and Coverage-aware Clustering Scheme for Wireless Sensor Networks

International Journal of Automation and Computing

7(4), November 2010, 500-508 DOI: 10.1007/s11633-010-0533-5

A Power- and Coverage-aware Clustering Scheme for Wireless Sensor Networks Liang Xue1 1

Xin-Ping Guan1, 2

Zhi-Xin Liu1

Qing-Chao Zheng1

Research Office of Networking Control, Institute of Electrical Engineering, Yanshan University, Qinhuangdao 066004, PRC 2

School of Electronic, Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, PRC

Abstract: A common and critical operation for wireless sensor networks is data gathering. The efficient clustering of a sensor network that can save energy and improve coverage efficiency is an important requirement for many upper layer network functions. This study concentrates on how to form clusters with high uniformity while prolonging the network lifetime. A novel clustering scheme named power- and coverageaware clustering (PCC) is proposed, which can adaptively select cluster heads according to a hybrid of the nodes0 residual energy and loyalty degree. Additionally, the PCC scheme is independent of node distribution or density, and it is free of node hardware limitations, such as self-locating capability and time synchronization. Experiment results show that the scheme performs well in terms of cluster size (and its standard deviation), number of nodes alive over time, total energy consumption, etc. Keywords:

1

Wireless sensor networks, clustering, high-uniformity, energy and coverage efficiency, network lifetime.

Introduction

Clustering is one of the basic approaches for designing energy-efficient, robust and highly scalable distributed sensor networks[1−5] . In such architecture, all the nodes fall into two classes: cluster-head node (cluster head) and noncluster-head member node (member node or cluster member). The cluster head is responsible for scheduling its member nodes to collect sensing information. In addition, since a large amount of nodes are deployed for specific applications, some neighbor sensors within one cluster coverage may detect the same event or phenomena simultaneously. Therefore, it is also necessary for the cluster head to perform local data aggregation, and then cluster head retransmits the compressed data to the base station, through which it reduces data redundancy and the hops data traversed[6] . In this paper, we propose PCC, a scheme that results in energy efficiency for data gathering application in wireless sensor networks (WSNs). In PCC, the cluster-head node receives data from its cluster members, performs signal processing functions on the data (e.g., data aggregation), and transmits data to the remote base station. Therefore, the cluster-head node is much more energy-intensive than the member node. In addition, to ensure that the energy level of each cluster head can evenly degrade, it is crucial to rotate the cluster-head node dynamically to increase transmission reliability. In consideration of above design requirements, the PCC clustering process is divided into two phases. In the cluster formation phase, by using the repulsive interactions between clusters, the scheme induces emergent formation of clusters that are an efficient cover of the network. Further, in the steady-state phase, the elected cluster head synthesizes the local information, including residual energy and loyal degree of its member node, to determine whether it needs to abdicate or maintain working in the subsequent Manuscript received June 5, 2009; revised November 11, 2009 This work was supported by National Basic Research Program of China (No. 2010CB731800), National Natural Science Foundation of China (No. 60934003), and Educational Foundation of Hebei Province (No. 2008147).

data-transferring round adaptively. As elected cluster head issues abdication message within a cluster, it also promotes a more qualified node to be the new head to undertake data receiving-aggregating-transferring task. Fig. 1 depicts the clustering process of PCC.

Fig. 1

2

Overview of PCC clustering scheme

Related work

Many clustering algorithms in various literatures have been proposed[1, 6, 7−10] . In general, these algorithms can be divided into two kinds, as determined by the nature of cluster-head selection. One kind is based on random number generating, and the other does not. Low energy adaptive clustering hierarchy (LEACH)[7] included in the first kind, pioneered clustering protocol applied in wireless sensor networks, aims at proposing a two-phase mechanism based on the random number each node generates. However, LEACH causes cluster-head nodes less evenly distributed in the network. Hybrid energy-efficient distributed (HEED) clustering[8] is another randomized method, which can select cluster heads through O(1) time iterations. According to the metric applied, HEED adopts corresponding cost types (e.g., minimum degree cost, maximum degree cost, and average minimum reachability power) towards cluster formation. Since a tentative cluster-head node can

