Performance Evaluation of Mac Transmission Protocol

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Performance evaluation of MAC transmission power controlin wireless sensor networks

Javier Vales-Alonso *, Esteban Egea-Lopez, Alejandro Martnez-Sala,Pablo Pavon-Marino, M. Victoria Bueno-Delgado, Joan Garca-Haro

Department of Information Technologies and Communications, Polytechnic University of Cartagena, Spain

Received 1 February 2006; received in revised form 3 July 2006; accepted 4 August 2006

Available online 12 September 2006

Responsible Editor: E. Chong

Abstract

In this paper we provide a method to analytically compute the energy saving provided by the use of transmission powercontrol (TPC) at the MAC layer in wireless sensor networks (WSN). We consider a classical TPC mechanism: data packetsare transmitted with the minimum power required to achieve a given packet error probability, whereas the additional MACcontrol packets are transmitted with the nominal (maximum) power. This scheme has been chosen because it does not mod-ify the network topology, since control packet transmission range does not change. This property also allows us to analyt-

ically compute the expected energy savings. Besides, this type of TPC can be implemented in the current sensor hardware,and it can be directly applied to several MAC protocols already proposed for WSN. The foundation of our analysis is theevaluation ofL ratio, defined as the total energy consumed by the network using the original MAC protocol divided by thetotal energy consumed if the TPC mechanism is employed. In the L computation we emphasize the basic properties of sensornetworks. Namely, the savings are calculated for a network that is active for a very long time, and where the number ofsensors is supposed to be very large. The nodes position is assumed to be random a normal bivariate distribution isassumed in the paper and no node mobility is considered. In the analysis we stress the radio propagation and the distri-bution of the nodes in the network, which will ultimately determine the performance of the TPC. Under these conditions wecompute the mean value ofL. Finally, we have applied the method to evaluate the benefits of TPC for TDMA and CSMAwith two representative protocols, L-MAC and S-MAC using their implementation reference parameters. The conclusion isthat, while S-MAC does not achieve a significant improvement, L-MAC may reach energy savings up to 1020%. 2006 Elsevier B.V. All rights reserved.

Keywords: Energy saving; MAC; Network lifetime; Transmission power control; WSN

1. Introduction

Wireless sensor networks (WSNs) consist of alarge set of autonomous wireless sensing nodes [1].They are designed and deployed to accomplishspecific tasks, e.g. environmental monitoring,

1389-1286/$ - see front matter 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.comnet.2006.08.001

* Corresponding author. Tel.: +34 968 326588; fax: +34 968325973.

E-mail addresses: [email protected] (J. Vales-Alonso),[email protected] (E. Egea-Lopez), [email protected] (A. Martnez-Sala), [email protected] (P. Pavon-Marino), [email protected] (M. Victoria Bueno-Delgado),[email protected] (J. Garca-Haro).

Computer Networks 51 (2007) 14831498

www.elsevier.com/locate/comnet
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industrial sensing or space exploration. As a conse-quence, WSNs have specific traffic patterns and net-work topologies, which are strongly applicationdependent. WSNs also inherit key properties fromad-hoc networks: decentralized control, common

transmission channel, broadcast nature, multihoprouting, and ephemeral topologies, among others.Besides, there are two WSN basic constraints. First,the expected hardware, program, and data memoryresources are scarce, consequently imposing limita-tions on the protocol complexity. Second, theamount of energy available per node is finite if theyare battery powered. Therefore, the development ofenergy-efficient protocols and applications is amajor challenge in current WSN research, in orderto develop systems that run unattended (withoutbattery replacement) for an arbitrary long time

(e.g. years).In fact, the major sources of energy waste are

related to radio communication issues [2,3]. Forinstance, communicating one bit of informationconsumes as much energy as executing hundredsof instructions in typical sensor nodes like Mica2motes [4]. The radio interface consumption dependson its state, which can be one of the following:

Transmission state (tx). Packet transmission.Power consumption is proportional to the radi-

ated output power, which can be selected froma set of discrete values (e.g. from 20 to 5 dBmin steps of 1 dB in the Mica2 motes, see Table1). However, in practice the output power is keptfixed at a nominal value (usually the maximumpossible output power).

Reception- and listening- state (rx). Packet recep-tion and channel listening (carrier sense). It alsoconsumes a significant amount of power whetherreceiving actual data or just listening (e.g.35.4 mW in the Mica2 motes).

Sleep state (sl). Radio off. Negligible power con-sumption (e.g. 3 lW in the Mica2 motes).

From the medium access control (MAC) layerperspective consumption may be minimized if thenodes sleep during inactivity instead of being inthe reception state. Thereby the average consump-tion is significantly reduced. This strategy requirescoordination among the nodes (all the neighborsmust sleep and awake simultaneously), and a trade-off between the sleeping time and the achievablethroughput (since nodes cannot send or receive data

in the sleep state). Consumption may also be

reduced using only the power needed for each datatransmission. Fig. 1 illustrates this idea. Node 1reaches nodes 2 and 3 with power Q1, howevernodes 4, 5 and 6 are only reached at power Q2. Inthis case Q2 is the nominal power that guaranteesfull connectivity. But, if power is set fixed, there is

Table 1Path-loss model (a = 3.95) ranges and consumptions for theMica2 output powers

Output power Consumption (mW) Range (m)

20 dBm (0.0100 mW) 25.8 19.30

19 dBm (0.0126 mW) 26.4 20.46

18 dBm (0.0158 mW) 27.0 21.6917 dBm (0.0200 mW) 27.0 22.9916 dBm (0.0251 mW) 27.3 24.3815 dBm (0.0316 mW) 27.9 25.8414 dBm (0.0398 mW) 27.9 27.3913 dBm (0.0501 mW) 28.5 29.0312 dBm (0.0631 mW) 29.1 30.7811 dBm (0.0794 mW) 29.7 32.6210 dBm (0.1000 mW) 30.3 34.589 dBm (0.1259 mW) 31.2 36.668 dBm (0.1585 mW) 31.8 38.867 dBm (0.1995 mW) 32.4 41.196 dBm (0.2512 mW) 33.3 43.67

5 dBm 0.3162 mW) 41.4 46.294 dBm (0.3981 mW) 43.5 49.073 dBm (0.5012 mW) 43.5 52.012 dBm (0.6310 mW) 45.3 55.131 dBm (0.7943 mW) 47.4 58.44+0 dBm (1.0000 mW) 50.4 61.95+1 dBm (1.2589 mW) 51.6 65.67+2 dBm (1.5849 mW) 55.5 69.61+3 dBm (1.9953 mW) 57.6 73.79+4 dBm (2.5119 mW) 63.9 78.22+5 dBm (3.1623 mW) 76.2 82.92

Node 2

Node 3

Node 4

Node 6

2Q

1Q

Node 1

Node 5

Fig. 1. Discrete output powers.

