Collaborative neighbor discovery in directional wireless sensor networks: algorithm and analysis
 Fernaz Narin Nur†^{1},
 Selina Sharmin†^{1},
 Md. Ahsan Habib†^{1},
 Md. Abdur Razzaque^{1}Email author,
 Md. Shariful Islam^{2},
 Ahmad Almogren^{3},
 Mohammad Mehedi Hassan^{3} and
 Atif Alamri^{3}
https://doi.org/10.1186/s1363801709036
© The Author(s) 2017
Received: 19 November 2016
Accepted: 12 June 2017
Published: 3 July 2017
Abstract
In directional wireless sensor networks (DSNs), sensor nodes with directional antennas provide extended network lifetime and better coverage performance. However, one of the key challenges of directional nodes is to discover their neighbors due to difficulty in achieving synchronization among their directed transmissions and receptions. Existing solutions suffer from high discovery latency and poor percentage of neighbor discovery either due to lack of proper coordination or centralized management of the discovery operation. In this work, we develop a collaborative neighbor discovery (COND) mechanism for DSNs. Each COND node polls to directly discover its neighbors in a distributed way and collaborates with the already discovered nodes so as to allow indirect discovery. It helps to increase the neighbor discovery performance significantly. A Markov chainbased analytical model is developed to quantify theoretical performances of the proposed COND system. The performance of the COND system is evaluated in Network Simulator Version 3, and simulation results reveal that it greatly reduces the discovery latency and increases neighbor discovery ratio compared to stateoftheart approaches.
Keywords
Directional sensor networks Directional antenna Synchronization Indirect neighbor discovery Discovery latency Discovery ratio Performance analysis1 Introduction
In directional wireless sensor networks (DSNs), sensor devices with directional antennas sense data and deliver them in a multihop fashion toward the sink node. Nowadays, DSNs are being used for the implementation of many realtime applications including infrastructure monitoring, healthcare monitoring, robotic exploration, battlefield surveillance, target tracking, and disaster response [1, 2]. The directional sensors have been proved to provide better energy efficiency, sensing quality, bandwidth utilization, etc. [3, 4]. However, the directional transmissions and receptions of the sensor nodes have made the development of data communication and networking protocols for DSNs more challenging.
Neighbor discovery is defined as the problem of identifying all nodes within the communication range of a sensor device. The problem of neighbor discovery in directional sensor network not only is more challenging than that in its omnidirectional counterpart but also requires complete redesign and implementation. The key fact behind this requirement is that the directional nodes have limited width of communication sectors, and thus, two nearby nodes must steer their communication sectors to each other for a successful communication [5–7]. Efficient strategies need to be employed so that a pair of neighbor nodes eventually beamform their antennas to each other at a certain time instance and can discover themselves. The primary challenge lies in increasing the number of nodes discovered in bounded delay through better coordination in a distributed way, when the nodes are not clocksynchronized.
In the literature, the problem of neighbor discovery with omnidirectional antenna has well been explored [1, 8]. Nevertheless, recently, a few neighbor discovery mechanisms are developed that are based on directional communications. A neighbor discovery algorithm based on contentionbased and contentionfree approaches have been developed in [8], where only the sink node uses directional antenna, whereas the other nodes use omnidirectional one, resulting in asymmetryingain problem [9, 10]. A scanbased asynchronous neighbor discovery algorithm (SBAN) is proposed in [11], where the neighbor discovery is based on fully directional transmissions and receptions. The probabilistic HELLO message broadcasting with fast reply mechanism reduces collisions among the sensors. A randomized twoway neighbor discovery algorithm has been developed in [12]. The authors have presented an asymptotic analysis of oneway and twoway directional neighbor discovery algorithms and have designed a twoway neighbor discovery mechanism with selective feedback that reduces the neighbor discovery time. However, both the works [11, 12] lack in guaranteeing responder the reception of reply packets which increases the discovery latency for a dense network. A fully directional and centralized sectored antenna neighbor discovery (SAND) algorithm is developed in [13], where a token is passed among the nearby nodes to successfully learn each other. However, for token management, a central node is required that is not feasible for many applications of DSNs, especially in achieving scalability. Moreover, the rotational latency of a token affects the neighbor discovery accuracy and it increases the overall neighbor discovery latency. None of these works have wellthoughtout the directional coordination between two nodes.
In this paper, a collaborative neighbor discovery (COND) algorithm is proposed, where the directional sensors discover their neighboring nodes collaboratively by sharing the discovered neighborhood information with the surrounding nodes. The key idea behind the COND mechanism is that each directional node performs neighbor discovery in each sector using a contentionbased polling mechanism. The goal of neighbor discovery mechanism is to increase the number of discovered nodes with minimum delay using a twoway collaborative polling mechanism. The preliminary concept of this work has been published in [14]. In this paper, we augment the detail operation method of indirect neighbor discovery through collaboration. We carry out theoretical analysis using Markov chain model that quantifies expected number of discovered neighbors and the corresponding delay incurred. We also present performance analysis and results for average discovery latency per node, sensing wastage, and energy cost per neighbor discovery. The results show that the proposed COND mechanism greatly outperforms the stateoftheart systems—randomized twoway [12] and SAND [13].