501

L. Xue et al. / A Power- and Coverage-aware Clustering Scheme for Wireless Sensor Networks

change into a regular node in subsequent clustering intervals, the data packets are prone to lose during node state transition within allocated time slots. In non-randomizing-based clustering algorithms[1, 11−16] , they are commonly classified into three branches: weightbased, topology-based, and heuristic-based algorithms. As for weight-based algorithms, three classical weight-based clustering algorithms are proposed in [11–13]. In [11], the author introduces a weighted cost function, through which node chooses its cluster-head by considering fully energy saving and workload balancing of cluster heads. The weight-based distributed clustering algorithm is proposed in [12], which takes into account a combined effect of four crucial system parameters. By assigning reasonable weighing factors for the corresponding system parameters, clusterhead selection solely relies on comparison of the combined weight among neighboring nodes. Power-efficient gathering in sensor information systems (PEGASIS)[1] is a topologybased clustering approach, which improves the performance of LEACH and prolongs the network lifetime significantly using a chain topology. The chain-shaped cluster will break up at particular node due to the sparse density of some region, which shortens the network lifetime, although the formed cluster can still work as two chain-shaped clusters. Other types of non-randomizing-based clustering techniques are nearly heuristic in nature. Gerla and Parekh[14, 15] originally proposed the highest-degree, also known as connectivity-based clustering. The node with maximum number of neighbors is chosen as a cluster head, and any tie is broken by the unique node ID. However, such a system has a low rate of cluster head change, and the throughput is low. Similarly, Lowest-ID[16] heuristic also assigns unique ID to each node, and it chooses the node with minimum ID as a cluster head. The inadequacy of this heuristic lies in its bias towards nodes with smaller IDs, which may lead to battery drainage of certain nodes. The scheme proposed in this paper attains a scaleindependent emergent clustering algorithm, through which it performs highly uniform cluster distribution with less overlap between clusters. In addition, PCC requires only a small constant amount of communications overhead, and it achieves clustering despite the overall number of nodes in the network. Furthermore, a virtual migration-based rotation strategy of the cluster-head node is introduced into PCC. Once a cluster head detects its inadequate power, the head will indicate unwillingness to return to the scheme. Consequently, PCC can also ensure the reliability of data transmission.

3

Radio model for PCC

We apply a simplified radio model as discussed in [7], including energy dissipated by transmitter and receiver. The transmitter dissipates ET x (l, d) J energy to run the radio electronics and the power amplifier. The equations used to calculate transmission costs for an l-bit message and disTable 1

tance d are shown below: ( l × Eelec + lεfriss-amp d2 , ET x = l × Eelec + lεtwo-ray-amp d4 ,

d < dcrossover d > dcrossover

(1)

where l is the message length in bits; Eelec represents the electronics energy; d is the distance between the transmitter and receiver; εfriss-amp and εtwo-ray-amp are propagation loss factors as inversely proportional to d2−4 ; dcrossover depicts the threshold distance for Friss and two-ray ground attenuation models. Similarly, when receiving the l-bit message, the radio expends energy: ERx = l × Eelec . (2) In addition, the cluster head dissipates EBF J/bit to perform beam-forming computations on data aggregation. In our simulations, all the tested clustering algorithms use the same constants for calculating energy costs, which are given in Table 1. For more details, readers can refer to [7] if necessary.

4

PCC scheme

4.1

Notations and definitions

To describe the PCC scheme, we use the following notations (shown in Table 2). These notations are classified into three types: network layer notations, node layer notations, and cluster layer notations. For the network layer notations, we assume that all nodes are scattered in a square sensing region, whose area is L×L. With limited power capacity, radio ranges of all nodes are predefined as R in PCC. As for node layer notations, all nodes located within the sensing region together form the set of generic nodes P . A node in PCC can have three possible states: it can be non-clustered (not a member node of any cluster), member node or it may be a cluster-head. We mark aggregates of these nodes with status as Ps−n , Ps−m , Ps-c , respectively, which are different subsets of P . To distinguish any two different nodes in P , representative element p is added with an inferior character, e.g., pv and pu . Node layer notations are almost without node status distinctions. Likewise, cluster layer notations reflect the subordinate relationship between cluster-head and member nodes. CH represents a set, which includes all the current cluster heads. To specify a particular cluster-head, elements in CH are indexed by its sequence number, e.g., CHi . Mi depicts the collection of CHi 0 s member nodes, and it has the same subscript as of CHi , because the subscripts are having oneto-one correspondence. Besides, we define the sum of elements in finite set A as card(A). For example, formula (3) gives the degree of node pv . Ndegree(pv ) = card({pkp C pv } ∪ pv ). (3)

System parameters for energy cost

Parameter

Eelec

l

εfriss-amp

εtwo-ray-amp

dcrossover

Value

50 nJ/bit

4000 bit

10 pJ/bit/m2

0.0013 pJ/bit/m4

87 m

502

International Journal of Automation and Computing 7(4), November 2010 Table 2 Notation L×L

Notations in PCC

Meaning The area of the sensing region

R

Radio range

P

The set of generic nodes in the network

Ps-n , Ps-c , Ps-m

Subset of nodes with status, which is either non-clustered, cluster head or member node Representative element in P without subscript

p pv , pu

To differentiate, representative elements in P with diverse subscripts

p / pv

Node p locates in pv 0 s radio range (excluding pv )

CH

The set of cluster heads

CHi

The cluster-head node in CH with sequence number i

Mi

The set of member nodes belong to CHi (exclude CHi )

mij

The j-th member node in Mi

Eresidual(pv )

The residual energy of node pv

p · CHi

p is one of the elements in Mi

Intuitively, the degree of node pv is the total number of pv 0 s one-hop neighbors (including pv ). In PCC, we are more concerned about the member node mij 0 s loyal degree, which gives the number of mij 0 s loyal members, and its mathematical expression is shown in (4).