1484 J. Vales-Alonso et al. / Computer Networks 51 (2007) 14831498


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a waste when data packets are delivered to nodes 2and 3 at power Q2. Selecting the best output powerin each transmission may reduce the output powerconsiderably, and thus the total consumption. Thistype of strategy is called Transmission Power

Control (TPC). Up until now only the formerscheme coordinated sleeping has been exhaus-tively studied as a technique for energy saving inWSNs, since idle listening avoidance has beenwidely considered the dominant factor to reducepower consumption. This has been the major designobjective of a large set of specific WSN MAC proto-col proposals [3,58].

In this paper, we are interested in the additionalbenefits, in terms of energy saving, that the use ofTPC may provide to WSN MAC protocols. First,we have to select a TPC mechanism suitable (or at

least adaptable) for the vast majority of the WSNMAC approaches, in order to evaluate the perfor-mance of TPC. We have selected a well-knownapproach for TPC [9]: the considered TPC mecha-nism uses the minimum power necessary to transmitthe network layer packet data units with a boundedpacket error probability, and the nominal (maxi-mum) power to transmit the additional MACcontrol packets. For instance, in the exampledepicted in Fig. 1, considering the IEEE 802.11 pro-tocol [10]: RTS/CTS/Data/ACK1 sequence. If node

1 has to send a data packet to node 2, then node 1would start transmiting the RTS at the maximum(nominal) power Q2. Afterwards, node 2 wouldanswer with the CTS at the same nominal power.The data is then exchanged, but at the reducedpower Q1, and finally the ACK is transmitted withthe nominal power Q2.

This approximation does not modify networktopology since control packet transmission rangeis not modified. Thereby, upper layer behavior isnot affected. This property allows us to fairly com-pare the energy consumption between TPC andnon-TPC protocols.

As a drawback, this type of TPC requires thatnodes have an exact knowledge about the outputpower needed for every packet exchange. Neverthe-less, since we are interested in the maximum energysaving achieved by an ideal TPC, we will assumethat this information is already known by the nodes.

To evaluate such a mechanism, we compute theratio of the energy without TPC to the energy using

the TPC algorithm after a very long running time.We denote this ratio as L. We find that, for a givennode distribution, L depends on two factors: (i) onecharacterizes the geometrical distribution of thenodes and the other (ii) is mainly influenced by

the MAC protocol and the traffic of the network.Both parameters are evaluated under the mostwidely accepted WSN assumptions (see Section 4),stressing the geometrical distribution and the trans-mission properties of the network. It is shown thatL converges if the number of nodes is large. Thistheoretical framework can be applied to a widerange of MAC proposals just by adjusting theparameters of the model according to a givenMAC operation. As an example, it is applied to aset of traffic loads and nodes densities for twoMAC protocols, a TDMA one (L-MAC) [8] and a

contention one (S-MAC) [3]. The results reveal thatenergy savings are considerable for L-MAC (from10% to 20%), while rather average for S-MAC(


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the aim of increasing the capacity in wireless mediaby means of channel reuse, or to ensure networkconnectivity. Two types of strategies have alreadybeen considered: (i) In network layer TPCs trans-mission power control is used to select the best sub-

set of the actual neighbors to be reached, that is, fortopology control purposes (e.g. COMPOW [12] andPSP [13]). And (ii), the MAC layer TPCs, wherepower is selected for each packet to improve chan-nel reuse, or to reduce packet collision probability(e.g. PCM [14], PCDC [15], PCMA [16] andDCAPC [17]). The three latter proposals are basedon multichannel devices, using the additional chan-nels to signal incoming transmissions and tocompute the best output power to be used. Besides,the PCM protocol must run on specialized radiohardware that allows very fast output power

variation.These solutions effectively reduce collisions and

improve capacity, which is the major issue inMANETs. However, in WSN the primary concernis energy consumption efficiency, rather than highchannel throughput and reusability. Moreover,WSN protocols are constrained by the scarce mem-ory, CPU and radio resources available. Sensornodes are too limited to support most of the previ-ously mentioned approaches proposed for MAN-ETs. For instance, multichannel proposals cannot

be implemented since current sensors are mainlymonochannel.

There is a number of TPC algorithms designedspecifically for sensor networks. In [18] a set ofdistributed TPC algorithms is proposed. Thesemechanisms select a single transmission power levelfor each node. The different proposals are comparedto one another, using network connectivity and life-time as performance metrics, but no comparisonwith non-TPC protocols is provided. In this paper,on the contrary, we evaluate the expected energysavings that can be achieved by using a genericTPC protocol, without describing a particular wayof finding the power level necessary to reach aspecific neighbor. Thus, our analysis provides anideal upper bound on energy saving.

Analytical studies on several aspects of TPC canalso be found in the scientific literature. In [19] theauthors look for the optimal transmission rangethat maximizes a parameter called expected one-hop progress in the desired direction, but energyconsumption is not considered. In [20], an analyticalcomparison between common range and variable-

range TPC for MANETs is provided. The study is

focused on the impact of TPC on network connec-tivity, capacity and routing protocols. An energyconsumption model, as a function of the packet size,MAC protocol and radio characteristics, is used in[21] to derive an optimal transmission power in

terms of end-to-end energy consumption. Ourapproach focuses on the improvement that TPCmay provide. In addition, the TPC mechanism usedin our evaluation can be combined with proposalsfocused on network layer operation. It should benoticed that the network topology is determinedby the range of control packets, which here is setto the maximum (nominal) transmission power.Therefore, this nominal transmission power can beselected in order to achieve a desired network prop-erty, such as full connectivity, allowing TPC to beused for data transmission.

