1Pushback: A Hidden Markov Model Based Schemefor Energy Efficient Data Transmission in Sensor

NetworksSha Liu, Rahul Srivastava, Can Emre Koksal, and Prasun Sinha

Department of Computer Science and Engineering Department of Electrical and Computer EngineeringThe Ohio State University The Ohio State University

Columbus, Ohio 43210 Columbus, Ohio 43210{liusha,prasun}@cse.ohio-state.edu {srivastr,koksal}@ece.osu.edu

Abstract In sensor networks, application layer QoS require-ments are critical to meet while conserving energy. One of theleading factors for energy wastage is failed transmission attemptsdue to channel dynamics and interference. Existing techniquesare unaware of the channel dynamics and lead to suboptimalchannel access patterns. We propose a MAC layer solution calledpushback, that appropriately delays packet transmissions to over-come periods of poor channel quality and high interference, whileensuring that the throughput requirement of the node is met. Ituses a Hidden Markov Model (HMM) based channel model thatis maintained without any additional signaling overhead. Thepushback algorithm is shown to improve the packet success rateby up to 71% and reduce the number of transmissions neededby up to 38% while ensuring the same throughput.

Keywords - sensor networks; channel aware MAC; channelestimation; hidden Markov model

I. INTRODUCTIONSensor networking applications often have stringent require-

ments for QoS parameters such as throughput and delay. Inbattery operated sensor networks, such QoS requirements mustbe met while consuming the least amount of energy. Since ahigh percentage of the energy is spent on data communication,support for efficient and reliable communication is critical.However, high variability in channel quality caused by factorssuch as fading, mobility, and time-varying multiuser interfer-ence make it difficult to achieve those objectives. Indeed, Wooet al. [1], and Zhao and Govindan [2] have both observeda significant variability in link quality in wireless sensornetworks with radios in the 433 MHz band. The former paperpoints out that the instantaneous packet error probability variesby approximately 30% around its mean. The latter paper, aswell as Willig et al. [3], both show that the packet-errorstochastic process exhibits significant long-term dependence.

Without any effort for adapting to the variability, the systemresources are consumed highly inefficiently. Due to highpacket loss rates, a high fraction of the energy of a node isconsumed by multiple retransmissions per packet. However,in the currently available sensor hardware platforms (suchas MicaZ or iMotes from Crossbow Inc.), the computationalpower rules out sophisticated control actions for adaptation.Only very simple strategies (e.g., transmit or do not transmita packet at a given time) are implementable. Our objective

in this paper is to design an optimum packet transmissionstrategy that meets the required throughput constraint whileconsidering the dynamics of the channel.

The existing CSMA protocol is an example of an adap-tive transmission technique. The CSMA protocol uses carriersensing to avoid collisions and backoffs to address the problemof contention among nearby nodes. However, packet transmis-sions may fail due to cumulative interference from other nodesin the network. Indeed in our testbed experiments with Mica2nodes, we have observed that with interfering sources that aresufficiently far away, 69% of the packets for which the CSMAgranted a transmission permit are lost. From this example, wecan conclude that the combined effect of a large number ofinterfering sources can be very detrimental and the CSMAbased protocols - designed to suppress collisions - are noteffective in avoiding such losses. Immediate solution to thisproblem is reducing the carrier sense threshold that triggers abackoff and consequently increasing the carrier sense range.This, in effect, would enable a node to sense this combinedinterference and hidden terminals to some extent, and avoidpart of the losses. However, the increase of carrier sense rangemakes a node overly conservative with respect to interferenceand it leads to a lower effective throughput. Therefore, simpleadjustment of the carrier sense range is not sufficient to avoidtransmissions during poor channel conditions.