Nloyal − d(CHi ) = card({ p| p · CHi , p / CHi } ∪ {CHi }∪ { p| p ∈ Ps−n , p / CHi } ∪ {CHi }) = card({ p| p · CHi } ∪ {CHi }∪ ∅ ∪ {CHi }) =

Nloyal−d(mij ) = card({ p| p · CHi , p / mij } ∪ {mij } ∪ { p| p ∈ Ps−n , p / mij } ∪ {CHi }).

card({ p| p · CHi } ∪ {CHi }).

(4)

The loyal members of mij include three main parts, { p| p · CHi , p / mij } ∪ {mij } denotes the set of member nodes which have CHi as their cluster head, and these member nodes exist simultaneously within mij 0 s neighbor set; { p| p ∈ Ps−n , p / mij } represents the non-clustered nodes that will be mij 0 s member nodes if mij declares that it is a cluster head. The last part in (4) {CHi } implies that if CHi abdicates its current head position, it could be a member node of mij , as mij is being promoted to a new cluster head. We illustrate the above explanations in Fig. 2.

(5)

Note that p·CHi denotes a member node that has CHi as its cluster head, whereas p / CHi indicates that the node0 s physical location is within CHi 0 s radio range. In PCC, one node0 s physical location may be within some clusterhead0 s coverage, but it does not mean that the node belongs to that cluster. Therefore, it can be deduced that { p| p · CHi } ⊆ { p| p / CHi }. Especially, when some node pv is in non-clustered status, i.e., pv is an element in Ps−n , Nloyal−d(pv ) can be given as Nloyal−d(pv ) = card({ p| p ∈ Ps−n , p / pv } ∪ {pv }).

(6)

PCC clustering scheme mainly consists of two phases: cluster formation phase, in which it makes cluster heads distribute well in the network; steady-state phase, in which a novel virtual migration mechanism is introduced by taking account of energy and coverage preserving. Details of these two phases are in the following subsections.

4.2

Fig. 2

Illustration of node loyal degree

Similar to Nloyal−d(mij ) , we can also obtain Nloyal−d(CHi ) (see in (5), mij is replaced with CHi ), which is the sum of loyal members of CHi .

Cluster formation phase

1) Network initialization For initialization, all nodes are in the non-clustered status. Nodes implement the PCC scheme at slightly different times due to clock discrepancy. These nodes viewed as elements in Ps−n start up neighbor-detection procedure, through which they obtain an incomplete neighbor list recording part of their neighbors. Some of the nonclustered nodes in Ps−n declare themselves as candidate cluster heads, which have higher number of neighbors. The non-clustered nodes maintain their status unless hearing the CANDIDATE HEAD MSGs and randomly choose a single


cluster for membership. CANDIDATE HEAD MSGs include the global unique ID assigned to each node when first deployed. It is worth to note that some node pv is possible to receive more than one CANDIDATE HEAD MSGs. However, pv will select only one cluster from the received CANDIDATE HEAD MSGs. Then, pv also broadcasts a JOIN MESSAGE to notify all nodes (which satisfy p/pv ) its current state. Similarly, if node pv leaves an existing cluster, it also broadcasts a LEAVE MSG locally. Node p (p / pv ) keeps track of these messages, and it updates Nloyal−d(p) dynamically. In real application scenario, due to unsynchronized startup time, the node may affiliate itself to some clusters even if it possesses the largest Ndegree . It leads clusters to overlap each other seriously. Some gaps may hold the space among two or more close neighboring clusters. To attain uniform clustering distribution, remedial measures should be taken according to different clustering status. 2) Circumstance 1 If node pv is a cluster head, e.g., pv is CHf . CHf polls all member nodes in Mf to find whether there exists member node mf j whose Nloyal−d(mf j ) is larger than Nloyal−d(CHf ) . If such a node exists, CHf prepares to transfer its head position to a node whose loyal degree is the largest. As the composition of loyal members has been given, the migration generates repulsion effect among clusters, and the formed clusters could be forced to depart from each other. The best migrating direction resides in the least overlap with current clusters. CHf promotes mf j as the new selected cluster head by issuing an ELECTION MSG. All member nodes in Mf receive the announcement, realizing that CHf will abdicate its position to mf j . They keep listening communication channel for responding. Further, mf j broadcasts a CANDIDATE HEAD MSG including its ID as a reply to CHf . Nodes that are common neighbors of mf j and CHf become member nodes of mf j . In the mean time, when CHf receives mf j 0 s declaration of being the new cluster head, CHf abdicates the current head position and gets itself one member node of mf j . Additionally, member nodes of CHf which are not the neighbors of mf j leave CHf . These nodes change themselves into non-clustered status due to cluster migration. 3) Circumstance 2 In the other case, when node pv is in non-clustered status, pv checks the number of its neighbors to verify whether Nloyal−d(pv ) is larger than a time-variant decreasing function fthreshold (t).

