battery recovery aware sensor networkspaws.kettering.edu/~ywang/file/wiopt.pdf · battery recovery...

1

Battery Recovery Aware Sensor NetworksChi-Kin Chau∗†, Muhammad Husni Wahab∗, Fei Qin∗, Yunsheng Wang∗, Yang Yang∗

∗EE Department, University College London.†Computer Laboratory, University of Cambridge.Email: [email protected],{m.wahab, f.qin, uceeywa, y.yang}@ee.ucl.ac.uk

Abstract—Many applications of sensor networks require bat-teries as the energy source, and hence critically rely on energyoptimisation of sensor batteries. But as often neglected bythenetworking community, most batteries are non-ideal energyreser-voirs and can exhibit battery recovery effect — the deliverableenergy in batteries can be replenished per se, if left idlingfor sufficient duration. We made several contributions towardsharnessing battery recovery effect in sensor networks. First, weempirically examine the gain of battery runtime due to batteryrecovery effect, and found this effect significant and duration-dependent. Second, based on our findings, we model the batteryrecovery effect in the presence of random sensing activities bya Markov chain model, and study the effect of duty cycling andbuffering to harness battery recovery effect. Third, we propose amore energy-efficient duty cycling scheme that is aware of batteryrecovery effect, and analyse its performance with respect to thelatency of data delivery.

Index Terms—Sensor Networks, Energy Efficiency, BatteryRecovery, Duty Cycling

I. I NTRODUCTION

Wireless sensor networks are created by networks of smallsensors integrated with tiny embedded processors, wirelessinterfaces, and MEMS micro-sensors. Many applications ofwireless sensor networks require batteries as energy sourcefor the sensors. However, small form factors of devices oftenprohibit the uses of large and long lasting batteries. Moreover,ad-hoc deployment of sensor networks and the inconvenienceof battery recollection usually constrain frequent replacementof batteries. Hence, the design of energy-efficient controlal-gorithms and protocols is a crucial topic in sensor networking.

There are a variety of energy optimisation studies in theliterature that mostly consider batteries as ideal energy reser-voirs, from which energy can be drained at constant discharg-ing voltage, and can be halted and resumed at anytime toregain the same voltage. However, most commercial batteriesare governed by complex non-linear internal chemical reac-tions to provide energy. Such chemical reactions are known bychemical engineers to be dependent on a variety of environ-mental factors and operational parameters (e.g. temperature,discharging duration, discharging current, memory of pastdischarging profiles) [1].

1Chi-Kin Chau is grateful to The Croucher Foundation for financial support,and to Basu Prithwish for helpful discussion. Yang Yang’s research waspartially supported by the UK Engineering and Physical Sciences ResearchCouncil (EPSRC) under the project EP/F004532/1. The authors also wouldlike to thank the reviewers for detailed comments. This research is continuingthrough participation in the International Technology Alliance sponsored bythe U.S. Army Research Laboratory and the U.K. Ministry of Defence.

Particularly, there is a subtle phenomenon calledbatteryrecovery effect, which refers to the process that the chemicalsubstances in a battery will replenish themselves if left idlingfor sufficient duration, and hence, the deliverable energy of abattery can be recharged per se. Thus, we are motivated todesign and engineer control algorithms and protocols that canharness battery recovery effect.

In this paper, we first empirically examine the gain of bat-tery runtime due to battery recovery effect, through extensivetest-bed experiments on commercial sensors. We found thatsuch gain can be significant under appropriate duty cyclingcontrol. Our experiments also show that there exists a satura-tion threshold, by which more consecutive idling periods willnot contribute to more recovery. The ramification is that if wecarefully adjust the idle periods of batteries before reachingthe saturation threshold, we can maximise battery recoveryeffect without wasting too much idling time that may hamperthe quality of service.

Our experiments consider periodic constant battery con-sumptions. To investigate the behaviour of battery recoveryeffect in the presence of random sensing activities, we for-mulate a Markov chain model and provide analytical insightson the gain of expected battery runtime. Then, we study theeffect of duty cycling and buffering to harness battery recoveryeffect. It is common that RF transceiver operations in a sensorwill consume most of the energy (even in listening mode), ascompared to the processing and sensing activities. Thus, dutycycling is frequently employed to regulate the on/off periodsof the RF transceiver, while keeping the rest of sensor moduleon (e.g. the sensing and processing units are on to detect andbuffer the sensing data before the RF transceiver is awake fortransmission.2) It is important to design proper duty cyclingand buffering strategies that can maximise the battery recoveryeffect. Here, we propose a more energy-efficient duty cyclingscheme by setting the sleep duration of the RF transceiveras the saturation threshold of the battery, which can take themaximal advantage of the duration-dependent battery recoveryeffect. We verify the usefulness of our scheme by simulationstudies.