In the context of transmission rate adjustment for 802.11networks, several solutions have been proposed based onestimated channel conditions [4][7]. In contrast, our objectivein this paper is to optimize the energy consumption withconstraint on the throughput. Our solution methodology is alsodifferent as it explicitly models the channel based on rigor-ous estimation techniques. Existing MAC layer solutions forsensor networks such as [8][11], have not considered directmodeling of the time-varying channel quality for optimizationof transmission attempts. MAC layer protocols such as [12],[13] model the bursty nature of wireless channel as a Markovmodel. However these techniques do not directly incorporatechannel estimation into the transmission scheduler. Severalback-pressure based mechanisms have been proposed at thelink layer [14][17] to address high interference and networkcongestion. These approaches are orthogonal to our proposedsolution, and can be used in conjunction with our solution to

2CSMA with Exponential Backoff

Plain CSMA

CSMA withExponential Backoff andTransmission Pushback Pushback period

(based on channel estimation)

Channel Quality Indicator

(for illustration only) Poor

Transmitted packet Transmitted but dropped packet

Time

Good

CSMA Resumed

Fig. 1. Transmission Pushback: CSMA unnecessarily transmits during poor channel conditions. With exponential backoff, there will be fewer transmissionsduring poor channel conditions, however opportunities to transmit during good states will also be lost. With transmission pushback CSMA can avoid periodswith poor channel quality, while making use of good channel states.

improve performance, as shown in Section V.In this paper, we systematically study the problem of

addressing packet losses due to cumulative interference, andpropose a binary control technique over CSMA. Our approachis based on exploiting the temporal correlations of the interfer-ence process. We introduce a new concept called transmissionpushbacks, which refers to an appropriately computed delayintroduced at the MAC layer in order to avoid periods withbad-channel quality while considering a nodes throughput re-quirement. Therefore, we reduce the number of transmissionsper packet as well as the number of transmission attempts perunit time. In case of bursty losses, avoiding the bad channelstate may also lead to a higher throughput (visible at higherlayers) despite lower number of transmission attempts.

The main idea of transmission pushbacks is to defer packettransmission attempts for an appropriately selected periodupon failed packet transmissions. Figure 1 illustrates thebenefits of using transmission pushbacks in comparison withCSMA based approaches in the presence of time-varyingchannels. Plain CSMA leads to failed transmissions, and thuswasted energy, during periods with poor channel quality.CSMA with exponential backoff may reduce such failedtransmissions, but it also cuts down the transmission attempts,even at times of improved channel quality. Our proposedtransmission pushback mechanism predicts the duration forwhich the channel quality will remain poor. Thus, unnecessarytransmissions can be avoided to conserve energy and the goodchannel states are taken advantage of. The contrast is alsohighlighted in Table I which shows that Pushback along withCSMA with exponential backoff can handle various types ofpacket losses. Observe that as pushback operates over theCSMA algorithm, improvements of the CSMA mechanismsuch as [18] are orthogonal to pushback.

To determine the pushback time, we need to estimate thechannel quality and how it varies over time. We use anadaptive channel prediction technique, based on estimatingthe parameters of a simple hidden Markov model (HMM),which represents our channel. The parameters of the HMMare dynamically updated based solely on the binary ACK

TABLE ITYPES OF LOSSES ADDRESSED BY VARIOUS MECHANISMS

Mechanisms Designed for Designed for interferencecollision losses and channel losses

CSMA Plain Partially NoCSMA/EB Yes PartiallyCSMA/EB+Pushback Yes Yes

sequence (transmission success or failure) for the previouspacket transmissions. We choose the appropriate pushbackperiod by considering the throughput requirement measuredby the incoming data rate, and the predicted quality of thechannel. Such an adjustment in rate, based on the throughputrequirement is also seen in lazy packet schedulers (e.g., [19]).Designing an optimal sleep-wake scheduling solution thatintegrates with pushback is beyond the scope of this paper.The main complexity of that task is caused by the missedreceive opportunities: during pushback, if a node goes intosleep mode, then it will miss opportunities to receive packetsfrom other nodes. We assume that nodes are awake at all timesfor potential received packets. However, nodes do not spendextra energy in sensing the channel since the calculation ofthe deferral time depends solely on the ACK/NACK packets.The proposed approach is simple to implement over existingCSMA based MAC solutions, as well as queue and congestioncontrol algorithms. Therefore it is highly suited for existingsensor network platforms.

This paper makes the following contributions: Using data collected from a sensor network testbed,

temporal characteristics of the channel variations and theinterference are studied.

