic transmission model with selfish nodes and the encounter probability analysis model. In Section 3, this paper elaborates the proposed opportunistic transmission scheme. The simulation results are presented in Section 4. Finally, this paper concludes our paper in Section 5.

2. System Model

2.1. Opportunistic Transmission Model with Selfish Nodes

In this paper, the opportunistic transmission-enhanced integrated UAV–ICV network consists of N ICVs and R UAVs. As shown in Figure 1, both ICVs and UAVs can be regarded as communication nodes, with functions such as information storage, carrying, and forwarding. In integrated UAV–ICV networks, the behavior of each communication node is typically social rather than isolated [6]. For example, a bus node may only forward message copies belonging to its bus company. Specifically, selfish behaviors can be categorized into two types: drop and non-forwarding. The “drop” behavior refers to a communication node receiving a message copy from another node but not forwarding it, instead dropping it. In contrast, the “non-forwarding” behavior refers to a communication node refusing to receive the message copy entirely.

Additionally, this paper classifies the node types in integrated UAV–ICV networks into three categories. Specifically, selfish nodes are private cars without public service attributes, and they neither broadcast nor forward information when encountering traffic congestion. Normal nodes are ICVs (e.g., taxis and passenger cars), which have partial public service attributes and generate or forward traffic information based on demand. Voluntary nodes are government vehicles or UAVs with public service attributes, and they generate or forward traffic information whenever they move. To analyze the impact of selfish behavior on integrated UAV–ICV networks, this paper defines the degree of node cooperation. The cooperation level is evaluated based on a metric that is negatively linearly correlated with the selfishness of nodes. When the cooperation level of a node is 0, it is considered completely non-cooperative. When the cooperation level is 100, it represents the ideal state of full cooperation, where each node forwards information as expected. Based on this analysis, this paper defines the three types of nodes and provides specific calculation methods.

Node cooperation type I (defined as $i_1$): This type represents the ideal state. In this case, all nodes in integrated UAV–ICV networks do not exhibit selfish behavior and only drop message copies due to energy exhaustion or a full cache. The cooperation level of type I is defined as $C_{\mathrm{I}}$. The total number of dropped message copies is denoted as $E_{\mathrm{drop}}$, and the total number of message copies that need to be forwarded is denoted as $E_{\mathrm{forward}}$. For type I, the node cooperation level can be calculated as

$$\begin{array}{c}\hfill C_{\mathrm{I}}=1-{\displaystyle \frac{E_{\mathrm{drop}}}{E_{\mathrm{forward}}}}.\end{array}$$

(1)

Therefore, when the relay type is type I, information is directly forwarded. The number of hops experienced by the message copy is increased by one.

Node cooperation type II (defined as $i_2$): In practical integrated UAV–ICV networks, there are inevitably some selfish nodes. It is assumed that different types of communication nodes are allowed to exchange messages with each other. However, selfish communication nodes drop all message copies from other nodes that need to be forwarded. In contrast, non-selfish communication nodes do not drop the message copies from other nodes that need to be forwarded. Let the number of non-selfish communication nodes be $N_{\mathrm{non}-\mathrm{sel}}$ and the number of selfish communication nodes be $N_{\mathrm{sel}}$. In this case, for type II, the node cooperation level $C_{\mathrm{II}}$ is given by

$$\begin{array}{c}\hfill C_{\mathrm{II}}=1-{\displaystyle \frac{N_{\mathrm{sel}}}{N_{\mathrm{non}-\mathrm{sel}}+N_{\mathrm{sel}}}}.\end{array}$$

(2)

Therefore, when the relay type is type II, if the communication node carrying the source node’s message copy is also of type II, the message is forwarded. In this situation, the number of hops experienced by the message copy is increased by one. Otherwise, the message copy is not == forwarded, and the number of hops experienced by the message copy remains unchanged.

Node cooperation type III (defined as $i_3$): In integrated UAV–ICV networks, this paper adds voluntary nodes to improve the performance of on-board information distribution [17]. This paper assumes that the number of voluntary nodes is $N_{\mathrm{pub}}$. For type III, the node cooperation level $C_{\mathrm{III}}$ can be expressed as

$$\begin{array}{c}\hfill C_{\mathrm{III}}=1-{\displaystyle \frac{N_{\mathrm{sel}}}{N_{\mathrm{non}-\mathrm{sel}}+N_{\mathrm{sel}}+N_{\mathrm{pub}}}}.\end{array}$$

(3)

Therefore, when the relay type is type III, if the communication node carrying the source node’s message copy contains information relevant to the relay node, the message is forwarded. In this situation, the number of hops experienced by the message copy is increased by one. In addition, if the communication node carrying the source node’s message copy contains information unrelated to the relay node, the message is not forwarded, and the number of hops experienced by the message copy remains unchanged.

