a delay-aware data collection network structure

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IEEE SENSORS JOURNAL, VOL. 11, NO. 3, MARCH 2011 699

A Delay-Aware Data Collection Network Structurefor Wireless Sensor Networks

Chi-Tsun Cheng, Member, IEEE, Chi K. Tse, Fellow, IEEE, and Francis C. M. Lau, Senior Member, IEEE

AbstractWireless sensor networks utilize large numbers ofwireless sensor nodes to collect information from their sensingterrain. Wireless sensor nodes are battery-powered devices. En-ergy saving is always crucial to the lifetime of a wireless sensornetwork. Recently, many algorithms are proposed to tackle theenergy saving problem in wireless sensor networks. In thesealgorithms, however, data collection efficiency is usually compro-mised in return for gaining longer network lifetime. There arestrong needs to develop wireless sensor networks algorithms withoptimization priorities biased to aspects besides energy saving.In this paper, a delay-aware data collection network structurefor wireless sensor networks is proposed. The objective of theproposed network structure is to minimize delays in the data

collection processes of wireless sensor networks. Two networkformation algorithms are designed to construct the proposednetwork structure in a centralized and a decentralized approach.Performances of the proposed network structure are evaluatedusing computer simulations. Simulation results show that, whencomparing with other common network structures in wirelesssensor networks, the proposed network structure is able to shortenthe delays in the data collection process significantly.

Index TermsCentralized control, distributed control, net-works, optimization methods, topology.

I. INTRODUCTION

STRONG adaptability, comprehensive sensing coverage,and high fault tolerance are some of the unique advantages

of wireless sensor networks. Wireless sensor networks consistof large amounts of wireless sensor nodes, which are compact,light-weighted, and battery-powered devices that can be usedin virtually any environment. Because of these special charac-teristics, sensor nodes are usually deployed near the targets ofinterest in order to do close-range sensing. The data collectedwill undergo in-network processes and then return to the userwho is usually located in a remote site. Most of the time, wire-less sensor nodes are located in extreme environments, whereare too hostile for maintenance. Sensor nodes must conserve

Manuscript receivedJanuary 12, 2010; revised March 31, 2010; accepted July25, 2010. Date of publication September 23, 2010; date of current version Jan-uary 26,2011. This work wassupported byThe Hong Kong Polytechnic Univer-sity under internal grant G-YF51. The associate editor coordinating the reviewof this paper and approving it for publication was Dr. Robert Schober.

C.-T. Cheng is with the Department of Electrical and Computer Engi-neering, University of Calgary, Calgary, AB T2N 1N4, Canada (e-mail:[email protected]).

C. K. Tse and F. C. M. Lau are with the Department of Electronicand Information Engineering, The Hong Kong Polytechnic Univer-sity, Hung Hom, Kowloon, Hong Kong (e-mail: [email protected];[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JSEN.2010.2063020

Fig. 1. (a) Data collection in a two-hop network and (b) data collection in animproved multihop network. Circles with CM represent the cluster members.Circles with CH represent the cluster heads. Filled circles with BS represent the

base stations. A dashed arrow represents the existence of a data link and thedirection of the arrow shows the direction of data flow.

their scarce energy by all means and stay active in order tomaintain the required sensing coverage of the environment.

Much prior work has focused on conserving energy by clus-tering. A network with clustering is divided into several clus-ters. Within each cluster, one of the sensor nodes is elected asa cluster head (CH) and with the rest being cluster members(CM). The cluster head will collect data from its cluster mem-bers directly or in a multihop manner. By organizing wirelesssensor nodes into clusters, energy dissipation is reduced by de-

creasing the number of nodes involved in long distance trans-mission [1]. The number of data transmissions and energy con-sumption can be further reduced by performing data/decisionfusion on nodes along the data aggregation path. Clustering pro-vides a significant improvement in energy saving. In sensor net-works with cluster, it is common for a cluster head to collectdata from its cluster members one by one. Let be the av-erage transmission delay among nodes. Data packets generatedby sensor nodes are considered as highly correlated, and thusa node is always capable of fusing all received packets into asingle packet by means of data/decision fusion techniques [2],[3]. Referring to the situation shown in Fig. 1(a), a base stationwill take 4 to collect a complete set of data from the net-work. By transforming the network into a multihop network, asshown in Fig. 1(b), it can be shown that the time needed by thebase station to collect a full set of data from the network canbe reduced to 3 . In the modified network, apart from re-quiring a shorter delay in data collection, cluster members willneed smaller buffers to handle the incoming data while waitingfor the belonging cluster head to become available.

The aim of this paper is to investigate the characteristics of adelay-aware data collection network structure in wireless sensornetworks. Two algorithms for forming such a network structureare proposed for different scenarios. The proposed algorithmsare operating between the data link layer and the network layer.

The algorithms will form networks with minimum delays in the1530-437X/$26.00 2010 IEEE


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700 IEEE SENSORS JOURNAL, VOL. 11, NO. 3, MARCH 2011

data collection process. At the same time, the algorithms will tryto keep the transmission distance among wireless sensor nodesat low values in order to limit the amount of energy consumedin communications. The rest of this paper is organized as fol-lows. Section II briefly reviews related work. Section III definesthe proposed network structure. Section IV explains the algo-rithm for forming the proposed network structure in differentscenarios. A numerical analysis is given in Section V to showhow different network structures perform in terms of delays indata collection processes. Simulation results and their analysiswill be given in Sections VI and VII, respectively. Finally, thispaper is concluded in Section VIII.

II. RELATED WORK

Due to the energy constraint of individual sensor nodes, en-ergy conservation becomes one of the major issues in sensornetworks. In wireless sensor networks, a large portion of theenergy in a node is consumed in wireless communications. Theamount of energy consumed in a transmission is proportional to

the corresponding communication distance. Therefore, long dis-tance communications between nodes and the base station areusually not encouraged. One way to reduce energy consump-tion in sensor networks is to adopt a clustering algorithm [1].A clustering algorithm tries to organize sensor nodes into clus-ters. Within each cluster, one node is elected as the cluster head.The cluster head is responsible for: 1) collecting data from itscluster members; 2) fusing the data by means of data/decisionfusion techniques; and 3) reporting the fused data to the remotebase station. In each cluster, the cluster head is the only node in-volved in long distance communications. Energy consumptionof the whole network is therefore reduced.