fthreshold (t) = γ(1 −

γ=

t ), cT

c > 1, c ∈ N, t 6 cT

card(P XP ) 1 Ndegree(pi ) P) card(P i=1

503

cT denotes the duration of cluster formation phase. An issue of utmost importance is that how to determine the value of c. If the value of c is set small, all non-clustered nodes will soon announce themselves as cluster-head nodes despite imbalance in σcluster , leading to considerable variation in the cluster size; meanwhile, the virtual migration of cluster heads will not take effect distinctly. Else if c is too large, cluster formation phase needs a relatively longer period. In fact, time needed for cluster formation phase is merely 2–3 iteration times. To evaluate the performances of the PCC scheme, we set the value of c as 5, but it does not mean that c should be kept invariant. In PCC, a non-clustered node pv will generate a new cluster whenever it finds Nloyal−d(pv ) is larger than fthreshold (t). Afterwards, the new generated cluster migrates routinely as other formed clusters. New generated clusters can fill in the gaps among clusters continuously. Performances of the PCC clustering scheme are not or less influenced by the node distribution or density. One can get that: the function value of fthreshold (t) decreases monotonically with time t; when time t equals cT , fthreshold (t) reaches its minimal value 0. Essentially, positive integer c denotes the iterations required for cluster formation phase. Considering one of the extreme circumstances-even after the end of cluster formation phase, some node pv , which is located in the sparse density region, did not receive any CANDIDATE HEAD MSGs or announce itself as a candidate cluster head. However, the loyal degree of node pv is surely larger than fthreshold (t) after cluster formation is completed. Then, node pv gets itself a single node cluster head, which possesses merely one member node, i.e., pv . 4) Circumstance 3 Likewise, if node pv is a member node, it is just obedient to its cluster head. When the cluster head abdicates its position, pv adjudicates independently to be a member of the new generated head or gets it non-clustered. 5) Convergence analysis In the following, we give some analysis about the convergence. We simplify the problem by assuming that N (N < P )) nodes in P are placed in a line (see Fig. 3), and card(P supposing only one cluster head can be moved along the line. Radio range R is a constant in PCC despite node status.

(7) Fig. 3

(8)

where γ represents the average number of each node0 s neighbors in P . Essentially, γ is a global system parameter that cannot be pre-calculated. However, it can be approximated P )/(l × l) × πR2 and embedded into all nodes in by card(P P . T is the estimated time interval between two iteration times. t is the time passed since the start-up time.

Simplified virtual migration

If 0 < R < min({ d| d = kpi − pj k }) (∀pi , pj ∈ P ; i 6= j), there will be no cluster head migrations in the network, and cluster formation phase can obviously converge. Thus, each non-clustered node just waits iteration times out, and becomes a cluster head individually. If kpj − pj+1 k < R < kpi − pi+1 k (∃ pi ∈ P ; 1 6 j < i), the cluster head can virtually migrate. However, the maximal idealized migrating steps are i − 1.

504

International Journal of Automation and Computing 7(4), November 2010

By taking into account the loyal degree as well as radio range restrictions, we can also obtain the following conclusion. If radio range R does not satisfy the above distance restrictions, then the value of R makes the one and only cluster move along the line with no barriers. In other words, if kpi − pi+1 k < R < kpi − pi+2 k (∀pi ∈ P ), and if Nloyal−d(pi ) < Nloyal−d(pi+1 ) , then the total migrating steps can be recalculated as N − i. Keeping the distance qualifications unvaried, if Nloyal−d(pi ) < Nloyal−d(pi+1 ) , and node pj with Nloyal−d(pj−1 ) < Nloyal−d(pj ) < Nloyal−d(pj+1 ) exists, where (∀pi ∈ P ; i 6 j). The converging steps can be calculated by j − i. Although discussions have been simplified, actually, it points out four causes of migrating termination.