Furthermore, we consider the setting of multi-hop sensornetwork, where each sensor can act as a relay to forwardthe sensing data for other sensors to the sink. In this setting,there requires a coordination scheme among the duty cycling

2Here we do not want to jeopardise the accuracy of sensing data, and hencedo not consider to turn off the sensing and processing units for the sake ofenergy conservation. Note that such duty cycling control onthe RF transceiveronly affects the timeliness of sensing data.

This paper appears in the proceedings of the 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc,and Wireless Networks (WiOpt), 2009.

2

sensors, such that each sensor can discover the appropriatetimeslot to transmit data without wasting energy to probe theavailability of their relays. We adapt a distributed randomisedcoordination scheme from [2], and extend it to be aware ofbattery recovery effect. In this scheme, each sensor inferstherandom duty-cycling schedule of the relay based on pseudo-random sequence, and the random duty-cycling schedule isset to take advantage of battery recovery effect by forcing asensor to sleep when it has been awake for certain duration.We then analyse the performance of our scheme, by extendingthe latency analysis of pseudo-random duty cycling scheme inprevious work [3]. We obtain analytical results of the latencyof data delivery.

In this paper, our contributions are threefold, as summarisedas follows:

1) We provide experimental evidence on the significantgain of battery runtime by battery recovery effect, andfound that the gain is duration-dependent, characterisedby a saturation threshold.

2) We study the behaviour of duration-dependent batteryrecovery effect in the presence of random sensing ac-tivities, and the effect of duty cycling and buffering,through analysis and simulations.

3) We propose a more energy-efficient duty cycling schemeand a distributed coordination scheme among duty cy-cling sensors, extending the pseudo-random duty cyclingscheme to be aware of battery recovery effect. We alsoanalyse the performance on the latency of data delivery.

Because of space constraint, the proofs of analytical resultsare omitted in this paper, but can be found in the full paper[4].

II. RELATED WORK

Sensor networks commonly use rechargable batteries, suchas Nickel-cadmium (NiCd), Nickel-metal hydride (NiMH),Sealed lead-acid (SLA), Lithium-ion (Li-ion), and Lithium-polymer (similar to Li-ion). Different batteries have differentproperties. NiCd and NiMH are more commonly used insensor networks. NiCd has longer cycle life, while NiMH hashigher energy density.

There have been numerous studies about the performanceof batteries in chemical engineering [1]. In networking, [5]carried out an empirical study to measure the performance ofbattery-powered sensors, but did not examine the saturationthreshold. Although battery consumption has been modeledextensively in networking, many extant models ignore orover-simplify the realistic battery characteristics (e.g. allow-ing unlimited battery recovery). There are two main modelsconsidering realistic battery characteristics.

First, the kinetic battery models [6]–[8] attempt to model thedetailed chemical reactions and diffusion process betweentheelectrode and electrolyte in a battery through a set of partialdifferential equations. These models aim to fully capture thenon-linear dynamics in a battery. However, these models areless tractable, and different form factors of batteries cansignificantly affect the accuracy of the models.

Second, there are stochastic battery models [9]–[13] thatcapture the battery dynamics using probabilistic Markovianmodels. But most of them do not consider the effect ofidle time. [14] considers idle time in embedded systems, butdoes not address the performance in sensor networking. Weremark that while all these stochastic battery models attemptto imitate the kinetic battery model with smaller complexity,the uses of probabilistic battery recovery is different from thedeterministic kinetic battery models. Moreover, these modelsare also less tractable, with few analytical insights provided.

In this paper, we present a more analysable Markov chainmodel that simplifies the stochastic battery models [10], [11],[14]. Particularly, our model uses deterministic battery recov-ery, yet is able to capture realistic battery characteristics, suchas limited recovery and the effect of idle time. More impor-tantly, useful analytical insights of realistic battery behaviourcan be derived from our model.

There are a number of approaches of energy managament insensor networks, including topology management and networklayer optimisation. But relevant to our work are the onesbased on MAC layer, which aim to reduce redundant radiooperations in MAC protocols: 1) idle listening, 2) overhearing,3) collisions, and 4) protocol overhead (headers or signallingmessages). Since both listening and reception consume signif-icant energy in common sensors. In this paper, we focus onreducing idle listening and overhearing by duty-cycling andexploiting battery recovery effect.

III. E XPERIMENTAL RESULTS

We present the experimental results on the significanceof battery recovery effect from our sensor network test-bed.The experiments have been carried out on two types ofcommercial sensors from Crossbow: TelosB and Imote2. Bothare popular models for wireless sensor networking. TelosBis consisted of MSP430 (1.8mA active and 5.1µA standby)as MCU and CC2420 (23mA active and 21µA standby) asthe RF transceiver. Imote2 is consisted of PXA271 as CPUand CC2420 as the RF transceiver. TelosB and Imote2 havedifferent system architectures — TelosB involves more energy-saving designs with less energy overhead, whereas Imote2is equipped with high computation ability (from 13MHz to400MHz) that requires higher energy overhead. The twomodels reflect different applications with two extreme energyconsumption requirements.

