QoS supporting and optimal energy allocation for a cluster based wireless sensor network

QoS supporting and optimal energy allocation for a cluster

based wireless sensor network

Shensheng Tang,Wei Li

*

Department of Electrical Engineering and Computer Science,University of Toledo,Toledo,OH 43606,USA

Available online 3March 2006

Abstract

Wireless sensor networks (WSNs)have become a very active and important area of research due to their potential in civil and military applications.A lot of research works focus on energy e?cient routing protocols due to the limited energy of battery-powered nodes.Currently,the increasing interest in multimedia applications has made the QoS (quality of service)supporting an unavoidable task.In this paper,we perform the analysis of QoS supporting and optimal energy allocation issues by presenting a cluster based WSN.A QoS supporting scheme is developed for dynamic tra?c conditions by controlling data generating rates at individual clusters.In addi-tion,an explicit solution on the energy distribution at di?erent clusters in the WSN is investigated based on an optimal energy allocation criterion.The localized QoS controlling scheme is useful in WSNs due to ?exibility and scalability,and the obtained network energy distribution formula is particularly convenient for node deployment design in WSNs and three speci?c situations are discussed as applications.

ó2006Elsevier B.V.All rights reserved.

Keywords:Wireless sensor network;Clustering;Data loss rate;Source-to-sink delay;QoS;Optimal energy allocation

1.Introduction

Recently,wireless sensor networks (WSNs)have received more and more attention due to their potential in civil and military applications as well as the advances in micro-electro-mechanical systems (MEMS)technology.Sensor networks are composed of a large number of sen-sors equipped with limited power and radio communica-tion capabilities.They can be deployed in extremely hostile environment,such as battle?eld target area,earth-quake disaster area,and inaccessible area inside a chemical plant or nuclear reactor to measure environmental changes or other needed information.A typical network con?gura-tion consists of sensors working unattended and transmit-ting their observation values to some processing or control center,the so-called sink node,which serves as a user inter-face [1].If these sensors are managed by the sink directly,

control overhead,management delay,and management complexity could make such a network less responsive and less energy e?cient.Clustering has been proposed by researchers to group a number of sensors,usually within a geographic neighborhood,to form a cluster [2].Using a clustering approach,sensors can be managed locally by a cluster head,a node elected to manage the cluster and relay the collected data.In addition,clustering provides inherent optimization capabilities at cluster-heads,such as data pre-processing.

Due to the limited transmission range,data generated from sensors that are far away from the sink must be relayed through a number of intermediate clusters (i.e.,multi-hop communications).Most applications for WSNs involve battery-powered nodes with limited energy.Their batteries may not be convenient for recharging or replac-ing.When a node exhausts its energy,it cannot sense or relay data any more.Thus,current research on sensor net-works mostly focused on protocols with energy e?cient mechanisms [3–6].However,the increasing interest in multimedia applications by employing imaging and video

0140-3664/$-see front matter ó2006Elsevier B.V.All rights reserved.doi:10.1016/https://www.360docs.net/doc/219145255.html,com.2006.02.007

*

Corresponding author.Fax:+14195308146.

E-mail addresses:stang@https://www.360docs.net/doc/219145255.html, (S.Tang),wli@https://www.360docs.net/doc/219145255.html, (W.Li).

https://www.360docs.net/doc/219145255.html,/locate/comcom

Computer Communications 29(2006)

2569–2577

sensors,such as target tracking in battle environments and disaster ?eld,has posed additional challenges [7–9],such as controlling the source-to-sink delay (SSD),data loss rate (DLR)or data pass rate (DPR)within acceptable range.These performance metrics are usually referred to as qual-ity of services (QoSs)of networks.Therefore,in the design of WSNs both energy-e?cient and QoS supporting issues should be considered in order to ensure e?ective ?eld data collection and optimal network energy allocation.

In this paper,we present a cluster based linear WSN topology to perform analysis of the two aspects,i.e.,QoS supporting and optimal energy allocation.Each cluster is managed by a cluster-head,which is modeled by a single server ?xed rate (SSFR)node with ?nite capacity and with di?erent data arrival rate depending on the total (relaying)tra?c from other clusters and the tra?c generated from its own cluster.All the tra?c is relayed from a cluster to another until to the sink.Based on the system model,some important performance metrics are analyzed,such as DLR,DPR,and the mean sojourn time for a data unit at individ-ual clusters and the maximum SSD in the network.Then we develop a QoS supporting scheme which can control the packet loss at individual clusters,and also quantitative-ly investigate the energy distribution in di?erent clusters based on an optimal energy allocation criterion.The obtained energy distribution formula is particularly useful for node deployment design of WSNs and three application situations are discussed as well.