4.3

Steady-state phase

At the end of the cluster formation phase, there are no cluster migrations or cluster regenerations in the networks. In the steady-state phase, member nodes transmit the sensing information (e.g., the acoustic and seismic signal, light intensity, temperature, or pH value, etc.) to their cluster heads. Next, cluster heads aggregate the data and relay them to the base station. Since the base station may be far away and the data messages are large, this is a high-energy transmission. Therefore, to be a cluster head, it will consume much more energy than member nodes. To take full use of the node0 s conserved energy and to extend the system lifetime, rotating head position should be introduced into the PCC clustering scheme. To avoid misunderstanding in the following, we mark all system parameters in the k-th round with subscript k, e.g., CHi changes it into CHi,k . CHi,k polls its entire member nodes in Mi,k to determine dynamically whether it needs to remain at the head position for the oncoming round. The criterion is in accordance with both the node residual energy level Eresidual(mij,k ) and node loyal degree Nloyal−d(mij,k ) . To attain better coverage performance and longer working duration, we define the following cost threshold Ethreshold(CHi,k ) for CHi,k picking out the qualified nodes in Mi,k .

Ethreshold(CHi,k ) =

1 card(Mi,k )

card(Mi,k )

X

Eresidual(mij,k )

j=1

(9) where Ethreshold(CHi,k ) implies the average power level of cluster CHi,k . By comparing Eresidual(mij,k ) with Ethreshold(CHi,k ) , CHi,k establishes the qualified nodes set Q(CHi,k ) . In Q(CHi,k ) , element nodes possess a relatively higher power level to be the qualified successor of CHi,k in the (k + 1)-th round. QCHi,k = { p| p · CHi,k } ∪ {CHi,k } ∩ { p| Eresidual(p) > max(ECHi,k , Ethreshold(CHi,k ) )}

(10)

where max(ECHi,k , Ethreshold(CHi,k ) ) gives a lower limit to the residual energy level of nodes in QCHi,k . By this limitation, the energy level of the qualified successor in the

(k + 1)-th round could not be less than ECHi,k . Otherwise, the succession node will possibly exhaust energy during one transmission process. (ECHi,k is defined in Section 5.1) Similar to the cluster formation phase, CHi,k abdicates its cluster head position once it is no longer an element in QCHi,k . To decrease overlap between clusters and stretch, the sensing area to fully converge, the most potential node MCHi,k ⇒ in QCHi,k can be promoted, only if it has the largest number of loyal degrees. MCHi,k ⇒ = max(Nloyal−degree(p) ), ∀p ∈ QCHi,k .

(11)

Next, the virtual migration process of the cluster head is the same as that of the cluster formation phase. Remark 1. PCC clustering scheme is independent of strict time synchronization mechanism both in the cluster formation phase and in the steady state phase. Design of the cluster formation phase happens to be based on the clock discrepancy phenomena. For the steady state phase, if mij,k previously randomly selects CHi,k as its cluster head, and mij,k is also located within CHv,k 0 s radio range, i.e., mij,k · CHi,k and mij,k / CHv,k . Then, when CHv,k migrates its head position to MCHv,k ⇒ , it is possible that mij,k has not completed data transmission to CHi,k . In this case, CHv,k just polls member nodes in Mv,k without waiting for mij,k . Remark 2. The initialization of the steady state phase is triggered by the basestation. Afterwards, every data collection round serves basestation needs, i.e., when basestation has to examine the sensing information, it broadcasts instruction information to the whole network. On receiving instruction successfully, all cluster heads in CHk respond to the instruction information. They relay the aggregated data to the basestation immediately. Elements of CHk select their successors independently, which is in a time-unsynchronized way as described in Remark 1. It is worth to note that the interval between two approximate instructions should be longer than the time length of both data transmission and cluster head migration time. Remark 3. At the end of each round, there may still be a small quantity of nodes that are uncovered by some clusters. These non-clustered nodes can transmit sensing data to their one-hop neighbors, which have already been member nodes of current clusters. For details, we give the following two definitions about two-hop members. Definition 1. We mark the start time of the k-th instruction information as tk . Likewise, the start time of (k +1)-th instruction information is marked as tk+1 . Therefore, the duration of k-th round Tk is given as Tk = tk+1 −tk . Tk is set a little longer than the longest processing time Tplongest , which is the maximal time required for specific cluster completing data collection-aggregation- relaying and cluster head migration. Definition 2. Within (Tk − Tplongest ), given nonclustered node pv , ∃pu · CHi,k and pv / pu , pv is deemed as one of CHi,k 0 s two-hop member. Similarly, the n-hop member of CHi,k is an analogue of Definition 2, and we do not repeat it here. The small quantity of non-clustered nodes could finally transfer its data to destination by multi-hops.

