WIR. COMM. AND MOBI. COMPU. Wirel. Commun. Mob. Comput. 00: 1–16 (0000) Posted online (wiley inter science) DOI: 10.1002/wcm.0000 Adaptive Low-Energy Clustering In Slotted Beacon-Enabled IEEE 802.15.4 Networks Hamidreza Tavakoli 1 , Jelena Miˇ si´ c 2 , Majid Naderi 3 and Vojislav B. Miˇ si´ c 2 1 Hakim Sabzevari University, Sabzevar, Iran 2 Ryerson University, Toronto, ON, Canada 3 Iran University of Science and Technology, Tehran, Iran Summary We present, model, and evaluate a novel clustering algorithm running on top of IEEE 802.15.4 wireless sensor networks operating in slotted, beacon-enabled mode. The Adaptive Low-Energy Clustering (ALEC) algorithm provides randomized sleep and randomized rotation of the cluster-head role so as to maximize the useful lifetime of the network by improving efficiency and balancing the lifetime of individual nodes. We model the ALEC algorithm through probabilistic analysis and show that its parameters can be tuned to extend the network lifetime and reduce the delay and energy overhead imposed by clustering. Copyright c 0000 copyright owner, Ltd. KEY WORDS: Wireless sensor networks; IEEE 802.15.4; clustering; randomized sleeping; rotation of cluster- head role; energy efficiency 1. Introduction Wireless sensor networks used for data collection in industry, healthcare, and other areas are often implemented using IEEE 802.15.4, a recent network communication technology [12]. In many applications where WSNs operate on battery power, battery replacement is costly or even impossible, and extending the lifetime of the nodes and, consequently, the network itself is one of the most important goals in WSN design [15, 27, 26]. Extending node lifetime is achieved by minimizing the energy consumption for each node individually, but also by ensuring balanced energy consumption of all the nodes in the network [17]. The latter is often achieved by clustering, a procedure whereby the nodes are divided into groups [3, 4], as shown in Fig. 1, in order to obtain the following benefits: • By reducing the number of direct com- munications with the base station, reduced transmission power can be used for intra-cluster communication and the number of collisions is considerably reduced. As the result, substantial energy savings and lifetime extension can be achieved, while latency is reduced [16]. • Under contention-based Medium Access Con- trol (MAC) algorithms, dividing the network into clusters reduces the number of contending nodes [31] which lowers the probability of colli- sions during medium access and improves both bandwidth utilization and energy efficiency. • Finally, routing overhead may be reduced through clustering as the routing tables need not be updated as often [4]. In each group or cluster, one of the nodes is chosen as a leader or Cluster-Head (CH). A CH node collects the sensing data from individual nodes in its cluster and delivers it to the base station (BS). Since this functionality results in higher energy consumption for CH nodes, they are likely to die Copyright c 0000 copyright owner, Ltd. LaTeX’ed with wcmauthX.cls [Version: 2007/01/09 v1.00]
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WIR. COMM. AND MOBI. COMPU.Wirel. Commun. Mob. Comput. 00: 1–16 (0000)Posted online(wiley inter science) DOI: 10.1002/wcm.0000
Adaptive Low-Energy Clustering In Slotted Beacon-EnabledIEEE 802.15.4 Networks
Hamidreza Tavakoli1, Jelena Misic2, Majid Naderi3 and Vojislav B. Misic2
1Hakim Sabzevari University, Sabzevar, Iran2Ryerson University, Toronto, ON, Canada3Iran University of Science and Technology, Tehran, Iran
KEY WORDS: Wireless sensor networks; IEEE 802.15.4; clustering; randomized sleeping; rotation of cluster-head role; energy efficiency
1. Introduction
Wireless sensor networks used for data collectionin industry, healthcare, and other areas are oftenimplemented using IEEE 802.15.4, a recent networkcommunication technology [12]. In many applicationswhere WSNs operate on battery power, batteryreplacement is costly or even impossible, andextending the lifetime of the nodes and, consequently,the network itself is one of the most important goalsin WSN design [15, 27, 26]. Extending node lifetimeis achieved by minimizing the energy consumption foreach node individually, but also by ensuring balancedenergy consumption of all the nodes in the network[17]. The latter is often achieved by clustering, aprocedure whereby the nodes are divided into groups[3, 4], as shown in Fig. 1, in order to obtain thefollowing benefits:
• By reducing the number of direct com-munications with the base station, reduced
transmission power can be used for intra-clustercommunication and the number of collisions isconsiderably reduced. As the result, substantialenergy savings and lifetime extension can beachieved, while latency is reduced [16].
• Under contention-based Medium Access Con-trol (MAC) algorithms, dividing the networkinto clusters reduces the number of contendingnodes [31] which lowers the probability of colli-sions during medium access and improves bothbandwidth utilization and energy efficiency.
• Finally, routing overhead may be reducedthrough clustering as the routing tables need notbe updated as often [4].
In each group or cluster, one of the nodes ischosen as a leader or Cluster-Head (CH). A CHnode collects the sensing data from individual nodesin its cluster and delivers it to the base station(BS). Since this functionality results in higher energyconsumption for CH nodes, they are likely to die
2 H. TAVAKOLI, J. MISIC, M. NADERI, AND V. B. MISIC
Fig. 1. Topology of the network for round i.
earlier. To reduce this imbalance, the CH role has tobe periodically reassigned to different nodes in thecluster so that most, if not all, nodes act in that rolefor a certain period of time, which may be a constantor random value that follows a predefined probabilitydistribution. However, the manner in which the CHrole is assigned to individual nodes must be carefullydesigned in order to maintain the desirable featuressuch as low data latency and coverage.
In this paper, we describe, analyze, and evaluatea novel clustering algorithm referred to as AdaptiveLow-Energy Clustering (ALEC). ALEC is basedon probabilistic sleep of individual nodes andprobabilistic rotation of the CH role through a simpleand efficient distributed election, specifically tailoredfor use in IEEE 802.15.4 beacon-enabled networks.As far as we know, this is one of the first proposalsthat includes both probabilistic sleep and probabilisticrotation of the CH role, and the first to presenta comprehensive analytical treatment of the impactof clustering on node and network lifetime thatincorporates realistic models for node operation atboth MAC and physical (PHY) layers. Using thesemodels, we evaluate the performance of a WSN thatuses ALEC, and show the impact of various networkand ALEC parameters. We also discuss the choice ofparameters to ensure balanced power consumption inorder to help prolong network lifetime.
