A New Hybrid Hierarchical Roadside Unit Deployment Scheme Combined with Parking Cars

Abstract

This paper proposes a new hybrid hierarchical roadside unit (RSU) deployment algorithm that combines traditional RSU deployment strategies with temporary RSUs (t-RSUs) selected from many parked vehicles. The driving vehicles in the corresponding RSU coverage section are divided into clusters and the demand is thus summarized. We first solve the problem of how to choose the appropriate cars serving as t-RSUs and then optimize the RSU deployment with the dynamic existing t-RSUs. We simulate the deployment application in a downtown area of Shanghai, China, using the simulation of urban mobility (SUMO), version 1.11.0, an open-source traffic simulation package, and its traffic-control interface (TraCI) with Python. The simulation results show that, within a given economic cost, the proposed hybrid hierarchical RSU deployment algorithm outperforms the maximum vehicle coverage deployment algorithm (MVCD) and the random deployment algorithm (RandDeploy) in terms of overall vehicle coverage and point-to-point vehicle connectivity ratio. Our scheme provides new solutions and ideas for the deployment of RSUs in future urban traffic environments.

1. Introduction

As one of the most promising technologies in intelligent transportation systems [1], vehicular ad hoc networks (VANETs) play a crucial role in driving assistance, traffic accident warnings, traffic management, and internet services. VANETs are a specialized form of mobile ad hoc networks (MANETs) in the transportation field [2]. The basic communication forms of VANETs are mainly vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I). V2V communication facilitates the exchange of information such as road congestion and traffic accidents among vehicles. However, the high density of nodes and their high-speed movements can negatively affect the information transmission capabilities of VANETs, resulting in increased packet loss and delays. Roadside units (RSUs) can mitigate these issues; however, the installation and maintenance costs of RSUs are substantial. Therefore, devising an applicable and effective RSU deployment strategy is imperative, particularly for urban areas. To this end, it is essential to introduce the new concept of “t-RSUs”, which refers to using parked cars as temporary RSUs (t-RSUs), as illustrated in Figure 1.

Figure 1 depicts a scene where parked cars along the roads form a mesh network automatically, which can be utilized as t-RSUs. The working mechanism of the t-RSU deployment scheme based on V2V and V2I connections in a VANET environment with t-RSUs can certainly solve the dilemma of difficult and complex radio signal attenuation due to buildings and other obstacles by enhancing the signal strength in those areas. In the research scenario, it is assumed that all communication terminals of mixed traffic flow are uniformly connected to the traffic information network. To better achieve the goal of serving users and improving the connectivity of the network, roadside units are used to assist in achieving efficient communication in the VANET. Then, the connectivity problem in the urban traffic information transmission network needs to be solved. To enable each vehicle user to access the traffic information network to the greatest extent, under the existing RSU equipment layout conditions, the connectivity of all vehicles needs to be maximized, and a practical roadside unit deployment scheme is required for roads in urban areas.

2. Related Work

The conventional RSU deployment schemes mainly focus on network connectivity, traffic coverage, and information dissemination. Early in 2008, Lochert et al. proposed a genetic algorithm that was able to find good positions for static RSUs in order to cope with the highly partitioned nature of a VANET in an early deployment stage [3]. In 2010, O. Trullols et al. considered a given number of infrastructure nodes (called Dissemination Points, DPs) to be deployed for disseminating information to vehicles in an urban area, formulating the problem as a Maximum Coverage Problem (MCP) [4]. In 2013, Barrachina et al. proposed a density-based roadside unit deployment policy (D-RSU) specifically designed to create an efficient system with the lowest possible cost to alert emergency services in the case of an accident. This was based on deploying RSUs in inverse proportion to the expected density of vehicles [5].