A novel concept called pushbacks is introduced, that isused to increase the packet success rate while consideringthe throughput constraint at each node.

Through simulations it is shown that significant gains inenergy and/or throughput can be observed in all scenariosusing the proposed technique.

The rest of the paper is organized as follows. Section IIpresents related work. Section III presents our approach tomodel the channel losses. Section IV presents a description of

3our pushback algorithm. Section V presents evaluation of theproposed scheme. Finally, Section VI concludes the paper andpresents pointers to future research directions.

II. RELATED WORKTransmission Rate Adaptation: Transmission strategiesbased on channel estimation has been considered in the contextof 802.11 [4][7] and other wireless [12], [13] networks.More specifically, the past packet success and failure reportshave been used to design strategies to dynamically adapt thephysical layer transmission rate to optimize the throughput.ARF [4] uses a heuristic to predict the channel quality based onpast transmission success and failure records, but it is obliviousto the underlying time-varying properties of the channel.RBAR [5] uses RTS/CTS to get immediate feedback fromthe destination to learn about the quality of the channel anddetermine the transmission rate. However, these packets havehigh overhead especially in sensor networks where the datapacket sizes are comparable to the size of RTS/CTS packets.In OAR [6] during good channel periods the transmitteropportunistically transmits multiple packets back-to-back ata high data rate. In contrast to the opportunistic nature of[6], our solution uses a rigorous channel model to predict theduration for which the channel will continue in a poor state.In [7], authors present a history based mechanism to predictthe quality of the channel and adjust the transmission rate.

In [12], [13], [20], [21], authors consider different oppor-tunistic transmission schemes which use a two-state Markovchannel similar to the one used in this work. In [20], thetransmitter simply retransmits a packet as soon as it is foundin error. The authors concentrate on calculating the latenessprobability of such packets, and do not use the ARQ infor-mation to determine whether the channel is good or bad fortransmission. On the other hand, [12], [13], [21], follow asimilar approach to ours by detecting a bad channel state uponreceipt of a NACK. However, the way they respond to a badchannel condition is different, since the transmission rate isreduced and the channel is probed periodically. The transmitterreturns to normal operation when the channel improves. Asmentioned previously, in the context of sensor networks, theoverhead of such probe packets can be substantial. In contrast,we develop an algorithm that estimates the channel conditionbased on ARQ-level information, which is freely available. Weuse the ARQ information to find the Maximum Likelihood(ML) estimate of the channel state and accordingly schedulethe transmission. The computational overhead of our approachis also minimal and our algorithm requires two table look-upsand three basic arithmetic operations. In [13], the transmitterswitches to a greedy mode (immediate retransmission on error)when the buffer level exceeds a certain threshold to ensure thatthe quality of service (QoS) requirement is being met. Ouralgorithm is able to dynamically adapt to the QoS requirementby predicting the incoming traffic flow rate and thus settingan optimal pushback period that supports this throughput.

Cognitive Medium Access (CMA) [22] is a design for cog-nitive radio which uses a two-state continuous-time Markovchain approximation for the channel. The main objectiveof this work is to optimize the throughput of a cognitive

(secondary) radio while limiting the interference experiencedby the WLAN (primary radio). The authors have used asense-before-transmit strategy in this case, which requires atransmitter design that incorporates a channel sensing mecha-nism. In addition, since CMA considers a frequency hoppingradio, it has an additional freedom to choose the channel totransmit. Our objective of optimizing energy consumption (bydeferring transmission) for a given throughput constraint isdifferent. Since, our work uses the already available ARQinformation for channel estimation, it does not rely on extraphysical layer information and it can be implemented onexisting radios without any hardware modification.