The remainder of the paper is organized asfollows. Section 2 reviews most relevant resultsfrom the literature. Section 3 describes the ALECalgorithm. Sections 4 and 5 present the analyticalmodel for energy consumption of ALEC algorithm.Section 6 evaluates ALEC algorithm’s performance
and discusses the results. Summary and somedirections for future research are given in Section 7.
2. Related work
Clustering has been shown to increase scalability andlifetime of wireless sensor networks [6]. Dependingon the manner in which the CH role is assigned toindividual nodes, we distinguish between distributedand centralized methods. Distributed approachestypically use probabilistic methods in which selectionof CH nodes is based on various criteria such asthe number of clusters, age of CHs [9], residualenergy of nodes [8], amount of traffic, number ofneighbors [2], and density of sensor nodes [20].However, distributed approaches suffer from the factthat individual sensor nodes do not possess completeknowledge of the network - the only such nodeis the BS, which has more energy and higherprocessing power than ordinary nodes. However,centralized elections necessitate periodic exchangeof status information between BS and sensor nodes[10] which may lead to extra power consumption[28]. Furthermore, CH selection and clustering mayinterfere with data communications and thus lead toexcessive delay overhead [3].
We note that CH election is often linked to re-clustering, i.e., re-distribution of nodes into clusters,which imposes additional power consumption as wellas delay overhead, since the transmission of sensingdata is reduced or completely suspended during thisprocess [20]. To reduce communication costs, [14]reinforces clustering only among nodes in closeproximity to each other. Alternatively, an energythreshold may be introduced so that only the CHswith lower energy level are allowed to take part inthe election, while others retain their role during thefollowing round [11].
Regarding analysis of WSNs with clustering,probabilistic analysis is often used to model event-based and query-based applications in order todetermine clustering efficiency and lifetime of thenetwork. Assuming fixed shapes for clusters, authorsin [21], derive the probability of achieving a desiredcluster lifetime under random assignment of nodes toclusters.
Proposed MAC protocols for sensor networks pro-vide either contention-based access, usually throughsome form of CSMA-CA, or time division multipleaccess (TDMA) [5]. The latter offer better powerefficiency since individual nodes can enter inactivestate until their allocated time slots [5], and they also
ADAPTIVE LOW-ENERGY CLUSTERING IN 802.15.4 NETWORKS 3
eliminate packet re-transmissions caused by packetcollisions. However, designing a collision-free TDMAschedule with minimum number of time slots andmaximum slot usage is an NP-complete problem[5, 13, 24], even without accounting for the need tosynchronize the nodes [3].
In comparison to TDMA protocols, contention-based MAC protocols are scalable, more efficient,and easier to implement. One of the most widelyused technologies with a contention-based MAC isthe IEEE 802.15.4 standard [12] that is specificallytailored towards networks with raw data rate below250kbps. Therefore, we have chosen this technologyas the foundation for our clustering protocol.
3. Adaptive Low-Energy Clustering: ALEC
We assume that all clusters operate in beacon-enabled, slotted CSMA-CA mode, with their CHsacting as coordinators. Additionally, CHs form aseparate cluster under the control of the BS. For allclusters, the time is divided into intervals determinedby beacons transmitted by CH nodes [12]; the timeinterval between two successive beacons is referredto as beacon interval BI = 48 · 2BO unit backoffperiods, while the duration of an active interval ofa superframe is SD = 48 · 2SO unit backoff periods.The variables BO and SO denote the so-calledbeacon order and superframe order, respectively; theirvalues are chosen so that 0 ≤ SO ≤ BO ≤ 15. If theoperating frequency of the network is 2.4GHz, theinterval known as a unit backoff period, is 320µswhich translates into 10 bytes and results in rawdata rate of 250Kbps. Both uplink and downlinkcommunications use CSMA-CA method at backoffboundaries. However, downlink communications cantake place only after announcement of a packet by CHnode and downlink request by the corresponding non-CH node [18].
In the inactive part of a superframe, non-CH nodessleep to reduce energy consumption while CH nodessynchronize to the BS superframe in order to deliverdata. As soon as a CH node delivers its data to theBS, it returns to its own cluster and resumes the CHrole by sending the beacon frame. If the CH nodedoesn’t succeed in delivering the data to BS in onesuperframe, it will freeze its backoff counter untilthe next communication to BS, much like ordinarynodes that do not succeed in sending their data to therespective CHs.
Activity management by adjusting frequency andratio of active and inactive intervals of sensor nodes
is used to reduce energy consumption [23, 25]. Eventsensing reliability R, i.e., the number of packetsshould be received by BS in a suitable time unit,is periodically announced by BS, together with thecurrent number of nodes aliveN . Then, each CH nodecalculates the portion of reliability for its own clusteras Rk = R(Nk/N), where Nk is the number of nodesin cluster k, and broadcasts it to the nodes in its cluster.Using this information, ordinary nodes calculatemean sleep period between transmission attempts;individual sleep periods are calculated randomly inorder to reduce collisions [17].
If a node wakes up with a packet in its buffer, it turnsits radio on in order to synchronize with the beacon.After finding the beacon, the node transmits the packetand goes back to sleep. If a node wakes up and findsits buffer empty, it will immediately begin a new sleepperiod. We refer to the sequence of sleep time, beaconfinding and packet transmission as a microcycle, asshown in Fig. 2.
After Nµ microcycles, CH nodes are due for re-election. Each node i generates a random number inthe range 0 to 1 and compares it with a threshold; ifthe value is below the threshold, the node becomes anew CH. The threshold depends on the index of theelection as
T (i, r) =
Nc
N −Nc(r mod NNc
), i ∈ G
0, otherwise(1)
where Nc is the desired number of CHs, and G isthe set of nodes that were not CHs in the previousr mod N/Nc elections. In this manner, the number ofnodes that compete for election is kept small (ideally,it should be equal to the number of clusters) whichminimizes the duration of the re-election intervalduring which data transmission does not take place.
The time interval during which a given node acts asthe CH is referred to as a round. As shown in Fig. 3,each round is composed of a set-up phase, in whichCH elections are held and clusters are formed, anda steady-state phase, in which data transmissions arecarried out. Each steady-state phase is composed ofNµ packet transmissions, and its duration is referredto as clustering period.
If all intra-cluster communications in the steady-state phase were to occur at the same channel, inter-cluster interference may result. As the IEEE 802.15.4standard operating in the 2.4GHz ISM band allowsthe use of 16 channels, inter-cluster interference canbe reduced through channel assignment [22]. Still,
4 H. TAVAKOLI, J. MISIC, M. NADERI, AND V. B. MISIC
0,ad
0,mp
0,cr
sleep
0,p
0,cd0,dr 0,d
c
µ
Fig. 2. Pertaining to the operation of ALEC.
communications in the set-up phase must occur ona single channel, the most suitable being channel 26which is the only one that is free from interferencefrom 802.11 (WiFi) networks [30]. (Channel 26 willalso be used by the BS-controlled cluster for datacommunications during the steady-state phase.)