3. Performance analysis

In this section, we introduce the calculation ofthe energy saving which can be obtained from theTPC mechanism selected. Let n be the number ofnodes in the network. Let Titx(t), T

irx(t) and T

isl(t)

be stochastic processes representing the accumu-lated time that node i, for i= 1, . . . , n, is in eachstate transmission (tx), reception (rx) and sleep(sl) during the interval [0, t). Then, we can define

the total network accumulated time in each state,adding all the nodes contributions, Ttx(t), Trx(t)and Tsl(t), as

Ttxt Xni1

Titxt;

Trxt Xni1

Tirxt;

Tslt Xni1

Tislt:

1

Let us define Ptx, Prx and Psl accordingly, as thepower consumptions associated to each state. Then,the total energy consumed until an arbitrary instantt, E(t), is given by Eq. (2).

Et PtxTtxt PrxTrxt PslTslt: 2We should specify a way to measure the energetic

efficiency improvement due to the application of theTPC mechanism to a particular MAC protocol. Onemetric may be the increase in the lifetime of the net-work. However, this is difficult to define in a general

way, since it is unclear when the network (as a



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whole) stops operating properly (which usuallydepends on the application). Instead, we can com-pute a metric of the efficiency (we name it L) ofTPC based on the asymptotical ratio for a large tof the energy consumption of the network in both

cases (with and without TPC) through Eq. (3).

L limt!1

Etjno-TPCEtjTPC

: 3

This expression can be further developed takinginto consideration the assumption that controlpackets are always sent at the maximum power.Therefore, neither network topology, nor Titxt,Tirxt and Tislt, changes when TPC is used.

Let us assume that the network is composed ofhomogeneous sensors with p possible transmission

output powers (Qj,j= 1, . . . ,p). Let us denote Ptxias the power consumption associated to outputtransmission power Qi. Let Qp be the nominal (max-imum) transmission output power, and hence Ptxp isthe nominal consumption. Indeed, the transmissiontime of each node can be decomposed into twocontributions: data and signaling. Let us define thestochastic processes Tidatat, Tisignt for i= 1, . . . , nas the accumulated transmission time dedicated todata and signaling respectively for each node. LetTdatat P

n

i1Tidatat, Tsignt P

n

i1Tisignt. In

addition, Ti

datat can be further subdivided in thetime spent transmitting at each output power j:Tidatajt. Let us define Tdatajt

Pni1T

idataj

t forj= 1, . . . ,p.

Then, assuming that the power consumption dur-ing the sleep periods is negligible, the energy con-sumption without and with TPC is given by Eqs.(4) and (5), respectively.

Etjno-TPC TdatatPtxp TsigntPtxp TrxtPrx; 4

EtjTPC Xpj1

TdatajtPtxj TsigntPtxp

TrxtPrx: 5

Therefore, from Eqs. (3)(5)

L limt!1

TdatatPtxp TsigntPtxp TrxtPrxPpj1TdatajtPtxj TsigntPtxp TrxtPrx

:

L can be rewritten dividing both numerator and

denominator by PtxpTdatat; we obtain

L limt!1

1 TsigntTdatat

PrxTrxtPtxpTdatatXp

j1PtxjTdatajtPtxpTdatat

TsigntTdatat

PrxTrxtPtxpTdatat

: 6

Now, let us define the variable n as

n limt!1

TsigntTdatat

Prx

Ptxp

TrxtTdatat

!: 7

Besides, let Q be the output transmissionpower random variable that assigns, to each trans-mission output power Qj, its corresponding proba-bility Pr[Q= Qj] (i.e., the probability that a datatransmission occurs in the jth power quantum).Let us note that

PrQ Qj limt

!1

TdatajtTdata

t

: 8

Hence,

L 1 nPpj1

Ptxj

PtxpPrQ Qj n

: 9

Finally, calling s Ppj1 PtxjPtxp PrQ Qj, we arriveto

L 1 ns n : 10

This expression says that the energy ratio of the

two approaches converges after a long running timeto a value that is a function of two variables: s and n.

On the one hand, s-coefficient characterizes thegeometrical distribution of the network since itdepends on the relative distance between neighbors,which determines the output power required. More-over, s values are always within the interval (0,1].Low values indicate that nodes are closer, and sav-ings are thus more noticeable (larger values of L).High values indicate that it is unlikely that the out-put quantum can be reduced. In fact, s = 1 meansthat no saving is possible at all. In this case TPClacks interest.

On the other hand, the n-coefficient measures thebalance between the time devoted to data transmis-sion and the time used for signaling and reception.Note that oL/on = (s 1)/(s + n)2 < 0 for alls 2 (0,1). Therefore, L decreases as n increases. Pro-tocols with a good balance have a low n value, yield-ing to a higher L ratio, that is, larger savings.

Finally, let us note that both coefficients areinfluenced by the traffic properties, and that if eitherthe position of the nodes or the number of sensors

changes, these variables (s and n) will also change,

J. Vales-Alonso et al. / Computer Networks 51 (2007) 14831498 1487


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and so will the L factor. That is, L is a function ofthe number of nodes and their positions. Hence, ifnodes position is random (a likely case in WSN),the L factor is also random.

We will compute the mean of L, L, in the next

sections. We will show that for large values ofn

,in a representative WSN deployment, L is givenby the following expression:

L 1 n

s n : 11

Both s and n (and, therefore, L) are evaluated inthe following sections applying the realistic assump-tions for WSN discussed in Section 4.

4. WSN model

At this point, we aim at computing the general Lfunction derived in the previous section for a repre-sentative WSN model. Such scenario is specified by:(i) a suitable propagation model, (ii) a node distri-bution, (iii) a traffic pattern and (iv) a multipleaccess scheme.

4.1. Propagation model

WSN media can be considered a time-invariant

narrow-band channel, which can be modeled usinga path-loss approximation [22]. In this case, the

transmission power required (cPtx ) to achieve a tar-get probability error (bpe ) for nodes at a given dis-tance d is

cPtx daXbpe 12being a the propagation coefficient of the path-lossmodel and X a function that depends on bpe andthe communication environment. Appendix A de-scribes how this expression is found.

For instance, for the Mica2 motes hardware, apacket size of 100 bytes, a target error probabilitybpe 103, a = 3.95 (value experimentally obtainedin our test-beds [11]), and a bit rate of 30 Kbps,we have X % 97.5 dB.2 For the discrete transmis-sion output powers of the Mica2 motes, the associ-ated distances using the previous parameters aresummarized in Table 1.

Maximum range. Additionally, receivers have asensitivity (PS% 102 dBm for the Mica2 motes)that establishes the maximum distance betweennodes (dS). For instance, for the path-loss modelwith the previous propagation coefficient

(a = 3.95) the associated maximum distancedS is89.92 m.