2.2. Encounter Probability Analysis Model

As mentioned above, there are three different types of node cooperation in the considered integrated UAV–ICV networks. In this paper, when communication node i, which carries a message copy, moves into the communication range of the next-hop relay node j, communication nodes i and j are referred to as a communication node pair, denoted as ${\phi }_x=\left(i,j\right)$. All communication nodes in integrated UAV–ICV networks can be represented by a set $\phi$, $\phi =\left\{{\phi }_1,...,{\phi }_x,...,{\phi }_n\right\}$. Based on the different node types, there are nine distinct states of communication node pairs in integrated UAV–ICV networks, namely, $\left(\mathrm{Node}\left(i_1\right),\mathrm{Node}\left(i_1\right)\right)$, $\left(\mathrm{Node}\left(i_1\right),\mathrm{Node}\left(i_2\right)\right)$, $\left(\mathrm{Node}\left(i_1\right),\mathrm{Node}\left(i_3\right)\right)$, $\left(\mathrm{Node}\left(i_2\right),\mathrm{Node}\left(i_1\right)\right)$, $\left(\mathrm{Node}\left(i_2\right),\mathrm{Node}\left(i_2\right)\right)$, $\left(\mathrm{Node}\left(i_2\right),\mathrm{Node}\left(i_3\right)\right)$, $\left(\mathrm{Node}\left(i_3\right),\mathrm{Node}\left(i_1\right)\right)$, $\left(\mathrm{Node}\left(i_3\right),\mathrm{Node}\left(i_2\right)\right)$, and $\left(\mathrm{Node}\left(i_3\right),\mathrm{Node}\left(i_3\right)\right)$. Therefore, depending on the node type, three different behaviors are generated: (1) forwarding all message copies of the nodes; (2) forwarding message copies of some nodes; (3) refusing to forward message copies of all other nodes. In this situation, we need to consider both the reception and packet loss of message copies to evaluate the behavior of communication nodes.

When communication node i moves into the communication range of the next-hop relay node j, the probability that node j successfully receives the message copy from node i mainly depends on the size of the message copy, the number of copies, and the cache size of node j. Let t be the current time and $\Delta t$ be the duration of contact between nodes i and j. By using (4), this paper derives the cumulative distribution function (CDF) $F\left(X\right)$ of the random variable X as

$$\begin{array}{c}\hfill F\left(X\right)={\int }_{-\infty }^{x}f\left(t\right)\mathrm{d}t,\end{array}$$

(4)

where $f\left(t\right)$ is the probability density function (PDF) of successfully receiving a message copy for a pair of communication nodes. We have $f\left(t\right)\ge 0$, $t\in \left(-\infty ,+\infty \right)$, and ${\int }_{-\infty }^{+\infty }f\left(t\right)\mathrm{d}t=1$. Similarly, the PDF $f\left(\Delta t\right)$ of $\Delta t$ is given by

$$\begin{array}{c}\hfill f\left(\Delta t\right)={\lambda }_{i,j}\times exp\left(-{\lambda }_{i,j}\Delta t\sum _{k=1}^n{X}_k\left(t\right)\right),\end{array}$$

(5)

where ${\lambda }_{i,j}$ is the encounter probability between nodes i and j, and $X_k\left(t\right)$ is an index that represents whether the node buffer is full, $X_k\left(t\right)\in \left\{0,1\right\}$. In addition, $X_k$ can be further expressed as

$$\begin{array}{c}\hfill X_k=\left\{\begin{array}{cc}1,& L_u\left(i\right)\le L_r\left(j\right)+{\displaystyle \sum _{z\left(m\right)}}{L}_m\left(j\right),\\ 0,& L_u\left(i\right)>L_r\left(j\right)+{\displaystyle \sum _{z\left(m\right)}}{L}_m\left(j\right),\end{array}\right.\end{array}$$

(6)

where $L_u\left(i\right)$ is the size of the message copy that node i needs to transmit; $L_r\left(j\right)$ is the remaining cache size of node j; $L_m\left(j\right)$ is the size of the message copy cached by node j; $z\left(m\right)$ is the priority function, which is used to indicate that the priority of the message copies cached in node j is lower than the number of message copies transmitted by node i.