505


5

Evaluation

5.1

. N N k 6 Einitial [( L×L πR2 × l × Eelec ) + ( L×L πR2 + 1) × l×

Evaluation metrics

To explain how system parameters affect the clustering metrics, we first analyze how many rounds that node can sustain, and then define some general criterions for evaluating clustering performances. We adopt Piggyback technology: accompanied by the regional sensing information, each member node0 s residual energy information is also included in the sensing data. Once member node mij in Mi transmits l bits sensing data to CHi , and then CHi executes receiving-aggregatingtransferring task. When received successfully, a cluster head node compresses all the received data into l bits aggregated data and then transmits the aggregated data to the base station. The ratio of data aggregation at CHi is (card(Mi ) + 1) : 1, where card(Mi ) + 1 denotes the number of member nodes belonged to CHi , which also includes CHi itself. The energy consumption for mij and CHi are shown as follows. Emij = l × Eelec + l × εfriss−amp × d2mij →CHi

EBF + (Eelec + εfriss-amp d2CHi →BS ) × l]× 200 (dmij →CHi < dcrossover ) (17) or . N N k 6 Einitial [( L×L πR2 × l × Eelec ) + ( L×L πR2 + 1) × l× EBF + (Eelec + εtwo-ray-amp d4CHi →BS ) × l]× 200 (dmij →CHi > dcrossover ) (18) where N = 100 node, Eelec = 50 nJ/bit, L = 100 m, R = 20 m, EBF = 5 nJ/bit, Einitial = 2 J/node, 75 m < dCHi →BS < 185 m. When 75 < dCHi→BS < dcrossover , we get that 3.26 < kupperbound1 < 3.34; otherwise, when dcrossover < dCHi →BS < 175 m, 1.13 < kupperbound2 < 3.26. The synthetic analysis of the upper bound of k can be given as

(12) 1.13 < kupperbound < 3.34.

if dCHi →BS < dcrossover : ECHi = card(Mi ) × l × Eelec + (card(Mi ) + 1) × l× EBF + (Eelec + εfriss-amp d2CHi →BS ) × l

(13)

else if dCHi →BS > dcrossover : ECHi = card(Mi ) × l × Eelec + (card(Mi ) + 1) × l× EBF + (Eelec + εtwo-ray-amp d4CHi →BS ) × l.

(14) According to (13), the energy consumption of ECHi is composed of three parts: data receiving, data aggregation, and data transmission. The final item (Eelec + εtwo−ray−amp d4CHi →BS ) × l in (14) accounts for the energy used to transmit the aggregated data to the base station. If CHi continues to undertake cluster head, in the k-th round (definition of round is given in Definition 1), Eresidual(CHi ) , the residual energy of CHi , can be approximated by Einitial(CHi ) − kECHi , where Einitial(CHi ) represents the energy level when nodes are first deployed. The maximal rounds that CHi can sustain are expressed by (15), with the assumption that the member node transmits 200 frames to the cluster head in every round, and each frame length in bits is 4000 bit/frame, Einitial − kECHi > 0.

(15)

Thus, k6

Einitial . ECHi

Further, card(Mi ) can N πR2 /(L × L). Therefore, in this case,

be

(16) approximated

to

(19)

Particularly, for the case when system parameters are not restricted to the above values, we vary radio range R and dCHi →BS to verify how they can affect ECHi . By comparing with Einitial surface, the boundaries of R and dCHi →BS are marked by the black color, which makes ECHi lower than Einitial surface. In our PCC scheme, radio range was set less than 25 m, and dCHi →BS ranges from 75 m to 185 m. As shown in Fig. 4, through setting proper system values in PCC, CHi will not use up its own energy during one data transmission process. However, the finite energy of the node could merely maintain data relaying three times at most just as (19) shows.

Fig. 4

Variation of ECHi

1) Metrics of energy i) Ratio of nodes alive We model the ratio of nodes alive Ralive,k as the metric to evaluate the energy load balancing in the PCC scheme. If Ralive,k decreases quickly with round increments, the clustering algorithm has poor load balancing capability.

506


card({ p| Eresidual(p) > ECHi,k , p ∈ P }) × 100 %. P) card(P (20) For brevity, ECHi,k is unified into ECHi,k (l, (185+75)/2), which is the average energy consumption when CHi,k happens to be located in the centre of the sensing region. Ralive,k does not mean that a node has used up its energy, but for preventing the node to be abruptly dead within one transmission. ii) Total energy consumption To give an overview of energy consumption, Wtotal represents the sum of energy depletion when all nodes execute clustering. Lower Wtotal shows that the clustering algorithm can save more energy within fixed operation time. Ralive,k =

P) card(P

Wtotal,k =

X

(Einitial − Eresidual(pi,k ) ).