The rest of paper is organized as follows.Section 2pre-sents the system model of the WSN.Section 3proposes the QoS supporting scheme.Section 4focuses on optimal ener-gy allocation issues.Section 5presents the results and dis-cussions.Section 6?nally concludes the paper.2.System model

Consider a multi-hop WSN consisting of M clusters arranged linearly as shown in Fig.1.Cluster i has n i sensing nodes and a cluster-head which is used for management and relaying,i =1,2,...,M .The distance between the sink and the 1st cluster is d 1and between the (i à1)st cluster and the i th cluster is d i .The total distance from the sink to the farthest cluster is P M

i ?1d i .The linear topology model under study rep-resents a common WSN where the cluster formation and net-work layer route discovery are assumed to be accomplished.A cluster-head not only collects data from the sensing nodes of its cluster but also relays collected data from other cluster-heads.This many-to-one data routing paradigm leads to

non-uniform tra?c distribution in di?erent clusters of the WSN.The cluster-heads closer to the sink transfer more traf-?c than those located at farther region.

Sensors and cluster-heads are assumed to be stationary or limited moving inside clusters.Sensors receive com-mands from and send data to its cluster-head,which does pre-processing for the data and forward them to other clus-ter-heads.A cluster-head is located within the communica-tion range of all the sensors of its cluster and can communicate with its neighbor cluster-heads.Since a clus-ter-head forwards tra?c to other cluster-heads with longer distance as compared to its sensing nodes,in some applica-tions it is more powerful than the sensing nodes in terms of energy,bandwidth and memory [10,11](in such cases,some pre-processing such as data aggregation/fusion [12]will be performed in cluster-heads),while others select clus-ter-heads from the deployed sensors [13,14].When a clus-ter-head is under failure due to insu?cient power,another cluster-head will be selected among the sensors (assume a sensor can adjust its transmission power to a larger value (for relaying requirement)once it is selected as a cluster-head.The details on transmission power con-trol issues are referenced in for example [15,16]).The clus-ter-based architecture raises many interesting issues such as cluster formation,cluster-head selection and cluster main-tenances,which are beyond the scope of this work.Here,we only focus on modeling the tra?c behavior along with the multi-hop cluster-heads.

The system model consists of three parts:(1)sensing part,the sensors around the target area are responsible for probing the target/event and send the collected data to their cluster-head;(2)relaying part,the collected data are relayed among the cluster-heads until to the sink;(3)sink,the sink performs system-level data analysis and pro-cess for an overall situation awareness.

The tra?c ?ow behavior in the linear network can be modeled by M ?nite queues linked in tandem.Each queue i is a single server ?xed rate (SSFR)node with ?nite capac-ity of K i (including the one in service),i =1,2,...,M .Assume that data units in each queue are served in a FCFS (?rst come ?rst served)manner.However,other service dis-ciplines,such as LCFS (last come ?rst served),priorities,processor sharing,etc.,could also be considered in the pro-posed model,since in some applications with for example LCFS-PR rule,it is of interest to get the freshest data avail-able.Assume that the data generating process for individ-ual sensors at cluster i is Poisson with rate g i (it can be adjusted through the command of the cluster-head)and the occurrence of every sensing event is independent of all the other events in the network.From the superposition property of Poisson process,the arrival process to the i th cluster-head is also Poisson with rate k i .Assume the service time of cluster-head at the i th cluster is exponentially dis-tributed with rate l i .Then the i th cluster-head can be mod-eled as an M /M /1/K i queue system with arrival rate k i ,i =1,2,...,M .The arrival rates to di?erent clusters are easily determined

by:

2570S.Tang,W.Li /Computer Communications 29(2006)2569–2577

k M?n M g M;

k i?n i g itk it1?1àp it1eK it1T

?n i g it

X M

j?it1n j g

j

Y j

k?it1

?1àp keK kT ;

i?1;2;...;Mà1;

e1T

where p i(K i)is the blocking probability of cluster i.By using routine approach[17],the steady-state queue-length distribution of the i th cluster-head is

p i ejT?

e1àq iTq j i

1àq K it1

i

;where q

i

?

k i

l i

.e2TThen many performance metrics can be easily obtained,

such as the data loss rate(DLR)(alternatively,data loss probability(DLP)),data pass rate(DPR)and the mean sojourn time at the i th cluster-head as well as the maximum source-to-sink delay(SSD)in the network.

