A Distributed MultiHop IntraClustering Approach Based on Neighbors TwoHop Connectivity for IoT Networks
Abstract
:1. Introduction
1.1. Network Architecture
1.2. Motivation
 A new connectivity metric is introduced to elect the set of appropriate CHs. The novelty of this metric is taking into account the twohop connectivity of the current node and its surrounding neighborhood (instead of using the traditional direct neighbors connectivity), in order to strengthen the clusters stability.
 The design of the algorithm is inspired from the distributed selfstabilizing systems. We prove that the algorithm converges within $O(n+k)$ rounds, which represents the upper bound of the time complexity, n is the number of network nodes and k is the depth threshold of the clusters. This perspective allows network devices to efficiently tolerate potential failures that can occur locally in the dynamic topology.
 The proposed approach generates clusters with an energy efficient topology by reducing the distance between nodes and their respective CH. The adopted approach is peculiar in that it constructs the intracluster links in a distributed manner rather than using a centralized algorithm executed by the CH.
2. Literature Review
3. Network Model and Algorithm Objective
4. Proposed Approach
 Twohop connectivity ratio (TCR): this parameter represents the connectivity ratio of a node relative to its neighborhood. The $TCR$ value of a given node i is calculated using Equation (2). Each node computes the average connectivity within its two hop neighborhood (${N}_{\le 2}\left(i\right)$) using ${\Phi}_{i}$, then compares the obtained value with the local degree to define the $TC{R}_{i}$. A negative $TC{R}_{i}$ value ($\leftN\left(i\right)\right{\Phi}_{i}\le 0$) reflects the low connectivity proportion of the node i relatively to its surrounding environment. Higher $TC{R}_{i}$ value means that node i is surrounded by a large number of neighbors and these neighbors are well connected with many other nodes, thus i is a suitable CH candidate to maintain network connectivity. Therefore, it covers the largest number of nodes within the maximum hop constraint k and generates more fault tolerant and stable cluster topology. Indeed, in case of potential CH failure, the neighborhood of this node is well connected and the replacement of the current CH does not affect the cluster performance.$${\Phi}_{i}=\frac{\left[{\displaystyle \sum _{j=1}^{{N}_{\le 2}\left(i\right)}}\leftN\left(j\right)\right\phantom{\rule{4pt}{0ex}}/\phantom{\rule{4pt}{0ex}}j\in {N}_{\le 2}\left(i\right)\right]+\leftN\left(i\right)\right}{{N}_{\le 2}\left(i\right)+1}$$$$TC{R}_{i}=\leftN\left(i\right)\right{\Phi}_{i}$$
 Residual energy (${E}^{ratio}$): the remaining energy of network nodes is introduced in the CH election process. The ratio of remaining energy of a node i is computed as:$${E}_{i}^{ratio}=\frac{{E}_{i}^{residual}}{{E}_{i}^{init}}$$
 Communication link quality (RSSI): DC2HC uses Radio Signal Strength Indicator (RSSI) as a metric to measure the quality of communications. The RSSI value (the received transmission power ${P}_{r}$) can be represented by the Log Distance Path Loss Model [53] as follows:$${P}_{r}\left(d\right)\left(\mathrm{dBm}\right)={P}_{t}\left(\mathrm{dBm}\right)10\times \alpha \phantom{\rule{4pt}{0ex}}log\left(d\right){X}_{\sigma}$$${P}_{t}$ represents the power of the transmitter’s radio signal in dBm. The distance d between the sender and the receiver is measured in meter. $\alpha $ is the path loss exponent that depends on the environmental conditions ($\alpha =2$ in the free space propagation model). ${X}_{\sigma}$ is a Gaussian random variable used in case of shadowing effect. Otherwise, it equals zero.
4.1. Initialization Phase
Algorithm 1 Initialization phase. 

4.2. Cluster Head Election Phase
Algorithm 2 Cluster Head election phase. 

4.3. Maintenance
4.3.1. Cluster Leaving
4.3.2. Cluster Joining
5. Energy Model and Transmission Reliability
6. Convergence
7. Complexity
7.1. Theoretical Analysis
 (a)
 After 2 rounds and in all following rounds, i is a cluster head ($Myc{h}_{i}=I{D}_{i}$ and $Dist(i,Myc{h}_{i})=0$).
 (b)
 After $2\times k+2$ rounds and in all following rounds, the neighbors of node i at distance $\le k$ form a cluster, where $\forall j\in {N}_{\le k}\left(i\right):(Myc{h}_{j}=i)\wedge (Dist(i,j)\le k)$.
7.2. Clustering Property
7.2.1. Safety Property
7.2.2. Liveness Property
8. Simulation
8.1. Experimental Settings
8.2. Experimental Results
8.2.1. Cluster Head Cardinality
8.2.2. Average Exchanged Messages and Consumed Energy
8.2.3. Average Network Lifetime
9. Conclusions and Future Works
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Protocol  Frequency Band  Data Rate  Range  Energy Consumption  Usage Area 

