energy-efficient network design via modelling: optimal designing point for energy, reliability,...

www.ietdl.org

Published in IET NetworksReceived on 31st January 2012Revised on 24th November 2012Accepted on 29th November 2012doi: 10.1049/iet-net.2012.0024

Special Issue on Resilient Network Design

ISSN 2047-4954

Energy-efficient network design via modelling:optimal designing point for energy, reliability,coverage and end-to-end delayMohammad Saeed Ansari1, Ali Mahani2, Yousef S. Kavian3

1Department of Electrical and Electronic Engineering, IUST, Tehran, Iran2Department of Electrical and Electronic Engineering, Shahid Bahonar University, Kerman, Iran3Faculty of Engineering, Shahid Chamran University, Ahvaz, Iran

E-mail: [email protected]

Abstract: Considering that practical wireless sensor networks are mostly built upon energy-constrained sensor nodes, networklifetime becomes a key deployment factor for sustainability of such networks initiating an attempt for prolonging the lifetime.Adopting a new multi-mode switching protocol for sensor nodes between active and sleep states, in this study, the authorspropose a new mathematical method using an embedded simulation-based computing of an energy-efficient strategyperformance metric to maintain resiliency of the network against side effects appearing in duty-cycling protocols. Here, theauthors use a Monte Carlo simulation to estimate network reliability. Then the proposed mathematical model enables us tobuild a decision for optimised performance upon trade-offs between consumed energy, reliability, coverage intensity and end-to-end delays by locating a network’s operational points. The authors show the trade-off operational significance of the modelagainst the percentage of sleeping probability via some design factors including figure of merit.

1 Introduction

With major advances in the development of wireless sensornetworks (WSNs) and on account of their features such astheir low cost, easy installation, wide range and high safety,many experimental and commercial deployments are takingplace in recent years [1, 2]. WSNs are widely used invarious applications such as military surveillance,agriculture monitoring and emergency rescue. Theseapplications, however, oftentimes require thatbattery-operated sensors be deployed in a large area,requiring (i) multi-hop data transmissions over error-pronewireless links, and (ii) longer network lifetime as it isdifficult or costly to change the batteries because of safetyreasons or the sensor network’s deployment scale.Therefore reliability and energy efficiency become twoconcerns in the ubiquitous deployment of WSNs [3].While designing a wireless sensor system, a major concern

is the cost: one-time deployment cost and the long-termmaintenance cost. The one-time deployment cost includesthe cost to purchase/develop the sensor nodes, the labourwork required to deploy the nodes etc. The long-termmaintenance cost, is the energy cost [4].Then to design and implement a practical WSN with a long

lifetime and reliable communication, two main objectivesshould be considered.

1- Energy-efficient communication: Unfortunately thesesensors are not always accessible, so it is infeasible to

IET Netw., 2013, Vol. 2, Iss. 1, pp. 11–18doi: 10.1049/iet-net.2012.0024

replace the sensors which have run out of energy. Hence,energy-efficient communication is necessary in WSNs.2- High reliability: WSNs are exposed to faults andvulnerability. Faults may happen because of hardware/software failures, message bit error rate, collisionprobability etc. [5–8]. Hence, the reliability analysis ofWSN in order to guarantee safe packet transmission is ofgreat importance.

There are various approaches to reduce energy consumption,including data fusion to minimise data transmissions,controlled flooding to lower the communication overhead,duty-cycling MAC protocols to reduce idle-listening. Sincewireless sensors consume similar power in transmitting data,receiving data and being idle, the network lifetime canbe significantly improved by putting sensors to sleep(turning off the sensors’ transceiver) when the sensors arenot used [9].The aim of WSN design is to guarantee its longevity

under the given energy constraint. The MAC plays acentral part in this design, since it controls the active andsleeping state of each node. The MAC protocols henceneed to trade longevity, reliability, fairness, scalabilityand latency [10].Some researchers have focused on the effects of active/

sleep periods on performance metrics. For example, in [11],Misic et al. have studied a new scheduling of inactive andactive periods at sensor nodes as a technique to controlevent reliability and device utilisation in the clustered