DLR i?k i p ieK iT;or DLP i?p ieK iT;

DPR i?k i?1àp ieK iT .

e3T

The mean number of data units at the i th cluster-head can be calculated as

E?L i ?

X K i

j?1jp

i

ejT?

q i

1àq i

à

eK it1Tq K it1

i

1àq i i

.

By Little’s law,the mean sojourn time at the i th cluster-head is

E?S i ?E?L i DPR i

?

1

el iàk iT?1àp ieK iT

à

eK it1Tq K i i

l ie1àq K it1

i

T?1àp ieK iT

.e4T

To determine the maximum SSD,we need?rst to ana-lyze the delay-related factors in a multi-hop path.In wire-less mobile networks,the end-to-end packet delay is the total time delay to deliver a packet from source to destina-tion node.It is the sum of delays at all links in the end-to-end path.The delay at an intermediate node usually includes the following components if a retransmission is not considered[18]:(a)processing delay,the time from the arrival of a packet to when it is assigned to a queue for transmission;(b)queuing delay,the time the packet is in queue before transmission starts;(c)transmission delay, the time between transmission of the?rst bit and last bit of the packet;(d)propagation delay,the time for signals to traverse the link.In the above components,processing delay and propagation delay are very small as compared to the queuing delay and transmission delay along a mul-ti-hop path.Therefore,the maximum SSD can be mainly attributed to the sum of the queuing delay and transmis-sion delay at all links between the farthest cluster and the sink,i.e.,SSD max?

X M

i?1

E?S i ;e5T

where the computation should be performed from cluster M to cluster1due to the fact that evaluating cluster i re-quires the information of cluster i+1.

3.QOS supporting

The tra?c in multi-hop WSNs often shows dynamic characteristics due to multimedia applications.Proper traf-?c control scheme should be employed in WSNs to main-tain the QoS requirements under dynamic tra?c conditions.In the above analysis,the cluster-heads are modeled as SSFR nodes with?nite queue capacity.This is due to the fact that sensor nodes are usually constrained in processing and storage capabilities[8].Thus,the node gets full from time to time.Once the node gets full,the next arriving data is rejected and the data is lost.For simplicity, the DLP at individual nodes,DLP i,i=1,2,...,M,are chosen as the QoS metric in this section.Another reason to choose DLP is that the QoS metric is based on individ-ual cluster-heads,which ensures the localized control in cluster-level(rather than network level)and thus less con-trol overhead.The cluster-head is in charge of measuring the DLP of its cluster and controls the data generating rate according to the QoS requirements by exchanging informa-tion with the sensors of its cluster.From Eq.(2),we know that the DLP tends to increase with the increase of tra?c load.Thus,when the DLP i goes above a prede?ned thresh-old due to for example burst tra?c,a command for decreasing data generating rate is broadcast inside the clus-ter.If the DLP i is still unacceptable when the data generat-ing rate reaches the minimum value(assume each cluster is given a minimum data generating rate to maintain appro-priate measuring accurateness),the cluster-head will send a request of decreasing data generating rate to its upstream cluster,and so forth until the QoS metric is controlled under the threshold value.By analysis and experience,we observe that the DLP metric at the cluster closer to the sink always exceeds the threshold earlier.Sometimes the DLP at every cluster is found to be far away below the threshold value,a command for increasing data generating rate is broadcast in the network.The reason for increasing data generating rate is to capture more accurate?eld informa-tion.This,however,also consume more energy from the network.Therefore,tradeo?exists between them.General-ly,it is appropriate to maintain the DLP parameter at a certain range under the threshold,i.e.,b*Th i,where we de?ne0.56b61to maintain the appropriate range of DLP parameter.It should be noted that frequent rate adjustment takes the risk of network oscillations.Proper oscillation elimination method should be adopted in vari-ous QoS control schemes.

Now,we present a QoS supporting scheme which can control the QoS metric within a prede?ned threshold by continuously adjusting the data generating rate at individ-

S.Tang,W.Li/Computer Communications29(2006)2569–25772571

ual clusters.The basic idea is:if the DLP i(usually at the clusters closer to the sink)is larger than the threshold Th i,the i th cluster will decrease the data generating rate by a small delta D i.A simple implementation method is to de?ne D i by a?xed value.However,the prede?ned value is di?cult to accurately select and in such way the resulting scheme cannot adapt well to varying load.Instead of using prede?ned value,a better method would be to predict how much adjustment amount should be every time according to certain rule.Here,we directly locate our objective at the QoS requirement,and then derive an explicit solution to D i with accurate adjusting amount.