In the experiments, we use an analogue-digital conversion(ADC) interface card and LabVIEW to measure and record thedischarging profiles of a pair of communicating sensors (seeFig. 1). Each sensor is powered by standard AAA NiMH 600mAh batteries (TelosB has two batteries, whereas Imote2 hasthree). When the supply voltage of the battery is lower than acertain threshold (called stop voltage), the device can no longeroperate, which is considered as to be completely discharged.We set different duty cycling rate on the sensors by puttingthe sensor in wake-up and sleep modes periodically, andmeasure the induced battery runtime. The duty cycling rate isdefined as the fraction of wake-up periods. Figs. 3 and 5 show


3

Fig. 1. The experimental setup.

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Time (0.1Second)

Cur

rent

(A)

Fig. 2. Measurement from LabVIEW on Imote2.

the discharging profiles for TelosB3 and Imote2 respectively,which are rescaled by multiplying the duty-cycling rate. Also,Figs. 4 and 6 show the gain of battery runtime under differentduty-cycling rates, as compared to continual discharging.

There are a number of key observations from the experi-ments:

• There are clear signs of battery recovery effect. Keepingthe same wake-up duration, longer sleep duration caninduce longer (rescaled) battery runtime, and hence largerdeliverable energy of battery.

• The effect of sleep duration is non-linear. It appears thatsleep periods more than a certain threshold will contributemuch less to battery recovery, we call asaturationthreshold.

• TelosB has a lower stop voltage, whereas Imote2 has ahigher one. This is due to TelosB involves lower energyoverhead. Since Imote2 has high energy overhead andlong boot-up time, battery recovery effect appears lessprominent when shorter wake-up duration is used.

• Both models of sensors exhibit non-uniform dischargingprofiles. For TelosB, the initial stage of dischargingappears to be slightly convex, followed by a concavedrop. For Imote2, the whole discharging profile is convex.This is due to the higher stop voltage of Imote2, whichcan only show partial discharging process, comparedto TelosB’s one (or the well known turn ‘S’-shapeddischarging curve of Ni-based battery).

• Even the sensor is in sleep mode, there is still energyconsumption due to the timer and other background pro-cesses. TelosB consumes 6.1µA in sleep mode, whereasImote2 is 0.38mA. Since battery recovery effect can stillhappen under low battery consumption, we found theimpact of background consumption is not substantial.

• We observe that most AAA NiMH batteries can be over-recharged. Although the standard initial voltage of an

3Because TelosB has a much longer battery runtime, we use a lowersampling rate, which gives a smoother profile curve.

AAA battery is stated as 1.2V, we found that a batterycan be recharged up to 1.3V by standard battery charger.The exact value is dependent on battery memory.

• Although our measurement of gain of battery recoveryeffect differs in other environmental settings (e.g. temper-ature), the insight revealed by our experiments will stillbe useful to the modelling and optimisation of batteryrecovery effect in sensor networks.

Finally, we discuss a major difference in the system ar-chitectures of TelosB and Imote2. In general, Imote2 cannotbe switch into and back from sleep mode fast. TelosB is ofMCU+RF architecture, where it is easy to turn the MCU intosleep mode by issuing internal commands. But Imote2 is ofCPU+RFIC and PowerControl IC. When Imote2 switches intosleep mode, it first needs to store it memory into flash, sendingcommand to PowerControl IC, then hibernates itself. WhenImote2 switches into awake mode, it simply restarts itself.It is found that in the experiment that Imote2 need severalseconds to boot up, and in this period Imote2 consumes muchmore than the normal operations (see the current plot forImote2 in Fig. 2). We remark that the difference in the systemarchitectures reflects the different roles of both models: TelosBusually acts as a leaf node, whereas Imote2 is supposed to bethe data processing node.

IV. M ODEL OF BATTERY CONSUMPTIONS

Our experimental findings confirm the usefulness of batteryrecovery effect, and show the characteristics of duration-dependence. We are motivated to model and study duration-dependent battery recovery effect in more realistic situationsconsidering random sensing activities as follows. For simplic-ity, we assume a discrete setting. The state of a battery canbe characterised by a tuple〈n, c, t〉, where n, c, t are non-negative integers.c is the theoretical capacity determined bythe amount of chemicals in the electrode and electrolyte,n isthe nominal capacity determined by the amount of availableactive chemicals for chemical reactions in the battery, andt isthe idle duration since the battery has stopped discharging.


4

AwakeH10sLSleepH0sL

AwakeH10sLSleepH2sL

AwakeH10sLSleepH4sL

AwakeH10sLSleepH6sL

AwakeH10sLSleepH8sL

AwakeH10sLSleepH10sL



0 200 400 600 800 1000 1200 1400Time HminL2.20

2.25

2.30

2.35

2.40

2.45

2.50

2.55

2.60VoltageHVL

Fig. 3. The discharging profiles of TelosB with respect to differentduty cycling rates.