11& The Institution of Engineering and Technology 2013

www.ietdl.org
sensor network with star topology. Luo et al. [12] and Munirand Ross [13] have studied the impact of active/sleepdynamics and node buffer size on the trade-off betweenpower efficiency and quality of service (QoS) requirements.Their model investigates the impact of active/sleepdynamics and buffer size on network performance metricsin terms of average power consumption, packet delay, lossrate and throughput.As mentioned above, the key idea for energy saving in
WSNs is to put nodes to sleep as long as possible whileavoiding deafness and reducing overhearing and overhead[9]. Hence, in the duty-cycling protocols such as, BMAC,X-MAC, CMAC, DPS-MAC, TICER, WOR, MX-MAC,MFP, STEM, MHMAC, SP, LPL, ZMAC and … eachsensor node chooses its active schedule independently ofother nodes around. The main side effect of duty-cyclingprotocols is connection delay (connection delay: given apair of sensors, the connection delay δ is the time intervalbetween the current time slot and the first time slot at whichboth sensors are active).Low coverage intensity and low network reliability are

other side effects of duty-cycling MAC protocols inproviding desirable QoS for applications that use WSNs.Since wireless channels are error-prone, and multi-hopcommunications are oftentimes necessary in variousapplications, network reliability over multi-hoptransmissions may be significantly degraded. Also node’sswitching on/off schedules is not coordinated at all, andthe durations of on/off period are such that the numberof active nodes at any particular time is so low that thenetwork is always disconnected. Network reliability isthe main factor in scalability analysis and multi-pathrouting manipulation. Hence, it is important that sensorsleeping solution prolongs the network lifetimewith reliability guarantee under varying networkconditions [4, 14].In this paper we try to propose a mathematical model to

calculate the link failure rate and then analyse the effectsof sleep probability as an energy-efficient strategy ontwo terminal reliability, coverage intensity and alsoend-to-end delay. In fact, it is important to obtain a longnetwork lifetime without sacrificing crucial aspects ofQoS such as coverage intensity, reliability and delay.This model helps us to find the optimum point, in whichthe network is in desired reliability and satisfies theperformance requirements while maximising networklifetime.This paper is organised as follows: Section 2 presents

Monte Carlo simulations (MCSs) to estimate networkreliability and also the performance metrics aredemonstrated. In Section 3, the simulation results areconsidered. Finally, Section 4 gives the conclusion.

2 Network reliability

Despite all possible faults, many applications (such asmilitary, disaster management, healthcare etc.) expectreliable communication.The reliability of a WSN is affected by the following main

factors:

† node reliability factors such as hardware/software failuresor battery depletion;† link reliability factors such as signal-to-noise ratio (SNR)and collision probability.


In this paper it is assumed that the nodes are fault free andso link reliability is calculated as the main factor oftwo-terminal reliability.

2.1 Link reliability

In wireless links, the link failure rate is affected by twoimportant faults, bit error rate and collision probability. Inthis section, a mathematical model for link reliability ispresented.

† Bit error rate. This is related to the changed bit because ofthe environmental factors.

To model this fault the SNR is used, γ. The SNR isdependent on the distance between transmitter and receiver,(1).

g(d) = 10× log4d

l

( )(1)

where l indicates the wavelength (the frequency is 2.4 GHz).The probability that one bit changes because of noise can

be calculated through

Pbiterror = 0.5e−g/2 (2)

However, we have a fault-free communication if all theframe’s bits are received correctly. The probability ofhaving a fault-free communication is given by

Pnobitchanges = 1− Pbiterror

( )8F(3)

in which F indicates the frame length, consists of preamble,network payload and cyclic redundancy code (CRC).

† Collision probability. The generated traffic of the networkincreases the number of collisions between packets, whichleads to packet loss increases. We calculate the collisionprobability through the below formula.

First the average contention window is calculated asfollows.