Intensive research [2][5] has been conducted on reducingenergy consumption by forming clusters with appropriate net-work structures. Heinzelman et al. proposed a clustering algo-rithm called LEACH [2]. In networks using LEACH, sensornodes areorganized in multiple-cluster 2-hop (MC2H)networks(i.e., cluster members cluster head base station). Using theidea of clustering, the amount of long distance transmissionscan be greatly reduced. Lindsey and Raghavendra proposed an-other clustering algorithm called PEGASIS [3], which is a com-pletely different idea by organizing sensor nodes into a single-chain (SC) network. In such networks, a single node on thechain is selected as the cluster head. By minimizing the numberof cluster heads, the energy consumed in long distance trans-

mission is further minimized. Tan and Krpeoglu developedPEDAP [4], which is based on the idea of a minimum span-ning tree (MST). Besides minimizing the amount of long dis-tance transmission, the communication distances among sensornodes are minimized. Fonseca et al. proposed the collectiontree protocol (CTP) [5]. The CTP is a kind of gradient-basedrouting protocol which uses expected transmissions (ETX) asits routing gradient. ETX is the number of expected transmis-sions of a packet necessary for it to be received without error[6]. Paths with low ETX are expected to have high throughput.Nodes in a network using CTP will always pick a route withthe lowest ETX. In general, the ETX of a path is proportional tothe corresponding path length [7]. Thus, CTP can greatly reduce

the communication distances among sensor nodes. All these al-gorithms show promising results in energy saving. However, a

TABLE ICLUSTER MEMBERS RANK DISTRIBUTION IN THE PROPOSED NETWORK

STRUCTURE WITH NETWORK SIZE N = 2 , WHERE p = 1 ; 2 ; . . .

network formed by an energy efficient clustering algorithm maynot necessarily be desirable for data collection. An analysis onhow these network structures perform in terms of data collec-tion efficiency will be given in Section V.

The focus of this paper is on investigating the data collec-tion efficiency of networks formed by different clustering algo-rithms. Therefore, event triggering algorithms such as TEEN[8]and APTEEN [9] will not be considered in this paper. A relatedwork on data collection efficiency was done by Florens et al.[10]. In their work, lower bounds on data collection time arederived for various network structures. However, the effect ofdata fusion, which is believed as one of the major features of

sensor networks, was not considered. Wang et al. [11] proposedlink scheduling algorithms for wireless sensor networks whichcan raise network throughput considerably. In their work, how-ever, it is assumed that data links among wireless sensor nodesare predefined. In contrast, the objective of this paper is to formdata links among wireless sensor nodes and thus to shorten thedelays in the data collection processes. Another related workwas done by Solis and Obraczka [12] who studied the impactof timing in data aggregation for sensor networks. Chen et al.[13] investigated the effects of network capacity under differentnetwork structures and routing strategies. A similar work wasdone by Song and He [14]. In their work, the term capacity isdefined as the maximum end-to-end traffic that a network can

handle. The delay in a data collection process is not their majorconcern.

III. THE PROPOSED NETWORK STRUCTURE

The proposed network structure is a tree structure. To deliverthe maximum data collection efficiency, the number of nodesinthe proposed network structure hasto berestricted to ,where . It will be shown in a later part that suchrestriction can be relaxed by giving up some performance. Eachcluster member will be given a rank, which is an integer between1 and . A node with rank will form data links withnodes, while these nodes are with different ranks starting

from up to . All these nodes will becomethe child nodes of the node with rank . The node with rankwill form a data link with a node with a higher rank. This higherrank node will become the parent node of the node with rank .The cluster head will be considered as a special case. The clusterhead is the one with the highest rank in the network. Instead offorming a data link with a node of higher rank, the cluster headwill form data link with the base station. By following this logic,the distribution of the rank will follow an inverse exponentialbase-2 function, as shown in Table I.

An example of the proposed network with is shownin Fig. 2. In this example, it takes 5 for the base station tocollect all data from 16 nodes. By dividing the time domain into

time slots of durations , the above process will last for fivetime slots.


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CHENG et al.: A DELAY-AWARE DATA COLLECTION NETWORK STRUCTURE FOR WIRELESS SENSOR NETWORKS 701

Fig. 2. Proposed network structure with network size N = 1 6 . Circles withCM represent the cluster members. Circle with CH represents the cluster head.Filled circle with BS represents the base station. Rank of each node is repre-sented by the variable k . A dashed arrow represents the existence of a data linkand the direction of the arrow shows the direction of data flow.

Lemma 1: Consider a network with , where. Data packets generated by sensor nodes are considered

as highly correlated, and thus a node is always capable of fusing

all received packets into a single packet by means of data/deci-sion fusion techniques. Through adopting the proposed networkstructure, a node of rank (where ) requirestime slots to collect data from all its child nodes.

Proof: Consider a network with , where. For a node of rank , the time slots required for it

to collect data from all its child nodes is equal to the number ofchild nodes it has, which is 1. Thus, the case for is true.Now, let us assume that any node of connection requires

time slots to collect all data from its child nodes. For nodeof rank , it has directly connected child nodes.

Each of these directly connected child nodes has different ranks

ranging from 1 to . Thus, they need 0 to time slots to col-lect data from all their sub-child nodes plus one extra time slotto report their aggregated data to node . Therefore, the max-imum time slots required for node to collect data from all itschild nodes is . By induction, the Lemma is proved.