0 2 4 6 8 10 12 14Sleep periodHsL0

5

10

15

20

25

30GainH%L

Fig. 4. The maximum gain of battery runtime is around25% forTelosB. The saturation threshold is around 5 sec.

AwakeH1minLSleepH0minL

AwakeH1minLSleepH0.33minL

AwakeH1minLSleepH0.67minL

0 500 1000 1500 2000 2500 3000Time HsecL3.65

3.70

3.75

3.80

3.85

3.90

VoltageHVL

Fig. 5. The discharging profiles of Imote2 with respect to differentduty cycling rates.

0.0 0.5 1.0 1.5 2.0 2.5Sleep periodHminL0

10

20

30

40GainH%L

Fig. 6. The maximum gain of battery runtime is up to37% for Imote2.The saturation threshold is around 0.5 min.

In the discharging process, bothn andc are decreasing. Theamount of available active chemicals constrains the energyofa battery can deliver, despite the presence of unused chemicalsin the battery. Hence,n ≤ c. But when the battery stopsdischarging, there is a recovery process, as a diffusion processbetween electrode and electrolyte to replenish available activechemicals, and effectively increasesn (though cannot increasethe theoretical capacityc)4. There is a saturation threshold fort, such that more consecutive idle periods will not contributemore recovery.

A. Normal Operations

To model random sensing activities under normal operationswithout duty cycling, we assume the consumption of a batteryis a Poisson random variable, which is reasonable if thesensing data follow Poisson distribution. We model the batterybehaviour as a Markov chainMbat with state set defined as:

{

〈n, c, t〉 : n, c, t are non-negative integers, andn ≤ c}

And the transition probabilities from states ofn ≥ 1 is definedas:

4Experimental studies [1] have shown that the recovery process is a non-linear dynamics, which critically depends on the state of battery 〈n, c, t〉. Ingeneral, the higher values ofn and c are, the more significant the recoveryeffect is observed. The recovery effect is more prominent when the battery hasconsecutive idle periods than sporadic idle periods. Thereis also a saturationthreshold fort, such that more consecutive idle periods will not contributemore recovery.

a) Discharging: The transition probability of

〈n, c, t〉a

−→ 〈n-k, c-k, 0〉 is pλpo(k) =

λke-λ

k!

for k ≥ 1 andn-k ≥ 1. The consumption is a Poissonrandom variable, whereλ captures the rate of batteryconsumption in a timeslot.

b) Completely Discharged: The transition probability of

〈n, c, t〉b

−→ 〈0, c-n, 0〉 is∞∑

k=n

pλpo(k) =

∞∑

k=n

λke-λ

k!

That is, whenever the consumption is higher than orequal to the nominal capacityn, the battery will becompletely discharged.

c) Idling with Recovering: The transition probability of

〈n, c, t〉c

−→ 〈n+1, c, t+1〉 is pλpo(0) = e-λ

for c ≥ n+1 and t < tsat. That is, there is recoverywhen no battery consumption, and the consecutive idleduration is lesser than the saturation thresholdtsat.

d) Idling without Recovering: The transition probability of

〈n, c, t〉d

−→ 〈n, c, t+1〉 is pλpo(0) = e-λ

for c < n+1 or t ≥ tsat. That is, there is no recov-ery when the nominal capacity reaches the theoreticalcapacity, or the consecutive idle duration reaches thesaturation threshold.


5

e) Otherwise, the transition probabilities for all other statetransitions equal 0.

Note that〈0, c, t〉 is an absorption state that will not transit toother states, corresponding to a complete discharged state. InFigs. 7-8 we illustrate the state transitions, assumingtsat = 1.

We remark that there are several simplifications in thismodel. First, we assume the saturation thresholdtsat is in-dependent ofn and c. Second, the recovery process is thesame for any state below the saturation threshold. While theseassumptions cannot capture the complete non-linear dynamicsin real batteries, they are sufficient to represent a genericmodelof battery behaviour. With the minimum number of parameter(only tsat), our model does not rely on extensive experimentsto determine further parameters as in a more complete modelthat otherwise critically depend on the types of batteries andother environmental factors (e.g. temperature)5. Moreover, thismodel enables simple analytical results to yield useful insightsfor harnessing battery recovery effect.

Let Wtm(n) be the expected battery runtime at state

〈n, n+m, t〉 in Markov chainMbat (i.e. the expected numberof timeslots a battery can last until reaching an absorptionstateas being completely discharged).