Gao et al. [6] proposed an RSU deployment scheme that focuses on the one-dimensional RSU deployment problem. The results of their greedy algorithm typically yield solutions close to the optimal. In view of the deployment cost of RSUs and the low market penetration of VANETs, Liu et al. aimed to deploy a minimum number of RSUs [7]. Silva et al. [8] introduced a heuristic algorithm based on Greedy Randomized Adaptive Search Procedure 2-multi-hop (GRASP2MH) to deploy a minimum number of RSUs to meet quality of service (QoS) requirements. Yang et al. addressed the problem of the RSU deployment scheme with constraints on delay and cost [9]. They first transformed the road network diagram into a weighted graph and then formulated the problem as a variant of the 0–1 knapsack problem. Mokhtari et al. introduced a new RSU deployment strategy that is more efficient by increasing V2I access opportunities compared with the simple use of the 0-1 knapsack algorithm [10]. Moura et al. proposed an approach that enhances vehicles’ connectivity coverage threshold time in VANETs across different traffic scenarios by integrating betweenness centrality preprocessing, community detection, and efficient search space reduction techniques [11]. Jiang et al. [12] highlighted that even with sparsely distributed roadside units, effective traffic predictions can be achieved by placing RSUs strategically, considering communication ranges and penetration rates of connected vehicles, and optimizing the deployment strategy. All those RSU deployment schemes mentioned above are constrained with the precondition that the parked cars are not utilized to act as temporary roadside units. Moreover, Silva et al. propose two new deployment strategies for RSUs in intelligent transportation systems: Gamma Deployment and Gamma-Reload Deployment, aiming to optimize the deployment of RSUs for delivering streaming content to connected vehicles, ensuring that a specific share of vehicles periodically encounter the communication infrastructure within a given time threshold [13]. Feng et al. have developed a comprehensive mathematical model that captures the essential elements of RSU deployment, including network, communication, and computation. Their proposed solution aligns with the specific communication requirements of road vehicles [14]. In fact, as early as 2011, Liu et al. first proposed the idea that the parked cars join VANETs as static nodes, assisting to improve connectivity [15]. Later, in 2014, Sommer et al. addressed the challenges of radio signal attenuation caused by buildings and other obstacles, proposing that parked cars are a means to mitigate these issues [16]. In 2017, B. Reis et al. introduced a self-organizing network approach allowing parked cars to function as RSUs, forming a vehicular support network [17]. Furthermore, recently, they further introduced a new approach for parked car self-organization, which advances existing techniques in several ways; the proposed mechanisms optimize networks of parked cars beyond their initial grouping, which leads to a more efficient selection of cars to act as RSUs [18].

Inspired by all the conventional and new concepts mentioned above, we propose a new hybrid hierarchical deployment scheme for roadside units incorporating parked cars as temporary roadside units for VANETs. In our approach, we first solve the problem of how to choose the appropriate cars serving as temporary RSUs. We then optimize the deployment of RSUs by considering the dynamic nature of temporary RSUs, which requires sufficient connectivity robustness.

3. Backgrounds

In this section, a new layered hybrid roadside unit deployment scheme is proposed, which introduces the idea of using the parked car as the temporary roadside unit t-RSU of VANET in the new concept.

Mobile Mode Analysis for Traffic Multi-Agent

For the mixed traffic flow, Zeng et al. [19] have already explained the concept of which components are the various categories of vehicles. Zhao et al. consider the design of a real-time cooperative eco-driving strategy for a group of vehicles with mixed automated vehicles (AVs) and human-driven vehicles (HVs), proposing a receding horizon model predictive control (MPC) method to minimize the fuel consumption for platoons and drive the platoons to pass the intersection on a green phase [20]. To better integrate ITS into a whole, first, it is necessary to analyze and summarize the information characteristics of the user side, as shown in Figure 2.

Figure 2 illustrates a mixed vehicle traffic flow consisting of trams, ordinary vehicles, and autonomous vehicles, where ordinary vehicles and autonomous vehicles can be divided into communication with the RSU and no communication. The wireless network provided by RSU can provide communication services for many mobile users. Different types of vehicles communicate with the RSU through a wireless link, forming multiple mobile units, and all RSUs are connected by high-speed wired Ethernet. Vehicles in the RSU coverage area can use V2I communication to communicate with the RSU, while vehicles outside the RSU coverage area can forward information with V2V communication of other vehicles. The movement pattern of different vehicles in mixed traffic flow is an important factor affecting the design of urban traffic-communication systems.

For the proposed layered hybrid roadside unit deployment scheme with t-RSU, the problem of how to select the appropriate vehicle as t-RSU is first addressed. Then, the existing t-RSU is dynamically updated. Since t-RSUs are not always static and the number and location of parked vehicles may change over time, sufficient connection robustness is required in this case.

