Title the Chews First Delaunay Triangulation refinement Scheme-based positioning of RSUs for optimal network coverage in VANETs

: The temporal network fragmentation and uncertain vehicle mobility are considered to impact the communication connectivity among the vehicular nodes of the network. In this context, Road Side Units (RSUs) play an anchor role in enhancing the vehicle-to-vehicle (V2V) communication connectivity and support Vehicle-to-Infrastructure (V2I) communication. In the current scenario, deploying a huge number of RSUs in the vehicular networks at an initial stage is completely impossible as it incurs high installation cost and authority restriction. Moreover, the optimal placement of RSUs in the vehicular network needs to be enforced for attaining maximized network coverage. In this paper, Chews First Delaunay Triangulation Refinement Scheme (CFDTRS) is proposed for optimal positioning of RSUs in order to attain optimal network coverage in the vehicular network with minimized cost. This CFDTRS considered the factors of vehicular density, number of obstacles in the map, intersection popularity and global coverage into account during the placement of RSUs. It is proposed with the objective of deploying required number of RSUs within the range of data transmission in order to achieve maximal coverage in the convex map, such that each area of the convex map is completely covered with at least a single RSU in the existence of multiple number of obstacles. The simulation results of the proposed CFDTRS attained from the real time situations of simplex, moderate and complex maps confirmed improved packet delivery rate of 9.32%, throughput by 10.74% with minimized packet loss of 9.14% and reduced end-to-end delay of 19.31$, compared to the benchmarked schemes considered for investigation.


Introduction
From the recent decade, Vehicular ad-hoc network (VANET) is considered to be the emerging technology that has invited huge amount of attention in the field of academics and industry [1]. The inclusion of VANETs in the Intelligent Transportation System (ITS) is determined to wide opened the way for predominant enhancement of the road safey and guaranteed reliable real time services with efficient through vehicle-to-vehicle (V2V) communications and vehicle-to-infrastructure (V2I) communications [2]. The V2V communications is facilitated by incorporating on-board units (OBUs) over the vehicles, while V2I communications is attined by deploying roadside infrastsructure such as LTE base stations or road side units (RSUs) with the comprehensive support of wireless technology such as cellular networks or Dedicated Short Range Communication (DSRC) [3]. In this context, the cellular networks refers to the potential future 5G developments. both LTE and advanced LTE-Advanced. The diverse communication requirements associated with different applications cannot be satisfied, even when the complete communications solely relies on V2V and V2I as they possesses a highly dynamic characterirtics of VANETs [4]. Hence, the communications of V2V and V2I need to coexist in order to improve the performance of the network. Moreover, RSUs as a critical entity of V2I communications that plays an anchor role in improving the quality of service (QoS) facilitated to the users by preventing the degradation of services that are introduced by areas of congestion, non line of sight problems and security issues, etc [5]. In specific, RSUs acts as a gateways to the Internet and other systems infrastructure (for instance, ITS) and enhances the degree of traffic information dissemination that extends the level of message coverage in the network [6]. But, the deployment of RSUs in order to attain complete network coverage is definitely not possible during the initial stage of VANETs as they incur a high cost during the their placement and further maintenance [7].
In the urban area, RSUs need to potentially deployed for handling the influence introduced by the maximum number of obstacles present in the vehicular environment [8]. The process of identifying the possible regions of RSUs deployment is determined to be highly challenging due to the hiderance introduced by the tall buildings, tall trees, constructions and water bodies [9]. The regions considered for deploying RSUs may not exits in the rectangle or square geometric shape [10]. Moreover, the regions considered for RSUs deployment may be complex and has the possibility of introducing potential challenges that incurs high communication delay in the process of V2I communication [11]. At this juncture, the concept of Constrained Delaunay Triangulation (CDT) is considered to be indispensable for optimal RSUs deployment in order to reduce deployment cost and network coverage [12]. This concept of CDT relies on the core principle that emphasies that the deployment of RSUs need to be attained only along its vertices [13]. This CDT aids in handling the issue of RSU deployment cost and network coverage based on the estimation of transmission range and distance between the RSUs. Further, the challenge of transmission delay is handled through the potential properties of CDT as they are always updated regularly. In this context, the method of triangulation is determined to the suitable and reliable candidate for covering the convex region that need to be covered through the optimal deployment of RSUs [14]. This method of trangulation plays a vital role in the construction of triangular meshes that aids in estimating the significant position at which the RSUs can be deployed for maximized coverage and minimized deployment cost. Furthermore, location for RSUs deployment need to be estimated based on the strategy of optimization that concentrates on cost incurred in deploying RSUs and end-to-end delay essential for interacting with the neighbourhood RSUs that lies with a close proximity [15]. Moreover, the delay incurred in V2I communication can be potentially minimized based on the selection of ideal number of RSUs with their best position that exists within the communication range. At this juncture, Chew First Delaunay Triangulation Refinement Scheme is considered as the first predominant CDT technique that can be potentially used in the process of optimal RSUs placement.
. In this paper, Chews First Delaunay Triangulation Refinement Scheme (CFDTRS) is proposed for identifying the optimal number of RSUs that could be significantly placed during V2I communication with the objective of covering maximum area with minimized deployment cost. This CFDTRS is proposed by inheriting the factors of vehicle density, different number of obstacles, intersection popularity and global coverage into account for attaining optimal RSUs placement in the convex map. It was proposed with the characteristic merits of CDT that focusses on deploying required number of RSUs with necessitated transmission range for achieving maximized coverage in the convex map, such that each and every region of the map can be suitably convered by atleast one RSU, independent to the number of obstacles present in the map. The comparative investigation of the proposed CFDTRS and the benchmarked schemes are achieved based on the simulation experiments conducted over the complex, moderate and simple maps that portrays real time road traffic scenarios. The simulation results confirmed that the proposed CFDTRS is capable enough in improving the packet delivery rate by 9.16$, reduced packet loss by 8.62% and minimized end-to-end delay by 18.42%, superior than the baseline schemes used for comparison and investigation.
The remaining sections of the paper is organized as follows. Section 2 depicts the literature review of the existing RSU optimal placement strategies proposed for V2I communication over the recent years with their pros and cons. Section 3 describes the complete details of the proposed CFDTRS scheme and their significant triangular mesh construction process with the strategy included for optimal RSUs selection that minimizes the cost of RSUs placement. Section 4 demonstrates the simulation results of the proposed CFDTRS scheme and the baseline approaches evaluated in terms of packet delivery ratio, throughput, packet loss, network coverage, end-to-end delay and RSUs placement cost under different number of RSUs, transmission range and vehicular densities. Section 5 concludes the paper with major contributions with the future scope of research.