The set-up phase contains the following activities.
1. Advertisement: after electing as a CH, a nodebroadcasts its status to other nodes.
2. Membership: each non-CH node determines theCH that requires the minimum transmissionpower (usually the closest one) and sends it ajoin request.
3. Channel Request: all CHs inform the BS aboutthe membership of their respective clusters, bysending their IDs along with other IDs theyreceived in membership phase to the BS.
4. Channel Assignment: the BS allocates fre-quency channels to individual clusters andinforms the newly elected CHs accordingly.
5. Channel Declaration: each CH node informs itscluster members about the allocated channel.
The time interval of nc = N/Nc rounds – which is,in fact, the period of the function used to determine thethreshold in r-th election, eq. (1) – will be referred toas a macrocycle. As shown in Fig. 2, a node undergoesa number of macrocycles during its lifetime, and actsas a CH for exactly one round in each macrocycle.
Unlike other clustering algorithms, ALEC intro-duces randomness at different levels: first, the timeinterval between successive intervals of CH duty israndom due to the election process; and second, theduration of CH duty is random due to the random sleeptime of ordinary nodes, random time to transmit thepacket due to CSMA-CA backoff time, and possibilityof packet collision and packet corruption due to noise.
ADAPTIVE LOW-ENERGY CLUSTERING IN 802.15.4 NETWORKS 5
rand(i,r) < T(i,r)
n = n + 1r = r + 1
Send membership message to chosen CH node, along with
other CH IDs, using CCC
Wait for Cluster-Head (CH) advertisements on Common
Control Channel (CCC)
START
n < Nµ
n = n + 1
Node i chooses a random number, rand(i,r), uniformly between 0 and 1
Advertise Cluster-Head (CH) status using Common Control
Channel (CCC)
Wait for membership messages, along with other
CH IDs, on CCC
Send ID along with other CH IDs to BS using CCC
Wait for Assigned Channel (AC) from BS on CCC
Send Assigned Channel (AC) to cluster members using CCC
(n=0)
Wait for Assigned Channel (AC) from CH on CCC (n=0)
Wait for data from cluster members on AC
Send data to BS using AC
Send data to CH node using AC
Node i calculates the threshold T(i,r) of the current round
n < Nµ
E < ET
Yes
No
r = 0
BS
BS
BS
END
Yes
No
Yes
No
NoYesSe
t-up
pha
seSt
eady
-sta
te p
hase
Fig. 3. Flowchart of node operation under ALEC.
4. Modeling ALEC Clustering
Let us now investigate the performance of the ALECalgorithm. We will model activities of individualnodes in the network using Discrete Time MarkovChain (DTMC) with a hierarchical structure. Asexplained above, a microcycle contains one or morerandom sleeps with mean duration determined fromthe event sensing reliability in the cluster, followedby packet transmission. The sequence of microcyclesspent in a cluster under a given CH coordination isdenoted as a round. In each round, each node willtransmit exactly Nµ packets after the set-up phase.A sequence of nc rounds comprises a macrocycle.We note that the transition between successivemacrocycles occurs with probability of one, as do thetransitions between rounds within a macrocycle and
transitions between microcycles within a round. Asthe result, the DTMC representing these transitionsis irreducible, recurrent and aperiodic, and henceforthergodic and has a stationary distribution. (We assumethat the steady-state of DTMC lasts sufficiently longtime.)
A Markov chain for one packet transmission isshown in Fig. 4 (adapted from [18]). The transmissionof a packet can start after the current beacon or itcan start immediately after the next beacon. The latertakes place when transmission of a packet cannot becompleted during a superframe [12]. The probabilityof deferring transmission of a packet to the nextbeacon (shown as block x in Fig. 4) is Px. Theindex x uses to discriminate between data packets(p), advertisement packets (ad), membership packets(mp), channel request packets (cr), downlink request
6 H. TAVAKOLI, J. MISIC, M. NADERI, AND V. B. MISIC
CSMA-CA Markov Chain building block
0,2,W0-1 0,2,W0-2 0,2,1 0,2,01
0,1,0
0,0,0
m,2,Wm-1 m,2,Wm-2 m,2,1 m,2,0
m,1,0
m,0,0
1
1
1
(1-Px)αx
βx
1-βx
1-βx
(1-Px)(1-αx)
uniformly distributed among the Wm states
uniformly distributed among the W0 states
block x
Px
1
(1-Px)αx(1-Px)(1-αx)
block x
Px
γxδx
1-γxδx
Tr
Tr
γxδx
1-γxδx
Tr
Tr
1
γyδyτ0,yfrom previous stage
to next stage
γxδxτ0,x
βx
Fig. 4. Markov chain for a packet transmission underCSMA-CA, adapted from [18].
packets (dr), downlink packets (d) and channeldeclaration packets (cd).
A single packet transmission takesDx = 2 +Gx +1 +Gack; this time is composed of two Clear ChannelAssessments (CCA), the time for actual transmission(Gx), the time for waiting the acknowledgement(one backoff time in the relation) and the timefor transmission of acknowledgement (Gack). Alladministrative packets are assumed to last for 3 unitbackoff periods and, thus, contain up to 30 bytes whichwas deemed sufficient. All data packets last for 12 unitbackoff periods and, thus, contain up to 120 bytes ofdata.
Success probabilities for first Clear ChannelAssessment, second Clear Channel Assessment andtransmission of the packet are labeled as αx, βx andγx, respectively. The actual transmission, shown withblock Tr, is composed of Dx backoff durations. Theimpact of noise and interference is modeled via theprobability of a packet being properly received isδx = 1− PER = (1−BER)Gx+Ga , where BERdenotes bit error rate. We assume to have areliable MAC layer which mean that the transmissioncontinues until the reception of acknowledgement.
In the Markov chain, a block {a, b, c} shows astate of the node in which a ∈ {0 . . m} indicatesthe number of backoff the node currently spends(m has a constant value of 4); b indicates thenumber of left Clear Channel Assessments (b ∈{0, 1, 2}); c ∈ {0 . . Wj − 1} indicates the numberof backoffs left before Clear Channel Assessments
(Wj = 2min(i+macMinBE,5) where macMinBE has aconstant value of 3). The probability of successfullymedium access by a node is denoted as τ0,x.
We will now describe specific features regardingtransmission of packets of different types.