A fully distributed novel neighbor discovery mechanism, collaborative neighbor discovery (COND) algorithm is developed for sensor nodes in DSNs.

A twoway pollingbased collaborative mechanism is designed to decrease the possibility of conflict and to speed up the handshaking process. In this mechanism, each node learns about its neighbors collaboratively by direct and indirect neighbor discovery through sharing information of already discovered nodes to and from its neighbors.

We develop a Markov chain model to analyze theoretically the expected number of neighbors discovered and the number of iterations required for discovery.

Finally, the results of performance evaluations, carried out in Network Simulator Version 3 (NS3) [15], show that our proposed COND mechanism outperforms SAND and randomized twoway mechanisms in terms of neighbor discovery latency and ratio, energy consumption, etc.
The rest of the paper is organized as follows. We give a detailed description of related stateoftheart works in Section 2. In Section 3, we describe the network model and assumptions. The proposed algorithm for the neighbor discovery using directional antenna is discussed in detail in Section 4, and the theoretical analysis and performance studies for the given algorithm are discussed in Sections 5 and 6, respectively. Finally, we conclude the paper in Section 7.
2 Related work
Directional sensor networks (DSNs) are gaining much popularity in the recent years, due to their improved performance gains through directional antennas [7, 16–21]. Even though the problem of neighbor discovery was well investigated in the literature for omnidirectional and wireless ad hoc networks, that for directional sensor networks kept less focused. However, in recent years, we find a few of neighbor discovery algorithms that are based on directional antennas. The existing works can broadly be categorized in two types: oneway broadcasting mechanisms [22–27] and two or threeway handshaking mechanisms [11, 13, 14, 28–30].
In oneway broadcastbased neighbor discovery mechanisms, nodes periodically broadcast their presence. On reception of at least one message successfully, a nearby node discovers the sender node. A probabilitybased neighbor discovery algorithm, namely ISBA is proposed in [27], where nodes transmit, receive, and remain idle with certain probabilities. The mechanism decreases number of collisions among the neighboring nodes when the probabilities are selected properly. Nevertheless, with the growing number of nodes in the network, the possibility of directional synchronizations among the nodes is gradually decreased. In [23], authors develop a directional neighbor discovery mechanism where the number of slots for neighbor discovery is dependent on the order of the average number of nodes in the network. The base station sends a beacon signal toward all the nodes in the network to start the discovery process, and all the nodes are timesynchronized with each other. Their neighbor discovery mechanisms exploit hybrid usage of omnidirectional and directional antennas; hence, with the increasing number of nodes in the network, the mechanism initiates extra overhead for the node synchronization. A directional neighbor discovery protocol was developed in [25], which is based on oneway broadcast mechanism. A HELLO message is broadcasted by each node, and after hearing the message, the neighboring nodes learn about information of that node.
In none of the above oneway broadcastbased neighbor discovery mechanisms, the sender nodes know whether the neighboring nodes receive their message successfully or not. Thus, the oneway neighbor discovery algorithms might be suitable for omnidirectional networks but not for directional sensor networks, because the later requires synchronization between the transmitting and receiving nodes to make the communication a successful one. Therefore, two or threeway handshaking protocols are more desirable for DSNs.
In twoway handshakingbased neighbor discovery mechanisms, a receiver node, after reception of a message, sends back a REPLY message toward the sender node, facilitating both nodes to discover each other in one event of communications. In directional transmission, a receiver node can only hear the message if it faces its antenna toward the sender and thus a feedback message is very important for neighbor discovery among the nodes. Hence, at least twoway handshaking is required for effective directional neighbor discovery as the nodes can agree on a future period for communication after the discovery. A fully directional scanbased asynchronous neighbor discovery algorithm is proposed in [11], where each node senses the medium and transmits HELLO message in a random direction and gathers location of the neighbor nodes, reducing the number of collisions among reply packets.