Related Work
In this section, the review of the existing works of the literature proposed for optimal placement of RSUs in the vehicular network is presented with their pros and cons.
A constrained Delaunay triangulation (CDT) method named new spanner was proposed for optimal placement of RSUs with the view to improve network area coverage with minimized end-to-end delay [19]. This new spanner method attained the objective of RSUs placement based on the requirements of network and geometric properties. This method of CDT construction minimized the hops count between the network graph nodes by including a small collection of edges into the local Delaunay triangulation process. The simulation results of new spanner confirmed its potential in reducing the hops count from the source to the destination. It was determined to minimize jitter, delay and improve the throughput on par with the baseline planarized local Delaunay triangulation, local Delaunay triangulation, relative neighborhood graph and Gabriel graph-based triangulation approaches. A partial mobility information-based optimal RSUs placement scheme was proposed for targeting on the process of road network partition that aids in better RSUs deployment [20]. This RSUs deployment policy included the merits of migration ratios that are estimated betweeb the neighboring urban cells for determining the optimal location of RSUs placement. It targeted on the identification of some specific number of locatios that maximizes the degree of V2I contact opportunity. This partial mobility information-based optimal RSUs placement scheme was determined to be better than the full mobility information and no mobility information-based optimal placement scheme.
A RSU deployment strategy was proposed for addressing the issue of computational demand and network coverage during placement [21]. This RSUs deployment framework was proposed for generating different number of placement models through the characteristics of area targeted for installation. It was utilized the infrastructure providers who played a vital role in the design of smart city. The results confirmed its significance by improving the packet delivery rate by 12.21%, minimized end-to-end delay by 10.38% and reduced RSUs cost of 8.74%, better than the existing approaches. Then, a realistic coverage scheme named Geocover was proposed for handling the challenges of resource constraints, mobility patterns and different service area that are common during RSU deployment in vehicular networks [22]. It was proposed geometry-based sparse coverage protocol that incorporated the geometrical attributes of networks and facilitates a buffering operation that gets adapted with respect to different kinds of road topology. This Geocover was proposed with the capability of discovering hotspots and predicted mobility patterns to an acceptable level. It included the merits of quality constraints and budger constraints into account for resolving the problem of resource constraints. It further used greedy and genetic algorithm for handling the problem of coverage.
Further, a Constrained Delaunay Triangulation (CDT) method of RSUs placement was proposed for assigning transmission range in the convex map, such that every individual map position can be perfectly covered by any one of the deployed RSUs independent to the number of obstacles [23]. This CDT approach initially determined the RSUs position for optimal deployment of RSUs in the obstacle free region. Then, an optimization method was included for determining the more potential location on which the RSUs deployment can be facilitated for attaining minimized end-to-end delay and RSUs cost. It also achieved a RSU selection strategy based on the merits of a multi-criteria decision making that aided in superior communication between I2V and V2I communication. The experimentation conducted with the simple, moderate and complex maps of Manhattan, Erlangen and Rome confirmed improvement in packet delivery rate of 7.7%, minimized packet loss of 9% and reduced end-to-end delay of 22%, compared to the existing CDT schemes.