4. Scenario Description and Basic Definition

4.1. The Concept of the t-RSU and Its Mechanism

The U.S. Department of Transportation (DoT) was expected to deploy roadside infrastructure nationwide in 2008 but was impeded due to the lack of cooperation, funding, etc. Therefore, when it comes to the RSUs’ deployment, it is of great necessity to take the RSUs’ installation cost into consideration. Actually, we have proposed a connectivity-oriented maximum coverage RSU deployment scheme (CMCS) aiming to maximize the V2I communication performance in 2015 [21]. However, the notion of making the parked cars as temporary RSUs is not taken into consideration.

In this research, we have systematically integrated an appropriate temporary RSU strategy with the CMCS. Hereinafter, we call the parked cars that are functioning the character of temporary RSU as t-RSU. The hybrid hierarchical roadside unit deployment scheme is divided into two parts: (1) For a specific parked car in a fixed area, whether it will serve the role as the t-RSU is determined by its coverage area, the existing coverage area (ECA) and whether it brings new coverage area or redundant coverage area (RCA). The areas of a single car are divided into many cells and the number of the cells is decided by the maximum transmission range of the parked cars, and the SCA represents the self-coverage area of the parked car. (2) We then optimize the deployment of the RSUs and the t-RSUs. The proposed RSU deployment scheme aims at maximizing the RSU connectivity while ensuring that the total installation cost does not exceed a given cost (referred to as $C$ hereafter).

Figure 3 gives a detailed description of the formation of t-RSU and SCA, ECA, and RCA. The green part of the graph indicates the coverage ECA of the existing t-RSU. The mixed color part represents the overlapping coverage area RCA of the current parked vehicle and the t-RSU. The white part represents the communication coverage SCA of the existing vehicle. For a specific parked vehicle in a fixed area, whether it can play the role of t-RSU depends on its coverage area, i.e., the existing coverage area and whether it brings a new coverage area or redundant coverage area.

We assume that the batteries of parked cars are energy-free for providing temporary RSU services. In fact, a typical IEEE 802.11p on-board unit (OBU) will not drain more than 1 W on average, which is a very generous upper limit. Considering that a small car’s battery provides 480 Wh to 840 Wh [22], the temporary RSU service can last for about 20 days under the circumstances of fully draining the battery. All the VANET vehicles are assumed to have the same maximum transmission range. To make the t-RSU work in a relatively fixed place, which is of great necessity for the afterward RSU’s installation deployment, it is necessary to give a detailed standard for choosing the candidate parking place. The candidate parking place may contain lots of parked cars. Before starting, the parking place is partitioned into many parts that here are defined by the vehicle’s 2-hop maximum transmission range.

For cooperative awareness applications (CAM), the European Telecommunications Standards Institute (ETSI) suggests that CAM messages at fixed broadcasting frequencies be in the range of 1 Hz to 20 Hz [23]. For energy-saving purposes, 1 Hz is used for the frequency of updating the information between the parks and the t-RSU in a single partition. A self-organizing method is here proposed by making the sleeping parked cars wake up regularly and listen to the IEEE 802.11p control channels (CCH) so that they can react to the changing situations in a parking area. While it is possible to obtain an optimized strategy result given complete geographic parking information, it is often impractical due to the huge computation cost. Another reason is that the states of the parking cars are dynamic and the constantly changing parking information. To solve the problem, we can use the online algorithm to make every single tiny area constrained by a parked car’s 2-hop transmission range be in a locally optimum state.

In Figure 4, we give the detailed process of the online algorithm which enables a practical implementation for the limited computation resources circumstance. After implementing the online algorithm for every single parking lot simultaneously in a distributed manner, it is crucial to set the strict candidate t-RSU area selection strategy that ensures the RSU functions effectively as a real RSU in the real world. The candidate t-RSU area selection strategy is simple but strict: First, the entire parking area is at least parked with one car for over 95% of the duration a day, a condition that can be investigated through a detailed transportation survey. Second, the parking area is located along the roadside on the ground.

The algorithm to calculate the exact score for determining whether the specific parked car should serve as t-RSU is shown in Algorithm 1.

