1 Introduction
2 Related work
3 Method/experimental
3.1 Preliminaries
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The nodes are organized into clusters where each cluster has a CH and all CMs can transmit data directly to the CH. The CH forwards the data to the BS via multiple hops.
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Every node has a minimum transmission range (\(Tr_{\min }\)) and data transmission range (\(Tr_{\mathrm{d}}\)). These ranges are defined based on the specification of the sensing device such as Telosb Tmote Sky platform [16].
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Throughput is defined as number of packets reaching to BS and originated from member nodes.
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The nodes are aware of their physical location.
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Nodes are uniformly distributed and randomly located.
3.2 Problem statement
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The average LEH among CHs is greater than the transmission range in the case of LEACH. This is due to variable inter-cluster topologies generated due to random CH selection.
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The LEH and transmission range are strongly related. Maximum LEH should be smaller than the transmission range. However, maximum network lifetime cannot be achieved if transmission range is not large enough.
3.3 Improved Clustering and Routing (ICR) Protocol
3.3.1 Clustering area distribution
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Definition 1 (Fixed Area (A)) the given minimum transmission range (\(Tr_{\min }\)) of the node, fixed area can be defined as the area where Width = Height = (\(Tr_{\min }\)). This is the area that acts as a clustering area for all nodes inside it.
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Definition 2 (Cluster) the set of nodes C(z) having the same cluster (K) can be denoted as follows:where A(x) is the fixed Area, R(x) is region W of sensing node x in the area K, and S is all the sensor nodes.$$\begin{aligned} C\left( {z}\right) = x:A(x) =K \cap x:R(x)=W; x \in S \end{aligned}$$(4)
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Definition 3 (Forward and Backward Nodes) Given the Area A(K) of node (x), the forward nodes, F(x), are from the Area (\(K-1\)) within the data transmission range (\(Tr_{d}\)), and Backward nodes, B(x), are from the Area (\(K+1\)) with nodes within the data transmission range (\(Tr_{d}\)).$$\begin{aligned} F\left( {x}\right) = x:distance(x,u) < Tr_{d} \cap A(u)=K-1 \end{aligned}$$(5)$$\begin{aligned} B\left( {x}\right) = x:distance(x,v) < Tr_{d} \cap A(v)=K+1 \end{aligned}$$(6)
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Definition 4 (Equal Nodes) The nodes within the same Area(K) such that:$$\begin{aligned} E\left( {x}\right) = x:distance(x,m) < Tr_{d} \cap A(m)=K \cap \forall R \in A(K) \end{aligned}$$(7)
Variable | Definitions |
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BSPosition | Position of sink node |
BS | Base station responsible for data collection |
NetArea | Network area size |
EInit | Initial energy of nodes |
Nd | Node |
NumNd | Total number of nodes |
\(N_F\) | Number of forward nodes |
\(N_B\) | Number of backward nodes |
NdPosition | Position of nodes |
Round | Current round of simulation |
MaxRound | Maximum number of rounds |
NdLive | Number of alive nodes in network |
SubAreasList | List of sub-areas based on transmission range of node |
ThrshdDist | Threshold distance |
CHList | List of CHs |
CH | Cluster head node of a cluster |
CM | Member node of a cluster |
EDissip | Energy dissipation |
SNd | Source node that sends packets |
TNd | Target node that receives packets |
T | Back-off timer of a node |
Nc | Number of clusters in the area based on transmission range |
CHSelect | Selection of CH |
NdWeights | The accumulative weight of node to be candidate for CH |
WeightList | Sorted list of nodes based on accumulative weights inside a cluster |
EConsumed | Energy consumed |
3.3.2 Cluster-head selection
3.3.3 Routing
ID | Forward | Backward | Equal | Hop-count |
---|---|---|---|---|
7 | BS | 4 | 8 | 1 |
8 | BS | 4, 5, 6 | 7 | 1 |
9 | BS | 5,6 | Nil | 1 |
ID | Forward | Backward | Equal | Hop-count |
---|---|---|---|---|
4 | 7, 8 | 1 | Nil | 1 |
5 | 8, 9 | 1, 2, 3 | 6 | 1 |
6 | 8, 9 | 2, 3 | 5 | 1 |
3.3.4 Cluster head probabilities