Proposed Chews First Delaunay Triangulation Refinement Scheme (CFDTRS) for optimal RSUs placement
The proposed Chews First Delaunay Triangulation Refinement Scheme (CFDTRS) is proposed as a potential CDT approach that focuses on the optimal placement of RSUs with the view to achieve maximized global coverage with minimized deployment costs during reliable data dissemination. This CFDTRS scheme derives the merits of Chews First Delaunay Triangulation Refinement technique [25] and determines the optimal number of RSUs that can be significantly placed during V2I communication for reducing cost and maximizing network coverage within a given range of data transmission. It is developed with Chews First Delaunay Triangulation Refinement strategy for ensuring better network coverage, which is considered as a significant approach over the constrained Delaunay triangulation based RSUs deployment strategy implemented by Ghorai and Banerjee [23]. The first objective of this proposed CFDTRS targets on the placement of RSUs in an urban area in which possible number of obstacles such as trees, water bodies, buildings and other constructions portraying a concave or convex polygon exists in the specified region. In this situation, the RSUs placement is completely impractical within such kind of polygons, even when there exists a possibility of placing RSUs on its sides. The primary goal of this CFDTRS scheme aims in placing the RSUs in an urban region for attaining complete network coverage, even when the area is completely obstructed by the existence of obstacles. It is also a reliable computational geometry approach of RSUs placement with an optimization strategy of Complex Proportional Assessment of alternatives (COPRAS) adoped for estimating the more potential RSUs position of deployment [24]. The secondary objective concentrated on the minimization of communication delay during V2I communication based on the utilization of multiple metric RSUs selection strategy, which plays an anchor role in selecting the best RSUs among the number of RSUs available in the range of data communication.
This proposed CFDTRS scheme of CDT construction achieved a larger minimized angle threshold of 28.32 degrees, which is estimated as a significant improvement over the CDT constructed by the baseline CDT scheme [23]. It is proposed with the potentiality of constructing unform CDTs that are considered as the ideal candidate for modeling real time practical scenarios. This uniform density CDTs construction is also necessary for minimizing the number of RSUs that are deloyed with the view ro reduce their deployment cost and improve the coverge area of the network to a maximized degree. Moreover, the proposed CFDTRS scheme is considered to construct non uniform triangular meshes with the minimum and maximized angle of 27.92 ∘ and 122.64 ∘ , respectively. The proposed CFDTRS scheme consists of two significant parsts such as, i) Initial RSUs position estimation based on CFDTR triangulation with optimization and ii) COPRAS-based multicriteria decision making strategy for RSU selection.

Initial RSUs position estimation based on CFDTR triangulation
The detailed view of the proposed CFDTR triangulation scheme that concentrated on the placement of optimal RSUs is described as follows. This RSUs optimal placement policy is explained based on Figure 1, which considered three RSUs such as A,B and C deployed in the vehicular network area.