The urgent requirement of synchronization in between a transmitter and a receiver is kept unexplored in the above works. Moreover, nodes wait at each sector for a fixed period of time for neighbor discovery, which is highly inefficient. In [29], a directional neighbor discovery mechanism has been developed, where only the sink node of the network uses directional antenna, whereas the other sensors use omnidirectional antennas. The sink node applies contentionbased and cotentionfree methods to medium access and sequentially scans all its sectors to discover its neighbors. To minimize the medium access delay, the authors presented an optimization method for selecting the beam width and the persistence probability of neighbor discovery. This mechanism results asymmetryingain problem [9] due to the difference between the antenna gain patterns of the sink node and other sensors. A randomized twoway neighbor discovery mechanism is proposed in [12], where the authors have presented an asymptotic analysis of oneway and twoway directional neighbor discovery algorithms. Their twoway neighbor discovery mechanism exploits selective feedback policy so as to reduce collisions among the reply packets and thus to decrease neighbor discovery time. However, the reception of a reply packet is not certain in the above works due to lack of synchronization between the sender and receiver nodes.
A fully directional and centralized threeway sectored antenna neighbor discovery (SAND) algorithm is proposed in [13], where a token is passed among network nodes sequentially to discover their surrounding neighbors. However, for token management, it requires a central node, which is not only often infeasible for many DSN applications but also limited by scalability. Furthermore, the rotational latency of a token affects the neighbor discovery accuracy and increases the overall neighbor discovery latency. The SAND mechanism also has not considered the directional synchronization issue among the nodes, causing deafness problem, and as a central controller controls the whole mechanism, the discovery latency sharply increases.
Our work is different from the above studies in that we develop a fully distributed neighbor discovery mechanism, where both the transmissions and receptions are directional and nodes collaborate with their (already discovered) neighbors to find other neighbors, reducing neighbor discovery latency significantly. This indirect neighbor discovery and selective feedback policies jointly help our algorithm to decrease the collisions in the network. In addition to that, a COND node employs dynamic waiting time at different directions while discovering nodes in the neighbor that greatly helps to mitigate the deafness problem.
3 Network model and assumption
Each node has one transceiver and can form one directional beam in a sector at a given time. For the network nodes, all transmissions and receptions are directional and they do not require any additional omnidirectional antenna. Note that the usage of both directional and omnidirectional antennas causes additional hardware cost, complexity, and two other major problems. First, the transmission ranges of the omnidirectional antenna and directional antenna are different, which introduces asymmetry gain problem in communication links. Again, the spatial reuse benefits are greatly reduced since omnidirectional communication inhibits more simultaneous transmissions.
The communication radius (r) of all nodes in the network is homogeneous. Nodes in the network are not clocksynchronized with each other. Each node independently discovers its neighbors. The success event of a transmission is probabilistic; however, our dynamic polling period and selected response REPLY to HELLO messages decrease the probability of collision and increase the number of successful transmission events. If the discovery message is exchanged between two nodes for at least half of a slot, two nodes can discover at the same time slot [7]. Subsequently, in a distributed system, without any clock synchronization, two sensor nodes can discover each other within a bounded delay.
List of notations
Symbol  Definition 

\(\mathcal {S}\)  Set of all sensor nodes 
\(\mathcal {M}\)  Set of sectors of directional antenna 
P _{ t }  Transmission probability 
r  Communication radius of each sensor 
\(\mathcal {K}\)  Delay tuning parameter 
A  Deployment area of the network 
ρ  Network density 
\(\mathcal {T}_{a}\)  Neighbor table of node \(a \in \mathcal {S}\) 
E _{ n }  Expected number of nodes in the neighborhood 
\(\mathcal {N}_{e}^{m}\)  Number of expected neighbor nodes in a sector \(m \in \mathcal {M}\) 
\(\mathcal {N}_{d}^{m}\)  Number of discovered neighbor nodes after an iteration 
\(\mathcal {F}\)  Flag indicating a neighbor is discovered directly or indirectly 
\(\mathcal {R}\)  Iteration for neighbor discovery 
x ^{′}  Mini subslot of a slot x 
δ _{ m }  Parameter that tunes \(\mathcal {K}\) 
4 Collaborative neighbor discovery mechanism