Theorem 1: Consider a network with , where. Data packets generated by sensor nodes are considered

as highly correlated, and thus a node is always capable of fusingall received packets into a single packet by means of data/deci-sion fusion techniques. By adopting the proposed network struc-ture, the number of time slots required for the base stationto collect data from the whole network is given by

(1)

Proof: Consider a network with , where. Through adopting the proposed network structure, the

cluster head is the only node with the highest ranking which is

From Lemma 1, the number of time slots required for acluster head, with rank , to collect data from all its childnodes is

Thus, the number of timeslots requiredfor the basestationto collect data from the whole network is the time slots requiredby the cluster head to collect data from all its child nodes plusone, i.e.,

IV. NETWORK FORMATION ALGORITHM

It has been proven in the last section that the delay in the datacollection process of a wireless sensor network can be greatlyreduced by adopting the proposed network structure. Since en-ergy consumption is always a major issue in the study of wire-less sensor networks, the objective of the proposed network for-mation algorithms is, therefore, to achieve the proposed networkstructure while keeping the energy consumption in the data col-lection process at low value.

A wireless sensor node can be considered as a device built up

of three major units, namely the microcontroller unit (MCU),the transceiver unit (TCR), and the sensor board (SB). Each ofthese units will consume a certain amount of energy while op-erating. The energy consumed by a wireless sensor node canbe expressed as

(2)

where represents the energy consumed by the MCU,represents the energy consumed by the TCR, and

represents the energy consumed by the SB. Here, canbe further expressed as

(3)

where denotes the energy consumed by the TCRin receiving mode, while denotes the energyconsumed by the TCR to transmit for a distance of . The totalenergy consumed by a network of sensor nodes is expressedas

(4)

Normally, , , and are constants.On the other hand, is a function of which is


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heavily depending on the network structure. Therefore, (4) canbe simplified as follows:

(5)

where is a constant. Assume that the path loss exponent is

equal to 2, can be further expressed as

(6)

where is the energy consumed by the TCRselectronic circuitry, while denotes the energy con-sumed by the power amplifier of the TCR. Bothand are constants and, therefore, (5) can be ex-pressed as

(7)

where and are constants. Here, (7) shows that the total

energy consumption of the network can be minimized by re-ducing . Thus, the objective of the proposed networkformation algorithms is to construct the proposed network struc-ture, while keeping at low value. In this section, twonetwork formation algorithms, namely the top-down and thebottom-up approaches, are proposed to achieve the objectivementioned above.

A. Top-Down Approach

The top-down approach is a kind of centralized control algo-rithm. In this approach, the base station is assumed to have thecoordinates of all sensor nodes in the network. The whole ap-proach is going to be executed at the base station. At the end ofthe optimization process, the base station will instruct the sensornodes to establish the essential data links and form the appro-priate network structure.

The network constructions for and aretrivial. For networks with nodes, where ,the proposed network structure can be constructed according tothe following algorithm.

1) The algorithm starts with considering the whole networkas a fully connected network. In this paper, the termconnected refers to the existence of a data link betweentwo wireless sensor nodes which is used to transmit datapackets in the data collection processes. Two wireless

sensor nodes are defined as disconnectedfrom each otherif there does not exist any direct data link between them.The connection degree of a wireless sensor node is tellingthe number of data links associated with such node. Anode with connection degree of 3 implies that such a nodehas formed three data links with three other nodes. For anetwork of nodes, where , each nodewill begin with degree equal to . The nodes willform the set . Set .

2) Select nodes from set to form set , such thatis maximized. Here, denotes the geo-

graphical distance between node and node . The restof the nodes from will form set . The algorithm

will then remove all connections (data links) among nodeswithin . Set iterators and .

Fig. 3. Network formation of the proposed network structure using centralized

top-down approach (N 4

).

3) Repeat step 2 until . Set .4) Nodes with degree form set . Nodes with degree

greater than form set such that set and setare of the same number of nodes. Connections among

nodes in the two sets are reduced until each node in setis only connected to a single node in set . Here, data

links are removed according to their distance. Details ofthe optimization method are given in the later part of thissection. After reducing the number of connections, set

.5) Repeat step 4 until .A flow chart of the network formation algorithm is given in

Fig. 3. The two nodes belonging to the last set of step 4 arehaving the highest connection degree among the nodes in thenetwork. These two nodes are, in fact, the nodes belonging to theset instep2,when .Since thesenodes arefrom thelast set generated fromstep 2,they havenotgone through theintraconnection removalprocess. Therefore, these two nodes areinterconnected with each other. Because of this, the connectiondegrees of these two nodes are always higher than the others.As a result, these two nodes are always included in the set instep 4. By the end of step 4, each of these two nodes will have

directly connected child nodes with unique rankings, providedthat the rankings of the child nodes are lower than the two nodes.These two nodes are, therefore, with connection degrees equalto .

Among these two nodes, the one which is located closer to thebase station will be selected as the cluster head and be connecteddirectly to the base station. Therefore, the cluster head will havea degree of which is the highest within the cluster.Notice that the connection degree of a node is in fact denotingits rank. By substituting connection degree with rank, theproposed network structure is achieved.

Accordingto the definition of the proposed network structure,half of the sensor nodes (i.e., ) in the network will have con-

nection degrees equal to 1. In addition, a quarter of the sensornodes (i.e., ) will have connection degrees equal to 2. The


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pattern goes on and follows the trend as shown in Table I. Ex-cept for the nodes with degree , no node in the proposednetwork structure will connect to another node with the sameconnection degree. Therefore, if a set of nodes are selected tohave the same connection degree, all edges among these nodesmust be removed.Nevertheless, in order to reduce the total com-munication distance in the final network structure, the length ofthe edges to be removed should be maximized. In the proposedtop-down approach, the selection of nodes to have the same con-nection degree is done by the procedures in step 1 and the re-moval of edges among those selected nodes is done by the pro-cedures in step 2.