From Eq.(2),we know that DLP i is approximately pro-portional to q K i i.If the data generating rate g i is reduced to

a new value g0

i ,then DLP i will be decreased.In view of this,

we construct the following equation:

DLP ien i g0

i

tk it1TK i?Th ien i g itk it1TK i.e6TThen,we obtain

g0 i ?

n i g iàex ià1Tk it1

x ián i

;where x i?

?????????????????????

DLP i=Th i

K i p.

In order to maintain a minimum requirement for envi-

ronment monitoring,we construct a compensation factor

1i in the above equation to ensure that g0

i is not less than

the minimum data generating rate g i_min.Then,we de?ne

g0 i ?

n i g

i

à1iex ià1Tk it1

x ián i

;

where0<1i6n i g iàx i n i g i min

ex ià1Tk it1

.Note that k M+1=0.Thus,

every time the resulting new DLP i will serve as an input

for the next adjustment until returning the threshold value.

The amount of adjustment is calculated as

D i?g iàg0

i

?

ex ià1Ten i g it1i k it1T

x ián i

.e7T

The algorithm for the QoS supporting scheme with

reducing network oscillation mechanism is summarized in

Fig.2.Some simulation results for the algorithm’s execu-

tion are presented in Section5.

4.Optimal energy allocation

For a simpli?ed power consumption model of radio

communication[6,19],the energy consumed per bit in

transmission is

e b?e tete ta d ate re;e8T

where e te is the energy per bit needed by the transmitter elec-

tronics(including the cost of startup energy),e re is for the

receiver electronics,e ta is the consumption of the transmit-

ting ampli?er to send one bit over one unit distance,d is

the transmission distance,a is the path loss factor depending

on the radio frequency environment and is generally between

2and4.This basic model is used for single hop situation.It

can be extended for our multi-hop linear cluster-based WSN.

By combining Eq.(8)with the cluster-based WSN mod-

el in Fig.1,we know the energy consumed at the cluster-

head is much larger than that at individual sensing node.

The reason is as follows:(1)the cluster-head needs to relay

all the tra?c of the cluster;(2)for each data unit,the clus-

ter-head needs to transmit longer distance due to transmis-

sion between clusters,while the sensing nodes just transmit

data inside the cluster.In view of this,let c i and C i be,

respectively,the energy dissipated per data transmission

inside cluster i and between cluster i and cluster(ià1).

Let E i denote the total initial energy in the i th cluster,

i=1,2,...,M.Then the total initial energy in the network

is E?

P M

i?1

E i.With the passage of time,energy is dissipat-

ed from each cluster until one cluster runs out of its energy

after time period T,which is known as the disconnection

time or the lifetime of the network[5].Let R i(t)be the

residual energy at the i th cluster after time t,then we have

R ietT?E iàc i n i g i tàC i k i t

?

E iàec itC iTn i g i tàC i

P M

j?it1

n j g j t

Q j

k?it1

?1àp keK kT ;16i6Mà1;

E Màec MtC MTn M g M t;i?M.

8

><

>:

e9T

Let T i denote the disconnection time of the i th cluster,

then cluster i will exhaust its energy after time T i,i.e.,

R i(T i)=0.In our linear WSN model,the lifetime of the

WSN,T,is de?ned as the time period when the energy at

any one of the clusters exhausts,i.e.,T=min{T1,T2,

...,T M},since the energy exhaustion of any cluster could

lead to the failure of data transmission in the

WSN. 2572S.Tang,W.Li/Computer Communications29(2006)2569–2577

Now,we are interested in?nding an optimal energy allo-cation criterion in the WSN which maximizes the network lifetime.Note that the WSN model has the form of many-to-one data routing paradigm and the clusters closer to the sink transfer more tra?c.If the equal energy allocation pol-icy is used for each cluster,then the closest cluster(to the sink),cluster1,is always the?rst one to exhaust its energy due to the largest amount of data transmission,leading to the failure of the network.However,at this time the other clusters still have some residual energy,leading to unutilized energy in the network and a reduced value of network life-time.Naturally,the ideal(optimal)energy allocation criteri-on is to make all clusters have the same exhaustion time and thus maximizes the network lifetime.From this criterion,we can?gure out the energy distribution formula at individual clusters and the network lifetime,which are the foundation to node deployment design in WSNs.