Initialization of neighbor discovery with appropriate value of a delay tuning parameter (\(\mathcal {K}\))

Discovery of neighbor nodes in different sectors using contentionbased polling mechanism

Maintaining and updating the neighbor tables of COND nodes in collaborative fashion
What follows next, we present the detail operations of the COND steps.
4.1 Initialization
Note that the numerical values in Eq. (6) are not strict choices; rather, the values are depicted through numerous simulation experiments for a given network environment (stated in Section 6), and they are tunable by the network administrator. In the case the number of already discovered nodes in a certain sector crosses the expected number of neighbors, the node may stop staying in that sector. Hence, it may happen that a node misses a good number of neighbors to discover if the calculation of expected number of neighbors is incorrect (due to distortions in deployment). Therefore, we allow a COND node to continue the discovery process until it fails repeatedly (say, up to two iterations) to find a new neighbor in a particular sector.
4.2 Contentionbased polling mechanism
Each slot is further divided into several mini subslots, as shown in Fig. 2 a. If a node decides to transmit a HELLO message in a slot, it does so in the first minislot and listens to the channel for any REPLY message(s) from its neighboring node(s). The HELLO message contains the node’s ID, (x,y) coordinate, sector number, and neighbor table, i.e., \(\Gamma _{H} = \{ID,\ \text {coord}(x,y),\ m,\ \mathcal {T}\}\). On reception of HELLO message, the surrounding nodes update their neighbor tables and relay back their information in a randomly chosen minislot. Thus, the nodes develop their neighbor tables for each sector with so far discovered nodes. The structure of the neighbor table is represented by the tuple, \(<ID, \text {coord}(x,y), m, \mathcal {F}>\), where the fourth field is a flag that contains 1 if the designated neighbor is discovered through direct exchange of messages and 0 if it is discovered indirectly. The details of direct and indirect discovery processes are discussed in the following section.
4.3 Collaborative discovery of neighbor nodes
The key challenge in reducing neighbor discovery latency in DSNs is the synchronization of HELLOREPLY transmissions among the nodes in a neighborhood. Therefore, in addition to discover neighbors through direct exchange of messages, we allow COND nodes to share their neighbor tables with each other and to update their tables collaboratively so as to further decrease the discovery latency. Thus, some neighbor nodes are discovered indirectly (via other nodes).
4.3.1 Direct discovery
When two nodes are beamformed to each other and successfully exchange HELLO and REPLY messages, they can directly discover each other. After the HELLOREPLY handshaking, two nodes update their neighbor tables accordingly. Thus, it is highly dependent on the synchronization of corresponding sectors of two neighbors. In Fig. 2 b, when the node a discovers a neighbor node b through direct handshaking, the flag entry for b in a’s neighbor table is set to 1. Unlike existing works in the literature that depend only on direct discovery, we allow indirect discovery of neighbor nodes through collaboration among them.
4.3.2 Indirect discovery
In omnidirectional communication, only direct discovery is sufficient for neighbor discovery. For directional nodes, it is the most important that two nodes are beamforming their antennas to each other; otherwise, the handshaking between the nodes would never occur. So, it may happen that when a node is broadcasting HELLO message in a particular sector, some of the neighbor nodes cannot receive the message because of the deafness problem [9]. Hence, the strict requirement of directional synchronization among nodes upsurges the discovery latency among the sensor nodes.