4.2. Nodes distribution

In a general WSN deployment, the position ofthe nodes may not be controlled, and it is a prioriunknown. In this paper we consider a reasonabletype of node position pattern, where nodes are con-centrated around a point of interest. This pattern islikely in several cases, such as natural disaster zones,where sensing nodes are thrown close to a targetarea. A simple way to model this scenario is to selectnodes with a random normal bivariate distributionaround the coordinates of the focus point. Thetypical deviation parameter r will control the nodedispersion. An example of this type of distributionis plotted in Fig. 2, for n = 250 nodes and r = 100.

Let us assume, without lost of generality, that thefocus point is situated in the center of the realplane. Then, the position of the ith node is (Xi,Yi), being Xi, Yi independent and identically distrib-

uted random variables N(0,r). The quadratic dis-tance between two nodes i, j is d2 = DX2 + DY2,being DX= Xi Xj, DY= Yi Yj. The probabilitydensity function (pdf) ofd2 is (see Appendix B):

fd2x 1

4r2exp x

4r2

: 13

2 This value has been calculated for Manchester codification,

which doubles the baud rate.

-400

-300

-200

-100

0

100

200

300

400

-400 -300 -200 -100 0 100 200 300 400

Fig. 2. 250 nodes positioned with a normal bivariate distribution

of parameter r = 100.

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spatial region of the network3 (and, therefore, thereare no collisions), whereas in CSMA-like proposalsall the nodes with information to transmit contendto access the channel.

5.

n Evaluation

Let c(t) be the number of timeslots until instant t.Notice, that c(t) is the same for all the nodes in thenetwork. Let us denote K as the number of linksthat exists in the network. Let m(t) be the stochasticprocess representing the number of packets sent ineach one of the K network links until time t. Thus,m(t) = c(t)q. In addition, let vi(n) be the randomvariable representing the number of neighbors ofthe i-th node, for i= 1, . . . , n. Obviously, it dependson the total number of nodes n. Let us define

vn Pni1vin, the sum of the neighbors that eachnode has. Note that v(n) = 2K, as each neighbornode corresponds to a link in the network, whichis counted twice in the sum. Then, the followingrelationship holds:

ct 2Kmtvnq : 14

Besides, it is now possible to compute theamount of time that nodes are in each state. Let mbe the bit transmission time of the radio transceiver.

Until time t, m(t) packets have been sent in eachlink, and c(t) timeslots have passed in each node.Then, the contributions to each time are thefollowing,

Data transmission: B bits for each packet sent.Km(t) packets altogether.

Tdatat BmKmt: 15Signaling transmission: B0p bits out of every C times-lots per node (nc(t) altogether). B0l Ba bits for eachpacket sent.

Tsignt B0pmC

nct B0l BamKmt: 16

Reception: Bp bits during C 1 out of every Ctimeslots (in the remaining timeslot, the node trans-mits its own preamble, and only listens to the chan-nel Bp B0p bits). Bl bits for each timeslot in whichthe node itself does not transmit (if the node trans-mits it listens only Bl B0l bits). B+ Ba bits for eachpacket received.

Trxt mBpCB0p

CnctBlmnct

B0lmKmtBBamKmt

nctm BpCB0p

CBl

KmtmBBa B0l

17Using these equations and Eq. (14), we have that

(notice that m disappears in the fractions since it wasboth in denominator and numerator)

TsigntTdatat %

B0pnCct B0l BaKmt

BKmt

2B0p

BCq

n

vn B0l Ba

B18

and

TrxtTdatat %

nct BpCB0p

CBl

KmtBBa B0l

BKmt

2BpCB0p

CBl

Bq

n

vnBBa B0l

B:

19These equations are approximations, since pack-

ets can be partially transmitted at instant t. How-

ever, this approximation will be fine for largevalues oft. Thus, as t tends to infinity, n is equal to

n 2B0p

BCq

n

vn B0l Ba

B

PrxPtxp

2

BpCB0pC

BlBq

n

vn B Ba B0l

B

26643775:20

To sum up, notice that the n coefficient depends

on the power ratios (a hardware parameter), andon the traffic load and message lengths (a protocolparameter). Also, n is a function of n/v(n), which,for random topologies like the one considered, is arandom variable.

Proposition 1. The mean of the random variable

n/v(n) is

En

vn& '

1v

1

n

1

1

exp

d2S

4r2 !; 21

3 Obviously, timeslots may be reused spatially in the network

without causing collisions.



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where v denotes the average number of neighbors of a

node in a network of n nodes.

The expression for v is obtained in Appendix C.We have no direct proof for the former expression.Instead, we have analyzed its correctness using

intensive computing. Fig. 4 shows some of theresults. For r values of 50, 100 and 150 we havedropped random networks of n nodes and calcu-lated the mean and typical deviation ofn/v(n) using10,000 samples. The lines in Fig. 4 are the mean the typical deviation obtained in the experiments,while the points represent the analytical computa-tion of 1/v. As can be clearly observed, the probabil-ity concentrates around the expected value as ngrows.

Using the previous expression, the mean of n is

given by Eq. (22).

n 2B0p

BCq

1

vB

0l BaB

PrxPtxp

2

BpCB0pC

BlBq

1

vB Ba B

0l

B

26643775:

22

Fig. 5 represents n evaluated versus q for differentdata packet sizes (B) using n = 100 nodes. Theparameters used to compute these plots are Bp B0p 100 bits, Bl B0l 400 bits, Ba = 400 bits,C= 20 and Prx = 35.2 mW, Ptxp 76:2 mW. Packetlengths have been chosen as representative values ofa WSN configuration, and the consumption powerscorrespond to actual Mica2 motes consumptions.

The curves show that the expected value of ndecreases as q increases, and that the value is greaterfor lower values of B.

6. s Evaluation

As shown in Section 3, the energy savingobtained depends on the value of the s coefficient.This coefficient is a function of the mass probabilityfunction of the random variable Q found in Section3 and given by Eq. (23).

s Xpj1

Ptxj

PtxpPrQ Qj: 23

Indeed, s is actually a function of the position ofthe nodes and the number of nodes. Since the posi-tion is random, s is also random.