�W = (1− c− c× (2× c)m)

1− 2× c×W0

2(4)

where m indicates the number of allowed retransmission andW0 is the stage 0 contention window. Then, the nodestransmission probability (τ) is given by

t = b0�W

(5)

where b0 is the probability that a randomly selected node hasat least one packet to transmit and the collision probability isgiven by

c = 1− (1− t)n−1 (6)

n shows the number of neighbour nodes plus the node itself.Hence, pt,1 shows the probability that at least one of the nodes


www.ietdl.org
(neighbours + itself) sends a packet
pt,1 = 1− (1− t)n (7)

The probability of a successful transmission is given by

ps,1 =n× t× (1− t)n−1

1− (1− t)n(8)

Now, let us write the expression for medium occupation time,Ts, corresponding to successful transmission and the mediumoccupation time, Tc, corresponding to collision.

Ts = tDIFS + tSIFS + tRTS + tCTS + tSIFS + tACK+ s+ tMAC + tPHY + E[p]

Tc = tDIFS + tSIFS + tRTS + tCTS

(9)

where E[p] is the average packet length and σ stands for slottime. The average time duration between two consecutivebackoff counter decrements is determined by

Tslot = 1− pt,1( )× s+ pt,1 × ps,1 × Ts + pt,1× 1− ps,1

( )× Tc(10)

The time to complete a transmission process would be

TRES = Tslot × �W (11)

So one packet transmission delay would be

B = TRES + Ts (12)

The new value of b0 is given by

b0,new = lB (13)

where λ is the unsaturated total traffic.According to the above formula the collision probability (c)

is achieved through a recursive algorithm. At the end of eachiteration, if the difference between b0 which is used in (4) andb0,new is less than ε (acceptable error), the collisionprobability which is obtained in (6) would be accepted.After modelling all the possible faults, we can now model

path reliability. The path is operating properly if none of thementioned faults occur. For a single link between twoneighbour nodes link reliability is given by

plink = Pno bitchanges × (1− c)

Then, from the two-terminal reliability points of view, a WSNcan be assumed as a graph with a huge set of vertexes andvery complicated edges. Hence, the MCS method would beone of the best options for two-terminal reliability calculation.

2.2 Paired-terminal reliability

As MCSs are robust methods in statistical works, they havebeen used to solve many network reliability problems [15].The reliability of a network can be calculated through a


network graph as shown in Fig. 1. To use the Monte Carlomethod for network reliability calculation, we need a set ofpaths from the source node to the sink. However, having allpossible paths especially in a large network is a non-deterministic polynomial (NP)-hard problem, so we aregoing to use minimal path set instead [15].The flowchart of making a minimal path is illustrated in

Fig. 2.where M is the number of repetitions and e is an auxiliary

node which is not sink node (s). Also i is the initial node.After finding the minimal path set, we are going to

approximate network reliability. Assuming R(m, n)determine the reliability of the link between two nodes mand n, then the random matrix u is generated, which is abinary-state matrix, u(m, n) = 1 if u(m, n) < R(m, n) elseu(m, n) = 0. By applying a simple logic operation on A andu the matrix B is obtained (B = A∧u). In fact, we considerthe effects of links reliability on the adjacency matrix, byusing matrix u. Finally, to approximate the reliability, thefollowing procedure is used as shown in Fig 3.In this way two-terminal reliability is calculated. In the

‘simulation results’ section, the effect of sleep mode onreliability and network performance metrics is explained.In the next section a mathematical model is proposed, in

which the relation between end-to-end delay and sleepprobability is recognised. Also coverage intensity and collisionprobability as a function of sleep probability are obtained.

2.3 Mathematical modelling

2.3.1 End-to-end delay: In our proposed mathematicalmodel, two possible scenarios for a WSN are considered:

1. Normal mode operation.2. Taking advantage of sleep mode or hybrid mode.

In the normal mode, the nodes take part in datatransmission till they die. In other words, in the firstscenario the sensor nodes do not have an alternativeoperational mode after turning on. However, in the hybridmode, the sensor nodes could switch between sleep andactive states randomly.The symbols with their definitions are listed below:

† Sleep probability ps,† Node density σ,† Number of neighbour nodes n − 1 = πr2σ,† The non-empty probability (the node’s queue isnon-empty) in which lead to packet transmission is τ.