The procedure in Step 2 is in fact the heaviest -subgraphproblem defined in [15]. The heaviest -subgraph problem is tofind the -vertex subgraph out of a given graph, such that thetotal weight of edges among these vertexes is maximized. Inthis paper, the weight of an edge (data link) connecting any twovertexes (nodes) and (wireless sensor nodes) is defined as

, where is the geographical distance between nodes and

. The proposed algorithm can always be modified to accommo-date different cost metrics by redefining the edge weights. Theproblem is a kind of combinatorial problem which is definedas NP-complete. Dynamic programming is commonly used tosolve combinatorial problem [16] and thus it is used to solve theheaviest -subgraph problem in this paper.

For each iteration of step 2, half of the nodes from setare selected to form set . The remaining nodes will formset . After the selection, all connections among the nodesin set will be removed. Therefore, in step 2, a larger setof will yield nodes with lower connection degrees, andvice versa. As half of the nodes from set are selected in eachiterations of step 2, the number of nodes with degree and

the number of nodes with degree greater than are alwaysequal in step 4.

Note that the proposed network structure is a tree-based net-work. In a tree-based network, a child node will connect itself toone parent node only (i.e., a node with higher rank in our case).Steps 1 and 2 of the proposed top-down approach will only re-move edges among nodes which are selected to have the sameconnection degree. Therefore, from the outcomes of step 2, achild node will be connected with more than one parent node.In the proposed top-down approach, steps 3 and 4 are designedto remove excess edges from the child nodes, provided that thetotal weight of the remaining edges are minimized. By the endof step 4, each child node will be connected to one parent nodeonly.

The nodes involved in the optimization in step 4 will form adistance matrix with each entry storing the distance between twonodes. The axis is representing the nodes from set , whilethe axis is representing the nodes from set . The two setsof nodes therefore form a bipartite graph and the optimizationproblem becomes a weighted matching problem. This problemcan be optimized by applying matching techniques such as Hun-garian Method [17], [18] or Munkres Assignment Algorithm[19]. In this paper, Munkres Assignment Algorithm is used tosolve the weighted matching problem.

For networks with number of nodes other than ,

where , dummy nodes are virtually added in thecalculation process to expand the network in order to fulfill the

network size requirement of the algorithm. These dummy nodeswill have infinite separations with the real nodes and have in-finite separations among themselves. The number of dummynodes will always be smaller than . At the end of the opti-mization process, these dummy nodes will allhave degree(rank)of 1 which can be ignored and removed without partitioning thenetwork. Since the condition , where isfulfilled during the network formation, Lemma 1 and Theorem1 still applied. Thus, the time slots required for complete datacollection will still be governed by (1), provided that the numberof nodes in (1) is replaced by the number of real nodesplus the number of dummy nodes . In general, (1) can bewritten as

(8)

where denotes the nearest integer larger than . Note thatthe top-down approach is mainly designed for sensor nodes with

communication distance long enough to cover thewhole sensingterrain. For scenarios where the diagonal of the sensing terrain islarger than the maximum communication distance of a node, thetop-down approach can still be applied by arranging the terraininto multiple subregions and performing the top-down approachto each subregion.

1) Example 1: The following example will show how theproposed network structure can be constructed by using the top-down approach.

1) Consider a network with [see Fig. 4(i)]. The top-down approach begins with a fully connected network with

. In the current example, is equal to 8. Therefore,all nodes are with connection degree equal to 7. These eight

nodes will form a set , where (i.e., ). Now,define parameter .

2) Select nodes from set (i.e., ) to form set(i.e., ) such that the total edge weight within set

is maximized. This combinational problem is solvedusing dynamic programming. In this example, the totaledge weight among nodes C, D, E, and F is the highest.Therefore nodes C, D, E, and F will form the set . Therest of the nodes, i.e., nodes A, B, G, and H will form set

(i.e., ). Cut all connections among nodes in set[see Fig. 4(ii)]. Set to (i.e., ) and set to

(i.e., ).3) Since , the previous step is repeated. Select

nodes from set (i.e., ) to form set (i.e., )such that the total edge weight within set is maximized.Since the total edge weight between nodes A, H, and thatbetween nodes B, G are the highest, one out of the twopairs is randomly selectedto bethe set . In this example,nodes A and H are selected as the set . The rest of thenodes, nodes B and G, will form set (i.e., ). Cutall connections among nodes in set [see Fig. 4(iii)]. Set

to (i.e., ) and set to (i.e., ).4) With , the algorithm proceeds and defines pa-

rameter . Nodes with degree equal to (i.e.,nodes A and H) form set . Nodes with degree

(i.e., nodes B and G) form set . Reduce connectionsamong nodes between set and until each node in set


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Fig. 4. An example of the top-down approach with N = 8 . Sensor nodes are represented by circles and the base station (B.S.) is represented by a rectangle. Eachnode is assigned with a unique letter for identification purpose. The numbers in the brackets represent the connection degrees of the nodes.

is only connected to a single node in set , providedthat the total edge weight is minimized [see Fig. 4(iv)]. Theweighted matching problem is solved by Munkres Assign-ment Algorithm. Set parameter to (i.e., ).

5) Since , the previous step is repeated. Nodeswith degree equal (i.e., nodes C, D, E, andF) form set . Nodes with degree (i.e., nodesA, B, G, and H) form set . Reduce connections amongnodes between set and until each node in set is onlyconnected to a single node in set , provided that the totaledge weight is minimized [see Fig. 4(v)]. Set parameterto (i.e., ).

6) When , the basic operation of the proposedtop-down approach is completed. The resultant networkwill now consist of two nodes with degree(i.e., nodes B and G) which are connected together. Amongthese two nodes, the one which is located closer to the basestation (i.e., node B) will be selected as the cluster headand be connected directly to the base station. Including theconnection with thebase station, the cluster head (i.e.,nodeB) will now have a connection degree of[see Fig. 4(vi)].

B. Bottom-Up Approach

Basically, the operation of the bottom-up approach is to joinclusters of the same size together. The bottom-up approach is,when comparing with the top-down approach, more scalable.It can be implemented in either centralized or decentralized

fashion. Specifically, a decentralized bottom-up approach canbe described as follows.