Proposition 2. The mean of the random variable s is

sPjp1j1 Ptxj exp

Qj1X

2=a

4r20B@ 1CA exp Qj

X 2=a

4r20B@ 1CA264 375Ptxp 1 exp

d2S4r2

!

exp Qp1X

2=a4r2

0BBB@1CCCA exp d2S4r2

1 exp d2S

4r2

! :24

0.001

0.01

0.1

1

100 1000

n/v(n)(logscale)

Number of nodes (n) (logscale)

=150=100=50

Fig. 4. n/v(n) evaluated versus n for different r.

1

10

100

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

Link load,

B=500B=750

B=1000B=1250B=1500

Fig. 5. n evaluated versus q for different data packet sizes (B).

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The aim of this section is to prove Proposition 2.A data transmission between two nodes uses

transmission output power Qj if the distancebetween them is within an interval Dj dminj ;dmaxj. If the link usage is equiprobable, then

Pr[Q= Qj] is just the probability that the distancebetween nodes is within Dj. TPC MAC algorithmsmust select a value of transmission power that guar-antees a given error probability bpe at the receiver (or,equivalently that the SNR be greater than a giventhreshold). Let Pr[Nodes in range] denote the prob-ability that the nodes are in range. For consistency,let Q0 = 0. Then, from Eqs. (12) and (13) we obtain

PrQ QjPrNodes in range PrQj1 6

cPtx ;Qj P

cPtx

PrQj1 6 cPtx 6 Qj PrQj1 6 daX 6 Qj

Pr Qj1X6 da 6

Qj

X

! Pr Qj1

X

26 da2 6 Qj

X

2" #

Pr Qj1X

2a

6 d2 6 QjX

2a

" #

exp Qj1X 2=a4r2

0B@ 1CA exp QjX 2=a

4r20B@ 1CA

25

for j= 1, . . . ,p 1. For the p-quantum there is anexpanded region between

Qj

X

2a

and d2S where recep-

tion is still possible, but with a higher error rate. Inthis case, the probability associated to the last quan-tum (nominal power) is

PrQ QpPrNodes in range Pr Qp1

X

2a

6 d2 6 d2S

" #

exp Qp1X

2=a4r2

0B@1CA exp d2S

4r2

: 26

The probability that nodes are in range is justPr[Nodes in range] = Prd2 6 d2S. Therefore, fromEq. (23), the average s coefficient (s) for a normal

distribution is

sPjp

j1Ptxj PrQQjPtxp

Pjp1j1 Ptxj exp

Qj1X

2=a4r2

0

BBB@

1

CCCA exp

Qj

X

2=a4r2

0

BBB@

1

CCCA

2

6664

3

7775Ptxp 1exp

d2S4r2

!

exp Qp1X

2=a4r2

0BBB@1CCCAexp d2S4r2

1exp d2S

4r2

! :27

We additionally verified Proposition 2 usingnumerical computation. Fig. 6 shows the results.For r values of 50, 100 and 150 we have droppedrandom networks ofn nodes and calculated the meanand typical deviation of s using 10,000 samples foreach point. The lines in the Fig. 6 are the mean typ-ical deviation obtained in the experiments, while thepoints represent the analytical computation of s(Eq. (24)). It can also be observed that the probabilityconcentrates around the expected value as n grows.

Fig. 7 shows an evaluation of this expression, for

different values of parameter r, and assumingX = 97.5 dB, and a = 3.95 (same values used inthe previous numerical examples). As it is clearlyobserved, lower values of parameter s (which implyhigher values ofL) are obtained for lower r distribu-tions, since the distance between nodes is also shorter.It should be noted that the resulting function has aninterval of fast growing for r 2 (10, 50). For the

0.7

0.72

0.74

0.76

0.78

0.8

0.82

0.84

0.86

100 1000

s(n)

Number of nodes (n)

=150=100=50

Fig. 6. s evaluated versus n for different r.



11/16

values r > 100 the function asymptotically increasestoward a limit value ofs

0:78.

7. L Evaluation

Based on the previous results, we can enunciatethe following proposition.

Proposition 3. For large values of n, the mean of the

random variable L converges to

Ljn)1 %1 ns n : 28

The reason behind this asymptotical behavior isthe concentration of the pdf around the mean of nand s as n grows (as can be seen in Figs. 4 and 6,respectively). Thus, for large values of n the uncer-tainty on the value ofn and s is very small and, there-fore, so is the uncertainty ofL. That is the reason thatallows us to substitute the random variables for theirexpected values in Eq. (28). Nevertheless, we have nodirect proof for Proposition 3. Instead, we haveperformed computational tests to verify this state-ment. Fig. 8 depicts the evaluation ofL for growingvalues of n. The experiments are similar to thoseshown in Figs. 4 and 6. For each point, 10,000 ran-dom networks are thrown and L is averaged. Themean typical deviation obtained are representedby lines depicted in Fig. 8. This figure also showsthe analytical results computed via Eq. (28) (points).The configuration used is similar to that of theprevious numerical examples: B= 800 bits, Bp B0p 100 bits, Bl B0l 400 bits, Ba = 400 bits,C= 20, Prx = 35.4 mW and Ptxp 76:2 mW.

At this point, the previous results can be appliedto a given MAC protocol just by adjusting the

model parameters properly. The s parameter

depends on the propagation model, the hardware

used and the distribution of nodes (see Section 4).The n parameter basically depends on the trafficmodel and the protocol operation. That is, theparameters of Eq. (22), Bp;B

0p;Bl;B

0l;B;Ba;C, take

their value according to the MAC protocol opera-tion. Therefore, someone interested in evaluating aMAC protocol with this method should analyze thedesired MAC protocol to determine the value of theseparameters. Their meanings are provided in Section4.4.

In the remainder of this section we show how to

do this evaluation. We apply the previous analysisto evaluate the benefits of TPC for two representa-tive WSN protocols: a TDMA protocol (L-MAC)and a contention protocol (S-MAC). Since we keepthe propagation model (path loss), hardware used(Mica2), and the distribution of nodes (normalbivariate) as in Section 4, we focus on the protocoloperation to determine n.

7.1. TDMA example: L-MAC

Lightweight medium access protocol (L-MAC) [8]is a TDMA protocol proposed for sensor networks,based on a modification of the Eyes MAC(E-MAC) [7]. In L-MAC each node selects a uniquetimeslot by using the slot occupancy informationfrom its one-hop neighbors. Once a node has selecteda slot, it always uses it to transmit either a controlmessage (preamble) or a control plus data message.