According to the above content, we can calculate the probability $P_{\mathrm{suc}}\left(i,j\right)$ of a pair of communication node $\left(i,j\right)$ successfully receiving message copies within $\Delta t$ time, which can be expressed as

$$\begin{array}{ccc}\hfill P_{\mathrm{suc}}\left(i,j\right)& =& F\left(t,\Delta t\right)\hfill \\ \hfill & =& {\int }_t^{t+\Delta t}f\left(t,\Delta t\right)\mathrm{d}\Delta t\hfill \\ \hfill & =& {\int }_t^{T_{max}}{\lambda }_{i,j}\Delta t\sum _{k=1}^n{X}_k\left(t\right)\mathrm{d}\Delta t,\hfill \end{array}$$

(7)

where $T_{max}$ is the TTL of the message copies.

After the relay node successfully receives the message copy, it may refuse to forward the message copy to non-destination nodes due to selfish behavior and drop this message copy. Therefore, in integrated UAV–ICV networks, the packet loss rate of node j can be estimated as

$$\begin{array}{c}\hfill P_{\mathrm{drop}}\left(j\right)={\displaystyle \frac{{\displaystyle \sum _{z\left(m\right)}}{L}_m\left(j\right)}{\sum L_{\mathrm{tot}}\left(j\right)}},\end{array}$$

(8)

where $L_{\mathrm{tot}}\left(j\right)$ is the total number of message copies in node j.

In summary, the probabilities that communication node i encounters the next-hop relay nodes of types I, II, and III can be represented as $P_{\mathrm{I}}$, $P_{\mathrm{II}}$, and $P_{\mathrm{III}}$, respectively. We have

$$\begin{array}{c}\hfill P_{\mathrm{I}}=P_{\left(i_1,i_1\right)}=P_{\left(i_2,i_1\right)}=P_{\left(i_3,i_1\right)}={\rho }_{\mathrm{I}}{\lambda }_{i,j}{P}_{\mathrm{suc}}\left(i,j\right),\end{array}$$

(9)

$$\begin{array}{c}\hfill P_{\mathrm{II}}=P_{\left(i_1,i_2\right)}=P_{\left(i_2,i_2\right)}=P_{\left(i_3,i_2\right)}={\rho }_{\mathrm{II}}{\lambda }_{i,j}{P}_{\mathrm{suc}}\left(i,j\right)\left[1-P_{\mathrm{drop}}\left(j\right)\right],\end{array}$$

(10)

and

$$\begin{array}{c}\hfill P_{\mathrm{III}}=P_{\left(i_1,i_3\right)}=P_{\left(i_2,i_3\right)}=P_{\left(i_3,i_3\right)}={\rho }_{\mathrm{III}}{\lambda }_{i,j}{P}_{\mathrm{suc}}\left(i,j\right)P_{\mathrm{drop}}\left(j\right).\end{array}$$

(11)

In (9)–(11), ${\rho }_{\mathrm{I}}$, ${\rho }_{\mathrm{II}}$, and ${\rho }_{\mathrm{III}}$ are the probabilities that communication nodes of type I, II, and III forward message copies, respectively.

3. Opportunistic Transmission Scheme for Integrated UAV–ICV Networks Enabled by Node Cooperation

Based on the node cooperation types elaborated in Section 2 and the constructed encounter probability analysis model, this paper evaluates the forwarding capabilities of each relay node. Specifically, the node cooperation type of a relay node can be determined by whether the value of $H_{max}$ changes, where $H_{max}$ changes, and $H_{max}$ is the maximum hop for information to reach the destination node or fail. Based on this, a decision can be made on whether to forward the information. Additionally, to prolong the network lifetime, the opportunistic transmission scheme should consider both the number of copies and transmission reliability. Taking into account the described practical factors, an opportunistic transmission scheme for integrated UAV–ICV networks enabled by node cooperation is proposed. The information transmission process in this scheme consists of two main parts: initial information flooding and UAV-assisted information transmission. The detailed flow chart of the proposed solution is shown in Figure 2.

3.1. Information Flooding

When the source node (UAV or ICV) generates information, it creates several message copies and forwards them to neighboring nodes that have not yet received this copy. During the forwarding process, the proposed opportunistic transmission scheme determines whether to transmit the message copy based on the encounter probability analysis model derived in Section 2.2 and then updates the encounter probabilities of the communication nodes. As discussed in [7], this paper uses Bayes’s theorem to establish the node transfer update equation, which is given by

$$\begin{array}{ccc}\hfill P_{\mathrm{Transfer}}& =& \sum P\left(\left.X\right|M,k_1,k_2,H_{max}\right)\hfill \\ \hfill & \times & P\left(\left.X\right|M,k_1,k_2,H_{max}\right),\hfill \end{array}$$