4.1. Transmission of packets of different types
Advertisement packets: After the election in thecurrent round, the new CH begins a backoffcountdown for the advertisement packet, startingimmediately after the beacon. Since the size of firstbackoff window is between 0 and 7 backoff periods,Pad = 1/8 denotes the probability that the chosenbackoff time is zero, in which case transmissionoccurs two backoff periods after the beacon. Thetotal transmission time is, then, Dad = 2 + 3 + 1 = 6backoff periods.
During a macrocycle, a node is in advertisementstate exactly once. Therefore, the probability offinishing the first backoff phase in the transmissionblock is
x(ad)0,2,0 =
τ0,pγpδpncNµ
+ τ0,ad(1− γadδad). (2)
If we define new variables C1,ad, C2,ad, C3,ad andC4,ad as
x(ad)0,1,0 = x
(ad)0,2,0(1− Pad)αad
= x(ad)0,2,0C1,ad
x(ad)1,2,0 = x
(ad)0,2,0(1− Pad)(1− αadβad)
= x(ad)0,2,0C2,ad
x(ad)0,0,0 = x
(ad)0,2,0((1− Pad)αadβad + Pad)
= x(ad)0,2,0C3,ad
C4,ad =1− Cm+1
2,ad
1− C2,ad
(3)
the transmission sub-chain can be described with thefollowing:
x(ad)i,0,0 = x
(ad)0,2,0C3,adC
i2,ad, i = 0 . . m
x(ad)i,2,k = x
(ad)0,2,0
(1− k
Wi
)Ci2,ad
i = 0 . . m, k = 0 . . Wi − 1
x(ad)i,1,0 = x
(ad)0,2,0C1,adC
i2,ad, i = 0 . . m
x(ad)0,2,k = x
(ad)0,2,0
(1− k
W0
), k = 0 . . W0 − 1
(4)
Access probability for a single advertisement packetis τ0,ad =
ADAPTIVE LOW-ENERGY CLUSTERING IN 802.15.4 NETWORKS 7
be combined with (2) to obtain
τ0,ad =C3,adC4,ad
τ0,pγpδpncNµ
1− C3,adC4,ad(1− γadδad). (5)
The sum of probabilities for the advertisement packettransmission sub-chain is
sad =
m∑i=0
Wi−1∑k=0
xi,2,k
+ (Dad − 2)
m∑i=0
xi,0,0 +
m∑i=0
xi,1,0
(6)
which can be simplified to
sad = x(ad)0,2,0C4,ad
(C3,ad(Dad − 2) + C1,ad
)+ x
(ad)0,2,0
m∑i=0
Ci2,ad(Wi + 1)
2
(7)
Membership packets: After the advertisement sub-phase, non-CH nodes start sending membershipmessages to their CHs. (Note that in a macrocycle,a node acts as an ordinary node in all rounds exceptthe one during which it acts as a CH.) Membershippackets, similar to advertisement packets, are sentafter the beacon, therefore Pmp = 1/8.
In the Markov chain, the probability of the firstbackoff being successful is x(mp)0,2,0 =
(nc−1)τ0,pγpδpncNµ
+
τ0,mp(1− γmpδmp). Following an approach similar tothe one outlined above, we get
τ0,mp =C3,mpC4,mp
(nc−1)τ0,pγpδpncNµ
1− C3,mpC4,mp(1− γmpδmp)(8)
The sum of probabilities for the transmission ofmembership packets can, then, be written as
smp = x(mp)0,2,0C4,mp
(C3,mp(Dmp − 2) + C1,mp
)+ x
(mp)0,2,0
m∑i=0
Ci2,mp(Wi + 1)
2
(9)
Channel request packets: Information on clustermembership gathered during the membership subphase is sent by the CHs to the BS. Channel requestpackets start after the beacon, therefore Pcr = 1/8,and their duration is assumed to be Gcr = 3 backoffperiods, as noted above.
In the Markov chain for a channel request packet,the probability of the first backoff being successful is
x(cr)0,2,0 = τ0,adγadδad + τ0,cr(1− γcrδcr). Following
an approach similar to the one outlined above for theadvertisement packets, we obtain
τ0,cr =C3,crC4,crγadδadτ0,ad
1− C3,crC4,cr(1− γcrδcr). (10)
The sum of probabilities for transmission of channelrequest packets can be, then, obtained as
scr = x(cr)0,2,0C4,cr
(C3,cr(Dcr − 2) + C1,cr
)+ x
(cr)0,2,0
m∑i=0
Ci2,cr(Wi + 1)
2
(11)
Downlink request packets: In order to applyfor a downlink request packet, the node starts abackoff attempt in the beginning of the superframe.Downlink request packets start after the beacon withprobability of Pdr = 1/8. Probability that the firstbackoff is successful for a downlink request packetis x
(dr)0,2,0 = τ0,crγcrδcr + τ0,dr(1− γdrδdr), and the
corresponding access probability is
τ0,dr =C3,drC4,drγcrδcrτ0,cr
1− C3,drC4,dr(1− γdrδdr). (12)
The sum of probabilities for the transmission ofrequest packets can be, then, obtained as
sdr = x(dr)0,2,0C4,dr
(C3,dr(Ddr − 2) + C1,dr
)+ x
(dr)0,2,0
m∑i=0
Ci2,dr(Wi + 1)
2
(13)
Downlink packets with channel assignment infor-mation: Downlink packets can be transmitted onlyupon successful acknowledgment of downlink requestpackets. Probability that a packet will be delayedis Pd = Dd/SD, where SD denotes the activesuperframe duration. Probability of finishing thefirst backoff phase in the transmission block for adownlink packet is x
(d)0,2,0 = τ0,drγdrδdr + τ0,d(1−
γdδd), while the corresponding access probability is
τ0,d =C3,dC4,dγdrδdrτ0,dr
1− C3,dC4,d(1− γdδd). (14)
The sum of probabilities for the transmission ofdownlink packets can be, then, obtained as
8 H. TAVAKOLI, J. MISIC, M. NADERI, AND V. B. MISIC
which can be simplified to
sd = x(d)0,2,0C4,dPdca + x
(d)0,2,0
m∑i=0
Ci2,d(Wi + 1)
2
(16)where Pdca = C3,d(Dd −2)+C1,d+Pd(Dd −1)/2.
Channel declaration packets: The transmission ofthese packets, which follow the downlink packets,begins in the second half of the current superframeor in the beginning of the next superframe,therefore Pcd = Dcd/SD. The duration of the channeldeclaration packet is Gcd = 3 backoff periods.