E i?ec itC iTn i g i TtC i

X M

j?it1

n j g j T

?

Y j

k?it1

?1àp keK kT ;16i6Mà1;e10T

T?

E M

ec MtC MTn M g M

.e11T

As applications of the above results,we discuss three application situations which lead to di?erent node deploy-ments.Finally,it is worthy to note that all the above anal-ysis,though based on a linear network,can be easily extended to a planar topology.

4.1.Energy e?cient solution in homogeneous WSNs

By the above the energy distribution formula,we can quantitatively determine the energy allocation at individual clusters.The cluster closer to the sink will be allocated more energy.If homogeneous sensors are used in the WSN,that is,each sensor has the same initial energy I e, then the cluster closer to the sink should be deployed with higher node density to achieve more total initial energy.By basic mathematics from Eqs.(10)and(11),we have

n i?

C i

ec MtC MTg Màec itC iTg i

X M

j?it1

n j g

j

?

Y j

k?it1

?1àp keK kT ;16i6Mà1.e12T

The above equation determines how many sensors each cluster should have,given the number of sensors at the far-thest cluster n M.In such a way,the node deployment design issues in WSNs can be accurately and e?ectively solved.Note that the dissipated energy of total data trans-mission per unit time at the farthest cluster g M should be greater than that at any other cluster.This is intuitive since the farthest cluster usually corresponds to the most impor-tant target?eld and thus the largest data generating rate.

It is noteworthy that this scheme requires the sensing nodes in high density clusters decrease their data generat-ing rate to save energy and to reduce the tra?c load.Other-wise,more sensors will generate more data and more energy will be needed for relaying.A more practical approach is that the cluster-head in a high density cluster schedules some nodes to enter sleep mode[20]in order to reduce the tra?c load and also keep more candidates for cluster-head.

4.2.Energy e?cient solution in heterogeneous WSNs

If heterogeneous sensors are used in the WSN,that is, each sensor has di?erent initial energy I e,i,j,where i denotes the i th cluster and j denotes the j th sensor in the cluster, 16i6M,16j6n i.Then sensors with larger batteries are selected?rstly as cluster-heads,and the cluster closer to the sink should be allocated more sensors with larger batteries to achieve more total initial energy.The detailed node deployment scheme can be theoretically determined from Eqs.(10)and(11)given the speci?c application requirement is provided,however,the mathematical expression of n i is hard to be obtained.

4.3.Energy e?cient solution by radio range adjustment

From Eq.(8),we know that radio transmissions are attenuated by a path loss in a power-law with distance. The total transmission energy can be reduced by decreasing the transmission distance.Thus,in the design of network topology,especially for a homogeneous WSN,clusters near the sink should be designed with shorter relaying distances to extend their energy usage,while clusters at the periphery should have longer distance to improve the relaying e?-ciency.For example,in Fig.1,we should design the follow-ing distance relationship:d1

5.Numerical analysis

In this section,we?rst present some numerical results to evaluate the performance metrics in terms of DLP,mean sojourn times at individual clusters and the maximum source-to-sink delay;then validate the QoS supporting algorithm by simulations;and?nally present some experi-mental examples to show the application of our network energy distribution formula.

5.1.Performance evaluation

As discussed previously,the many-to-one data routing paradigm of WSNs inevitably leads to non-uniform tra?c distribution,which will decrease the performance of the clusters closer to the sink.A feasible solution is to reduce data generating rates in these clusters.Now,we show, respectively,the e?ect of the same and di?erent data gener-ating rate at each cluster on di?erent performance metrics by Figs.3–6,and performance comparison will be observed

S.Tang,W.Li/Computer Communications29(2006)2569–25772573

naturally.The system con?guration is set as follows.There are M =4clusters involved in the considered system.The number of sensing nodes is n 1=n 2=n 3=n 4=100,and cluster-heads have service rates l 1=l 2=l 3=l 4=20and queue capacity K 1=K 2=K 3=K 4=100.The data gener-ating rates are given at di?erent ?gures.

Figs.3and 4show,respectively,the e?ects of same and di?erent data generating rates on DLP at individual clus-ters.First,we observe that the DLP will increase when the data generating rate increases,and drastically increase at the cluster closer to the sink as compared with that at periphery.This is understandable as the queue capacity is ?nite,leading to increased DLP with more data generation;and the cluster closer to the sink needs to relay larger tra?c load.Next,by comparing Figs.3and 4,we ?nd,as expect-ed,the DLPs at di?erent clusters have been decreased by appropriately reducing data generating rates.The e?ect is particularly obvious in the situation of low data generating rate at each sensor.