1) Each node is labeled with a unique identity and marked aslevel . The unique identity will only serve as an identifi-cation which has no relation with sensor nodes locationsand connections. Here, is a function which represents the

number of nodes in a cluster. For a cluster of nodes, itsvalue is equal to . Since nodes are disconnected

initially (i.e., no data link exists among wireless sensornodes), these nodes can be considered as level0 clus-ters. Within each cluster, one node will be elected as thesubcluster head. We denote as a subcluster headof a level cluster. In the bottom-up approach, a SCHcan only make connection (i.e., setup a data link) with an-other SCH of the same level. Since there is only 1 node ineach cluster, all nodes begin as SCH(0). The dimensions ofthe terrain ( , ) are provided to the sensor nodes beforedeployment.

2) Each SCH performs random backoff and then broadcastsa density probing packet (DPP) to its neighboring SCHswhich are within a distance of m.Note that the size of a DPP is much smaller than that ofa data packet. A SCH can use the number of received DPP,together with the dimensions of the terrain, to estimate thetotal number of nodes ( ) in the network. A SCH willuse the to adjust its communication distance .Definition of will be explained in the later part of thissection.

3) Each SCH will do a random back off and then broadcastan invitation packet (IVP) to its neighbors withinm. The IVP contains the level and the identity of the

issuing SCH. A SCH will estimate the distances to itsneighboring SCHs using the received signal strength of the


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IVPs received. A SCH will also count the number of IVPsreceived. If the number of IVPs received has exceededa predefined threshold or a maximum duration has beenreached, a SCH will send a connection request(CR) to thisnearest neighbor. If both SCHs are the nearest neighbor ofeach other, a connection will be formed between these two

SCHs.4) Once they are connected, the two SCHs and their be-longing level- clusters will form a composite level-cluster. One of the two involved SCHs will become thechief SCH of the composite cluster. The chief SCH willlisten to the communication channel and reply any CRfrom lower levels with a rejecting packet (RP). When nomore CR from lower levels can be heard, the chief SCHwill start to make connection with other SCHs of the samelevel.

5) If a RP is received, a SCH will send a CR to its next nearestneighbor in its database. If such neighbor does not exist, theSCH will increase its . The SCH will then broadcast a

CR using the new . Upon receiving the CR, a SCH ofthe same level will grant the request if it is still waiting fora CR.

6) If no connection can be made within a period of time, ei-ther all neighbors of the same level are unavailable or allCRs have been rejected, the SCH will increase its andbroadcast the CR again. This process repeats as long as

. If , the SCH willmake connection with the base station directly.

7) The above processes continue until no more connection canbe formed.

In the bottom-up approach, the communication distance

is defined as

(9)

Here, is a constant which is set to 0 initially. Parameter isthe estimated maximum rank of a node in the network, which isexpressed as

(10)

Initially, all SCHs are with and . There-

fore, the SCHs will start broadcasting their IVPs with. If a SCH has made a

connection with another SCH, its level will be increased by 1(i.e., ). After that, the chief SCH of the composite cluster

will broadcast its IVP with .The is designed to be increased with because whenSCHs are paired up to form composite clusters, the averageseparation among composite clusters will be increased. It ismore energy efficient to start the broadcasting with a longercommunication range. However, if no connection can be made,a SCH will increase its by one. This will increase ,which can facilitate the searching of available SCHs. A SCH

will increase its by incrementing until a connection canbe made. The sum of and is defined to be smaller than

to ensure is upper bounded by the diagonal of the sensingterrain.

In step 3 of the bottom-up approach, a SCH will send a CR toits nearest neighbor if the number of received IVPs has exceeded

. Here, is the expected number of IVPs to be received whichis expressed as

(11)

Parameter is the density of the network which can be estimatedusing the obtained before.

When being implemented in a decentralized control manner,the above algorithm may end up with multiple composite clus-ters i f the n umber of nodes i s not e qual t o , w here .SCHs of these composite clusters will communicate with thebase station directly. By virtue of pairing up composite clustersof same sizes, the algorithm will end up with composite clus-ters of completely different sizes. Considering the base stationas the root of the network, the number of time slots required by

the base station to collect data from all sensor nodes is

(12)

In contrast, the above algorithm can also be carried out at thebase station as a centralized control algorithm. The base stationis again assumed to have the coordinates of all sensor nodesin the network. When the number of nodes is not equal to ,where , dummy nodes can be virtually added in thecalculation process, depending on the application. If a singlecluster is required, dummy nodes should be virtually added tofulfill the requirement of , where . However,if multiple clusters can be formed, dummy nodes are not es-

sential. When dummy nodes are virtually added, these dummynodes will have infinite separations with the real nodes and withthemselves. Note that whenever a real SCH is connecting witha dummy SCH, the real SCH will always be the chief SCH ofthe composite cluster. This is to ensure the removal of dummynodes at the end of the calculation process will not partition thenetwork. The number of time slots required by the base stationto collect data from all sensor nodes will be governed by (8) (forsingle cluster) and (12) (for multiple clusters).

V. NUMERICAL ANALYSIS

Theorem 2: Assume that each sensor node can only commu-

nicate with one sensor node at a time, and that data fusion is ap-plicable. For a single-cluster network of nodes, where

, the minimum number of time slots required by thebase station to collect data from sensor nodes is

(13)

Proof: Given a period of time slots, a parent node cancollect data from at most directly connected child nodes, pro-vided that these child nodes are using different time slots tocommunicate. Within these child nodes, the node will re-port data at time slot , which implies the node can collectdata from at most directly connected child nodes of it-

self before it has to report data to its parent node. Therefore, fora period of time slots, a parent node can receive data from


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at most nodes (including itself). On the other hand, the min-imum number of time slots required for a parent node to collectdata from nodes (including itself) is . Thus, the min-imum number of time slots required for a base station to collectdata from nodes is .