(12)

where $P_{\mathrm{Transfer}}$ is the updated encounter probability, $\sum P\left(\left.X\right|M,k_1,k_2,H_{max}\right)$ is the likelihood function, and $P\left(\left.X\right|M,k_1,k_2,H_{max}\right)$ is the prior probability. In addition, in (12), M represents the number of communication nodes involved in the communication, $M\le N+R$; $k_1$ and $k_2$ are the number of type II and type III nodes participating in relay transmission in integrated UAV–ICV networks, respectively. It should be noted that for ICVs, the number of type I nodes is $N-k_1-k_2$, and all R UAVs are type I nodes. After the message copy reaches the relay communication node, $P\left(\left.X\right|M,k_1,k_2,H_{max}\right)$ can be further calculated as (13) based on the node type of relay nodes and the encounter probability analysis model. We have

$$\begin{array}{ccc}\hfill & & P\left(\left.X\right|M,k_1,k_2,H_{max}\right)\hfill \\ \hfill & =& \left\{\begin{array}{cc}\left[\left(N+R-k_1-k_2\right)-\left(M-k_1-k_2\right)\right]{\lambda }_{i,j}{P}_{\mathrm{suc}}\left(i,j\right),& \mathrm{if}X=\left(M+1,k_1,k_2,H_{max}+1\right),\\ \left(K_1+K_2-k_1-k_2\right){\lambda }_{i,j}{P}_{\mathrm{suc}}\left(i,j\right)\times \left[1-P_{\mathrm{drop}}\left(j\right)\right],& \mathrm{elseif}X=\left(M+1,k_1,k_2,H_{max}\right),\\ \left(K_1+K_2-k_1-k_2\right){\lambda }_{i,j}{P}_{\mathrm{suc}}\left(i,j\right)P_{\mathrm{drop}}\left(j\right),& \mathrm{elseif}X=\left(M,k_1,k_2,H_{max}\right),\\ {\lambda }_{i,j}{P}_{\mathrm{suc}}\left(i,j\right),& \mathrm{else}.\end{array}\right.\hfill \end{array}$$

(13)

where $K_1$ and $K_2$ are the number of type II and type III nodes in integrated UAV–ICV networks, respectively; X denotes the state of the transition model; D indicates that the relay node is the destination node, meaning the message copy will no longer be forwarded.

In addition, the forwarding conditions of message copies are related to the cooperation threshold of the communication nodes in integrated UAV–ICV networks and the type of message copies. These conditions are mainly divided into the following two cases:

• Case 1: When the next-hop node is a type II communication node, the transfer probability $P_{\mathrm{Transfer}}$ of the communication node is compared with the cooperation threshold $P_{\mathrm{Transfer}\mathrm{II}}$ of the type II communication node. If $P_{\mathrm{Transfer}\mathrm{II}}\le P_{\mathrm{Transfer}}$, the message copy is transmitted. If $P_{\mathrm{Transfer}\mathrm{II}}>P_{\mathrm{Transfer}}$, the message copy is not transmitted.
• Case 2: When the next-hop node is a type III communication node, the message copy type is first evaluated, with $M_{\mathrm{Mes}\_\mathrm{type}}$ defined as the message type. If $M_{\mathrm{Mes}\_\mathrm{type}}=1$, it indicates that the message copy is related to the relay node, and the message copy is transmitted. If $M_{\mathrm{Mes}\_\mathrm{type}}=0$, it indicates that the message is not related to the relay node, and the cooperation threshold $P_{\mathrm{Transfer}\mathrm{III}}$ must be compared. If $P_{\mathrm{Transfer}\mathrm{III}}\le P_{\mathrm{Transfer}}$, the message copy is transmitted. If $P_{\mathrm{Transfer}\mathrm{III}}>P_{\mathrm{Transfer}}$, the message copy is not transmitted.

3.2. UAV-Assisted Information Transmission

After the initial information flooding, the proposed opportunistic transmission scheme leads to a continuous decrease in the number of remaining message copies at communication nodes as the copies are forwarded. Generally, when a communication node has only one remaining message copy and fails to successfully transmit it to its destination node, the relay communication node can only encounter the destination node either by moving or waiting. However, this stage may introduce significant delays in information transmission. Therefore, the proposed opportunistic transmission scheme can be combined with the information forwarding probability in the Prophet routing protocol [9] and the UAV-assisted mechanism to transmit message copies.