By the definition of state transitions inMbat and thelinearity of expected values, we obtain:

W0

0(n) = 1 +

n-1∑

k=0

pλpo(k)W0

0(n-k), Wt

0(n) = W0

0(n) (1)

That is, if the consumption is ofk charges and is less thanthe nominal capacityn, then the expected battery runtime isW

00(n-k) + 1. Otherwise, it will be completely discharged (the

expected battery runtime is 1).For m ≥ 1,

Wt

m(n) =

1 + pλpo(0)Wt+1

m-1(n+1) +n-1∑

k=1

pλpo(k)W0

m(n-k) if t < tsat

1 + pλpo(0)Wtsat

m (n) +n-1∑

k=1

pλpo(k)W0

m(n-k) if t = tsat

(2)

B. Duty Cycling and Buffering

Next, we define Markov chainMbuf with duty cyclingon RF transceiver and buffering. We assume that the sensorwill sleep forbmax timeslots, immediately after the battery isconsumed for a burst of RF transmission. During the sleepperiods, the sensing unit is still on, and the data is bufferedfor at mostbmax timeslots. To take the maximal advantage ofbattery recovery effect, we setbmax ≤ tsat.

Now the state is defined as〈n, c, b〉, whereb ≥ 1 meansthe battery has been in buffered state forb timeslots. Ifb +1 > bmax, then the buffer will not hold any consumption and

5Other models (e.g. [11], [14]) attempt to incorporate more parameters,such as probabilistic recovery effect to capture non-linear battery behaviour.These models are often inconvenient for analysis, and yieldlittle analyticalinsights.

proceed to immediate discharging. We let the buffered batterybehaviour be a Markov chainMbuf with state set as:

{

〈n, c, b〉 : n, c, b are non-negative integers, andn ≤ c}

Define the transition probabilities from states ofn ≥ 1 as:

a’) Discharging: The transition probability of

〈n, c, 0〉a′

−→ 〈n-k, c-k, 1〉 is pλpo(k) =

λke-λ

k!

for k ≥ 1 andn-k ≥ 1.b’) Completely Discharged: The transition probability of

〈n, c, b〉b′

−→ 〈0, c-n, 0〉 is∞∑

k=n

pλpo(k) =

∞∑

k=n

λke-λ

k!

c’) Idling: The transition probability of

〈n, c, 0〉c′

−→

{

〈n+1, c, 0〉 if c ≥ n+1〈n, c, 0〉 if c < n+1

is pλpo(0) = e-λ

d’) Buffering: Define b+ , b+1(mod bmax+1) (i.e. the

number of buffered timeslots increases by 1, untilreaching the limit of buffered timeslots asbmax). Thetransition probability of

〈n, c, b〉d′

−→

{

〈n-k+1, c-k, b+〉 if c ≥ n+1〈n-k, c-k, b+〉 if c < n+1

is pλpo(k) =

λke-λ

k!

for 1 ≤ b ≤ bmax andn-k ≥ 1.e’) Otherwise, the transition probabilities for all other state

transitions equal 0.

Note that the above Markov chain will record the batteryconsumption during buffering periods, and hence automat-ically deduct the battery consumption when releasing thebuffer. In Figs. 9-10 we illustrate the state transitions whenbmax = 1.

Similarly, let Bbm(n) be the expected battery runtime with

buffering at state〈n, n+m, b〉 in Mbuf . Like Wtm(n), we

obtain:B

b

0(n) = W0

0(n) (3)

For m ≥ 1,

Bb

m(n) =

1 +n-1∑

k=0

pλpo(k)Bb

+

m-1(n-k+1) if b > 0

1 + pλpo(0)B0

m-1(n+1) +n-1∑

k=1

pλpo(k)B1

m(n-k) if b = 0

(4)whereb

+ , b+1(mod bmax+1) (i.e. the number of bufferedtimeslots increases by 1, until reaching the limit of bufferedtimeslots asbmax).

C. Analytical Results

In general, Wtm(n) and B

bm(n) appear with no simple

closed-form expression. However, we can obtain severalanalytical results as follows, which can offer useful insightsof the behaviour.


6

W00(n) W0

1(n)

n

c

1 2 30

0

1

2

3

4

5

t= 0

n

c

1 2 30

0

1

2

3

4

5

t= 0

d

aa

b

aa

b

c

Fig. 7. State transitions for Markov chainMbat at t = 0.

n

c

1 2 30

0

1

2

3

4

5

n

c

1 2 30

0

1

2

3

4

5

W02(n) W1

1(n)

t= 0 t= 1

d

a

a

b

a

c

aa

b

Fig. 8. State transitions fort = 1, whentsat = 1

n

c

1 2 30

0

1

2

3

4

5

b= 0

n

c

1 2 30

0

1

2

3

4

5

b= 1

c’

a’

b’

a’

a’

B11(n) B0

2(n)

Fig. 9. State transitions for Markov chainMbuf at b = 0.

c

1

2

3

4

5

c

0

1

2

3

4

5

n1 2 30n1 2 30

b= 0b= 1

c’

d’

d’

d’

b’

B11(n) B0

0(n)

Fig. 10. State transitions forb = 1, whenbmax = 1.

Theorem 1: The expected battery runtime is bounded by:

Wtm(n) ≤ W

0

m(n) ≤n+m-1

λ+

1

1 − e-λ

The bounds are intuitive, because the battery runtimeshould not exceedΘ(n+m) = Θ(c). Indeed, these upperbounds can be shown as tight.