Consider a scenario in Fig. 2 b, where pairs a and b and a and c have already discovered themselves in the present or previous time frame, but node b has not yet been discovered by c or viceversa, as their antenna directions did not match during the direct neighbor discovery process. In order to ease the problem and to accelerate the discovery process, we allow COND nodes to share their neighbor tables with already discovered nodes. That is, node a shares its table with b and c so that they can discover each other as a neighbor of the respective sectors by checking their coordinates. We term this update of neighbor table as indirect discovery, and the flag entry for such discovered node is set to 0.
The proposed collaborative neighbor discovery (COND) mechanism has been summarized in Algorithm 1. Initially, the neighbor table of each node remains empty. After getting a HELLO/REPLY message from any neighbor, a node updates its own table (lines 6–23). The node that receives a HELLO message checks its neighbor table to find whether the node is discovered earlier or not. If there exists a record, the node checks the flag value and if the value is 1, it does not give any REPLY message to that node assuming that it has exchanged messages in the earlier slots with that node; otherwise, it updates the information in the neighbor table and sends a REPLY message in a random subslot to the direction of the sender node (lines 15–22). If the sender node receives a REPLY message (without any collision) from any neighbor, it adds the node in the neighbor table (lines 8–12). In this way, two nodes discover each other using twoway handshaking. In the case, a node cannot discover any new node in a certain sector in consecutive two iterations, we stop COND process in that sector (lines 25–27).
The time complexity of Algorithm 1 for one iteration is quite straightforward to follow. The lines 1–31, enclosed in a loop, iterate \(\mathcal {M}\) times having a complexity of \(\mathcal {O}(\mathcal {M})\) in the worst case. Again, the statements 4–23 iterate T times in a nested loop. The rest of the statements have constant unit time complexities. Therefore, the overall time complexity of the proposed COND algorithm is \(\mathcal {O}(\mathcal {M} \times T)\).
5 Theoretical analysis of COND
At each iteration, a COND node performs neighbor discovery around its all sectors, and on completion of one iteration, the node gets an updated neighbor table with the newly discovered neighbors. In this section, we formulate a theoretical model for analyzing the neighbor discovery delay, average number of discovered nodes per iteration, and corresponding energy consumption of the COND system.
5.1 Discrete time Markov chain model
We have developed a discrete time Markov chain model for analyzing the performance of the proposed algorithm. In this model, a node can stay in one of the following six states: idle (I), Transmitting HELLO message (T), Listening REPLY message (L), Receiving HELLO message (R), Transmitting REPLY message (A), or Collided (C).
Here, L is the set of REPLY message listening states, i.e., \(L = \left \{ L_{0}^{2},\ L_{1}^{2}, \dots,\ L_{v}^{2} \dots L_{0}^{u},\ L_{1}^{u}, \dots, L_{v}^{u} \right \}\) and each \(L_{v}^{u} \in L\) denotes that the v number of neighbor nodes is discovered in reply minislot u. Similarly, R is the set of states after receiving a HELLO message, i.e., \(R = \left \{ R_{0}^{1},\ R_{1}^{1}, \dots,\ R_{v}^{1} \right \}\), where each state \(R_{v}^{1}\) represents that the v number of neighbors is discovered during the first minislot. The value of u is from 2 to the number of minislots (x ^{′}) available in a slot and the maximum value of v can be \(\mathcal {N}_{e}^{m}\), the expected number of neighbors in a certain sector m.
We can find the distribution vector at equilibrium by solving the equations P S=S and \(\sum \mathbf {S} = 1\).
where ξ=1+P _{ T }+(σ _{0}+σ _{1}+σ _{2}+σ _{3}+⋯+σ _{ v })(P _{ T }+P _{ R }+P _{ A } P _{ R })+P _{ T }[(σ _{0})^{2}+2σ _{0} σ _{1}+2σ _{0}(σ _{1})^{2}+2σ _{0} σ _{1} σ _{2} σ _{3}+2σ _{0} σ _{1}(σ _{2})^{2} σ _{3}(σ _{4})^{2}+⋯+(P _{ T })^{2}]+P _{ C }.
5.2 Comparison of analytical and simulation results
6 Performance evaluation
We have implemented our proposed COND system in NS3 [15], a discreteevent network simulator to verify the effectiveness of proposed algorithm. We have done a comparative study of COND performances with those of two stateoftheart algorithms—randomized twoway neighbor discovery mechanism [12] and SAND [13].
6.1 Simulation environment
Simulation parameters
Parameters  Value 