Specifically, in the proposed opportunistic transmission scheme, during the initial information flooding process, the encounter probability $P_{i,d}$ between node i and the destination node d, as well as the encounter probability $P_{k,d}$ between the next-hop relay node k and the destination node d, should be calculated. If $P_{i,d}\le P_{k,d}$ the information is transmitted. Otherwise, to prevent excessive message flooding, the transmission does not occur. However, under this scheme, there may still be cases where certain communication nodes have only one remaining message copy and fail to successfully transmit it to the destination node. In such cases, the message copy can be forwarded to a UAV. Compared to ICVs, UAVs have a wider communication range, greater cache size, and lack selfishness. Therefore, in integrated UAV–ICV networks, UAVs have more centrality. Strong node centrality means that, within the same time period, a UAV node can contact more communication nodes. According to the above analysis, UAV nodes are more suitable as relay nodes for message forwarding. The node centrality $D_{\mathrm{Centrality}}$ can be expressed as

$$\begin{array}{c}\hfill D_{\mathrm{Centrality}}=\sum _{k=1,k\ne i}^{N+R}{\displaystyle \frac{x_{i,k}}{N+R-1}},\end{array}$$

(14)

where $x_{i,k}\in \left\{0,1\right\}$. If nodes i and k are within each other’s communication range, $x_{i,k}=1$, otherwise, $x_{i,k}=0$.

This paper defines the initial energy of UAVs as $E_{\mathrm{init}\_\mathrm{UAV}}$ and its standby energy consumption as $E_{\mathrm{st}\_\mathrm{UAV}}$. The initial energy of ICVs is defined as $E_{\mathrm{init}\_\mathrm{veh}}$, with a standby energy consumption of $E_{\mathrm{st}\_\mathrm{veh}}$. The energy refresh cycle for both types of communication nodes is T. The energy consumed by the UAV and ICV for a single node detection is $E_{\det \_\mathrm{UAV}}$ and $E_{\det \_\mathrm{veh}}$, respectively. Moreover, the energy consumed by the UAV and ICV for a single information transmission is defined as $E_{\mathrm{tran}\_\mathrm{UAV}}$ and $E_{\mathrm{tran}\_\mathrm{veh}}$, respectively. Furthermore, during one refresh cycle, the UAV performs node detection and information transmission $N_{\det \_\mathrm{UAV}}$ and $N_{\mathrm{tran}\_\mathrm{UAV}}$ times, respectively. The ICV performs node detection and information transmission $N_{\det \_\mathrm{veh}}$ and $N_{\mathrm{tran}\_\mathrm{veh}}$ times, respectively. Based on the above analysis, for the l-th transmission, the remaining energy of the UAV and ICV, denoted as $E_{\mathrm{rest}\_\mathrm{UAV}}$ and $E_{\mathrm{rest}\_\mathrm{veh}}$, can be calculated by using (15) and (16), respectively.

$$\begin{array}{ccc}\hfill E_{\mathrm{rest}\_\mathrm{UAV}}\left(l\right)& =& E_{\mathrm{rest}\_\mathrm{UAV}}\left(l-1\right)-E_{\det \_\mathrm{UAV}}\left(l\right)\times N_{\det \_\mathrm{UAV}}\left(l\right)\hfill \\ \hfill & -& E_{\mathrm{tran}\_\mathrm{UAV}}\left(l\right)\times N_{\mathrm{tran}\_\mathrm{UAV}}\left(l\right)-E_{\mathrm{st}\_\mathrm{UAV}}\left(l\right),\hfill \end{array}$$

(15)

and

$$\begin{array}{ccc}\hfill E_{\mathrm{rest}\_\mathrm{veh}}\left(l\right)& =& E_{\mathrm{rest}\_\mathrm{veh}}\left(l-1\right)-E_{\det \_\mathrm{veh}}\left(l\right)\times N_{\det \_\mathrm{veh}}\left(l\right)\hfill \\ \hfill & -& E_{\mathrm{tran}\_\mathrm{veh}}\left(l\right)\times N_{\mathrm{tran}\_\mathrm{veh}}\left(l\right)-E_{\mathrm{st}\_\mathrm{veh}}\left(l\right),\hfill \end{array}$$

(16)

where $E_{\mathrm{rest}\_\mathrm{UAV}}\left(0\right)=E_{\mathrm{init}\_\mathrm{UAV}}$ and $E_{\mathrm{rest}\_\mathrm{veh}}\left(0\right)=E_{\mathrm{init}\_\mathrm{veh}}$.