Theorem 2: When λ is small or n is large, for someconstantsα,

W0

m(n) ≈n+m

λ+ α

Theorem 3: Consideringbmax = tsat, buffering is alwaysbetter:Bb

m(n) ≥ Wtm(n).

We carried out simulation studies for specificn and m.Figs. 11-12 depict the plots form = 40. We can see thatduty-cycling and buffering facilitates battery recovery,and canreach the upper bound closer. We remark that more drastic gapbetweenW0

m(n) andB0m(n) can be observed for largerm.

Figs. 11-12, we have seen that by duty-cycling and buffer-ing, there is a significant improvement of the battery runtime.In Fig. 13, we examine the gain of using duty-cycling andbuffering. We found then’s in Figs. 11-12 that maximise thedifference betweenW0

40(n) andB040(n) with respect to different

values ofλ andbmax, tsat, and plot the corresponding gain. Weobserve that the maximum gain can be up to200%. However,

the effectiveness decreases asbmax andtsat increase, becausethe larger saturation threshold means more likely batteryrecovery effect take place, so duty-cycling and buffering willnot improve too much.

tsat=bmax=1

tsat=bmax=2

tsat=bmax=3

0.0 0.5 1.0 1.5 2.0Λ0

50

100

150

200

Max GainH%L

Fig. 13. The maximum gain of using duty-cycling and buffering againstnormal operations over alln.

V. M ULTI -HOP SENSORNETWORKS

In this section, we consider multi-hop sensor networks,where each sensor can act as a relay to forward the sensingdata for other sensors to the sink. If we employ the dutycycling and buffering scheme as in Sec. IV on all the sensors,then there requires a coordination scheme among the duty


7

Λ=0.125

Λ=0.25

Λ=0.375Λ=0.5

Normal

Buffering

Bound

0 5 10 15 20n0

100

200

300

400

500Battery RuntimeHslotsL

Λ=0.625

Λ=0.75

Λ=0.875

Λ=1

Normal

Buffering

Bound

0 20 40 60 80 100 120n0

50

100

150

200


Fig. 11. Whenbmax = tsat = 1, we plot of the upper boundn+m-1λ

+ 1

1−e-λ, along with the battery runtime of normal operationsW0

40(n), and the

battery runtime with duty-cycling and bufferingB040

(n).

Λ=0.125

Λ=0.25

Λ=0.375Λ=0.5

Normal

Buffering

Bound

0 5 10 15 20n0

100

200

300

400


Λ=0.625

Λ=0.75

Λ=0.875Λ=1

Normal

Buffering

Bound

0 20 40 60 80 100 120n0

50

100

150

200


Fig. 12. Whenbmax = tsat = 3, we plot of the upper boundn+m-1λ

+ 1

1−e-λ, along with the battery runtime of normal operationsW0

40(n), and the

battery runtime with duty-cycling and bufferingB040

(n).

cycling sensors, such that each sensor can discover the appro-priate timeslot to transmit data. A simple scheme is to employa global coordinator that assigns a periodic/deterministic dutycycling schedule to each sensor in a-priori manner, and allsensors are provided the knowledge of the duty cycling sched-ules of their neighbours. However, this scheme suffers seriousscalability issue, and cannot cope with the rapid changingnetwork topology due to ad hoc sensor deployments.

Another simple duty cycling scheme is to turn RFtransceivers off and on independently randomly. Then, packetforwarding can only occur when the transmitting and receiv-ing nodes are both awake. This does not require a globalcoordinator among the devices, and is more resilient andself-configuring for ad hoc deployments. On the other hand,in periodic/deterministic duty cycling schedules, the on/offschedules of network nodes have to be carefully coordinatedsuch that efficient routing and forwarding can occur, whichare less robust than random duty cycling schemes. However,random duty cycling also suffers performance issue, such thata sensor needs to probe the availability of its relays.

Here, we adapt a distributed randomised coordinationscheme from [2], by which each sensor infers the randomduty-cycling schedule of the relays based on pseudo-randomsequence. We then extend this pseudo-random duty-cyclingscheme to be aware of battery recovery effect, is set to takeadvantage of battery recovery effect by forcing a sensor to

sleep when it has been awake for certain duration. We alsoobtain analytical results of the latency of data delivery, basedon the latency analysis of pseudo-random duty cycling schemein previous work [3].

A. Pseudo-random Duty-cycling Scheme

First, we describe the pseudo-random duty-cycling scheme.As in Sec. IV, we assume that when a sensor switches to sleepmode, only the RF transceiver is off, keeping the processingand sensing units for sensing activities on. Hence, it will notundermine the sensing functionality of the sensor networks.