Our generic protocol model (see Section 4.4) candirectly be applied to L-MAC operation. L-MACuses a pure TDMA access scheme, and it directlynotifies neighbors of transmission in the preamble

packet. Thus, the listening/notifying phase of our

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

20 40 60 80 100 120 140 160 180 200

s

Nodes position standard deviation

Fig. 7. s evaluated versus r.

1.04

1.05

1.06

1.07

1.08

1.09

1.1

1.11

1.12

1.13

100 1000

L(n

)

Number of nodes (n)

=150=100=50

Fig. 8. L evaluated versus n for different r.



12/16

model (see Fig. 3) is not necessary (thereforeBl = 0). Additionally, the timeslot period is C= 32and there are no acknowledgements, Ba = 0. There-fore, a L-MAC timeslot includes only a preambleand data (when corresponding).

The TPC can be used with this protocol withoutchanging the topology if nodes always transmit theirpreamble at nominal power. The following data sec-tion would be sent at a controlled power. Thus, inorder to evaluate L we directly set the followingparameters according to the L-MAC operation inEq. (22):

n = 100 nodes. Data size, B= 800 bits. Preamble, Bp B0p 96 bits. Signaling, Bl

B0

l 0 bits.

Auxilary, Ba = 0 bits. Preamble period, C= 32. Prx = 35.4 mW. Ptxp 76:2 mW.

Fig. 9 depicts the evaluation of L versus rthrough Eq. (28) for different link loads (q). Resultsshow considerable savings, in the order of 1020%,for mid-large values of r. Moreover, in Fig. 9 sav-ings are more noticeable for low r and high valuesof q. This trend is sound, since if network nodes

are close and transmit a high number of packets,the TPC is more effective.

7.2. Contention example: S-MAC

S-MAC [3] is a contention-based protocol pro-posed for WSN. It uses a timeslot structure, similarto Fig. 3. Nodes synchronize their active/sleep peri-

ods by means of the short SYNChronization(SYNC) packet. SYNCs are periodically broad-casted by stations in the preamble, which allowsnodes to correct time drifts. Data transmission isperformed by means of CSMA/CA, i.e the RTS/

CTS/Data/ACK sequence. The RTS/CTS packetsare transmitted in the listening/notifying stage indi-cated in Fig. 3. Finally, in the message exchangeperiod the data packet and the ACK are transmit-ted, corresponding respectively to lengths B andBa. Again, the analysis can be done just by settingthese parameters according to the S-MAC opera-tion in Eq. (15)(17). We have chosen the valuesemployed in the reference implementation of S-MAC for TinyOS [23], which are:

n = 100 nodes.

Data size, B= 800 bits. Preamble, Bp = 727 bits, B

0p 100 bits.

Signaling, Bl= 1226 bits, B0l 100 bits.

Auxillary, Ba = 100 bits. Preamble period, C= 20. Prx = 35.4 mW. Ptxp 76:2 mW.

Fig. 10 plots L versus r for different link loads(q). Results show a worse behavior than in theL-MAC case studied in the previous section. The

average saving is below 10% for mid-large valuesof r. The reason of this worsening is twofold. Onone hand, S-MAC nodes transmit more controlpackets (RTS, CTS) than L-MAC ones. Since thesepackets are always sent at nominal power, moreenergy is wasted. On the other hand, in L-MACnodes go to sleep just after the preamble (if they

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

0 20 40 60 80 100 120 140 160 180 200

L

=0.01=0.02=0.05=0.1

Fig. 9. L vs. r for different link loads (q) for L-MAC protocol.

1

1.1

1.2

1.3

1.4

1.5

1.6

0 20 40 60 80 100 120 140 160 180 200

L

=0.01=0.02=0.05=0.1

Fig. 10. L vs. r for different link loads (q) for S-MAC protocol.



13/16

are not the data receivers). In S-MAC all the nodeshave to wait always at least until the end of thelistening period to sleep.

We must remark that, although S-MAC is a con-tention protocol, we have assumed that no collisions

are possible in our analysis. Therefore, the real val-ues will be even worse than those predicted byFig. 10. This yields to the conclusion that S-MACis not a good candidate for TPC use.

7.3. Discussion

In the introduction we stated that we are inter-ested in the maximum energy saving that an idealTPC may provide. In this way, basically two strongassumptions have been made in this paper: (1) everynode knows in advance the power necessary to

reach its neighbors and (2) there are no collisions.Therefore, the results drawn in the previous sectionsshould be interpreted accordingly: they show thetrend of the energy saving obtained by the use ofTPC, that is, an estimate of what may be achieved.Clearly, the conditions of the real scenario willdetermine the actual saving, whether collisions arelikely or nodes implement some mechanism todecide the power needed to reach their neighbors.

In any case, our analytical method allows toquickly estimate the benefits of TPC in order to

decide if it is worth adding it to a MAC proposal.Let us take the case of L-MAC: since it is a pureTDMA protocol, the no-collision assumptionapplies. In this case, the saving may be close tothe upper bound derived here, and so it is worthdeveloping a heuristic to gather information aboutthe powers needed and performing simulations totest it. On the other hand, the results for S-MACclearly suggest not to use TPC: the upper bound isalready low and the energy saving will be furtherdecreased by collisions. In addition, in S-MACmore than one transmission schedule may beadopted [3], increasing the overall listening time.

8. Conclusions

In this paper we have developed an analyticalmethod to compute the energy savings providedby a general MAC TPC mechanism, which can beapplied to most of the current WSN MAC propos-als. We have shown that the average energy savings,measured through the L ratio, converge if the num-ber of nodes is large (a very likely condition in

WSN).

An upper bound of the energy saving achievableby TPC can be quickly obtained by adjusting theformula parameters according to the operation ofthe protocol under evaluation. We have shownhow to apply this method with two representative

protocols. The conclusion derived is that the TPCmechanism analyzed is worth being included insome proposals of WSN MAC layer. Energy sav-ings up to 1020% can be expected in TDMA accessprotocols like L-MAC, while contention ones, likeS-MAC, achieve no significative improvements.

Future work will include the computation of Lratio by means of simulation to verify the results,and to extend our work to a broader set of WSNMAC protocols, traffic patterns and random distri-bution deployments. Furthermore, we aim at testingthis type of TPC strategy in real test-beds using

Mica2 motes.