The probability of a channel declaration packetsuccessfully finishing the first backoff phase in thetransmission block is x
(cd)0,2,0 = τ0,dγdδd + τ0,cd(1−
γcdδcd), while the corresponding access probability is
τ0,cd =C3,cdC4,cdγdδdτ0,d
1− C3,cdC4,cd(1− γcdδcd)(17)
and the sum of probabilities for the corresponding sub-chain is
scd = x(cd)0,2,0C4,cdPcd + x
(cd)0,2,0
m∑i=0
Ci2,cd(Wi + 1)
2
(18)where, similar to the case of downlink packets withchannel assignment information, Pcd = C3,cd(Dcd −2) + C1,cd + Pcd(Dcd − 1)/2.
Data packets: A node that wakes up and findsa packet in its buffer will wait for the beacon tosynchronize and begin its backoff countdown in orderto send the packet to its CH. We denote Pp = 1/8as the probability of occurring transmission in thebeginning of the superframe because the first windowfor backoff attempt is 8. In this case, the CCAs willbe successful. The length of data packets is Dp = 12backoff periods, as noted above.
In the Markov chain for a data packet, theprobability that the first backoff is finished is
x(p)0,2,0 =
τ0,mpγmpδmp + (Nµ − 1)τ0,pγpδpNµ
+τ0,p(1− γpδp),(19)
and the corresponding access probability is
τ0,p =C3,pC4,pτ0,mpγmpδmp/Nµ
1−C3,pC4,p
((Nµ−1)γpδp
Nµ+(1−γpδp)
) .(20)
Sum of total probabilities for the sensing data packettransmission sub-chain is
sp = x(p)0,2,0C4,p
(C3,p(Dp − 2) + C1,p
)+x
(p)0,2,0
m∑i=0
Ci2,p(Wi + 1)
2
(21)
Synchronization times: Synchronization time isthe time interval between wake-up time and thesubsequent cluster beacon, for an ordinary node, orthe time interval between switching to the BS clusterand the subsequent BS cluster beacon, for a CH node.Since the distribution of synchronization period isuniform, the Probability Generating Function (PGF)can be determined as D(z) = 1−zBI
BI(1−z) . Sum of totalprobabilities within the beacon synchronization timeduring steady-state phase is
sss =τ0,mpγmpδmp+(Nµ−1)τ0,pγpδp
Nµ
BI∑i=0
i
BI
(22)The probability distribution of sleep period of
a node is geometric with the average value offrac1Psleep [17]. Sum of total probabilities that anode spends in a single sleep period is
ss1 =τ0,mpγmpδmp + (Nµ − 1)τ0,pγpδp
Nµ(1− Psleep). (23)
As noted above, when a node wakes up, it checks ifthere is a packet in its buffer and if so, it will attempt tosend it. The probability of the event is denoted as Pcand the value will be determined later. Sum of totalprobabilities that a node spends in a sleep cycle isss =
ss1(1−Pc) .
The normalization condition for the completeMarkov chain is
For a specific packet type, total access probabilitycan be determined as sum of the access probabilitiesin a macrocycle, taking into account that some ofactivities actually occur only once per round:
ADAPTIVE LOW-ENERGY CLUSTERING IN 802.15.4 NETWORKS 9
The analysis of the transmission of data packets andsynchronization times in the last two sub-subsectionsabove applies to both data transmissions from asensing node to its CH in an individual cluster, andto data transmissions from a CH to the BS in the BScluster.
4.2. Analysis of the packet queue at the node
MAC layer will be modeled as an M/G/1/K queuewith the following Markov points: sleep period,beacon synchronization, cluster set-up and servicetime of the packet. Packet arrivals to the queue of anode follow the Poisson process with average arrivalrate of λ. The buffer of nodes has the capacity ofL packets. The node that has packets will send asingle packet before going to sleep, which is knownas 1-limited scheduling policy [29]. The PGF of theduration of packet service time is denoted as Tt,x(z),where x ∈ {ad,mp, cr, dr, d, cd, p}; the exact valueof this PGF will be derived in Section 5. The buffer ofa node is modeled using the following Markov points.
Departure time of a data packet: The number ofpacket arrivals during service time of a packet has thePGF ofB(z) =
∑∞k=0 bkz
k = T ∗t,p(λ− zλ), in whichT ∗t,p() denotes the Laplace-Stieltjes Transform (LST)of service time [29] and the LST can be obtained byreplacing the variable z with e−s. The probability ofexisting j ∈ {0 . . L− 1} packets in the node bufferafter finishing the service time of a packets is denotedas νj .
End of a sleep period: After finishing transmissionof a packet (before ending the steady-state phase),the node starts a sleep period. a single sleep periodhas the PGF of V (z) =
∑∞j=1(1− Psleep)P
j−1sleepz
j =(1−Psleep)z1−zPsleep . According to [29], during a single sleep
period, number of packet arrivals to the buffer of anode has PGF of E(z) =
∑∞j=0 ejz
j = V ∗(λ− zλ).The probability of existing j ∈ {0 . . L} packets in thebuffer of a node after finishing a single sleep period isdenoted as ωj .
End of cluster set-up phase: According to Fig. 2,after ending the steady-state phase, the node starts acluster set-up, during which data packets cannot betransmitted. The set-up state can be assumed as avacation for the queue of data packet. The PGF ofthe duration of the set-up is Ts(z) and the number ofpackets arriving to the buffer during a set-up phase
has the PGF of H(z) =∑∞j=0 hjz
j = T ∗s (λ− zλ).The probability of existing j ∈ {0 . . L} packets in thebuffer of a node after finishing the cluster set-up isdenoted as εj .
End of the synchronization period: After endingof a sleep cycle, the node with a non-empty queue,has to find a beacon. The interval has a uniformdistribution between 0 and BI − 1 backoff, and itsPGF D(z) is given in 4.1. During a synchronizationperiod, number of packet arrivals to the buffer of anode has PGF of F (z) =
∑∞k=0 fkz
k = D∗(λ− zλ).The probability of existing j ∈ {0 . . L} packets in thebuffer of a node at the end of synchronization periodis denoted as δj .
Node buffer behavior in Markov points: Bymodeling the node buffer state in Markov points ofdifferent types, the steady-state equations for statetransitions are as follows:
10 H. TAVAKOLI, J. MISIC, M. NADERI, AND V. B. MISIC
together with the normalization equation
L∑k=0
(ωk + εk) +
L∑k=1
δk +
L−1∑k=0
νk = 1 (27)
where 1− p = 1/Nµ denotes the probability of beingin the last transmission of the current steady-statephase. After solving the equations, the probability ofthe queue length at Markov points will be found.Solving the equations results in obtaining the valueof Pc = ω0/
∑Li=0 ωi. Therefore, mean sleep cycle
(which can be composed of a number of sleep periods)is I = 1/ ((1− Pc)(1− Psleep)).