Figure 1: Optimal RSUs placement based on the proposed CFDTRS scheme
In the process of this CDT construction, the transmission range associated with the RSUs are assumed to be unequal contributing towards the generation of non-uniform triangular meshes that maximizes network coverage with minimized RSUs deployment. The significance of the proposed CFDTRS scheme and its indispensable role of CDT construction for optimal RSU placement is explained based on the following lemmas. with the minimum angle between the CDT sides is 27.92 ∘ , [25], then the maximized global network area coverage achieved during the implementation of the proposed CFDTRS scheme is always 3 times better than the total area enveloped by the constructed CDT.
TC represents the circles at the points A, B and C representing the network coverage area associated with each RSUs as illustrated in Figure 2. The network area covered by the RSUs-A, B and C in the constructed CFDTR triangle is m(Aed), m(Bfg) and (Cih), respectively, then the total area covered by the RSUs represented by m(ABC) can be computed based on the addition of three areas-m(Aed), m(Bfg) and (Cih). The maximum network coverage area of RSUs is considered to be achieved, if the total area covered by the RSUs is at least 3 times of the complete area covered by the CDT as the total area is partitioned into a number of CDTs. Thus, the total network area coverage facilitated by the three deployed RSUs are determined based on Equation (1) = (  Thus, the network area completely covered by the utilized RSUs as per the strategy of RDTRS scheme is confirmed to be 2.5 times ( > 3 × ) better than the area covered by a CDT constructed using CFDTRM and ICDT schemes. Moreover, the benchmarked CFDTRM and ICDT schemes were potent to cover only a total area of 2 times better than the area enveloped by the single constructed CDT Thus, the network area completely covered by the utilized RSUs as per the strategy of RDTRS scheme is confirmed to be 3 times ( > 3 × ) better than the area covered by a CDT constructed using CFDTRM and ICDT schemes. Moreover, the benchmarked CFDTRM and ICDT schemes were potent to cover only a total area of 2 times better than the area enveloped by the single constructed CDT  with the minimum and maximum angle ranging from 27.922 ∘ and 122.64 ∘ , confirmed that the complete area covered by the three RSUs is identified to guarantee 100% of the coverage.

2 Position estimation of significant RSUs
In this position estimation process of RSUs, the initial location of the RSUs are identified first based on the CFDTR riangularization method as described in Section 3.1. Then, an optimization method is incorporated for estimating the suitable position based on the initial position identified for each individual RSUs initially deployed in the vehicular network. If a number of RSUs, say ( ( ) = ( (1) , (2) , Where, ( ) highlights the minimum cost function calculated based on the lowest cost delay determined from the complete and feasible cost incurred during and every individual session.