For a single-cluster network with nodes, where

, the minimum number of time slots re-quired for a base station to collect data from nodes is

(14)

From Theorem 1 and (8), it can be shown that the proposednetwork structure is an optimum network structure in terms ofdata collection efficiency provided that:

1) each sensor node can only communicate with one sensornode at a time;

2) data fusion can be carried out at every sensor node;3) sensor nodes are belonging to a single cluster with a single-

cluster head.

The same idea can be applied to multiple-cluster network byconsidering the base station as the root of the network structure.Therefore, in multiple-cluster networks, the minimum numberof time slots required for a base station to collect data fromnodes is

(15)

Using (12), it can be shown that the proposed network structureis again an optimum network structure in terms of data collec-tion efficiency provided that:

1) each sensor node can only communicate with one sensor

node at a time;2) data fusion can be carried out at every sensor node;3) the network consists of multiple clusters.In a MC2H network with nodes organized in clusters,

where , the time slots required by the base sta-tion to collect data from all sensor nodes is minimized whenall clusters have different numbers of nodes. Therefore, eachcluster can communicate with the base station interleavingly.Meanwhile, the number of nodes in the largest cluster shouldbe minimized such that the total number of time slots requiredby the base station is also minimized. An example for isshown next.

1) Example 2: For a MC2Hnetwork of nodes organized in2 clusters (where ),in orderto achieve the maximumdatacollection efficiency, the number of nodes in these two clustersshould be equal to

(16)

The minimum number of time slots required by thebase station to collect data from all sensor nodes is equal to thenumber of nodes in the largest cluster. Therefore

is oddis even

(17)

In general, for a MC2H network of nodes organized inclusters, where , the number of nodes in thecluster can be written as

(18)

where denotes the nearest integer smaller than and. Thus, the minimum number of time slots

required by the base station to collect data from all sensor nodesis equal to

(19)

Based on(18), the optimum numberof clusters for a MC2Hnetwork in terms of data collection efficiency can be obtainedfrom the following inequality:

(20)

(21)

where is the number of nodes in the network, and is thenumber of clusters.

Theorem 3: For a MC2H network of nodes organized inclusters of completely different sizes, where .

The minimum number of time slots required by thebase station to collect data from all sensor nodes is equal to thenumber of clusters in the system, i.e., .

Proof: Consider the extreme case, which a MC2H networkof nodes is organized in clusters of completely differentsizes, where . These clusters will all have differentnumbers of nodes ranging from 1 to . The minimum numberof time slots required by the base station to collect datafrom all sensor nodes is equal to the number of nodes in thelargest cluster, which is . Suppose one node has to be removedfrom the network such that is reduced to . To maintainthe number of clusters in the network, this particular node mustbe removed from one of the clusters except the one with a singlenode. Removing a node from any of the clusters will cause two

clusters to have the same number of nodes. During a data col-lection process, the two clusters of the same size will have to dointerleaving, which will not affect . Therefore, the min-imum number of time slots required by the base stationis always equal to the number of clusters in the system.

In contrast, for a MC2H network with nodes organized inclusters, where , the number of time slots required by thebase station to collect data from all sensor nodes is maximizedwhen nodes are belonging to the same cluster. Theremaining clusters will all have a cluster size of 1, and wehave

otherwise(22)


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In a SC network, the number of time slots required by the basestation to collect data from all sensor nodes is minimized whenthe cluster head is at the middle of the chain, i.e.,

is oddis even

(23)

where is the number of nodes in the network.On the contrary, in a SC network, the number of time slots

required by the base station to collect data from all sensor nodesis maximized when the cluster head is at the end of the chain,i.e.,

(24)

where is the number of nodes in the network.In networks using MST and CTP, the number of time slots re-

quired by the base station to collect data from all sensor nodes islower bounded by (13) and (14). On the other hand, the numberof time slots required by the base station to collect data from allsensor nodes is maximized when the resultant networks of MSTand CTP are in single-cluster two-hop structure which is upperbounded by .

VI. SIMULATIONS

In this section, the proposed network structure will be com-pared with a MC2H network, a SC network, a MST network,and a CTP network. Networks having nodes with varyingfrom 4 to 64, with a step size of 4, will be distributed randomlyand evenly on a sensing field of 50 50 . The center of thesensing field is located at . In the simula-

tions, synchronization among wireless sensor nodes are main-tained by the physical layer and the data link layer. Wirelesssensor nodes are assumed to be equipped with CDMA-basedtransceivers [20]. Interference due to parallel transmissions canbe alleviated by utilizing different spreading sequences in dif-ferent data links. Media access control during network forma-tion is handled by the MAC sublayer and is assumed to be satis-factory. A node can either receive or transmit at any time. In thesimulation, a wireless sensor node is always capable of fusingall received packets into a single packet by means of data/deci-sion fusion techniques and the size of an aggregated packet isindependent to the number of packets received.

For each network, the averaged data collection time (DCT)will be used to indicate its data collection efficiency. The com-munication distance of a network is represented by thefollowingfunction:

(25)

where is an indicator to indicate cluster heads ( ) andcluster members ( ). Parameter is the distance be-tween a cluster head and the base station. Here, is an indi-cator to indicate the presence ( ) or absence ( ) of adata link between node and node . Furthermore, is the ge-

ographical distance between nodes and . In the simulations,the path loss exponent is assumed to be 2. The base station is

TABLE IIVALUES OF PARAMETERS USED IN THE SIMULATIONS

assumed to be at the center of the sensing field (i.e., ,).

For the simulations on network lifetime, each node is given50 J of energy. The energy model of the wireless sensor nodesis the same as the one introduced in Section IV. A network willperform the data collection process periodically. The lifetime ofa network is defined as the number of data collection processes(in terms of rounds)that a network can accomplish before any ofits nodes runs out of energy. Each data packet is bits long.Other packets are all regarded as control packets. Each controlpacket is bits long. Values of the parameters used in theenergy model are shown in Table II.