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The node(x) must have at least one forward node(u). This node(x) acts as the backward node of node(u) as well. For node(u) to be selected as the forward node of node(x), the probability P isAnd for node(x) to be the only CH that forwards data to node(u), the probability can be written as:$$\begin{aligned} \displaystyle \prod _{u} \big [1 - P(x,u) \big ] \cap u \in F(x) \end{aligned}$$(11)Where \(P(x,u)=P_{\rm CH}(u).P(F(x))\). This equation explain that if node (x) has to be selected as a CH then it should have a forwarding node (u) that should also be a CH node. This is required condition for network topology generation.$$\begin{aligned} \displaystyle P_{\rm CH}(x)= \big [1- \prod _{u}(1 - P(x,u)) \big ] \cap u \in F(x), A(x) \ne A(u) \end{aligned}$$(12)
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If there is no backward node of node(x), it means that the area of node(x) is the last area (Kth area), then the equation of node(x) to be CH can be written as follows:where m is the equal node of node(x) within same area but different region.$$\begin{aligned} \displaystyle P_{\rm CH}(x)= P(x,m) \cap N_B (x) = 0 \cap N_F (x) \ne 0 \end{aligned}$$(13)
3.3.5 Number of forward and backward nodes
ID | Forward | Backward | Equal | Hop-count |
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1 | 4, 5 | Nil | 2 | 1 |
2 | 5, 6 | Nil | 1, 3 | 1 |
3 | 5, 6 | Nil | 2 | 1 |
4 Results
Parameter | Value | Units |
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Sink position | 50, 100 | |
Number of nodes | 100, 200 | |
Initial energy | 0.25, 0.5, 1.0 | Joules |
Area | (100 m × 100 m) (200 m × 200 m) (400 m × 400 m) | Meters |
Packet size | 2000 | Bits |
Control packet (data frame overhead) length | 200 | Bits |
Transmitter energy \(T{_x}\) | 50 | nJ/bit/m\(^2\) |
Receiver energy \(R{_x}\) | 50 | nJ/bit/m\(^2\) |
Data aggregation energy | 5 | nJ/bit/m\(^2\) |
Transmit amplifier (free space) | 100 | nJ |
Transmit amplifier (multipath) | 0.0013 | nJ |
4.1 Network throughput/ aggregation/node density/node heterogeneity
Init energy | E with agg (ETX + EDA) | Pks to BS | Rounds | E without agg (ETX) | Pks to BS | Rounds |
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0.25 | 4.0364e−04 | 122,423 | 2087 | 6.0550e−05 | 35,638 | 504 |
0.5 | 7.1335e−04 | 228,028 | 3663 | 1.2300e−04 | 70,618 | 998 |
1.0 | 0.0016 | 495,250 | 8074 | 1.6275e−04 | 115,374 | 1607 |
4.2 Alive nodes vs number of nodes
Energy (J/node) | Protocol | Rounds 1st node dies | Rounds last node dies | Packet to BS | E-consumed (Tx + EDA) |
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0.25 | LEACH | 394 | 665 | 8500 | 41.6349 e−09 |
ICR | 350 | 1850 | 122,423 | 4.0364 e−04 | |
0.5 | LEACH | 932 | 1312 | 16,924 | 83.2754 e−09 |
ICR | 400 | 4300 | 228,028 | 7.1335e−04 | |
1 | LEACH | 1848 | 2608 | 29,731 | 148.0973 e−09 |
ICR | 750 | 9200 | 495,250 | 0.0016 |
Step | LEACH | JCR | ICR |
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Advertisement | All nodes sharing residual battery information | Gradient field setup | Cluster-sorting |
CH selection | Random selection of CH among nodes | CH selection using back-off timer | CH selection based on cumulative weights of parameters |
Cluster setup | The CH sends an advertisement message to the CM. The CM joins the desired CH | Similar to LEACH | The CH only sends its info to the CMs in the sub-area |
Scheduling | The CH generates the TDMA schedule and broadcasts it to all nodes in the network. All the nodes receive this message and accept or discard based on relevance | The CH sends the TDMA-based schedule information to all nodes in its transmission range | The CH sends the TDMA-based schedule information of only nodes in the sub-area |
Route selection | No routing is performed in LEACH | The BS initiates the path discovery and moves from one gradient to the next and selects the optimal the next gradient CHs | The ICR protocol develops a multihop route of the CHs to the BS. This routing is initiated by the BS |
Data transmission | The data transmission of LEACH is started from the CM to the CH. Since all the nodes are in the transmission range of each other, the probability of packet loss is very high | Data transmissions from the CM to the CH have a lower probability of collision compared with LEACH but more than that of ICR because of variable clustering ranges | Each clustering area has its own transmission range, the probabilities of packet loss in ICR are much less than LEACH |
Energy | Pkts-to-BS | Rounds | Pkts-to-BS | Rounds | Pkts-to-BS | Rounds |
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25 m | 50 m | 100 m | ||||
0.25 | 82,082 | 2552 | 122,423 | 2087 | 81,256 | 1535 |
0.5 | 187,403 | 4761 | 228,028 | 3663 | 168,638 | 3224 |
1.0 | 298,188 | 9135 | 495,250 | 8074 | 385,579 | 7291 |
No. | Init energy | Pkts to BS | Rounds | Pkts to BS | Rounds |
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Homogeneous | Heterogeneous | ||||
1 | 0.25 | 104,726 | 1622 | 78,823 | 1208 |
2 | 0.5 | 207,463 | 3269 | 131,270 | 2671 |
3 | 1.0 | 491,399 | 8000 | 272,134 | 4983 |