RSU selection based on COPRAS
In this final step, the method of COPRAS is ultilized as the multicriteria decision making process that aids in determing the process of RSU selection during V2I communication in order to reduce the transmission cost with maximized coverage and reduced delay. The method of COPRAS is included for selecting the suitable and ideal RSUs for effective routing of packets from the source to the destination vehicles for attaining reliable data communication in the network. This RSU selection process considered the collection of RSUs, criterions considered for RSU selection and their associated weights (already explained in Section 3.2). The steps involved in the process of RSU selection achieved through COPRAS is detailed as follows.
Step 1: Select the potential parameters (influencing criterions-say transmission range, RSU cost, delay and number of obstacles, etc.) that impact the selection of RSUs during V2I communication.
Step 2: Construct a decision making matrix ( DM M ) based on the aforementioned constraints using Equation (7) M = [ Where, ' ' and ' ' refers to the number of RSUs and the number of criterions considered for evaluating each of the RSUs deployed in the vehicular network.
Step 3: Determine the weight ( ) associated with the criterions (factors of selection indexes used for RSUs selection) for attaining the goal of optimal RSUs selection process.
Step 6: The weighted normalized values of the RSUs are determined based on the most preferable maximization parameters such as network coverage and throughput considered for optimization are added together as depicted in Equation (12) M _ ( ) = ∑ ∧ =1 (12) In the above mentioned Equation, ' k ' refers to the maximum and complete number of criterions considered for maximization or minimization. Moreover, the evaluation criterions that possesses the maximal optimal possibility are used identified before confirming the criterions that possess minimal optimal possibility in the matrix columns.
Step 7: Then, the weighted normalized values of the RSUs are also determined based on the most preferable minimization parameters such as RSUs cost, delay, number of obstacles and network transmission range considered for optimization are integrated together as specified in Equation (13) _ ( ) = ∑ ∧ = +1 (13) Step 8: Determine the minimized value associated with the most preferable minimization parameters-based weighted normalized values ( _ ( ) ) depending on Equation (14) ( _ ( ) ) = _ ( ) ; 1 ≤ ≤ (14) Step 9: Calculate the relative weight of each RSU 'i' based on Equation ( Step 11: Identify the priority of RSUs that possesses a greater weight ( ( − ) ) among 'm' RSUs deployed in the network in order to select them as the fittest RSUs that has the possibility of selection during V2I communication. Moreover, a degree of satisfaction with respect to each RSUs complies with the indices of selection that are either maximized or minimized during optimization process.
Step 12: Finally, the RSUs selection degree ( ( ) ) is computed based on Equation (17) Where, 10-100 in order to investigate their significance with respect to their increase and increase in the network with reference to network area coverage and deployment costs. The simulation experiments are attained with the protocols of MobileIP, AODV and UDP that corresponds to the network layer, transport layer and application layer based on the data traffic that satisfies the characteristics of Constant Bit Rate (CBR). data traffic. In addition, Table 1 depicts the simulation parameters considered for implementation of the proposed CFDTRS scheme. In the first of investigation, the proposed CFDTRS scheme and the baseline CRCCDT, PMIRSUP and NFDRSUP schemes are investigated based on network area coverage, mean throughput and average end-to-end delay with simple (Manhattan) and complex maps (Rome) and RSUs count varied from 10 to 100. Figure 2 and 3 presents the network area coverage and mean throughput of the proposed CFDTRS scheme and the baseline CRCCDT, PMIRSUP and NFDRSUP schemes with with simple (Manhattan) and RSUs count varied from 10 to 100. The network area coverage of the proposed CFDTRS scheme with systematic increase in the number of RSUs is considered to be significant on par with the baseline schemes, since the network area enveloped by the constructed triangular CDT is maximized. Moreover the mean throughput of the proposed CFDTRS scheme is also improved as the selection of optimal RSUs is attained through the inclusion of COPRAS multicriteria decision making strategy. Thus, the proposed CFDTRS scheme is confirmed to improve the network area coverage by 5.42%, 7.18% and 9.64%, better than the benchmarked CRCCDT, PMIRSUP and NFDRSUP schemes. Moreover, the mean throughput of the proposed CFDTRS scheme is determined to be enhanced by 6.14%, 8.52% and 9.18%, better than the benchmarked CRCCDT, PMIRSUP and NFDRSUP schemes.  Figure 4 demonstrates the average end-to-end delay of the proposed CFDTRS scheme and the baseline CRCCDT, PMIRSUP and NFDRSUP schemes with simple (Manhattan) and RSUs count varied from 10 to 100. The average end-to-end delay of the proposed CFDTRS scheme is visualized to be minimized on par with the benchmarked schemes, since optimal number of RSUs are deterministically selected based on the application of equal weights to each of the parameters considered for optimizing the placement of RSUs in the network. On the other hand, the proposed CFDTRS scheme is reliable in handling the impact of obstacles that completely hinders the communication between the source and destination vehicular nodes. Hence, the average end-toend delay incurred by the proposed CFDTRS scheme is proved be presominantly reduced by 7.21%, 8.28% and 9.02%, better than the benchmarked CRCCDT, PMIRSUP and NFDRSUP schemes.
Further, Figure 5 and 6 demonstares the network area coverage and mean throughput of the proposed CFDTRS scheme and the baseline CRCCDT, PMIRSUP and NFDRSUP schemes with with complex map (Rome) and RSUs count varied from 10 to 100. The network coverage area enveloped by the proposed CFDTRS scheme is determined to cover alteast three time the area coverage by a single CDT. Furthermore, maximized throughput is guaranteed in the network through the selection of RSUs that compulsorily prevents the drop of packets in the network. Thus, the network area coverage of the proposed CFDTRS scheme under complex map is confirmed to