(21)

i=1

2) Metrics of uniformity and coverage i) Standard deviation in cluster sizes Standard deviation in cluster sizes σcluster,k is given as follows, which can evaluate the differences of cluster heads0 communication load. 1 σcluster,k = × card(CH k) − 1 v u card(CH k ) ) ucard(CH X 1 t P k (card(M )− card(Mi,k ))2 . i,k card(CH k ) i=1 i=1 (22) ii) Number of cluster heads In each round, we expect the number of cluster heads Nhead,k remains unchanged. Nevertheless, most dynamic clustering algorithms are difficult to avoid the variations of cluster heads. Nhead,k = card(CH k ).

5.2

Fig. 5

Ratios of nodes alive

In the experiment shown in Fig. 6, we explore the energy consumption with a macroscopic point of view. With round increases, energy consumption Wtotal,k in PCC increases slowly. In the later 25th to 40th rounds, residual energy of the entire nodes is almost the same in the PCC scheme. Even energy threshold can select a high-energy candidate cluster head, but eligible nodes are less comparable with the circumstance when nodes are first deployed. Therefore, the performance gap between PCC and Lowest-ID is not significantly different. Due to randomizing-based mechanism, the irregularly distributed cluster heads in LEACH may locate far away from basestation. Besides, at the beginning of each round, candidate cluster heads broadcast declarations covering the whole network. The above-mentioned two reasons also cause a great deal of energy consumption in LEACH. Accordingly, LEACH performs worse than PCC and Lowest-ID in terms of Wtotal,k , especially in the middle and later rounds.

(23)

Simulation analysis

In Fig. 5, we first examine the impact of rounds on Ralive,k in the network. Obviously, the PCC clustering scheme has higher Ralive,k with the increase of rounds. In direct communication, the network is independent of cluster structure, each node transmits their sensing data to the base station directly, and the energy consumption is nearly proportional to the square of transmission distance. The uneven distribution of cluster heads in LEACH causes the number of member nodes diverging a lot from one cluster to another. To the dense cluster, the cluster head uses much more energy than its counterpart does in the sparse one. Lowest-ID is originally a static clustering algorithm regardless of the candidate node0 s energy level. In the meantime, once the cluster head is selected, they continue undertaking data relaying until energy is used up. However, in our simulation, Lowest-ID rotates cluster heads in every round for statistical convenience. The PCC scheme considers both the direction when head migrates and the residual energy of the candidate node. Additionally, energy conservation strategy in PCC suspends the decrease of Ralive,k .

Fig. 6

Total energy consumptions

Another appealing cluster property is minimizing the standard deviation in cluster sizes. For one clustering algorithm, we expect that the energy load can be distributed to all cluster heads evenlyby which it guarantees that the energy falling rate in CH k tends to be almost the same. In Fig. 7, the experiment shows the minor differences in


cluster sizes of PCC. Comparing LEACH and our PCC scheme, we find that local determination of head selection indeed reduces the deviation among clusters. In this sense, σcluster,k not only reflects the energy load distribution, but also reflects the evenness of cluster heads. Similar to PCC, Lowest-ID makes every node locally determine its ownership, and the cluster range essentially is equal to the radio range. There is no significant difference in σcluster,k between these two algorithms. Finally, we study the effect of rounds on the quantity of cluster heads. In the experiment, the number of selected cluster heads varies. The smaller the radius is, the larger the required number of cluster heads needed to cover the entire network. The number of cluster heads in PCC is comparable to those selected by LEACH and Lowest-ID. Fig. 7 shows that average Nhead,k in PCC remains almost constant in the earlier rounds, since PCC intends to select cluster heads that are based on the formed clusters in the cluster formation phase. As time goes by, fewer nodes are further capable of acting as cluster heads. Thus, Fig. 8 shows that Nhead,k decreases when high-energy nodes fall sharply. On the other hand, PCC can balance energy consumption among all nodes. Under the same settings, average operation time of PCC is the longest.

6

507

Conclusion and future work

In this paper, we describe a novel power- and coverageaware clustering scheme applied to periodical data gathering in sensor networks. PCC produces a uniform distribution of cluster heads through localized communication in the cluster formation phase. Moreover, PCC also adopts virtual migration mechanism and residual energy threshold among sensors in the steady state phase. To achieve a balance in energy consumption, eligible nodes take turns to be elected as the cluster heads. Simulation results show that PCC performs better than LEACH and the other two clustering algorithms in terms of conserving energy and meeting coverage requirement. Furthermore, PCC is independent of time synchronization, which will restrict clustering practical application. In order to verify our assumptions about PCC, we will extend it to the design of upper layer network protocols that require energy efficiency, scalability, and load balancing. Considering inter-cluster data transmission, there is still much space to improve the clustering performances.