Area deployment  500 m × 500 m 
Type of deployment  Uniform random 
Number of nodes deployed  100∼1000 
Number of sectors  2∼6 
Transmission range  100 m 
Slot duration  1 ms 
Packet size  40 bytes 
Initial energy  3 J 
Data transmission rate  1 Mbps 
Bandwidth  5 MHz 
Routing protocol  AODV 
Channel model  Yans WiFi model 
Propagation model  Friis propagation loss model 
Simulation time  1000 s 
6.2 Performance metrics

Average discovery latency per node: A round of node discovery is completed when a node finishes the operation in all sectors (either clockwise or anticlockwise). Average discovery latency per node is the ratio of total discovery time to the number of discovered nodes.

Sensing wastage is the count of wastage of time slots for neighbor discovery. A sensing time slot is regarded as wastage if no neighbor is discovered in it.

Average discovery ratio is the ratio of the number of neighbor nodes successfully discovered to the total number of nodes in the network.

Control byte overhead is the ratio of total number of control bytes (HELLO and REPLY messages) exchanged during the simulation period to the total number of neighbors discovered.

Average energy cost per node discovery is the measure of average amount of energy consumed during the simulation period for discovering a single node in the network.
6.3 Simulation results
The comparative performance results are plotted for varying number of sensors deployed in the network, number of sectors a node has, and the size of the sensing time frame.
6.3.1 Impacts of varying number of nodes
We have varied the number of nodes from 100 to 1000 and compared the performances of the proposed COND mechanism with those of other systems. The number of sectors for each node is fixed at 4, and we call a round of sensing is completed when a node is switched to all of its sectors for neighbor discovery. Each time frame contains 25 slots and each slot has 4 minislots.
As we have fixed the number of slots in each time frame, the sensing wastage is very high for a low dense network in all the studied approaches, causing poor utilization of time slots. The wastage of slots reduces with the growing number of nodes up to approximately 600 nodes in COND due to collision and conflicts of nodes in competing environment of node discovery. The COND has the minimum wastage of slots because of allowing indirect node discovery, whereas many slots are wasted in the other algorithms especially for the lack of sector synchronization, as shown in Fig. 6 b.
The graphs in Fig. 6 c depict the discovery ratio of the neighboring nodes during the simulation period. The discovery ratio is 100% for all the proposed algorithms when the network density is low. The discovery ratio decreases with the growing number of nodes. Our indepth look into the simulation trace files depicts that the last 10% of nodes take the longer time to discover. The COND mechanism performs better than the other two mechanisms with higher network density as the indirect discovery of COND mechanism increases the neighbor discovery ratio. In the twoway randomized protocol and SAND, the overheads are higher than that of COND because of additional control packet exchanges among nodes at random times due to collision and loss of token, as depicted in Fig. 6 d. The SAND has higher overhead among all the algorithms as it uses tokens to control and manage transmissions in the network.
6.3.2 Impacts of varying number of sectors
Directional antenna reduces the chance of collision among the neighboring nodes. The Fig. 7 c shows that the neighbor discovery ratio gradually increases with increasing sectors in all the mechanisms, which is as expected theoretically. Nevertheless, excessive reduction of sensing angle reduces the chance of direction synchronization among nodes, and thus, it decreases the neighbor discovery ratio. Yet again, higher number of sectors causes the nodes to switch from one sector to another frequently, resulting in transmission of more HELLO/REPLY messages. Hence, the control byte overhead is increased with the growing number of sectors, as shown in Fig. 7 d. Our COND mechanism outperforms the stateoftheart mechanisms as it needs less control byte overheads.
6.3.3 Impacts of varying number of time slots
The number of time slots per round are varied from 10 to 40 for the simulation. Here, we assume fixed number of 500 sensor nodes and each node has 4 sensing sectors.
6.3.4 Average energy cost for neighbor discovery
7 Conclusions
In this paper, we investigated distributed solutions to the problem of neighbor discovery in DSNs and introduced indirect neighbor discovery through collaboration among the already discovered nodes. We also introduced dynamic polling period in each sector following the number of already discovered nodes in it. The joint employment of the above strategies helped the proposed COND system to achieve excellent performances in neighbor discovery. Our indepth look into the simulation trace files depicts that the collaborationbased indirect neighbor discovery helped to reduce the discovery latency significantly while the utilization of time slots in each frame was greatly enhanced due to the use of dynamic polling periods. The results from simulation experiments, carried out in NS3, showed the achievements of as high as 80 and 75% performance gains in neighbor discovery latency and discovery ratio, respectively, compared to SAND, a leading work in the literature.
In the future, we shall concentrate on developing a theoretical model for analyzing delay tuning parameter and study the effects of node mobility on performances of the proposed neighbor discovery mechanism.
Notes
Declarations
Acknowledgements
This work was financially supported by the King Saud University through Vice Deanship of Research Chairs.
Competing interests
The authors declare that they have no competing interests.
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Authors’ Affiliations
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