Meanwhile, when transmitting message copies to communication nodes with higher centrality, the remaining cache space of these nodes must also be considered. In practical integrated UAV–ICV networks, the cache size of nodes is limited. Once the cache is full, the node is unable to store newly received information and mst drop these message copies, which reduces the delivery ratio of integrated UAV–ICV networks. Therefore, the selected UAV nodes must not only have high centrality and sufficient energy but also consider their remaining cache size. It is assumed that the initial cache space of UAV and ICV is $B_{\mathrm{init}\_\mathrm{UAV}}$ and $B_{\mathrm{init}\_\mathrm{veh}}$, respectively. In addition, the size of each message copy is $\alpha$. The number of message copies currently cached by the UAV and ICV is ${\beta }_{\mathrm{UAV}}$ and ${\beta }_{\mathrm{veh}}$, respectively. According to the above-mentioned analysis, for the l-th transmission, the remaining cache size of the UAV and ICV can be calculated by (17) and (18), respectively.

$$\begin{array}{c}\hfill B_{\mathrm{rest}\_\mathrm{UAV}}\left(l\right)=B_{\mathrm{rest}\_\mathrm{UAV}}\left(l-1\right)-\alpha \times {\beta }_{\mathrm{UAV}}\left(l\right),\end{array}$$

(17)

and

$$\begin{array}{c}\hfill B_{\mathrm{rest}\_\mathrm{veh}}\left(l\right)=B_{\mathrm{rest}\_\mathrm{veh}}\left(l-1\right)-\alpha \times {\beta }_{\mathrm{veh}}\left(l\right),\end{array}$$

(18)

where $B_{\mathrm{rest}\_\mathrm{UAV}}$ and $B_{\mathrm{rest}\_\mathrm{veh}}$ are the remaining cache sizes of UAVs and ICVs, respectively. We have $B_{\mathrm{rest}\_\mathrm{UAV}}\left(0\right)=B_{\mathrm{init}\_\mathrm{UAV}}$ and $B_{\mathrm{rest}\_\mathrm{veh}}\left(0\right)=B_{\mathrm{init}\_\mathrm{veh}}$.

Therefore, the selected UAV nodes for transmission should consider the node centrality, remaining energy, and remaining cache. The selection criterion is

$$\begin{array}{ccc}\hfill \Phi & =& lg\left(a\times D_{\mathrm{Centrality}}+10\right)\times lg\left(b\times E_{\mathrm{rest}\_\mathrm{UAV}}\left(l\right)+10\right)\hfill \\ \hfill & \times & lg\left(c\times B_{\mathrm{rest}\_\mathrm{UAV}}\left(l\right)+10\right),\hfill \end{array}$$

(19)

where a, b, and c are the tuned parameters. In (19), logarithmic operations are performed to eliminate heteroscedasticity of tuned parameters. Additionally, the higher the value of $\Phi$, the better the forwarding performance to that node. A diagram of UAV-assisted information transmission is shown in Figure 3.

4. Performance Evaluation

4.1. Simulation Parameters

In this section, the performance of the proposed opportunistic transmission scheme is evaluated through simulation experiments. This paper compared it with three state-of-the-art schemes: (A) Scheme 1 [21]; (B) Scheme 2 [22]; (C) Scheme 3 [23]. The employed simulation software was the opportunistic network environment (ONE). The mobility model for UAVs and ICVs is the shortest path map-based movement (SPMBM) model [29]. The SPMBM model utilizes a “shortest path map”, a method from graph theory, to predict and optimize the movement paths between network nodes (i.e., UAVs and ICVs). Therefore, the movement of nodes in integrated UAV–ICV networks is not completely random but depends on the physical distances between nodes and the communication opportunities available. In this model, each node is equipped with the global positioning system (GPS). Additionally, each node is represented as a graph to denote its position within the network, and the shortest paths between each node and all other nodes are taken into account. In the simulations, we considered scenarios where UAVs and ICVs equipped with smart Wi-Fi devices communicate in a real urban environment. Moreover, this paper classified ICVs into three types based on their cooperation level. The ratio of type II nodes to type III nodes is 1:1. Furthermore, the UAVs were defined as non-selfish nodes. When any node encountered a non-selfish node, information could be transmitted directly without an interaction request. However, when interacting with selfish nodes, an interaction request was required.

The simulation scenario settings are shown in

Table 1. Simulation scenario settings.