Figs.5and 6show,respectively,the e?ects of data gen-erating rates on the mean sojourn time of a data unit at individual clusters and the maximum SSD (i.e.,the delay from cluster M to the sink).As expected,when the data generating rate increases,the mean sojourn times at indi-vidual clusters will increase,and the increasing trend is gradually slow with the increase of data generating rate.This may be explained as:with the increase of data gener-ating rate,each cluster will hold more data units and each data unit will wait more time to be served;and the relaying tra?c will gradually play a dominant role at especially those clusters closer to the sink,leading to gradually small e?ect of sensing tra?c load.We also observe that the mean sojourn time at the cluster closer to the sink is much larger than that farther to the sink.This also attributes to the higher tra?c load at the cluster closer to the sink.Similar-ly,by comparing Figs.5and 6,we ?nd that both mean sojourn times and maximum SSD have been reduced by

2574

S.Tang,W.Li /Computer Communications 29(2006)2569–2577

appropriately reducing data generating rates.For example, when g=0.07,we have(E[S1]=5.0,E[S2]=4.0, E[S3]=0.17,and SSD max=9.14)in Fig.5and (E[S1]=4.5,E[S2]=0.5,E[S3]=0.14,and SSD max=5.22)in Fig.6.

5.2.QoS algorithm simulation

The numerical simulation is performed under M=4 clusters,we still use the same system con?guration as that in part A.In addition,in order to see how the QoS algo-rithm behaves under di?erent tra?c conditions,we per-form the simulation under heavy load and light load, respectively.For simplicity,the acceptable QoS threshold at each cluster is assumed as Th i=10à4,i=1,2,3,4, although it can be set with di?erent value in di?erent clus-ters.The other parameters in the algorithm are set as: g i_min=10à4,b i=0.9,1i is set to be0.3at heavy load and0.95at light load.The objective is to make the DLPs

in the clusters closer to the sink get back into the QoS threshold when they get out of the threshold(note that the closer clusters always break out of the QoS threshold earlier than the farther clusters due to the non-uniform tra?c distribution),and to make them go up to a certain level(i.e.,b i*Th i)when all of them are far away from the threshold.The detailed procedures of the simulation executions are shown in Figs.7and8.

Fig.7shows how the algorithm performs at the heavy tra?c condition.In the beginning,the DLPs in clusters1 and2are very high,so the algorithm is performed by decreasing the data generating rates in these clusters,while keep clusters3and4with no rate adjustment(since increasing the data generating rates in clusters3and4will further increase the DLPs of clusters1and2,which have already exceeded the threshold).Then,the DLPs of clusters 1and2gradually get down through continuous rate adjust-ments until below the threshold(10à4).We also observed that the DLP of cluster2got below the threshold at the 9th adjustment and the rate did not change any more (g2=0.0175),while the rate of cluster1had to be contin-uously adjusted because the DLP was close to but not yet below the threshold.After a couple of adjusting times, g2was changed from0.0175to0.0174at the15th adjust-ment,and the DLP of cluster1eventually got below the threshold with the same rate(g1=1.0877·10à4,which is very close to g i_min).By some investigation,we found that the regular new data generating rate would be 9.8152·10à5for the15th adjustment,which is smaller than g i_min and de?nitely not be able to use.So a request for decreasing data generation was automatically sent to cluster2,leading to the decrease of g2.This validates the e?ectiveness of the algorithm.

Fig.8shows how the algorithm performs at the light tra?c condition.In the beginning,the DLPs in all clusters are much lower than the threshold,so the algorithm is per-formed by increasing the data generating rate in each clus-ter.When the DLP of one of the clusters gets close to the prede?ned value(b*Th i),the algorithm will stop.

5.3.Applications of energy allocation

Now,we present some experiment examples to show how to apply the energy distribution formula in the WSN design.The system con?guration is the same as that in part A.In addition,for simplicity,we set the same cluster size and the same distance between two adjacent clusters,that means each cluster has the same c i and C i.Set c i=1energy unit,C i=5energy units,and network lifetime T is set as 100time units,which may be hours,days,weeks,etc.