Algorithm 1: t-RSU Score

Input: $SCA=\left\{sc{a}_1,sc{a}_2\dots sc{a}_n\right\},ECA=\left\{ec{a}_1,ec{a}_2\dots ec{a}_n\right\}$$, S\left(RCA\right)$ Output: the outcome score of weighted S(SCA, ECA), S(RCA) $\mathrm{Set} S\left(SCA, ECA\right)$$, S\left(RCA\right)$ as 0 $\hspace{1em} \mathbf{for} \mathrm{each} sc{a}_i$$\mathrm{in} \left\{sc{a}_1,sc{a}_2\dots sc{a}_n\right\}$ do $\hspace{1em}\hspace{1em}\hspace{1em} \mathbf{if} ec{a}_i<sc{a}_i$$\mathrm{and} sc{a}_i$$\mathrm{has} \mathrm{overlap} \mathrm{with} ec{a}_i$ then $\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} S\left(SCA,ECA\right)=S\left(SCA,ECA\right)+\left(sc{a}_i-overlap\left(sc{a}_i,ec{a}_i\right)\right)$       End $\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} S\left(RCA\right)=S\left(RCA\right)+overlap\left(sc{a}_i,ec{a}_i\right)$     End $Score=w_1·S\left(SCA,ECA\right)-w_2·S\left(RCA\right)$

Detailed explanations of the parameters shown in Algorithm 1 are given below:

• SCA represents the self-coverage area of the parked car, and $sc{a}_1,sc{a}_2\dots sc{a}_n$ are the $n$ partitions of the self-coverage area.
• ECA is the existing coverage area covered by other temporary t-RSUs; $ec{a}_1,ec{a}_2\dots ec{a}_n$ are the $n$ partitions of the temporary coverage area.
• RCA is the redundant area that overlaps between the currently parked car and other temporary t-RSUs. Meanwhile, since the overlapped area is 3D in the real world (due to the existence of underground and above-ground garages), here we use $overlap\left(sc{a}_i,ec{a}_i\right)$ for calculating it by projecting the area in the 2D map.
• $w_1$ and $w_2$ are the coefficients for the S(SCA, ECA) and S(RCA), respectively, which can be used to determine the score and set the threshold for whether a new parked car should become a t-RSU.

Algorithm 1 presents the pseudo-code to calculate the score for determining whether a single parked vehicle can function as a t-RSU. It quantitatively calculates the influence of each variable and outputs a score. If the score is positive, the parked vehicle is designated as a t-RSU. Otherwise, it is not.

In fact, concerning the real world, from an intuitive perspective, the distribution of parking lots is highly relevant to the prosperity of the district in a city. The central districts’ parking lots density is higher than the remote districts since there are more cars in the central rather than the remote. Though it is hard to compute the optimized strategy result of the entire city with all the data centralized at the same time, we can certainly solve this problem in a distributed manner. Furthermore, all the algorithms proposed above are just for calculating whether a specific area is with “a constant t-RSU” quantitively. For the future RSU installation deployment, we take multiple parked cars in the parking area and classify them into different clusters. Since we have already taken the parked cars’ two-hop maximum transmission range for a single partition in a given area, this strategy automatically forms a mesh network cluster. Furthermore, we can calculate the cluster’s score changing with the time quantitively, as shown in Equation (1):

$$S\left(cluste{r}_k,t\right)={{\displaystyle \sum }}_{j=1}^{m}Scor{e}_{j,t}$$

(1)

where $j=1\dots m$; $j$ is the sequence number of the parked cars in the given cluster, and m is the parked car’s total number for the current second. The subscript $t$ indicates that the score represents the cluster’s state at the current second, given that we set the updating frequency as 1 Hz. The subscript $k$ means the sequence number for the cluster, thanks to the fact that there are many clusters in an area. The cluster’s score can represent the current mesh network’s working status. To step further, with the appropriate threshold for a single parked car, the cluster can provide a networking service in a much bigger range and better quality with many t-RSUs working at the same time. The relatively fixed cluster can, therefore, be treated as a huge unconventional t-RSU.

So far, the first part of our proposed hybrid hierarchical roadside unit deployment scheme has been accomplished. The second part is naturally transferred into an optimization problem within an area with already-existing fixed unconventional “huge t-RSUs” distributed in different coordinates of the given area.

4.2. Optimize RSUs Deployment with Already-Existing t-RSUs

In this section, the main problem lies in how to make the RSUs to be deployed maximize the RSU connectivity and the number of covered vehicles with the constraints of limited cost. When the cars equipped with OBUs are running on the roads, maximizing the connectivity for all of them is the most important issue. First, we divide the running cars on the links or roads into many clusters, which is defined by Equation (2):

$$Cluste{r}_i=\left[{\displaystyle \frac{L_i}{R}}\right]$$

(2)

where $i$ refers to the identification (ID) of different roads. $L$ is the length of the road. R is the average communication range of all the vehicles equipped with OBUs. The notation $\left[·\right]$ denotes rounding the value up to the nearest integer. $Cluste{r}_i$ means the number of clusters for a given road $i$, as shown in Figure 5.