According to our previous work [16], the wireless channelat any moment is in one of the following states:

† idle state (Si),† collision state (Sc),† successful transmission state (Ss).

Fig. 1 Sample graph to show two-terminal reliability computation


www.ietdl.org

Fig. 2 Minimal path set construction procedure

In a multi-hop network in which nodes have (n – 1)neighbours, the following conditional probabilities aredefined:

pis: The probability that the wireless channel is idle.pss: The probability that the wireless channel is sensed busywhen a successful transmission occurs.pcs: The probability that the wireless channel is sensed busywhen a collision occurs.

All the above three probabilities are defined for a WSN innormal mode. Then, for a WSN in hybrid mode theprobabilities are pis, pss and pcs, respectively.Since n stations contend to access the medium and each

station transmits with probability τ, the state probabilitiesfor normal mode are given by

pis = (1− t)n (14)


pss = n1

( )t(1− t)n−1 = nt(1− t)n−1 (15)

pcs = 1− pis − pss (16)

And the state probabilities for hybrid mode are given by

pis = (1− t)n−nps (17)

pss = n− nps1

( )t(1− t)n−nps−1 (18)

pcs = 1− pis − pss (19)

Ts is the average time that the medium is sensed busy becauseof a successful transmission and Tc is the average time that themedium is sensed busy by each station when a collisionoccurs and σ is the duration of an empty slot. The values ofTs and Tc depend on the channel access mechanism


www.ietdl.org

Fig. 3 Reliability calculation procedure

assuming that all stations use the same channel accessmechanism [16].If α be the average length of slot time, then we have

a = pis+ pcTc + psTs (20)

For the backoff process, the binary exponential backoff isconsidered, in which Wmin and Wmax denote the minimumand maximum contention window, respectively, and wav isthe average backoff window.Finally, the total delay could be given by

D = H∗ a∗wav

( )+ packet length

Bandwidth

{ }(21)

where H is the average hop count between source node andsink.

2.3.2 Coverage intensity: Coverage intensity, which canbe considered as a QoS measurement of the WSNs, is affectedby sleep probability. As mentioned in Section 1 in order tosatisfy network lifetime, duty-cycling protocols are used.


However, taking advantage of duty-cycling protocols willreduce coverage intensity. Network coverage intensity is theratio of the time when a random point in the area of thenetwork is covered by at least one active node to the totaltime [17]. Hence, let f (x, y) denote the probability densityfunction (PDF) of uniform distribution and P(a, b) denotethe probability that a random point (a, b), is covered by atleast one node. Since we have distributed sensor nodes in acircular area, the PDF would be

f (x, y) = 1

pR2(22)

So we have

P(a, b) =∫∫

(x−a)2+(y−b)2,r2f (x, y) dx dy = pr2

pR2= r2

R2(23)

where R denotes the network area radius and r denotes thenode’s sensing radius.


www.ietdl.org
Finally, the coverage intensity of the network for normal
mode and hybrid mode is given by:

C = 1− (1− P(a, b))n

C = 1− (1− P(a, b))n−nps(24)

in which (n − nps) is the number of active nodes in hybridmode.

3 Simulation results

We developed the simulation program in MATLAB. The sinkis placed in the centre of the network area and the nodes areuniformly distributed around the sink. The simulation resultstry to consider the effects of sleep probability on networkperformance and two-terminal reliability of the network.The main assumptions are:

† Data transmission/reception is the main energy depletionactivity.† Sensor nodes are stationary.† Sensor nodes communicate with the sink along the shortestpath.† Nodes have limited energy.† Sensor nodes use contention-based MAC protocol.† Nodes switch between sleep and active mode randomly.† Synchronisation is not necessary and nodes can set theirwake up and sleep time in a decentralised fashion.† The network area is circular with radius R = 500 m.† The coverage area of each sensor node has radiusr = 100 m.† Total number of sensor nodes is N = 500, since sensorsdensity in the unit area is σ =N/πR2.† Packet length is 1024 bytes.† Data rate is 54 Mbps.