Fig.9quantitatively shows that the energy distribution with the same data generating rate at each cluster.The energy consumption is larger for the cluster closer to the sink due to the transmission of more tra?c.Thus,in the cluster based WSN design,the cluster closer to the sink should be allocated more energy to achieve optimal energy

S.Tang,W.Li/Computer Communications29(2006)2569–25772575

utilization.For our speci?c system con?guration,the quan-titative energy values at individual clusters are presented under various data generating rates.Fig.10shows the same problem with di?erent data generating rate at each cluster.Due to the intrinsic nature of non-uniform tra?c distribution in WSNs,we reduce the data generating rates of the clusters closer to the sink.By comparing Figs.9and 10,we observe that the needed energy in Fig.10is much less than that in Fig.9for maintaining the same network lifetime.This result shows that,by appropriately control-ling data generating rates at individual clusters,we can not only save energy of the network,but also provide QoS supporting through the developed algorithm under heavy tra?c condition.

Figs.11and 12show an energy e?cient solution exam-ple in homogeneous WSN.By designing di?erent data gen-erating rates at individual clusters,we can ?gure out the accurate number of sensors at every cluster with optimal

energy distribution (as shown in Fig.11),which is very use-ful for sensor deployment design in WSNs.Moreover,the DLP metrics at individual clusters under the designed sensor deployment also satisfy the QoS threshold,for example,at one designed deployment (n 4=180,n 3=300,n 2=367,and n 1=402),the DLPs are (DLP 4=2.732·10à45,DLP 3=3.061·10à19,DLP 2=6.236·10à9,and DLP 1=1.723·10à4).If the DLPs do not satisfy the QoS requirement,the QoS supporting algorithm will be applied.6.Conclusions

We have performed the analysis of QoS supporting and optimal energy allocation issues by presenting a cluster based WSN.A QoS supporting scheme is developed for dynamic tra?c conditions by controlling data generating

2576

S.Tang,W.Li /Computer Communications 29(2006)2569–2577

rates at individual clusters and the speci?c algorithm is pre-sented and validated by numerical simulations.Besides,an explicit solution on the energy distribution at di?erent clus-ters in the WSN is investigated based on an optimal energy allocation criterion.The localized QoS controlling scheme is useful in WSNs due to?exibility and scalability.The obtained network energy distribution formula is particular-ly convenient for node deployment design in WSNs and application situations are also discussed and presented by experimental examples.

Acknowledgements

The authors thank the anonymous referees for the care-fully reading of the original manuscript.Their comments and suggestions have led to a much better presentation of the paper.The second author of the paper would like to acknowledge that his work is partially supported by the National Science Foundation of US with Grant No. 0515263and partially supported by the National Natural Science Foundation of China with contract No.60474067.

References

[1]C.-F.Chiasserini,M.Garetto,Modeling the performance of wireless

sensor networks,in:IEEE INFOCOM’04,9–11March2004,Hong Kong,China.

[2]J.Deng,Y.Han,W.Heinzelman,P.Varshney,Scheduling sleeping

nodes in high density cluster-based sensor networks,ACM/Kluwer Mobile Networks and Applications(MONET).Special Issue on Energy Constraints and Lifetime Performance in Wireless Sensor Networks,10(6)(2005)825–835.

[3]C.E.Jones,K.M.Sivalingam,P.Agrawal,J.C.Chen,A survey of

energy e?cient network protocols for wireless networks,Wireless Networks7(4)(2001)343–358.

[4]R.Shah,J.Rabaey,Energy aware routing for low energy ad hoc

sensor networks,in:Proc.of IEEE Wireless Communications and Networking Conference(WCNC02),Orlando,FL,March2002. [5]V.Rai,R.Mahapatra,Lifetime modeling of a sensor network,in:IEEE

Intl.Conf.on Design,Automation and Test in Europe(DATE)2005.

[6]J.Haapola,Z.Shelby,C.A.Pomalaza-Ra′ez,P.Ma¨ho¨nen,Cross-

layer energy analysis of multi-hop wireless sensor networks,in: Proceedings of the European Workshop on Wireless Sensor Net-works,Jan.31–Feb.2,2005,Istanbul,Turkey.

[7]D.Chen,P.K.Varshney,QoS support in wireless sensor networks:a

survey,in:Proc.of the2004International Conference on Wireless Networks(ICWN04),June2004,Las Vegas,Nevada,USA.

[8]M.Younis,K.Akayya,M.Eltowiessy,A.Wadaa,On handling QoS

tra?c in wireless sensor networks,in:Proc.of International Confer-ence on System Sciences(HICSS-37),Hawaii,Jan.2004.