References [1] S. Lindsey, C. S. Raghavendra. PEGASIS: Power-efficient gathering in sensor information systems. In Proceedings of IEEE Aerospace Conference, IEEE, Monana, USA, vol. 3, pp. 1125–1130, 2002. [2] O. Younis, S. Fahmy. Distributed clustering in ad-hoc sensor networks: A hybrid, energy-efficient approach. In Proceedings of IEEE INFOCOM, Hong Kong, PRC, vol. 1, pp. 640, 2004. [3] S. Soro, W. B. Heinzelman. Cluster head election techniques for coverage preservation in wireless sensor networks. Ad Hoc Networks, vol. 7, no. 5, pp. 955–972, 2009. [4] H. Abusaimeh, S. H. Yang. Dynamic cluster head for lifetime efficiency in WSN. International Journal of Automation and Computing, vol. 6, no. 1, pp. 48–54, 2009. [5] C. Bean, C. Kambhampati. Autonomous clustering using rough set theory. International Journal of Automation and Computing, vol. 5, no. 1, pp. 90–102, 2008.

Fig. 7

Standard deviations in cluster sizes

[6] S. Bandyopadhyay, E. J. Coyle. An energy efficient hierarchical clustering algorithm for wireless sensor networks. In Proceedings of the 22nd Annual Joint Conference of IEEE Computer and Communications, IEEE, San Francisco, USA, vol. 3, pp. 1713–1723, 2003. [7] A. P. Chandrakasan, A. C. Smith, W. B. Heinzelman. An application specific protocol architecture for wireless microsensor networks. IEEE Transactions on Wireless Communications, vol. 1, no. 4, pp. 660–670, 2004. [8] O. Younis, S. Fahmy. HEED: A hybrid, energy-efficient, distributed clustering approach for ad hoc sensor networks. IEEE Transactions on Mobile Computing, vol. 3, no. 4, pp. 366–379, 2004. [9] H. W. Chan, A. Perrig. ACE: An emergent algorithm for highly uniform cluster formation. In Proceedings of the 1st European Workshop on Sensor Networks, Lecture Notes in Computer Science, Springer, Berlin, Germany, vol. 2920, pp. 154–171, 2004.

Fig. 8

Numbers of cluster heads

[10] J. Kamimura, N. Wakamiya, M. Murata. Energy-efficient clustering method for data gathering in sensor networks. IEIC Technical Report, Japan, vol. 103, no. 691, pp. 31–36, 2004.

508


[11] M. Ye, C. F. Li, G. H. Chen, J. Wu. EECS: An energy efficient clustering scheme in wireless sensor networks. IEEE Transactions on Mobile Computing, vol. 3, no. 4, pp. 366– 379, 2004. [12] M. Chatterjee, S. K. Das, D. Turgut. WCA: A weighted clustering algorithm for mobile ad hoc networks. Cluster Computing, vol. 5, no. 2, pp. 193–204, 2002. [13] S. Basagni. Distributed clustering for ad hoc networks. In Proceedings of the 4th International Symposium on Parallel Architectures, Algorithms, and Networks, IEEE, Fremantle, Australia, pp. 310–315, 1999. [14] M. Gerla, J. T. C. Tsai. Multicluster, mobile, multimedia radio network. Wireless Networks, vol. 1, no. 3, pp. 255-265, 1995. [15] A. K. Parekh. Selecting routers in ad-hoc wireless networks. In Proceedings of the SBT/IEEE International Telecommunications Symposium, Rio de Janeiro, Brazil, pp. 420–424, 1994. [16] A. Ephremides, J. E. Wieselthier, D. J. Baker. A design concept for reliable mobile radio networks with frequency hopping signaling. Proceedings of IEEE, vol. 75, no. 1, pp.56– 73, 1987. Liang Xue received the B. Eng. degree in automation from Yanshan University, Qinhuangdao, PRC in 2006. He is currently a Ph. D. candidate in Yanshan University. His research interests include protocol design of wireless sensor networks, cognitive radio networks, and industrial wireless networks. E-mail: [email protected] (Corresponding author)

Xin-Ping Guan received the master degree in applied mathematics in 1991, and the Ph. D. degree in electrical engineering in 1999, both from Harbin Institute of Technology, PRC. Since 1986, he has been with Yanshan University, PRC, where he is currently a professor of control theory and control engineering. In 2007, he also joined Shanghai Jiao Tong University, PRC. His research interests include robust congestion control in communication network, chaos control, and networked control system. E-mail: [email protected]; [email protected] Zhi-Xin Liu received the master degree in control theory and control engineering, and the Ph. D. degree in control science and engineering from Yanshan University, Qinhuangdao, PRC in 2003 and 2006, respectively. He is currently an associate professor in Yanshan University. His research interests include network congestion control, network rate control, and routing protocol for wireless sensor networks. E-mail: [email protected] Qing-Chao Zheng received the B. Eng. degree in automation from Sichuan Normal University, Chengdu, PRC in 2008. He is currently a master student in Yanshan University. His research interests include clustering and routing protocol design for wireless sensor networks. E-mail: [email protected]