Figure 5 gives a schematic diagram of the cluster and its connectivity. By calculating the number of clusters, the internal connectivity of the cluster is further analyzed. After calculating the cluster numbers of a road, the intra- and inter-cluster connectivity are thus to be analyzed.

$$Intra\_R_{i,k}={\displaystyle \frac{{{\displaystyle \sum }}_{m=n+1}^{N_{i,k}}{{\displaystyle \sum }}_{n=0}^{N_{i,k}-1}{R}_{m,n}}{C_{N_{i,k}}^2}}={\displaystyle \frac{{{\displaystyle \sum }}_{m=n+1}^{N_{i,k}}{{\displaystyle \sum }}_{n=0}^{N_{i,k}-1}{R}_{m,n}}{\frac{N_{i,k}·\left(N_{i,k}-1\right)}{2}}}=r-{\displaystyle \frac{{{\displaystyle \sum }}_{m=n+1}^{N_{i,k}}{{\displaystyle \sum }}_{n=0}^{N_{i,k}-1}{d}_{m,n}}{\frac{N_{i,k}·\left(N_{i,k}-1\right)}{2}}}$$

(3)

where $Intra\_R_{i,k}$ means the intra-connectivity for cluster $k$ in road $i$; $R_{m,n}$ is the path robustness between vehicle $m$ and $n$; $d_{m,n}$ refers to the Euclidean distance between vehicle $m$ and vehicle $n$; $\min \left(r_m,r_n\right)$ equals the minimum transmission range between vehicle $m$ and vehicle $n$; $N_{i,k}$ means the total number of vehicles for cluster $k$ in road $i$. For Equation (3), since the transmission ranges of all the vehicles are exactly the same which has been assumed before, $\min \left(r_m,r_n\right)$ equals to $r$. It can be easily obtained from the above equation that the robustness of a single cluster ranges from 0 to $r$.

For inter-cluster connectivity robustness, the circumstance becomes more complex due to the potential presence of varying numbers of t-RSU clusters (which could range from none to many) among the clusters. Thanks to the special conditions described above, it is necessary to design an appropriate strategy for solving this problem. First, we think about the fundamental circumstance. When it comes to the two adjusted clusters, we must check if there are t-RSU clusters existing between them or connecting them thus making them be in a larger and new cluster. In that way, then take them as a whole, i.e., a new cluster. We would apply this strategy until there are no t-RSU clusters existing between them or connecting them. If there are no other t-RSU clusters, then we begin to calculate the inter-cluster connectivity robustness. The inter-cluster robustness is defined as the transmission range minus the maximum Euclidean distance projected over a $\pi$ or $-\pi$ degree motion angle between the vehicle from one cluster and the vehicle from the adjacent cluster. In that way, it is easy to conclude that the bigger the new cluster is, the inter-cluster robustness is probably smaller and probably negative. Furthermore, if the two clusters are both initial ones without expansion, the inter-cluster robustness value range is $\left[-r,r\right]$. The formula is given in Equation (4):

$$Inte{r}_{\_}R=\min \left(r_m,r_n\right)-\max P_{\mathrm{roj}}\left(Ed\left(Ve{h}_m,Ve{h}_n\right)\right)=r-\max P_{\mathrm{roj}}\left(Ed\left(Ve{h}_m,Ve{h}_n\right)\right)$$

(4)

where $Inte{r}_{\_}R$ refers to the inter-cluster robustness. $\min \left(r_m,r_n\right)$ means the minimum vehicle transmission range in the two adjacent clusters, which equals $r$. $m$ and $n$ denote the vehicle ID in the two adjacent clusters, respectively. $P_{\mathrm{roj}}$ represents the projection. $Ed$ refers to the Euclidean distance; $Veh$ means vehicle. After modeling the robustness of the intra-cluster and inter-cluster, the next step is to establish the RSU deployment strategy. Within a given cost $C$, the number of the RSUs is set. Since the maintenance cost and the installation cost are relatively certain, here we assume them as constant. The total number of the RSUs to be deployed is calculated in Equation (5):

$$N=\left[{\displaystyle \frac{C}{C_m+C_i}}\right]$$

(5)

where $N$ is the maximum number of RSUs that can be deployed within the given cost. The notation [∙] denotes rounding down the value to the nearest integer. $C_m$ and $C_i$ refer to the maintenance cost and installation cost, respectively.