4.3. Transmission success probabilities
We assume the packet arrival events follow a Poissonprocess and there are nc = N/Nc nodes in a cluster.The traffic generated by all other nodes in a clusteris considered as background traffic for a given node,assuming that the cluster operates below the saturationregime [18].
Arrival rates of packets for background traffic:Since CH nodes are members of the BS cluster,we discriminate between packet arrival rates duringtheir CH and non-CH periods. Transmissions ofmembership and sensing packets can commencein the first eight backoffs in the beginning of asuperframe. The background packet arrival is λx =(nc − 1)τxSD/8, where x ∈ {mp, p}.
During CH periods, transmission of advertisement,channel request and downlink request packets cancommence in the first eight backoffs in the beginningof a superframe; the arrival rate of background trafficis λx = (Nc − 1)τxSD/8, where x ∈ {ad, cr, dr}.After a successful reception of a downlink requestpacket, the transmission of a downlink packet canstart. In this case, the arrival rate of background trafficof downlink packets is λd = (Nc − 1)τdSD/(SD −Ddr).
After learning about the assigned channel, theCH node starts transmission of channel declarationpackets in the second part of the current superframeor the first part of the immediately following one. Thearrival rate of the background traffic can be describedby λcd = (Nc − 1)τcd.
The first CCA will fail if any other transmission isin progress while the second CCA will fail if any othertransmission has just been started.
Medium behavior: Sensing, advertisement, mem-bership and channel request packets have successprobabilities of αx = 1
8
∑7i=0 e
−iλx , βx = e−λx , andγx = βDxx , respectively, where x ∈ {ad,mp, cr, p}.
Downlink request packets have successprobabilities of αdr =
18
∑7i=0 e
−i(λdr+λcd),
βdr = e−(λdr+λcd), and γdr = βmax(Ddr,Dcd)dr .
Success probabilities for downlink packetsare αd =
1SD−Ddr
∑SD−Ddr−1i=8 e−i(λdr+λd+λcd),
βd = e−(λdr+λd+λcd), and γd = βmax(Ddr,Dd,Dcd)d .
Finally, success probabilities for channel declara-tion packets are αcd = 1
SD
∑SD−1i=0 e−i(λdr+λd+λcd),
βcd = e−(λdr+λd+λcd), and γcd = βmax(Ddr,Dd,Dcd)cd .
Success probabilities for CH and non-CH nodes:There areNc clusters containing nc sensor nodes, eachhaving arrival rate of λ per node. We can assumeidentical traffic conditions in all clusters during around.
Before obtaining success probabilities, accessprobabilities have to be determined. For a specific typeof packet, in order to determine access probability, thepacket type x should be replaced for τx (25).
Access probabilities for packets sent by CHs can bemodeled as τx,CH = ncτx. As success probability forCH transmissions depends on all other CHs, we arriveat γx,CH = (1− τx,CH)Dx(Nc−1).
5. Analyzing Node Lifetime
For a specific type of packet x with constant lengthof kx backoffs, the PGF of length of packet will beassumed as Gx(z) = zkx . We will assume Ga(z) = zis PGF of duration of acknowledgment and tack(z) =z2 is PGF of duration of intervals between the data andacknowledgment. According to previous assumptions,PGF for duration of a transmission reception ofits acknowledgment is Tx(z) = Gx(z)tack(z)Ga(z).Then, for a specific type of packet x, the PGF of thetime interval needed to accomplish transmission of asingle packet [18] is
Ax(z) =
m∑i=0
(1−αxβx)iz2(i+1)αxβxTx(z)
i∏j=0
Bj(z)
αxβx
m∑i=0
(1− αxβx)i
(28)where Bj(z) = zWj−1
Wj(z−1) is the PGF for the durationof j-th backoff time prior to transmission. The LSTs
ADAPTIVE LOW-ENERGY CLUSTERING IN 802.15.4 NETWORKS 11
for energy consumption during wait and reception ofacknowledgment, two CCAs and packet transmissionare e−3sωr , e−2sωr , and e−kxsωt , respectively. Weassume that the length of beacon necessary forinforming the number of live nodes and eventsensing reliability is three; hence the LST for energyconsumption while receiving it is e−3sωr . Then, theLST for energy consumption during transmission ofthe data packet and reception of acknowledgmentwill be T ∗x (s) = e−skxωte−s3ωr . The LST for energyconsumption for a single transmission attemptbecomes
E∗Ax(s) =
m∑i=0
(1−αxβx)ie−2sωr(i+1)αxβxT∗x (s)B
αxβx
m∑i=0
(1− αxβx)i
(29)where B =
∏ij=0E
∗Bj
(s).Considering packet collisions [19], PGF
of the total packet service time becomes
Tt,x(z) =∞∑k=0
(Ax(z)(1− γxδx))kAx(z)γxδx which
can be simplified to Tt,x(z) =γxδxAx(z)
1−Ax(z)+γxδxAx(z) ,and the LST for the energy spent on a packet servicetime is E∗Tx(s) =
γxδxE∗Ax(s)1−E∗Ax(s)+γxδxE
∗Ax(s)
. Averagevalue of energy consumed for packet transmission isET x = − d
dsE∗T x(s)|s=0.
CHs send packets during advertisement, channelrequest, uplink request for channel assignment andchannel declaration sub-phases of a given set-up phase; they receive packets during membershipsub-phase and sub-phase of downlink data forchannel assignment. Non-CH nodes only sendpackets during membership sub-phase, and theyare in receiving mode during other sub-phasesof a given set-up phase. Therefore, the PGFof the duration of one set-up phase is Ts(z) =Tad(z)Tmp(z)Tcr(z)Tdr(z)Td(z)Tcd(z) and LST ofenergy consumption during a single set-up phase is
E∗s,C(s) = E∗T ad(s)E∗T cr(s)E
∗T dr(s)E
∗T cd(s)
· Tmp(e−sωr )Td(e−sωr )E∗s,nC(s) = E∗Tmp(s)Tad(e
−sωr )Tcr(e−sωr )
· Tdr(e−sωr )Td(e−sωr )Tcd(e−sωr )
(30)
for CH and non-CH nodes, respectively.As discussed before, each steady-state phase
is composed of a number (Nµ) of microcycleswhich is composed of three steps: sleep, beaconsynchronization and data transmission (CSMA-CA
uplink). However, all CH nodes are awake and inreceiving mode during a microcycle, therefore theaverage energy consumption is
E∗m,C(s) = I(e−sωr )D(e−sωr )e−s3ωrTp(e−sωr )
E∗m,nC(s) = I(e−sωs)D(e−sωr )e−s3ωrE∗T p(s)(31)
for CH and non-CH nodes, respectively.Then, the LST for energy consumption during a
given round is
E∗r,C(s) = E∗s,C(s)(E∗m,C(s))
Nµ
E∗r,nC(s) = E∗s,nC(s)(E∗m,nC(s))
Nµ (32)
for CH and non-CH nodes, respectively.During a macrocycle which is composed of nc
rounds each node has to act as CH for one round only;therefore, the LST for energy consumed during onemacrocycle is
E∗M (s) = E∗r,C(s)(E∗r,nC(s))
nc−1 (33)
If the battery budget is Ebat, the average numberof macrocycles during lifetime of a node is Ebat/EM ,where EM is the average value of energy consumedduring a macrocycle. Therefore, total lifetime of thenetwork is L = TMEbat/EM , where TM is averageduration of a macrocycle.