Pseudo-random duty cycling [2], [3] is proposed as a moreenergy-efficient approach than purely random duty cycling.Suppose that transmissions occur in slotted time. Usually,random duty cycling is determined by a pseudo-random se-quence generator at a node. In pseudo-random duty cyclingscheme, if a node knows the seed and the cycle positionof the neighbours’ pseudo-random sequence generators, thenit can deterministically predict its neighbours’ wake-up andsleeping timeslots. This prevents a node from sending packetsin the timeslots that all its neighbours sleep, and can effectivelyreduce energy for unnecessary RF operations. We suppose thatall transmitters will buffer all their outgoing packets until thetimeslot when their respective receivers are awake.

The pseudo-random duty-cycling scheme is described asfollows:


8

1) At bootstrapping, neighbouring sensors exchange theseed, cycle position and duty-cycling rate (the proba-bility threshold of a slot that it is awake or asleep) ofpseudo-random sequence generators.

2) At each slot, a sensor determines its state (being asleepor awake), and all the neighbours’ states in the next slot.

3) To forward packets, a sensor will wait until there is anawake neighbour on its shortest path to the sink, and thentransmit the packets with corresponding receiver ID inthe header. The receiver of the corresponding ID willcarry out the forwarding of the packets until reachingthe sink.

Note that we assume the arrival packet rate is not high, andignore the interference of simultaneous transmitters6. We alsoassume that the sensing events of all sensors follow the sameindependent Poisson distributionpλ

po(k). We defer the study ofcorrelated sensing events to the future work. In the following,we study the battery runtime of pseudo-random duty-cyclingscheme.

Give a network topology, we pick one node to be thesink, and all other nodes must send the random sensing data(as distributed as Poisson distributionpλ

po(k)) to the sinkusing multi-hop forwarding. We define thenetwork life asthe expected time that there is a relaying node running outof its battery. By simulation studies, we compare the networklife of pseudo-random duty-cycling scheme and the normalcase where all the sensor is always on. We consider that onlytransmission will consume energy (not listening), which isproportional to the amount of data transmitted.

First, we consider linear network topology, where there aren nodes. The rightmost node is a sink. Fig. 14 shows that thegain of pseudo-random duty-cycling scheme is around20%−35%.

Next, we consider 2D lattice network topology, and indexeach node as(i, j) by integersi, j. There is a link betweennodes(i, j) and(i′, j′), if ( |i-i′| = 1 andj = j′) or (|j-j′| = 1and i = i′). Without loss of generality, we denote node(0, 0)as the sink, and all other nodes send packets destined to it.

(0,0)

(k,l)

(i,j)

Fig. 16. A lattice where the orange node is the sink(0, 0), we consider thenumber of shortest paths from(i, j) via (k, l).

Suppose that each node only uses greedy forwarding (i.e.

6Even the packet rate is more moderate, duty cycling on sensors alreadycut down the number of potential collisions.

forwarding packets to only the neighbours on the shortest pathto the sink).

1) For i ≥ 1, node(i, 0) will forward to (i-1, 0).2) For i, j ≥ 1, node (i, j) for i, j ≥ 1 will randomly

forward to (i-1, j) or (i, j-1) with equal probability.Fig. 15 shows that the gain of pseudo-random duty-cyclingscheme can be up to50%.

B. Battery Recovery Awareness

To extend the pseudo-random duty cycling scheme to takeadvantage of battery recovery effect, we propose a simplescheme byforced sleep. Suppose that a sensor has been awakefor more thanwmax consecutive slots at the current slot, then itmust go to sleep for the nextbmax slots for somebmax ≤ tsat.This allows sufficient battery recovery process to maximisethedeliverable energy in the sensor network. A typical settingwillbe wmax = 1 andbmax = tsat.

VI. L ATENCY ANALYSIS

Increasing the sleep periods of sensor to maximise batteryrecovery effect will inevitably increase the latency of deliver-ing a packet to the sink. In this section, we provide analyticalresults for the latency of data delivery in sensor networks withpseudo-random duty cycling.

Suppose nodei is waiting to forward data, which has a setof neighboursNi and degree asdi. Each of these neighboursis performing pseudo-random duty cycling with probabilityρdc, such that in one time slot, each node is awake with i.i.d.probabilityρdc, and is sleep of probability1-ρdc.

Let L(i) be the random number of slots ati beforeone of the neighbours of i wakes up. Therefore,L(i) = min{L1, L2, . . . , Ldi

}, where Lj is the waitingtime random variable for neighbourj ∈ Ni.

Theorem 4: (See [3])E[L(i)] =1

1 − (1 − ρdc)di

Note that the expected per-hop latency decreases quicklywith decreasing node degreedi. For extremely low dutycycling rate (i.e. small valueρdc), we obtain:

E[L(i)] ≈1

1 − (1 − ρdcdi)=

1

ρdcdi

Theorem 5: For 2D lattice, let`(i, j) be the end-to-endlatency from(i, j) to (0, 0).