RSU deployment strategy is now based on how to find the strongest connectivity robustness path and covering the most vehicles for an observation time among those given N number of RSUs to be deployed. First, still starting from the simplest and most fundamental circumstance, the connectivity robustness between two RSUs is considered. For the specific RSU and another RSU, the path with the strongest robustness is calculated according to the formula in Equation (6):

$$Pat{h}_{\_}R={{\displaystyle \sum }}_{k\in R_{\mathrm{s}}}\min {\{Intr{a}_{\_}{R}_i,Inte{r}_{\_}{R}_{i,i+1}\}}_k$$

(6)

where $Pat{h}_{\_}R$ means the robustness of the path from one RSU to another with the strongest robustness. $R_{\mathrm{s}}$ is the set of the path with the strongest robustness. $i$ and $k$ refer to the ID of the cluster and road, respectively. $\min \{Intr{a}_{\_}{R}_i,Inte{r}_{\_}{R}_{i,i+1}\}$ represents a single road’s robustness since a road’s robustness is determined by its minimum intra-cluster and inter-cluster robustness.

For an observation time T, the average number of vehicles on a specific road or the path from one RSU to another with the strongest connectivity robustness can be obtained. Therefore, finally, the RSU deployment strategy is given by the following formula in Equation (7):

$$\left\{\begin{array}{c}\max {\displaystyle \sum }_{road=1}^{m}Num\left(road\right)·Boo{l}_{road}\\ \max {\displaystyle \sum }_{rsu=1}^{n}C\left(rsu\right)·Boo{l}_{rsu}\\ {\displaystyle \sum }_{rsu=1}^{n}Boo{l}_{rsu}\le N\end{array}\right.$$

(7)

where $Num\left(road\right)$ means the average number of vehicles during the observation time on the given road. $Boo{l}_{rsu}$ and $Boo{l}_{road}$ determine whether the RSU or road is selected with their values being either 0 or 1. $C\left(rsu\right)$ refers to the average connectivity robustness of an RSU with other RSUs. ${\displaystyle \sum }_{rsu=1}^{n}Boo{l}_{rsu}$ refers to the total number of RSUs to be deployed. It should be noted that to achieve the maximum average connectivity robustness and the highest average number of vehicles on the road for a given observation duration, it can be concluded that the sum ${\displaystyle \sum }_{rsu=1}^{n}Boo{l}_{rsu}$ should be set to $N$.

Branch and Bound Algorithm

The above problem is a multi-objective optimization problem. The proposed multi-objective problem can be transformed into a single-objective optimization problem and then solved by the branch and bound algorithm [24,25]. The algorithm flow is shown in Figure 6:

Figure 6 describes the flow of the branch and bound algorithm. The algorithm uses block calculation to exhaustively block the feasible solution of the problem until the algorithm obtains the optimal solution. A detailed description of the branch and bound method is shown in

Table 1. Branch and bound algorithm steps.

Step	Description
Step 1	If the problem is to minimize the solution, the current optimal solution is set as $\infty$.
Step 2	According to the branch rule, a node is selected from the nodes that have not been searched at present, and it is divided into several new nodes in the next level of the node.
Step 3	Calculate the lower limit of each new branch node.
Step 4	If either of the following conditions is satisfied, it is not considered: 1. The node does not contain a feasible solution. 2. The lower limit of the node is greater than or equal to the current A value. 3. If a feasible solution with a minimum lower limit value in the node is found, it is necessary to further compare the feasible solution with the current A value. If the latter is small, it needs to be discarded.
Step 5	Determine whether there are nodes that have not yet been searched. If there are, step 2 is performed. If not, the calculation is stopped, and the optimal solution is obtained.

.

As shown in Table 1, the detailed process of the branch and bound algorithm is divided into five steps. After obtaining the optimal solution of the model, the simulation software OpenStreetMap and SUMO (version 1.11.0) [26] are used to verify the above calculation results.

5. Simulation Analyses and Results

5.1. Simulation Analyses

The experimental simulation software is built on the following hardware configuration: AMD Ryzen 7 1800X Eight-Core Processor 3.60 GHz CPU processor (AMD, Santa Clara, CA, USA), Ubuntu 20.04 operating system, 8 GB RAM, NVIDIA GeForce GTX 1060 6 GB graphics processor (NVIDIA, Santa Clara, CA, USA). In the simulation, a 3D map of the real-world road network is obtained from OpenStreetMap and projected onto a 2D plane using the standard WGS84 coordinate system. SUMO is employed to simulate real traffic scenes with parked vehicles, which are considered to be t-RSUs. In this section, the simulations that are conducted using OpenStreetMap and SUMO (version 1.11.0) with its interface TraCI interacted with Python are described.