6. Performance evaluation
To evaluate the performance of the ALEC algorithm,we have solved the system of equations presentedin Sections 4 and 5 to obtain relevant performanceindicators. We have assume that the network has400 nodes, each of which is powered by two AAbatteries with total energy Ebat = 10260J . The effectof noise and interference is modeled with BER =10−4. The network operates in the ISM band at 2.4GHz, with raw data rate of 0.25 Mbps. Superframeand beacon order parameters were set to SO = 0 andBO = 1, respectively, which means that superframesize was SD = 48 unit backoff periods, while thebeacon interval was BI = 96 backoff periods.
To ensure realistic experimental values, we haveassumed that energy consumption per backoffperiod is ωs = 18.2× 10−9J , ωr = 17.9× 10−6J ,and ωt = 15.8× 10−6J , during receiving, sleep-ing and transmitting at 0 dBm, respectively [1].Regarding packet length, we note that increasingpacket length would result in reduced values forsuccessful transmission and reception rate (γx
12 H. TAVAKOLI, J. MISIC, M. NADERI, AND V. B. MISIC
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coefficient of variation (Nc=24)
skewness (Nc=8)
skewness (Nc=24)
(d) Coefficient of variation and skewness of around.
10 15 20
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0.015
0.02
Nc
coefficient of variation (R=10)coefficient of variation (R=50)skewness (R=10)skewness (R=50)
(e) Coefficient of variation and skewness of amacrocycle.
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3
x 10−3
Nc
R
(f) Coefficient of variation of lifetime.
Fig. 5. Performance vs. sensing reliability R and number of clusters Nc.
and δx, respectively), which translates into morefrequent retransmissions and lower energy efficiency.Therefore, we assumed that all packets have the samelength of kp = 3 unit backoff periods, except forsensing packets which have the maximum allowedpacket length of kp = 12 unit backoff periods. We alsoassume that each node has a buffer that can holdL = 2packets.
Our main performance indicators will be themean value of a random variable µ = − d
dsF∗(s)|s=0,
where F ∗(s) is its LST; the coefficient of variation
CV = σ/µ = 1µ
(d2
ds2F∗(s)|s=0 − µ2
) 12
, which is ameasure of dispersion around the mean; and skewnessγ = − 1
σ3
(d3
ds3F∗(s)|s=0 − 3µσ2 − µ3
), which is a
measure of the degree of asymmetry of a distributionaround its mean.
6.1. Variable event sensing reliability andnumber of clusters
We first investigate performance of ALEC undervariable event sensing reliability R (i.e., number ofpackets per second needed for reliable event detection)and variable number of clusters Nc, while keepingthe number of microcycles constant at Nµ = 500.The resulting mean duration of a round, macrocycle,and network lifetime, as well as their coefficient of
variation and skewness (except for network lifetime),are shown in Fig. 5. The required event sensingreliability values are obtained by varying the packetarrival rate in the range 0.025 to 0.125 packets persecond per node. The average duration of a microcycleis Tm = 1/r = I +D + 3 + T , from which we candetermine the mean inactive period I and sleepprobability Psleep.
As can be seen in Fig. 5(a), lower values ofR lead tohigher mean duration of a round. Since a macrocycle issum of nc independent and identically distributed (iid)random variables that correspond to individual rounds,mean duration of a macrocycle is the sum of averagesof rounds, as in Fig. 5(b). The network lifetime, shownin Fig. 5(c), is also sum of a number of iid randomvariables representing duration of macrocycles. Thecoefficient of variation and skewness of a roundand a macrocycle are shown in Figs. 5(d) and 5(e),respectively. The variance of the sum of a numberof iid random variables is the sum of their variances.Therefore, when the number of random variables tobe added increases, the numerator of coefficient ofvariation (standard deviation) decreases more rapidlythan its denominator, which means smaller dispersionaround the mean.
When the number of clusters increases, as shownin Fig. 5(e), the number of rounds in a macrocycledecreases, which results in higher dispersion around
ADAPTIVE LOW-ENERGY CLUSTERING IN 802.15.4 NETWORKS 13
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(d) Coefficient of variation and skewness of around.
200 400 600 800
0.01
0.015
0.02
0.025
0.03
0.035
0.04
Nµ
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(e) Coefficient of variation and skewness of amacrocycle.
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−3
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Fig. 6. Performance vs. sensing reliability R and number of microcycles Nµ.
the mean and, consequently, higher values ofcoefficient of variation. Also, a macrocycle has smallerskewness than a round, as can be seen in Figs. 5(d)and 5(e), which is due to the fact that, according tothe central limit theorem [7], sum of a number of iidrandom variables converges to a normal distributionwith zero skewness. Since the network lifetime iscomposed of macrocycles, the same argument holdswith respect to the coefficient of variation of networklifetime, shown in Fig. 5(f). Higher values of CVindicate higher variation of lifetime, which means thatthe network may cease to operate even though manynodes still haven’t exhausted their energy supply.Lower values for the coefficient of variation aredesirable as they indicate longer network lifetime andbetter energy efficiency.
6.2. Variable event sensing reliability andclustering period
In our second experiment, we have investigated theperformance of the ALEC approach under variableevent sensing reliability R and variable clusteringperiod, controlled by the number of microcycles Nµ.the results obtained with Nc = 16 clusters, whichmeans that each cluster had nc = N/Nc = 25 nodes,are shown in Fig. 6.