[9]K.Akkaya,M.Younis,An energy-aware QoS routing protocol for

wireless sensor networks,in:Proc.of the IEEE Workshop on Mobile and Wireless Networks(MWN2003),Providence,RI,May2003. [10]M.Younis,M.Youssef,K.Arisha,Energy-aware routing in cluster-

based sensor networks,in:Proc.of the10th IEEE/ACM Sym.on Modeling,Analysis and Simulation of Computer and Telecom Systems(MASCOTS’02),Fort Worth,TX,October2002.

[11]L.Subramanian,R.H.Katz,An architecture for building self

con?gurable systems,in:Proc.of IEEE/ACM Workshop on Mobile Ad Hoc Networking and Computing,Boston,MA,August2000. [12]J.N.Al-Karaki,A.E.Kamal,Routing techniques in wireless sensor

networks:a survey,IEEE Personal Communications11(6)(2004)6–28.[13]W.R.Heinzelman, A.Chandrakasan,H.Balakrishnan,Energy-

e?cient communication protocol for wireless sensor networks,in: Proc.of the33rd Hawaii International Conference on System Sciences,Jan.2000.

[14]S.Lindsey,C.S.Raghavendra,PEGASIS:power e?cient gathering in

sensor information systems,in:Proc.of the IEEE Aerospace Conference,Big Sky,Montana,March2002.

[15]M.Kubisch,H.Karl,A.Wolisz,L.Zhong,J.Rabaey,Distributed

algorithms for transmission power control in wireless sensor net-works,in:IEEE Wireless Communications and Networking Confer-ence(WCNC03),New Orleans,March2003.

[16]V.Kawadia,P.R.Kumar,Principles and protocols for power control

in ad hoc networks,IEEE J.Select.Areas Commun.23(1)(2005) 76–88.

[17]L.Kleinrock,Queueing Systems Volume1:Theory,Wiley,New

York,1975.

[18]D.Bertsekas,R.Gallager,Data Networks,second ed.,Prentice-Hall,

Englewood Cli?s,NJ,1992.

[19]Q.Gao,K.Blow,D.Holding,I.Marshall,X.Peng,Radio range

adjustment for energy e?cient wireless sensor networks,Journal of Ad Hoc Networks(2004).

[20]Y.Xu,J.Heidemann, D.Estrin,Geography-informed energy

conservation for ad hoc routing,in:Proceedings of ACMMobile’01, Rome,Italy,July2001,pp.

70–84.

Shensheng Tang received his BS degree in Tianjin

University,China in1990and MS degree in

China Academy of Telecommunications Tech-

nology(CATT)in1997,both in electrical engi-

neering.He is presently pursuing his PhD degree

in the department of electrical engineering and

computer science,University of Toledo,Ohio,

USA.He has over8years of industrial experience

in electronics and telecommunications areas,

which involves the development of electronic

instruments and mobile communication base stations as well as the research related to3G TD-SCDMA and WCDMA technologies.His current research interest focuses on wireless communi-cations and networking,including wireless LANs,mobile ad hoc net-works,wireless sensor networks,3G and future generations of wireless cellular

networks.

Wei Li received his PhD degree from the Chinese

Academy of Sciences in1994.He is currently an

Associate Professor in the Department of Elec-

trical Engineering and Computer Science at the

University of Toledo,USA.He was once an

Assistant Professor,Endowed Chair Professor in

Bell South Mobility/BORSF in Telecommunica-

tions at the University of Louisiana at Lafayette,

and also a recipient of US Air Force Summer

Faculty Fellowship.Dr.Li’s research interests are

in the wireless and mobile networks,mobile ad hoc networks,wireless sensor networks and queuing networks etc.Dr.Li has published over60peer-reviewed papers in professional journals,over 20referred papers in the proceedings of professional conferences and3 books.Dr.Li is currently serving as an Editor for EURASIP Journal on Wireless Communications and Networking,for International Journal of Computer and Their Applications,for International Journal of High Performance Computing and Networking,and for International Journal of Sensor Networks.He has also served as a TPC member for some professional conferences such as IEEE ICC’05,04,02,IEEE Glob-Com’05,03,IEEE WCNC’05,04,00,IEEE WirelessCom’05,Qshine’05,04, IEEE VTC’03,etc.

S.Tang,W.Li/Computer Communications29(2006)2569–25772577