Acknowledgements

This work has been cofunded by the Economy,Industry and Innovation Council, with the SOLID-MOVIL project (2I04SU044), supported by Funda-cion Seneca, with the ARENA Project (00546/PI/04), both from the Region of Murcia, the SpanishResearch Council with the ARPaq project(TEC2004-05622-C04-02/TCM), and by the Span-

ish Ministry of Industry, Tourism and Commercewith the project m:Ciudad (FIT-330503-2006-2).

Two anonymous referees made relevant com-ments that helped us to improve this paper.

Appendix A. Radio channel model

Let Ptx and Prx be the transmission and receptionsignal power, respectively. Let d be the distancebetween peers. WSN media can be considered atime-invariant narrow-band channel, which can be

modeled using a path-loss approximation [22],where

Prxd Ptx k4pd0

2d0

d

a29

being a the path-loss coefficient (typically, a 2 [2,4])calculated at a reference distance d0.

There are two main contributions to the noise inthe transmission: (1) the channel noise is usuallyconsidered Additive White Gaussian Noise(AWGN) with spectral power density N0 = KT,

where K is the Boltzmann constant and T is the



14/16

absolute temperature. And (2) the internal noise ofthe receiver, characterized by a noise figure(F% 1015 dB). Let Eb be the energy per bit, R bethe bit rate and B be the transmission bandwidth.The signal to noise ratio S

N is

SN

PrxKTBF

EbN0

RB

: 30

Mica2 motes use the NCFSK modulation, thenthe bit probability error (be) is [24]

be 12

exp 12

Eb

N0

: 31

And, consequently, the packet probability error(pe) for a packet of n bits is

pe 1 1 ben

: 32Given a target error packet probability (bpe ), the

necessary power transmission (cPtx ) can be obtainedfrom the previous equations. This objective errorpacket probability bpe is the quality (figure of merit)we would like to have in our communications. First,notice that

cEbN0

2 ln2bbe 2 ln 2 1 1 bpe

1n

h i : 33

And from Eq. (30),

cPrxKTBF

2 ln 2 1 1 bpe1nh i RB

cPrx 2KTFR ln 2 1 1 bpe1nh i : 34

Then, from Eq. (29), cPtx can be expressed ascPtx daX; 35where

X, 2KTRF ln 2 1 1 bpe1nh i 4pd0k 2

1

d0 a:

36

Appendix B. Probability density function of the

quadratic distance with normal distribution

Theorem 1. The pdf ofd2 for a Normal distribution is

fd2x 1

4r2exp x

4r2 : 37

Demonstration: First, notice that

DX Xi Xj N0;r N0;r N0;

ffiffiffi2

pr

DY Yi Yj N0;r N0;r 38 N0;

ffiffiffi2

pr:

Therefore,

DXffiffiffi2

pr

2 DYffiffiffi

2p

r

2 v22: 39

Thus,

d2 DX2 DY2 2r2v22: 40Since v22 exp 12

, the PDF ofd2 is

Prd2 6 x Pr2r2v22 6 x Pr v22 6x

2r2h i Zx2r20

12

exp u2

du

1 exp x4r2

: 41

And, finally, the pdf ofd2 is the derivate of thePDF:

fd2x d 1 exp x

4r2

dx

14r2

exp x4r2

:

42

Hence, proved.

Appendix C. Average number of neighbors with

normal distribution

Let n be the total number of nodes in the net-work. Let v be the random variable number ofneighbors of a node. Since nodes position isselected independently, the mpf ofv is

Pr

v

i

n1

i gi

1

g

n1i for i

1; . . . ;n

1;

43where g is the probability that two nodes indepen-dently selected are neighbors, that is the probabilitythat distance between nodes (d) is less than dS. Fromthe pdf ofd2 obtained in Appendix B, we know that

g Prd2 6 d2S 1 exp d2S

4r2

. Additionally, the

first order moment of v can be obtained

v

Xn1

i1i

n 1i gi1 gn1i gn 1: 44



15/16

References

[1] I.F. Akyildiz, W. Su, Y. Sankarasubramaniam, E. Cayirci, Asurvey on sensor networks, IEEE Communications Maga-zine 40 (8) (2002) 102116.

[2] J. Polastre, J. Hill, D. Culler, Versatile low power medium

access for wireless sensor networks, in: Proc. ACM Confer-ence on Embedded Networked Sensor Systems (SenSys2004), 2004, pp. 95107.

[3] W. Ye, J. Heidemann, D. Estrin, Medium access controlwith coordinated, adaptive sleeping for wireless sensornetworks, ACM/IEEE Transactions on Networking 12(2004) 493506.

[4] MICA MOTES. Online, available from: .

[5] T. van Dam, K. Langendoen, An adaptive energy-efficientMAC protocol for wireless sensor networks, in: Proc. ACMConference on Embedded Networked Sensor Systems (Sen-Sys 2003), 2003, pp. 171180.

[6] G. Lu, B. Krishnamachari, C. Raghavendra, An adaptive

energy-efficient and low-latency MAC for data gathering insensor networks, in: Proc. Int. Symp. on Parallel andDistributed Processing, 2004.

[7] L. van Hoesel, T. Nieberg, H. Kip, P. Havinga, Advantagesof a TDMAbased, energy-efficient, self-organizing MACprotocol for WSNs, IEEE VTC (2004).

[8] L. van Hoesel, P. Havinga, A lightweight medium accessprotocol (L-MAC) for wireless sensor networks, in: Proc.Int. Workshop on Networked Sensing Systems (INSS 2004),2004.

[9] Gomez, J., Campbell, A.T., Naghshineh, M., Bisdikian, C.,Conserving transmission power in wireless ad hoc networks,in: 9th Int. Conf. Network Protocols (ICNP 2001), 2001,pp. 2424.

[10] IEEE 802.11, 1999 Edition (ISO/IEC 8802-11:1999). Part 11:Wireless LAN Medium, Access Control (MAC) and PhysicalLayer (PHY) Specifications.

[11] A. Martnez-Sala, J.M. Molina-Garca-Pardo, E. Egea-Lopez, J. Vales Alonso, L. Juan-LLacer, J. Garca-Haro,An accurate radio channel model for wireless sensornetworks simulation, Journal of Communications and Net-works 7 (4) (2005) 401407.