As can be expected, values of sensing reliabilityaffect the mean duration of a round or a macrocyclein a similar way as in the previous experiment,although the dependency is much less pronouncedthan in Fig. 5(a). Increasing the number of microcyclesincreases the mean duration for both round andmacrocycle periods. As the macrocycle consists ofa number of rounds, increasing the number ofmacrocycles translates into lower values for bothcoefficient of variation and skewness, as the levelof rounds, Fig. 6(d), as well as at the levelof macrocycles, Fig. 6(e). However, skewness ofa macrocycle is smaller than that of a roundwhich implies that macrocycles are closer to normaldistribution. Since lifetime is composed of a numberof macrocycles, similar argument holds for thecoefficient of variation of network lifetime, shown inFig. 6(f). When the required event sensing reliabilitydecreases, the number of macrocycles during thenetwork lifetime decreases, which leads to higherdispersion around the mean value and higher valuesof coefficient of variation.
6.3. Variable number of clusters andmicrocycles
We have also investigated performance of the ALECapproach under variable number of clusters Nc and
14 H. TAVAKOLI, J. MISIC, M. NADERI, AND V. B. MISIC
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Nµ
(a) Mean duration of a round.
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15
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NµN
c
(b) Mean duration of a macrocycle.
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NµN
c
(c) Mean network lifetime.
200 400 600 800
0.05
0.1
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0.2
Nµ
coefficient of variation (Nc=8)
coefficient of variation (Nc=24)
skewness (Nc=8)
skewness (Nc=24)
(d) Coefficient of variation and skewness of around.
200 400 600 800
0.01
0.02
0.03
0.04
0.05
Nµ
coefficient of variation (Nc=8)
coefficient of variation (Nc=24)
skewness (Nc=8)
skewness (Nc=24)
(e) Coefficient of variation and skewness of amacrocycle.
1015
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1.6
1.8
2
x 10−3
NµN
c
(f) Coefficient of variation of lifetime.
Fig. 7. Performance vs. number of clusters Nc and number of microcycles Nµ.
variable number of microcycles Nµ, while keepingthe event sensing reliability and, consequently, packetarrival rate at constant value of R = 30 and r = 0.075packets per second per node, respectively. The resultsare shown in Fig. 7.
As can be seen, higher number of microcycles leadsto higher mean duration of a round, Fig. 7(a). Theduration of a macrocycle, being a sum of duration ofa number of rounds, increases when the number ofclusters decreases and/or the number of microcyclesincreases, as shown in Fig. 7(b). The network lifetime,on the contrary, increases when there are fewerclusters, but is rather insensitive to the number ofmicrocycles, Fig. 7(c), due to multiple levels ofsummation between the two.
Coefficient of variation and skewness for around and macrocycle are shown in Figs. 7(d) and7(e), respectively. When the round contains fewermicrocycles (below 200), coefficient of variation aswell as skewness are higher, which leads to higherdispersion around the mean value. Increasing thenumber of microcycles, which are summed to obtain around, results in lower dispersion around mean valuefor a round, and the same observation holds for amacrocycle. Again, the skewness of a macrocycle issmaller than that of a round, which means the durationof a macrocycle is closer to normal distribution.Coefficient of variation of lifetime is shown in
Fig. 7(f); as can be seen, lower dispersion aroundthe mean can be achieved by lowering the numberof clusters which, in turn, results in larger number ofrounds in a macrocycle.
6.4. Power consumption and delay overheads
The ALEC algorithm incurs some amount of overheaddue to clustering. As mentioned before, no data canbe transmitted to BS during the set-up phase, whichwill delay delivery of some sensing data. On theother hand, energy consumption during set-up phasedoes not directly contribute to data collection so itmay be considered as energy overhead. Obviously,minimizing both delay and energy overhead is aprimary measure of the efficiency of a clusteringalgorithm.
To evaluate the efficiency of the ALEC algorithm,we have also calculated the delay and energy overheadintroduced by the use of ALEC algorithm; the resultsare shown in Fig. 8, with delay overhead shown in thediagrams in the top row and energy overhead in thediagrams in the bottom row.
Regarding the delay overhead incurred by theALEC algorithm, results shown in Fig. 8(a) areobtained with the number of microcycles fixed at 500,those in Fig. 8(b) are obtained with the number ofclusters fixed at 16, and those in Fig. 8(c) are obtained
ADAPTIVE LOW-ENERGY CLUSTERING IN 802.15.4 NETWORKS 15
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Fig. 8. Overhead (in percent) due to ALEC algorithm.
with sensing reliability fixed at 30. Overall, the delayoverhead is below 0.65% in all three experimentswhich is rather low. As can be seen, lower valuesof delay overhead can be achieved by increasing thenumber of clusters or the number of microcycles.Delay overhead could also be decreased by loweringthe event sensing reliability – provided the applicationallows it.
The energy overhead incurred by the ALECalgorithm is calculated as the ratio of total energyconsumed by the network during the set-up phaseand the total energy consumption of the network. Asabove, the results in Fig. 8(d) are obtained with thenumber of microcycles fixed at 500, those in Fig. 8(e)are obtained at the number of clusters fixed at 16, andthose in Fig. 8(f) are obtained under sensing reliabilityfixed at 30. Overall, the energy overhead is less than0.15% in the observed range of independent variableswhich is negligible. Still, energy overhead may bereduced by increasing the number of clusters and/ormicrocycles. It may also be reduced by lowering theevent sensing reliability, as long as the applicationrequirements allow for such a reduction.
7. Conclusion
In this paper, we have presented the Adaptive Low-Energy Clustering (ALEC) algorithm for sensornetworks using sensor nodes operating in IEEE802.15.4 slotted beacon-enabled mode. Nodes in anALEC-operated network use random sleep to extendtheir lifetime. They also use clustering to improveefficiency, with the role of cluster-head taken bydifferent nodes in random periods in order to balancethe energy consumption and thus extend the usefullifetime of the network. We have used probabilisticand queuing analysis to investigate how differentALEC parameters such as the number of clusters andnumber of microcycles, as well as application-dictatedparameters such as event sensing reliability, impact theperformance of the network in particular the networklifetime and clustering overhead. Our results indicatethat energy consumption overhead and delay overheadof the ALEC algorithm are not only low, but are wellbelow the variability due to the randomness inherentto the ALEC algorithm. Moreover, low values of thecoefficient of variability and skewness indicate thatthe node energy consumption is well balanced, whichmeans all nodes will die at approximately the sametime, thus extending the useful life of the networkitself.
16 H. TAVAKOLI, J. MISIC, M. NADERI, AND V. B. MISIC
Our future work will focus on improving the ALECalgorithm by fine-tuning its parameters. We will alsoinvestigate the possibility of aggregating the senseddata in order to improve the transmission efficiency.
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