WiFi [28]  2.4/5.0 GHz  54 Mb/s  30 m  Medium  Home entertainment, Industrial 
Bluetooth [2]  2.4 GHz  1 Mb/s  10 m  Low  Industrial, Traffic management 
IEEE 802.15.4 [23]  868−915 MHz/2.4 GHz  250 kb/s  [10, 100] m  Low  Industrial, Traffic management, Smart home, vehicle monitoring 
LTE [29]  2.6 GHz  10 Mb/s  ≤15 km  High  Mobil telecommunications, Smart Cities 
Wireless HART [24]  2.4−2.5 MHz  250 kb/s  [1, 100] m  Low  Healthcare, Industry automation 
BLE [31]  2.4 MHz  1 Mb/s  200 m  Very Low  Healthcare, Home entertainment 
ZWAVE [26]  1 GHz  40 kb/s  30 m  Low  Home automation applications 
WAVENIS [22]  865−916 GHz  100 kb/s  ≤4 km  Very Low  Chemical and healthcare applications 
LoRaWAN [32]  868−900 GHz  50 kb/s  ≤15 km  Very Low  Smart City, industrial Monitoring, Agriculture 
NBIoT [30]  180 kHz  234.7 kb/s  ≤35 km  Low  Industrial Monitoring, Smart City 
Algorithm  Topology  Number of CH’s  Intra Clustering  Inter Clustering  Load Balancing  Energy Consideration  Benchmarks 

LEACH [43]  Distributed  Undetermined  Singlehop  Singlehop  No  No  MTE 
EPLEACH [44]  Distributed  Undetermined  Singlehop  Singlehop  No  Yes (CHelection)  LEACH, TEEN 
FLLEACH [45]  Distributed  Determined  Singlehop  Singlehop  Yes  No  LEACH 
Wu et al. [47]  Centralized  Undetermined  Singlehop  Singlehop  Yes  No  Not specified 
MHLEACH [46]  Distributed  Undetermined  Multihop  Singlehop  No  Yes (MultiHop transmission)  LEACH 
EPEGASIS [48]  Centralized  Determined  Multihop  Singlehop  No  No  PEGASIS, LBEERA 
EE3C [50]  Centralized  Undetermined  Multihop  Multihop  Yes  No  Not specified 
KECDS [49]  Distributed  Undetermined  Multihop  Multihop  No  No  ECDS, HEED 
Singh et al. [14]  Centralized  Undetermined  Multihop  Multihop  Yes  Yes (CHrotation)  EEUC, EUCA 
Turgut [19]  Distributed  Undetermined  Multihop  Singlehop  Yes  No  Not specified 
Mezghani [34]  Distributed  Undetermined  Multihop  Singlehop  Yes  Yes (intracluster routing)  MTE, HEED, APTEEN, EDC, THC, VCA 
Symbol  Description 

$I{D}_{i}$  Identity of device i 
${W}_{i}$  Weight of i (computed using Equation (5)) 
$Myc{h}_{i}$  Relative Cluster Head of i 
$CH\_weigh{t}_{i}$  Weight of $Myc{h}_{i}$ 
$Dist(i,Myc{h}_{i})$  Distance between i and $Myc{h}_{i}$ (in term of hops) 
${P}_{i}$  Parent of i in the aggregation path toward the relative CH 
$T{r}_{i}$  Transmitting range of i 
$Deg\left(i\right)$  Degree of i (Number of node in the neighborhood of i) 
$LS{V}_{i}$  Local State Variable of i 
$CR{L}_{i}$  Clustering Record List (Neighbors clustering information received) 
$TC{R}_{i}$  Twohop connectivity ration of i 
Parameter  Value 

Network size (${\Delta}^{2}$)  1000 × 1000 m${}^{2}$ 
Node density  $\delta \in [40,1300]$ 
Distribution of nodes  Random 
connectivity model  Unit Disk Graph (UDG [59]) 
Transmitting range ($Tr$)  70 m 
Maximum hop constraint k  $\{1,2,3\}$ 
$\alpha ,\beta ,\gamma $  1/3, 1/3, 1/3 
${E}_{elec}$  50 nJ/bit 
${\epsilon}_{FS}$  10 pJ/ bit/ M${}^{2}$ 
${\epsilon}_{Mfs}$  0.0013 pJ/ bit/ M${}^{4}$ 
Data packet size  100 bytes 
Initial energy  1 Joule 
Clustering Algorithm  IntraCluster Topology  

Singlehop  Twohop  Threehop  
Mezghani  6.9%  21.1%  27% 
MHLEACH  55.3%  64.2%  67.3% 
Clustering Algorithm  IntraCluster Topology  

Singlehop  Twohop  Threehop  
Mezghani  28.7%  37%  37.1% 
MHLEACH  10.6%  13.8%  3.1% 
Clustering Algorithm  IntraCluster Topology  

FND  LND  
Singlehop  Multihop  Singlehop  Multihop  
Mezghani  30.5%  24.2%  16.4%  10.2% 
MHLEACH  14.4%  14.7%  75.1%  41.8% 
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Batta, M.S.; Mabed, H.; Aliouat, Z.; Harous, S. A Distributed MultiHop IntraClustering Approach Based on Neighbors TwoHop Connectivity for IoT Networks. Sensors 2021, 21, 873. https://doi.org/10.3390/s21030873
Batta MS, Mabed H, Aliouat Z, Harous S. A Distributed MultiHop IntraClustering Approach Based on Neighbors TwoHop Connectivity for IoT Networks. Sensors. 2021; 21(3):873. https://doi.org/10.3390/s21030873
Chicago/Turabian StyleBatta, Mohamed Sofiane, Hakim Mabed, Zibouda Aliouat, and Saad Harous. 2021. "A Distributed MultiHop IntraClustering Approach Based on Neighbors TwoHop Connectivity for IoT Networks" Sensors 21, no. 3: 873. https://doi.org/10.3390/s21030873