Fig. 4 Two terminals network reliability against sleep probability


As we expect, increasing sleep probability, led to a high ofsaved energy in nodes and also longer network lifetime.However, as shown in Fig. 4, which illustrates two-terminalreliability against sleep probability, sleep probability has anegative effect on network reliability. It is clear thatincreasing the sleep probability leads to a longer pathbetween source and destination and so decreases thetwo-terminal reliability.Sleep probability, which is the main solution for

energy-efficient network design has a non-negligible andweighty negative effect on two-terminal reliability. Thenumber of active nodes decrease through increasing sleepprobability. This means a longer path from the source nodeto the sink and when data passes a longer distance, theprobability of fault occurrence increases and we have areduction in two-terminal reliability.Table 1 shows the hop count from five random selected

nodes as the source node to the sink for different sleepprobabilities. Hence, the numerical results of the table showthe effect of sleep probability on path length which provesour reasoning.Now, we will explain the effect of nodes sleep probability

on collision probability. The number of active nodes has adirect effect on collision probability. When the number ofactive nodes increases, the probability of packet lossoccurrence increases and accordingly the number ofretransmissions would increase which lead to highend-to-end delay too.The end-to-end delay is illustrated in Fig. 5, but as shown

in Fig. 5, despite path length growth through sleep probabilityincrement, the end-to-end delay does not show a strictbehaviour.In order to interpret this behaviour, the effect of sleep

probability on path length and also collision probability

Fig. 5 Sleep probability effect on end-to-end delay

Table 1 Effect of sleep probability on route length (from random source node to the sink)

Sleep probability Point 1 (numberof hops to sink)

Point 2 (numberof hops to sink)




0.00 9.01 10.47 13.57 15.47 17.250.05 9.30 11.42 13.75 16.95 18.450.10 10.63 12.82 14.95 17.37 19.700.15 11.1 13.11 15.80 18.75 20.950.20 12.63 14.22 16.83 19.80 22.51


www.ietdl.org

Fig. 6 Network coverage intensity against sleep probability


Fig. 7 Effect of r/R ratio on network coverage intensity

Fig. 8 FOM against sleep probability

should be discussed together. High sleep probability increasespath length (Table 1) and reduces collision probability. Theend-to-end delay depends on both collision probability andpath length. A longer path length clearly increases theend-to-end delay. Collision probability has the same effecton the end-to-end delay. Hence, by increasing sleepprobability, the end-to-end delay would not behave strictly.Then the plot can be divided into two regions. Theascendant region, in which the path length is the dominantfactor in end-to-end delay and the descendant region, inwhich the collision probability is the dominant factor.Another important factor which is affected by sleep

probability is coverage intensity. Fig. 6 shows the networkcoverage intensity against the nodes sleep probability. Thefigure shows that the network coverage intensity increasesas sleep probability decreases and Fig. 7, shows the effectof nodes sensing radius on coverage intensity.

Finally, a new figure of merit (FOM) is defined in whichcoverage intensity, reliability and end-to-end delay areconsidered. The proposed FOM is given by

FOM = (coverage intensity)∗(two− terminal reliability)

(normalised end− to− end delay)

The proposed FOM help us to find the optimum point inwhich the network has low delay and high coverageintensity and reliability (Fig. 8).

4 Conclusions

Upon an investigation of energy-constrained sensing nodessleeping protocols, this paper provides a design


www.ietdl.org
environment using a multi-mode protocol which switches thenetwork nodes randomly between two modes of sleep andactive. Calculating the link’s failure rate affected by twofault associated issues of (i) bit error rate and (ii) collisionrate upon a mathematical model obtains link reliability inthe network. Therefore the mathematical model analyses theeffects of sleeping probability on features of the systemnamely network lifetime, end-to-end delay and reliability ofthe network.The MCS, which is used to obtain network reliability and
the proposed mathematical models, help us to find theoptimum working point of a resilient WSN designprocedure accountable for reliability, coverage intensity andtotal delay, as well as the network lifetime.