[12] V. Kawadia, P.R. Kumar, Power control and clustering in adhoc networks, in: Proc. 22nd Annual Joint Conference of theIEEE Computer and Communications Societies (INFO-COM 2003), vol. 1, 2003, pp. 459469.

[13] C. Yu, K.G. Shin, B. Lee, Power-stepped protocol: enhanc-

ing spatial utilization in a clustered mobile ad hoc network,IEEE Journal on Selected Areas in Communications 22 (7)(2004) 13221334.

[14] E. Jung, N.H. Vaidya, A power control MAC protocol forad hoc networks, in: Proc. ACM Conference on MobileCommunications (MobiCom 2002), 2002, pp. 3647.

[15] A. Muqattash, M. Krunz, Power controlled dual channel(PCDC) medium access protocol for wireless ad hocnetworks, in: Proc. 22nd Annual Joint Conference of theIEEE Computer and Communications Societies (INFO-COM 2003), vol. 1, 2003, pp. 470480.

[16] J.P. Monks, V. Bharghavan, W.M. Hwu, A power controlledmultiple access protocol for wireless packet networks, in:Proc. 20th Annual Joint Conference of the IEEE Computer

and Communications Societies (INFOCOM 2001), vol. 1,2001, pp. 219228.

[17] Y.-C. Tseng, S.-L. Wu, C.-Y. Lin, J.-P. Sheu, A multi-channel MAC protocol with power control for multi-hopmobile ad hoc networks, in: Proc. DistributedComputing Systems Workshop, 2001, pp. 419424.

[18] M. Kubisch, H. Karl, A. Wolisz, L.C. Zhong, J. Rabaey,Distributed algorithms for transmission power controlin wireless sensor networks, in: Proc. IEEE WirelessCommunications and Networking, vol. 1, 2003, pp. 558563.

[19] H. Takagi, L. Kleinrock, Optimal transmission ranges forrandomly distributed packet radio terminals, IEEE Trans-actions on Communications 32 (3) (1984) 246257.

[20] J. Gomez, A. Campbell, A case for variable-range trans-mission power control in wireless multi-hop networks,in: Proc. IEEE INFOCOM 2004, vol. 2, 2004, pp. 14251436.

[21] Y. Chen, E.G. Sirer, S.B. Wicker, On selection of optimaltransmission power for ad hoc networks, in: Proc. 36th

Hawaii International Conference on System Sciences,2003.[22] T. Rappaport, Principles of Communications Systems,

second ed., Prentice Hall, 2002.[23] S-MAC Source Code for TinyOS. Online, available from:

.[24] J. Proakis, Digital Communications, Fourth ed., McGraw-

Hill, 2001.

Javier Vales-Alonso received the Tele-communications Engineering degreefrom the University of Vigo, Spain, in2000 and the Ph.D. in Telecommunica-tions from the Polytechnic University ofCartagena (UPCT), Spain, in 2005. InNovember 2002 he joined the UPCTwhere he is assistant professor of theDepartment of Information Technolo-gies and Communications. He has beeninvolved in several National and Inter-

national research projects related to cellular networks, opticalpacket switching, wireless and sensor networks and performanceevaluation issues. He is author or co-author of more than 15papers mainly in the fields of cellular and wirelesscommunications.

Esteban Egea-Lopez received the Tele-communications Engineering degree in2000, from the Polytechnic University ofValencia (UPV), Spain, the MasterDegree in Electronics in 2001, from theUniversity of Gavle, Sweden, and Ph.D.in Telecommunications in 2006 from thePolytechnic University of Cartagena.Since 2001, he is an assistant professor ofthe Department of Information Tech-nologies and Communications at the

Polytechnic University of Cartagena. His research interest isfocused on ad-hoc and wireless sensor networks.

http://www.xbow.com/http://www.xbow.com/http://www.isi.edu/ilense/software/smac/download.htmlhttp://www.isi.edu/ilense/software/smac/download.htmlhttp://www.xbow.com/http://www.xbow.com/


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Alejandro Martnez-Sala received theElectrical Science Engineering degrees(B.S. in 1998, M.S. in 2000) and thePh.D. in Telecommunications in 2006from the Polytechnic University ofCartagena (UPCT) in Spain. Since 2001,he is an assistant professor of theDepartment of Information Technolo-gies and Communications at the Poly-technic University of Cartagena. Hisresearch interest is focused on wireless

sensor networks and active RFID technology.

Pablo Pavon-Marino received the Tele-communication Engineering degree inTelecommunications in 1999 from theUniversity of Vigo (UVIGO), Spain. In2000 he joined the Polytechnic Univer-sity of Cartagena (UPCT), where he is anAssociate Professor at the Departmentof Information Technologies and Com-munications. He received the Ph.D.degree from this University in 2004. Heis involved in several National and

International research projects related to optical packet switch-ing, performance evaluation issues and wireless sensor networks.

M. Victoria Bueno-Delgado received theTelecommunication Engineering degree(B.S. in 2002, M.S. in 2004) from thePolytechnic University of Cartagena(UPCT) in Spain. Since 2005, she is an

assistant professor of the Department ofInformation Technologies and Commu-nications at the Polytechnic Universityof Cartagena. Her research interest isfocused on wireless sensor networks andactive RFID technology.

Joan Garca-Haro received the Tele-communication Engineering degree andthe Ph.D. in Telecommunications in1989 and 1995 respectively, both fromthe Polytechnic University of Catalonia(UPC), Spain. He has been an AssistantProfessor at the Department of AppliedMathematics and Telematics (DMAT-UPC) since 1992, and Associate Profes-sor since 1997. In September, 1999 he joined the Polytechnic University of

Cartagena (UPCT), Spain, where he is Professor of the Depart-ment of Information Technologies and Communications. He hasbeen involved in several National and International researchprojects related to electronic and optical packet switching, B-ISDN design and planning, next generation Internet, wireless andsensor networks, value-added services and performance evalua-tion issues. He was a visiting research scientific at Queens Uni-versity at Kingston, Ontario, Canada. He is author or co-authorof more than 50 papers mainly in the fields of switching and

performance evaluation. Since 1994 he served as regional corre-spondent of the Global Communications Newsletter (and Editorin Chief from April 2002 to December 2004) included in the IEEECommunications Magazine, Associate Technical Editor fromJanuary, 2000, and Technical Editor of the same magazine fromMarch 2001. He also holds an Honorable Mention for the IEEECommunications Society Best Tutorial paper Award (1995).


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