Category	Parameter	Value
Scenario	Simulation Time	24 h
	Simulation Range	$50\mathrm{km}\times 50\mathrm{km}$
	Simulation City	Xi’an
Node	Transmission Mode	Wi-Fi
	Transmission Range of ICVs	200 m
	Transmission Range of UAVs	1500 m
	Movement Speed	$\left[30,70\right]$ km/h
	UAV/ICV Cache Size	50/150 MB
Message	Message Size	$\left[1,2\right]$ MB
	Message TTL	5 h
	Generation Frequency	$\left[1,20\right]$ min
Communication	Transmission Mechanism	OFDMA
	Channel Bandwidth	180 KHz
	Transmission Power	30 dBm
	Path Loss Model (ICV-UAV)	$32.44+20lg\left[d\left(\mathrm{km}\right)\right]+20lg\left[f_c\left(\mathrm{MHz}\right)\right]$
	Path Loss Model (ICV-ICV)	LoS in WINNER + B1 [30]
	Noise Power	$-174\mathrm{dBm}/\mathrm{Hz}$

. In Table 1, OFDMA and LoS are abbreviations for orthogonal frequency division multiple access and line-of-sight, respectively. It should be noted that, to ensure a fair comparison, the simulation settings not only considered the proposed scheme but also included the baseline mechanisms. This allowed us to evaluate the performance of the proposed scheme in relation to existing solutions under the same conditions, ensuring that the results were meaningful and comparable. Moreover, we used Open Street Map (OSM) to export real-world road data and integrated OSM with the event-driven simulator by using the osm2wkt.jar package and Open Jump. Furthermore, we employed an opportunistic multihop multiple access control (MAC) protocol, which enables nodes to take advantage of brief opportunities to exchange data while they are within transmission range of each other.

4.2. Simulation Results

In this section, the obtained results are based on the scenario described in Table 1; we focus on two metrics: delivery ratio and average delivery delay.

• Delivery Ratio: This metric is the most important for evaluating the opportunistic transmission scheme in integrated UAV–ICV networks. A higher delivery ratio indicates greater accuracy in information delivery by the scheme.
• Average Delivery Delay: This metric can assess the transmission ability of the opportunistic transmission scheme in integrated UAV–ICV networks. Smaller delays indicate higher ability and efficiency of the scheme.

4.2.1. Performance Comparison Under Different Proportions of Selfish Nodes

Figure 4 and Figure 5, respectively, present the delivery ratio and average delivery delay of each scheme under varying proportions of selfish nodes. The results indicate that as the proportion of selfish nodes increases, the performance of all opportunistic transmission schemes shows a declining trend. However, the proposed opportunistic transmission scheme for integrated UAV–ICV networks exhibits the smallest performance degradation. When the proportion of selfish nodes increases from 20% to 50%, the delivery ratios of the proposed scheme, Scheme 1, Scheme 2, and Scheme 3 decrease by 6.7%, 25.8%, 22.9%, and 15.1%, respectively. This demonstrates that the performance of the proposed scheme is more stable compared to that of the other three schemes.

When the proportion of selfish nodes is 50%, the delivery ratio of the proposed opportunistic transmission scheme is 1.72 times, 1.39 times, and 1.22 times higher than that of Scheme 1, Scheme 2, and Scheme 3, respectively. Additionally, its average delivery delay is only 77.3%, 82.3%, and 89.7% of that of these three schemes. Notably, this disparity becomes particularly evident when the proportion of selfish nodes is high. The primary reason for this is that the proposed scheme does not blindly transmit message copies during the initial information flooding and UAV-assisted information forwarding processes. Instead, it prioritizes nodes with higher cooperation levels for relay transmission. Furthermore, the proposed scheme fully considers the energy and cache size of nodes, effectively improving the delivery ratio and reducing the average delivery delay.

Based on the aforementioned findings, it is evident that in VDTNs, the average delivery delay frequently exceeds 1000 s, attributed to the dynamic characteristics of their operational environment. The reason is that integrated UAV–ICV networks are designed to handle intermittent connectivity and high mobility, where continuous communication cannot be guaranteed. Particularly, UAVs and ICVs are in constant motion, leading to frequent changes in the network topology and connectivity, which results in disconnections. VDTNs typically rely on “store-carry-forward” transmission mechanisms, where data are temporarily stored at relay nodes until a viable communication opportunity arises, at which point the data can be forwarded. Despite such high delays, VDTNs remain valuable in specific scenarios, where the timely delivery of information is not always critical, but ensuring high reliability and extensive coverage is critical. For example, VDTNs can be used in applications such as real-time traffic management and entertainment information services, where data can be delivered in a delayed manner but still provide valuable services to users. The main difference between VDTNs and traditional direct data transmission is that VDTNs do not require continuous end-to-end connectivity.