5 References

1 Rosberg, Z., Liu, R.P., Dinh, T.L.: ‘Statistical reliability for energyefficient data transport in wireless sensor networks’, J. Wirel. Netw.,2010, 16, (7), pp. 1913–1927

2 Doohan, N.V., Mishra, D.K., Tokekar, S.: ‘Reliability analysis forwireless sensor networks considering environmental parameters usingMATLAB’. IEEE Third Int. Conf. on Computational Intelligence,Communication Systems and Networks, 2011, pp. 99–102

3 Yang, O., Heinzelman, W.: ‘Sleeping multipath routing: a trade-offbetween reliability and lifetime in wireless sensor networks’. GlobalCommunication Conf., GlobeCom, 2011, pp. 1–5

4 Yang, O.: ‘Sleeping strategies for wireless sensor networks’. PhDThesis, University of Rochester, New York, USA, 2011

5 Akyildiz, I.F., Su, W., Sankarasubramaniam, Y., Cayirci, E.: ‘A surveyon sensor networks’, IEEE Commun. Mag., 2002, 40, (8), pp. 102–114


6 Tubaishat, M., Madria, S.: ‘Sensor networks: an overview’, IEEEPotentials, 2003, 22, (2), pp. 20–23

7 Pottie, G.J., Kaiser, W.: ‘Wireless sensor networks’, ACM Commun. J.,2000, 43, pp. 51–58

8 Korkmaz, T., Sarac, K.: ‘Characterizing link and path reliability in largescale wireless sensor networks’. IEEE Wireless and Mobile ComputingConference (WiMob 10), 2010, pp. 217–224.

9 Bachir, A., Dohler, M., Watteyne, T., Leung, K.K.: ‘MAC essentials forwireless sensor network’, IEEE Commun. Surv. Tutor., 2010, 12, (2),pp. 222–247

10 Liang, Z., Ma, S., Zhang, Q.: ‘Analysis of wireless sensor sleepmechanism with group arrival queueing model’. The Eighth IEEEConsumer Communications and Networking Conf., 2011,pp. 570–574

11 Misic, J., Shafi, S., Misic, V.B.: ‘Activity management throughBernoulli scheduling in 802.15.4 sensor clusters’, IEEE BroadbandNetworks, 2005, pp. 538–547

12 Luo, J., Jiang, L., He, C.: ‘Finite queuing model analysis for energy andQoS tradeoff contention-based wireless sensor networks’, IEEE ICC07,2007, pp. 3901–3906

13 Munir, A., Ross, A.G.: ‘Markov modeling of fault-tolerant wirelesssensor networks’, IEEE Computer Communications and Networks(ICCCN), 2011, pp. 1–6

14 Yang, O., Heinzelman, W.: ‘Modeling and performance analysis forduty-cycled MAC protocols in wireless sensor networks’, IEEE Trans.Mob. Comput., 2011, 11, (6), pp. 905–921

15 Yeh, W.C., Lin, Y.C., Chung, Y.Y.: ‘Performance analysis of cellularautomata Monte Carlo simulation for estimating network reliability’,Int. J. Expert Systems with Application, 2010, 37, pp. 3537–3544

16 Mahani, A., Tahmasebi, F., Nezamabadi-pour, H.: ‘Two tiers wirelessmesh networks: optimal configuration’, ICCKE11, 2011, pp. 235–239

17 Peng, M., Chen, H., Xiao, Y., Ozdemir, S., Vasilakos, A.V., Wu, J.:‘Impact of sensor node distributions on coverage in sensor networks’,Elsevier Int. J. Parallel and Distrib. Comput., 2011, 71, (12),pp. 1578–1591


energy-efficient network design via modelling: optimal designing point for energy, reliability,...

Documents