NUMBER OF RSUs (COMPLEX MAP-ROME)
PROPOSED CFDTRS CRCCDT PMIRSUP NFDRSUP count varied from 10 to 100. With respect to complex map, the average end-to-end delay of the proposed CFDTRS scheme with different number of obstacles is confirmed to be minimized compared to the benchmarked schemes, since the included triangulation process is efficient and effective enough in determining minimal number of RSUs with maximized network coverage. This proposed scheme is effective in preventing the delay b selecting only the RSUs that considerably minimizes the drop of packets during V2I communication process. Thus, the average end-to-end delay incurred by the proposed CFDTRS scheme is proved be presominantly reduced by 5.18%, 7.92% and 9.14%, better than the benchmarked CRCCDT, PMIRSUP and NFDRSUP schemes.
In the second part of investigation, the proposed CFDTRS scheme and the baseline CRCCDT, PMIRSUP and NFDRSUP schemes are investigated based on network area coverage, mean rate of packet delivery, mean packet loss and average end-to-end delay with complex map (Rome) and density of vehicles varied from 10 to 100. Figure 8 and 9 depicts the network area coverage and mean rate of packet delivery achieved by the proposed CFDTRS scheme and the baseline schemes evaluated with respect to different vehicular densities. The network area coverage of the proposed CFDTRS scheme with different vehicle densities is identified to be improved by 7.21%, 9.42% and 11.68%, better than the benchmarked CRCCDT, PMIRSUP and NFDRSUP schemes. Moreover, the mean rate of packet delivery of the proposed CFDTRS scheme with different vehicle densities is identified to be improved by 7.21%, 9.42% and 11.68%, better than the benchmarked CRCCDT, PMIRSUP and NFDRSUP schemes.  Figure 10 and 11 demonstrates the mean packet loss and average end-to-end delay of the proposed CFDTRS scheme and the baseline schemes evaluated with respect to different vehicular densities. The proposed CFDTRS scheme with different vehicle densities is determined to be reduce the mean packet loss by 6.54%, 8.56% and 10.72%, superioe to the benchmarked CRCCDT, PMIRSUP and NFDRSUP schemes. In addition, the proposed CFDTRS scheme with different vehicle densities is identified to minimize the average end-to-end delay by 6.92%, 8.64% and 10.88%, better than the benchmarked CRCCDT, PMIRSUP and NFDRSUP schemes.

Conclusions
In this paper, CFDTRS scheme is proposed for better triangulation method that aids in better construction of CDT that focusses on minimizing deployment cost of RSUs with maximized network coverage in V2I communication. This proposed CFDTRS scheme was proposed for handling huge number of obstacles that hinders the network performance in urban environments. It was proposed with the merits of COPRAS for better multi-attribute decision making process that concentrated on the optimal RSUs selection that maximizes the network area coverage. This CFDTRS is proposed by inheriting the factors of vehicle density, different number of obstacles, intersection popularity and global coverage into account for attaining optimal RSUs placement in the convex map. The simulation results of this proposed CFDTRS scheme with different RSUs is confirmed to improve the network area coverage and mean throughput, on an average by 8.36% and 8.92%, better than the benchmarked CRCCDT, PMIRSUP and NFDRSUP schemes. With respect tto different vehicle densities, the proposed CFDTRS scheme improved the mean network area coverage, mean rate of packet delivery by 8.64% and 8.42% with minimized packet loss and average end-to-end delay by 9.12% and 9.54%, superior to the benchmarked CRCCDT, PMIRSUP and NFDRSUP schemes. In addition, the proposed CFDTRS scheme with different vehicle densities is identified to minimize the average end-to-end delay by 6.92%, 8.64% and 10.88%, better than the benchmarked CRCCDT, PMIRSUP and NFDRSUP schemes. As the part of the future scope, it is decided to formulate a Ruppert CDT-based triangulation method and compare it with the proposed CFDTRS scheme.

Data Availability Statement
Data sharing not applicableno new data generated, Data sharing is not applicable to this article as no new data were created or analyzed in this study.

Funding Information
There is no funding received for this research work