The network structures under test are classified into twotypes: Type I) single-cluster network structure; Type II) mul-tiple-cluster network structure. Under this classification, allstructures under test belong to Type I, whereas MC2H and theproposed network structure belong to both types. Note that asthe number of clusters in Type I and Type II network structuresare different, results obtained by different types of networkstructures should not be compared directly.

For the proposed network structure to work as a Type I struc-ture, either the top-down or the bottom-up approach can be ap-plied provided that sufficient dummy nodes are added. To workas a Type II structure, the proposed network structure can onlybe constructed by the bottom-up approach without adding anydummy node. The cluster number of the MC2H network is fixedto 1 when it works as a Type I structure. Here, of the MC2Hnetwork is minimized by selecting the node with minimum sep-arations from its fellow nodes as the cluster head. To work as aType II structure, cluster heads in the MC2H networks are se-lected in a random manner as given in [2], while the optimumnumber of cluster heads is selected according to (21). In both

configurations, cluster members are connected to their nearestcluster head.The SC network can only work as a Type I structure, and

the chain is formed by using a greedy algorithm as given in[3]. To minimize DCT, the node closest to the middle of thechain (in terms of hops) will be selected as the cluster head.Similar to the SC network, the MST network can only work asa Type I structure. Networks will be formed by using the Primsalgorithm as given in [4]. To minimize DCT, the node with thesmallest separation (in terms of hops) to all leaf nodes will beselected as the cluster head.

In networks using CTP, the node closest to the center of thesensing terrain is regarded as the root of the collection tree. The

ETX of a path is expressed as the squared value of the pathlength [6]. The root of the tree will have an ETX of 0. The ETX


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Fig. 5. Averaged data collection time of different single tree structures. Notethat results obtained from the proposed algorithm using the top-down approachare overlapping with those obtained from the bottom-up approach.

Fig. 6. Averaged of different single tree structures.

of an arbitrary node is the cumulated ETX from it, through itsparent nodes, to the root [5]. Each node will choose its best routeby selecting the path with the minimum cumulated ETX.

Simulation results are shown in Figs. 510. All results pre-sented in this paper are averaged over 100 simulations.

VII. ANALYSIS

As expected in Section V, the DCT of networks with the pro-posed network structure is the lowest among Type I structures.In simulations among the six TypeI structures, DCTof networkswith the proposed network structure is the lowest, followed bynetworks with CTP. Since the aim of the MST is to minimize thetotal weight of edges, it does not perform well in reducing bot-tleneck and therefore it ranks fourth. In a SC network, it takes avery long time for data to propagate from both ends of the chainto the cluster head at the middle. This explains why SC net-works have much higher DCT than networks with the proposed

network structure. With the single-cluster two-hop structure, thenetworks with MC2H structure do not have any advantage in

Fig. 7. Averaged lifetime of different single tree structures.

Fig. 8. Averaged data collection time of different multiple-cluster structures.

Fig. 9. Averaged of different multiple-cluster structures.

reducing DCT. The MC2H network is the one with the highestDCT among Type I structures.

In terms of minimizing , the MST network no doubt ranksfirst. The ETX used in network with CTP can greatly reduce


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Fig. 10. Averaged lifetime of different multiple-cluster structures.

the communication distances among sensor nodes and make itranks second. Nodes in networks with SC structure try to re-duce the total communication distance by connecting to theirnearest neighbors only. The strategy is effective for networkwith small number of nodes. However, to maintain a single-chain structure, it is unavoidable for the SC network to increaseits as the number of nodes increases. The SC network there-fore ranks third. Using the optimization techniques employedin Section IV, the of networks constructed using the pro-posed top-down or bottom-up approach does not increase dras-tically as increases and they ranks fourth and fifth. When

, the performance of the top-down approach in terms

of is better than that of the bottom-up approach. However,as further increases, the top-down approach is outperformedby the bottom-up approach. This is because all the optimizationtechniques employed in the top-down approach are carried outindividually. Although all the optimization techniques will pro-vide optimum solutions, there is lack of a global optimizationmethod. This makes the top-down approach more effective forsmall-scale networks, but at the same time, it is more prone tobe trapped in local optimum points as the network density in-creases. Therefore, the top-down and the bottom-up approachesare recommended for low density and high density networks, re-spectively. With all sensor nodes connected to a single-cluster

head, the MC2H network is the structure with the highestwithout question.In a data collection process, a node with connection degree

is required to receive data packets, perform timesof data fusion, and transmit 1 data packet. A node with a highconnection degree will certainly consume more energy that onewith a low connection degree. Therefore, a network which hasa uniform connection degree distribution is more likely to yielda longer network lifetime than one with a nonuniform connec-tion degree distribution. The minimum spanning property ofa MST network can make the connection degree evenly dis-tributed among nodes. Therefore, the MST network can achievethe highest network lifetime for networks with . In a

SC network, as most of the nodes are having connection de-grees equal to 2, the energy consumed by each node in receiving

and fusing data is relatively low. Therefore, the SC networkranks second. Similar to the simulations on the , network life-time of networks with CTP, the proposed top-down approach,and the proposed bottom-up approach rank third, fourth, andfifth, respectively. In a SC2H network, all cluster members areconnected to a single-cluster head. The cluster head is heavily

loaded and has a very high energy consumption, which explainwhy a SC2H network has the lowest network lifetime among allnetwork structures under test.

In simulations of the two Type II structures, networks formedby the proposed algorithm are shown to have the lowest DCT.Although the networks with MC2H structure have been tunedto give the optimum number of clusters, there is no control onthe distribution of sensor nodes in each cluster. The DCT of net-works with MC2H structure, therefore, greatly increases asincreases. For the same reason, network lifetime of networkswith MC2H structure decreases gradually as increases. Interms of , both the proposed and the MC2H network struc-tures give similar results when . For , networks

constructed by the proposed algorithm have lower than thoseconstructed in MC2H structure. The gap increases further as

increases. According to (21), a MC2H network is most ef-ficient if there are clusters, where is proportional to

. As increases, increases and thus more nodes are in-volved in long distance transmissions. The same thing happensto networks constructed by the proposed algorithm. Neverthe-less, due to the special topology of the proposed network struc-ture, the number of clusters increases at a lower rate. This ex-plains why of networks formed by the proposed algorithmis lower than those constructed in MC2H structure. This alsoexplains why networks formed by the proposed algorithm can

obtain a longer network lifetime than those constructed with theMC2H structure.