The simulations use a 1.91 km by 2.01 km real-world road topology from the area around Nenjiang Road, which is located at the Wujiaochang area of Jiangwan, Yangpu District, Shanghai, the downtown area of Shanghai, China. The parameters in the SUMO simulator (verison 1.11.10) are shown in

Table 2. Parameters of Simulation.

Parameter	Value
Density of Vehicles (veh/km2)	37.5, 112.5, 187.5
Total Given Cost	5 units
Simulated Area	Downtown area of Shanghai, China
Communication Range	100 m, 300 m, 500 m
Traffic Data Source	Historical traffic data in Shanghai
Car-Following Model	CarFollowingModel-Krauss [27]
Lane-Changing Model	LC2013 [28]

.

In the simulation, considering a confined geographical region, vehicles are entering and leaving the region continuously and the RSUs can be deployed at any position along the roads. Meanwhile, it is assumed that all drivers use the fastest routes through the network using the Djikstra routing algorithm. During the simulation, we compare our deployment algorithm with two other algorithms: the Random Deployment algorithm (RandDeploy) and the Maximum Vehicle Coverage Deployment (MVCD) algorithm. The RandDeploy algorithm randomly selects a vertex in a road network until the set visiting probability (SVP) of all the vertices to the result set meets or exceeds a predefined threshold [29]. The MVCD algorithm employs a greedy algorithm to maximize the coverage area of vehicles within the given cost, which consequently often leads to the inclination to deploy the RSUs in the intersections. Both the RandDeploy and MVCD are conventional algorithms and do not include the procedure of choosing the candidate virtual t-RSUs. To evaluate the performance of the hybrid hierarchical RSU deployment scheme with parked cars as t-RSUs against the other two deployment strategies, a critical cost constraint of 5 RSU units is applied. Furthermore, the three different vehicle densities in the given area represent the typical low, median, and high vehicle densities, respectively. The low density represents the vehicle at nighttime, while the median and density reflect the density during usual and peak hours in the daytime, respectively.

The paper uses the following evaluation metrics:

• Vehicle coverage ratio, which is the ratio between the total number of vehicles that come in contact with the RSUs or t-RSUs and the total number of vehicles in the confined area.
• Point-to-point connectivity, which is the reflection of the reachability between two random positions in the area.

5.2. Results

After the simulation in SUMO interacting with Python using traCI, the RSU deployment is calculated. Figure 7 shows the RSU deployment under the transmission range of 500 m, where the yellow dots represent the t-RSUs and the red dot represents the real RSU.

What can be obviously seen from Figure 7 is that the total number of RSUs (whether t-RSU or real RSUs) in (a) is larger than in (b) and (c), where half for t-RSUs and half for real RSUs. It seems unfair for the MVCP and RandDeploy under the circumstances without any assistance from t-RSUs. Therefore, it could be predicted that the t-RSUs would play a vital role in undertaking the responsibility of transmission in the near future. The vehicle coverage ratio given in Figure 8 describes the excellent performance with parked cars serving as t-RSUs in detail.

Figure 8a–c represent the vehicle coverage under the RSU information transmission range of 100 m, 300 m, and 500 m, respectively. It can be seen that due to the help of t-RSU, our algorithm significantly outperforms the MVCD and RandDeploy algorithms in terms of vehicle coverage under the three RSU information transmission ranges. Taking the RSU information transmission distance of 100 m as an example, when the vehicle density is 112.5 vehicles/km² and 187.5 vehicles/km², the vehicle coverage rate of the proposed hybrid layered roadside unit deployment algorithm for activating t-RSU is 22.40% and 24.66% higher than that of MVCD, respectively. Compared with RandDeploy, the vehicle coverage of the proposed hybrid layered roadside unit deployment algorithm for activating t-RSU is increased by 25.12% and 25.6%, respectively. In addition, three different vehicle densities in the simulation area represent typical low, medium, and high vehicle densities, respectively. Low density can represent the density of driving vehicles at night, while medium and high density can reflect the density of driving vehicles during usual and peak hours during the day, respectively. At the same time, for Figure 8a,b, when the RSU information transmission distance is 100 m and 300 m, respectively, the vehicle coverage of MVCD and RandDeploy decreases with the increase of vehicle density. This phenomenon is contrary to the intuitive impression because the number of RSUs deployed is insufficient to cover the given area. Specifically, when the vehicle density is low, coincidentally, most vehicles are located within the transmission range of the RSU of the RSU.