(1) E[`(i, 0)] = 1 +i-1ρdc

andE[`(0, j)] = 1 +j-1ρdc

(2) For i, j ≥ 1, E[`(i, j)] ≤ 1 +i+j-1ρdc

The above theorems enable sensor network designers auseful tool to balance and optimise the trade-off betweenincreasing battery runtime of sensor networks and the incurredlatency of data delivery. Here we discuss a useful applicationof our theorem. Suppose that we are designing a sensor net-work with a latency constraint. We let the maximum tolerablelatency beE[L(i)], and obtain the correspondingρdc fromTheorems 4-5.


9

Λ=1

Λ=2

Λ=4

Λ=8

Always On

Duty-cycling

0 5 10 15Network Size0

100

200

300

400Network Life HslotsL

0 2 4 6 8Λ0

5

10

15

20

25

30

35Max GainH%L

Fig. 14. Considering linear network topology, andbmax = tsat = 3, we compare the network life of pseudo-random duty-cyclingscheme and the normalcase where all the sensor is always on.

Λ=1

Λ=2

Λ=4

Λ=8

Always On

Duty-cycling

0 20 40 60 80 100 120Network Size0

20

40

60

80

100Network Life HslotsL

0 2 4 6 8Λ0

10

20

30

40

50Max GainH%L

Fig. 15. Considering 2D lattice network topology, andbmax = tsat = 3, we compare the network life of pseudo-random duty-cyclingscheme and thenormal case where all the sensor is always on.

VII. C ONCLUSION

This paper examines the gain of battery recovery effectand provides analytical results to shed light on harnessingthe battery recovery effect in sensor networks. In particular,we analyse battery recovery effect in the presence of randomsensing activities, based on our experiments. We derive upperbounds of battery runtime and study the benefit of duty-cycling and buffering. We then propose a more energy-efficientduty cycling scheme that is aware of battery recovery effect,by extending the pseudo-random duty cycling scheme. Weprovide analytical results that predict the latency of datadelivery in sensor networks when considering battery recoveryoptimisation. In future work, we aim to study a broader scopeof optimising battery recovery effect in conjunction with avariety of qualities of service observed in sensor networks,such as coverage, connectivity, reliability.

REFERENCES

[1] D. Linden, Handbook of Batteries and Fuel Cells. McGraw-Hill, 1994.[2] J. Redi, S. Kolek, K. Manning, C. Partridge, R. Rosales-Hain, R. Ra-

manathan, and I. Castineyra, “Javelen: An ultra-low energyad hocwireless network,”Ad Hoc Networks Journal, vol. 5, no. 8, 2008.

[3] P. Basu and C.-K. Chau, “Opportunistic forwarding in wireless networkswith duty cycling,” in Proc. of ACM Workshop on Challenged Networks(CHANTS), September 2008.

[4] C.-K. Chau, M. H. Wahab, F. Qin, and Y. Yang, “Harnessing batteryrecovery effect in sensor networks,” Tech. Rep.

[5] C. Park, K. Lahiri, and A. Raghunathan, “Battery discharge characteris-tics of wireless sensor nodes: An experimental analysis,” in Proc. IEEESecon, 2005, pp. 430–440.

[6] J.F.Manwell and J.G.McGowan, “Extension of the kineticbattery modelfor wind/hybrid power systems,” inProc. EWEC, 1994, pp. 284–289.

[7] M. Doyle and J. S. Newman, “Analysis of capacity-rate data for lithiumbatteries using simplified models of the discharge process,” J. AppliedElectrochem, vol. 27, pp. 848–856, JUL 1997.

[8] T. F. Fuller, M. Doyle, and J. S. Newman, “Newman. modeling ofgalvanostatic charge and discharge of the lithium polymer insertion cell,”J. Applied Electrochem, vol. 140, pp. 1526–1533, 1993.

[9] C. F. Chiasserini and R. R. Rao, “A model for battery pulsed dischargewith recovery effect,” inProc. IEEE WCNC, 1999, pp. 636–639.

[10] C.-F. Chiasserini and R. R. Rao, “Improving battery performance byusing traffic shaping techniques,”IEEE J. Selected Areas in Communi-cations, vol. 19, pp. 1385–1394, JUL 2001.

[11] C. F. Chiasserini and R. R. Rao, “A traffic control schemeto optimizethe battery pulsed discharge,” inProc. MILCOM, vol. 2. IEEE, 1999,pp. 1419–1423.

[12] S. Sarkar and M. Adamou, “A framework for optimal battery manage-ment for wireless nodes,”IEEE J. Selected Areas in Communications,vol. 21, no. 2, 2002.

[13] T. L. Martin and D. P.Siewiorek, “Nonideal battery and main memoryeffects on CPU speed-setting for low power,”Very Large Scale Integra-tion (VLSI) Systems, IEEE Trans., vol. 9, pp. 29–34, FEB 2001.

[14] V. Rao, G. Singhal, A. Kumar, and N. Navet, “Battery model forembedded systems,” inProc. Intl. Conf. on VLSI Design, 2002.


battery recovery aware sensor networkspaws.kettering.edu/~ywang/file/wiopt.pdf · battery recovery...

Documents