VIII. CONCLUSIONS

In this paper, a delay-aware data collection network struc-ture and its formation algorithms are proposed. To cater for dif-ferent applications, network formation can be implemented ineither centralized or decentralized manner. Two network for-mation approaches are derived to provide optimized results fornetworks with different sizes. The performance of the proposednetwork structure is compared with a multiple-cluster two-hopnetwork structure, a single-chain network structure, a minimum

spanning tree network structure, and a collection tree networkstructure. The proposed network structure is shown to be themost efficient in terms of data collection time among all the net-work structures mentioned above. The proposed network struc-ture can greatly reduce the data collection time while keepingthe total communication distance and the network lifetime atacceptable values.

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Chi-Tsun Cheng (S07M09) received the B.Eng.and M.Sc. degrees from the University of HongKong, Hong Kong, China, in 2004 and 2005, respec-tively, and the Ph.D. degree from the Hong Kong

Polytechnic University, Hong Kong, in 2009. Duringhis studies, he was the recipient of the Sir EdwardYoude Memorial Fellowship.

Since January 2010, he is a Postdoctoral Fellowwith the Department of Electrical and Computer En-gineering, University of Calgary, AB, Canada. He isinvolved in a GEOIDE project, which is supported

by the Government of Canada through the Networks of Centres of Excellenceprograms. His research interests include wireless sensor networks, bio-inspiredcomputing, and metaheuristic algorithms.

Chi K. Tse (M90SM97F06) received theB.Eng. (Hons) degree in electrical engineeringand the Ph.D. degree from the University of Mel-bourne, Melbourne, Australia, in 1987 and 1991,respectively.

He is presently Chair Professor and Head ofthe Department of Electronic and InformationEngineering, Hong Kong Polytechnic University,

Hong Kong. He is the author of Linear CircuitAnalysis (London, U.K.: Addison-Wesley, 1998) andComplex Behavior of Switching Power Converters

(Boca Raton, FL: CRC Press, 2003), coauthor of Chaos-Based Digital Com-munication Systems (Heidelberg, Germany: Springer-Verlag, 2003), ChaoticSignal Reconstruction with Applications to Chaos-Based Communications(Singapore: World Scientific, 2007), and Sliding Mode Control of SwitchingPower Converters: Techniques and Implementation (Roca Raton, FL: CRCPress, 2010), and co-holder of two U.S. patents and two other pending patents.In 2010, he was appointed the Chang Jiang Scholar Chair Professorship by theMinistry of Education of China and the appointment is hosted by HuazhongUniversity of Science and Technology, Wuhan, China. His research interestsinclude power electronics, complex networks and nonlinear systems.

Dr. Tsewas awarded theL. R. East Prize by theInstitutionof Engineers, Aus-tralia, in 1987, the IEEE TRANSACTIONS ON POWER ELECTRONICS Prize PaperAwardin 2001, and the International Journal of Circuit Theory and ApplicationsBest Paper Award in 2003. In 2007, he was awarded the Distinguished Interna-

tional Research Fellowship by the University of Calgary, Canada. In 2009, heand his co-inventors won the Gold Medal with Jurys Commendation at the In-ternational Exhibition of Inventions of Geneva, Switzerland, for a novel drivingtechnique for LEDs. He serves as Deputy Editor-in-Chief for the IEEE Circuitsand Systems Magazine and Editor-in-Chief of IEEE Circuits and Systems So-ciety Newsletter. He was/is an Associate Editor for the IEEE TRANSACTIONSON CIRCUITS AND SYSTEMS PART I from 1999 to 2001 and again from 2007 to2009. He has also been an Associate Editor for the IEEE TRANSACTIONS ONPOWER ELECTRONICS since 1999. He is an Associate Editor of the International

Journal of Systems Science, andalsoon theEditorial Boards of theInternationalJournal of Circuit Theory and Applications and International Journal and Bi-furcation and Chaos. He also servedas Guest Editorand Guest Associate Editorfor a number of special issues in various journals.

Francis C. M. Lau (M93SM03) received theB.Eng. (Hons) degree in electrical and electronicengineering and the Ph.D. degree from KingsCollege London, University of London, London,U.K., in 1989 and 1993, respectively.

He is an Associate Professor and Associate Headat the Department of Electronic and Information En-gineering, Hong Kong Polytechnic University, HongKong. He is the coauthor of Chaos-Based DigitalCommunication Systems (Heidelberg, Germany:Springer-Verlag, 2003) and Digital Communications

with Chaos: Multiple Access Techniques and Performance Evaluation (Oxford,U.K.: Elsevier, 2007). He is also a co-holder of one U.S. patent and two pendingU.S. patents. His main research interests include channel coding, cooperativenetworks, wireless sensor networks, chaos-based digital communications,applications of complex-network theories, and wireless communications.

Dr. Lau served as an Associate Editor for IEEE TRANSACTIONS ON CIRCUITSAND SYSTEMS II from 2004 to 2005 and the IEEE TRANSACTIONS ON CIRCUITSAND SYSTEMS I from 2006 to 2007. He was also an Associate Editor of Dy-namics of Continuous, Discrete and Impulsive Systems, Series B from 2004 to2007 and was a Co-Guest Editor ofCircuits, Systems and Signal Processing forthe Special Issue on Applications of Chaos in Communications in 2005. He iscurrently a Guest Associate Editor of the International Journal and Bifurcationand Chaos.

a delay-aware data collection network structure

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