When the vehicle density is medium and high, the situation begins to change because the road network is large (relative to the transmission range of 100 m and 300 m), and more vehicles exceed the information transmission coverage of the deployed RSU. With the help of t-RSU, this phenomenon is not obvious in the hybrid layered RSU deployment scheme. However, for the RSU information transmission coverage of 500 m, as the vehicle density increases, the vehicle coverage also increases. In this case, the transmission range is larger than the entire road area, so the deployed RSU can cover most of the area of a given simulation road.

The RSU information transmission range is set to 100 m, 300 m, and 500 m, respectively. For the three algorithms, the connectivity ratio between vehicle points is further compared. The results are shown in Figure 9.

Figure 9a–c represent the vehicle point-to-point connectivity ratios of the three algorithms under different vehicle densities in the three RSU information transmission ranges of 100 m, 300 m, and 500 m, respectively. In general, as the vehicle density increases, the connectivity ratio also increases. When the RSU information transmission distance is 100 m, and the vehicle density is low, with the help of t-RSU, the point-to-point vehicle connectivity ratio of the proposed hybrid layered RSU deployment scheme still reaches more than 50%, which shows excellent performance in the three deployment algorithms. Taking the RSU information transmission distance of 300 m and the vehicle density of 112.5 vehicles/km² as an example, compared with the MVCD and RandDeploy deployment algorithms, the proposed algorithm improves the vehicle point-to-point connectivity ratio by 30.85% and 33.27%, respectively. However, when the RSU information transmission distance is 300 m, and the vehicle density is 187.5 vehicles/km², the difference in the vehicle point-to-point connectivity ratio of the three algorithms is very small. Especially when the RSU information transmission range is 500 m, there is almost no difference in the vehicle point-to-point connectivity ratio of the three algorithms. At this time, the connectivity ratio of the three algorithms is close to 1, indicating that the network in this area is basically in full coverage. In addition, another phenomenon that is inconsistent with the intuitive view is that when the RSU information transmission distance is 100 m and 300 m, and the vehicle density is low density and medium density, as the vehicle density increases, the connectivity ratio even decreases slightly. This may be because the vehicle density of the entire road network is unsaturated, which makes the vehicle distribution sparse so that the connectivity rate is very small or even lower.

6. Conclusions and Future Work

6.1. Conclusions

This article proposes a new hybrid hierarchical RSU deployment algorithm for roadside unit deployment. The algorithm introduces a novel hybrid RSU deployment model that combines the traditional RSU deployment strategy with the strict selection rules on candidate t-RSUs chosen from multiple parking cars using an online algorithm. The concept of combining the candidate parking cars as temporary RSUs is first proposed, which contributes to saving RSU resources and improving network connectivity and vehicle coverage. The driving vehicles in the corresponding RSU coverage section are divided into clusters and summarized. The simulation results demonstrate that the hybrid deployment strategy, thanks to the use of t-RSUs, significantly outperforms the other two conventional deployment strategies (i.e., RandDeploy and MVCD algorithms) in terms of vehicle coverage ratio and point-to-point connectivity within given costs. For instance, when the transmission range is 100 m, the vehicle coverage ratio in the proposed model improves by 69.81% and 92.5% compared to the RandDeploy algorithm at median and high vehicle densities, respectively. Regarding the connectivity ratio, even at low density in a 100-m transmission range, the proposed deployment scheme achieves a connectivity ratio of over 50% with the assistance of the t-RSUs, demonstrating the best performance among the three deployment methods. The proposed scheme provides a new solution and idea for the future deployment of RSU in urban traffic environments.

6.2. Future Works

More detailed work about how to quantitively simulate the effects of building occlusion on the VANETs would also be conducted. Moreover, the continuing work would further focus on trying to develop an efficient geo-position-based routing protocol for VANETs, since the traditional protocols, especially topology-based routing protocols, are not working so well in the VANETs. Furthermore, 5G communication technology would also bring enormous change for the VANETs, in which case the evolution may just be occurring.