4.2.2. Impact of Different Node Cooperation Thresholds on Transmission Performance

Figure 6 and Figure 7, respectively, show the impact of different cooperation thresholds on the delivery ratio and average delivery delay under varying proportions of selfish nodes. The simulation results indicate that the delivery ratio and average delivery delay in integrated UAV–ICV networks are closely related to the cooperation threshold, exhibiting a trend of first increasing and then decreasing. Specifically, when the cooperation threshold is low, selfish nodes receive a large number of message copies from non-cooperative nodes. This leads to an inundation of message copies within integrated UAV–ICV networks, which in turn reduces the delivery ratio. Conversely, when the cooperation threshold is high, selfish nodes may refuse to receive message copies not only from non-cooperative nodes but also from cooperative nodes, which also results in a decrease in the delivery ratio. From the results in Figure 6 and Figure 7, it is evident that when the cooperation threshold is set at 0.6, the integrated UAV–ICV networks achieve a higher delivery ratio and a shorter average delivery delay.

In integrated UAV–ICV networks, since data transmission relies on opportunistic communications, the optimal cooperation threshold is difficult to express using a closed-form solution. Additionally, given that the network conditions are dynamic, the optimal cooperation threshold is not a fixed value and may vary over time. To address this, we conducted Monte Carlo simulations to explore the impact of different cooperation thresholds on transmission performance. While we analyzed a set of thresholds in Figure 6 and Figure 7, the optimal threshold may not be limited to just those values. Thus, the exploration of the optimal cooperation threshold is indeed an interesting topic for further investigation.

4.2.3. Impact of Different Number of Nodes on Transmission Performance

Figure 8 and Figure 9, respectively, illustrate the impact of the number of communication nodes on the delivery ratio and average delivery delay under varying proportions of selfish nodes. The results demonstrate that the delivery ratio is positively correlated with the number of nodes. As the number of nodes increases, the delivery ratio rises, while the average delivery delay decreases. With a cooperation threshold of 0.2, the delivery ratio is lower, and the average delivery delay is larger. This occurs because nodes with lower cooperation levels are selected for relay during the initial flooding process, hindering rapid delivery to the destination node and causing significant packet loss.

In contrast, with a cooperation threshold of 0.8, the delivery ratio is higher, as nodes with higher cooperation levels are chosen for each relay transmission. However, due to the opportunistic transmission mechanism in integrated UAV–ICV networks, the type of communication nodes encountered is highly uncertain. Under this condition, using a higher cooperation threshold necessitates waiting for nodes with higher cooperation levels for relay transmission, thereby increasing the average delivery delay. Therefore, it is essential to elaborately set a reasonable cooperation threshold to enhance transmission performance.

5. Conclusions

In VDTNs, the selfishness of communication nodes leads to relay nodes refusing to receive message copies from non-cooperative nodes, thereby reducing network performance. Although traditional incentive schemes promote cooperation among nodes, they result in high-resource consumption by non-selfish nodes with high centrality, which also decreases network performance. Motivated by the above, we investigated the opportunistic transmission problem in integrated UAV–ICV networks. By using the “store-carry-forward” transmission mechanism, an opportunistic transmission scheme for integrated UAV–ICV networks, enabled by node cooperation, was proposed. According to the selfish behavior of nodes in the actual use scenario, the cooperation type and encounter probability of nodes were modeled and analyzed. Then, by jointly considering the node centrality, energy consumption, and cache size, information was initially flooded and transmitted with the assistance of UAVs. Finally, this paper performed simulations using real maps to evaluate the performance of the proposed opportunistic transmission scheme. It was observed that compared to state-of-the-art schemes, the delivery ratio was improved, and the average delivery delay was reduced. Additionally, the influence of network parameters (e.g., the proportion of selfish nodes, cooperation thresholds, and number of nodes) on the delivery ratio and average delivery delay was fully demonstrated.

In addition to the issues outlined in the previous sections, numerous research issues warrant further exploration. First, this paper assumed that the communication range and rate for integrated UAV–ICV networks are fixed. However, in actual vehicular networks, the communication range and rate dynamically change with environmental factors such as building density, power, and spectrum. In future work, it is necessary to combine our previous work [14] to further optimize the transmission mechanism and improve network performance. Additionally, this paper sets the mobility model for both UAVs and ICVs based on the SPMBM model using the Dijkstra algorithm. However, the movement of UAVs should theoretically be constrained by regulations. Meanwhile, the mobility of ICVs is influenced by social attributes, and the mobility model should not be singular. Thus, we can further explore the impact of mobility models on the delivery ratio and average delivery delay. Nevertheless, the opportunistic transmission scheme proposed in this paper offers important insights and points out a promising direction for the design of relay selection protocols in the presence of selfish nodes within integrated UAV–ICV networks.