MAC and Link Layer for Sensor Networks: Various MAClayer protocols have been proposed to conserve energy insensor networks by sleep scheduling. These protocols canbe categorized as either synchronized or unsynchronized.SMAC [10], TMAC [23] and DMAC [11] are examples ofsynchronized MAC layer protocols. These MAC protocolsrequire periodic message exchange for synchronization. Inthese protocols nodes wake up for a short duration at synchro-nized times and sleep otherwise to conserve energy. In orderto address the overhead of synchronization, unsynchronizedapproaches have also been proposed. BMAC [24] and SP[25] are two such examples that make use of long preamblesbefore data transmission to ensure that the receiving node willreceive the packet. More recently, CMAC [9] and XMAC [8]have been proposed to avoid the overhead of long preambles.Anycasting has been considered in the joint design of MACand routing layers to operate in unsynchronized networks[26][29]. However, none of these solutions have consideredthe time-varying properties of the underlying channels in thedesign of the channel access mechanism.

In order to address high interference and network con-gestion, several back-pressure based mechanisms have beenproposed for sensor networks [14][17]. CODA [14] uses amoving average of channel samples to detect the onset ofcongestion and sends back-pressure messages to control thedata rate of upstream nodes. Fusion [15] uses the concept ofhop-by-hop flow control and prioritized MAC along with tokenbuckets to control the packet rate at each node. IFRC [16] andRAIN [17] use variations of the AIMD (Additive IncreaseMultiplicative Decrease) and the back-pressure mechanisms.Various schemes have been proposed, which select the backoffcounter [30] and the backoff window [31], [32] based on thechannel state. However, MAC protocols with backoffs tuned tochannel conditions do not address the time-scales associatedwith channel variations. Figure 1 illustrates that such protocolswill not be able to react quickly enough to changes in channelstate.

We conclude this section by observing that most of thesesolutions are unaware of the time-varying characteristics of thechannel, and hence still perform blind retransmissions obliv-ious to the current channel conditions. Even MAC protocolsthat set the backoffs according to the channel state do notaddress this problem completely. Solutions which considerthe time-varying channel incur a high overhead or requireadvanced transmitter design, both of which are not suitable

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Deferred Time Slots (m)

Condit

ional

Pro

babil

ity

of

Fail

ure

P(An+m

=F|An=S)

P(An+m

=F|An=F)

Fig. 2. Conditional probability of failure as a function of deferred time slotssetting p = 0.6 and = 0.8.

for sensor networks. On contrary, the pushback algorithmproposed in this paper can learn the channel characteris-tics and schedule retransmissions accordingly. Our solutionmethodology is also different as it uses rigorous estimationof dynamic channel properties. In fact, our solutions can beused in conjunction with the above link layer mechanisms andbring extra benefit as shown in our simulation results.

III. CHANNEL MODELIn this section we describe our channel loss model and

its parameters and give an experimental justification for ourmodel. We use this channel loss model to derive the theoreticalexpressions for Packet Success Ratio (PSR) and throughputas functions of channel and system parameters. We describehow to estimate these parameters based on the availablemeasurements at the sensor nodes in the next section.

A. Channel ModelLet An, n > 1 be the process, which takes on an S or

an F depending on whether a packet transmitted at time nis successfully decoded at the receiver or not. We assume thatonly one packet can be transmitted in each time slot and thatAn is a wide-sense Markov of order 1 for the packet errorprocess. We will discuss the validity of this assumption later,but first we describe An further.

A sequence An, n 1 is said to be wide-sense Markovif the probability of a future value, An+m, is completelydetermined by its most recent value, i.e. An and the timedifference (m) between the two events. The autocovariancefunction for such a process is exponential. More specifically,suppose the process is in steady state1 at time n and letP (An = F) = p. Then the autocovariance function of Anis KA(m) = p(1 p)|m| for some , || < 1. Here p is thelong-term loss probability and quantifies the coherence orcorrelation between a successful (failed) transmission in thefuture based on the present observation. The loss probabilityp increases with the number of interfering users and the noise

1We assume that the process started at time n = . In practice the datatransmission is only finite, however we make this technical assumption, sincewe do not have any information about the initial channel state.

in the channel and is a measure for the burst length for thefailed transmissions.

For this wide-sense Markov process, the probability of asuccessful (failed) transmission in a future time slot, condi-tioned on a successful (failed) transmission in the present slot,is unique (Appendix I):

P (An+m = F|An = S) = p(1 m) (1)P (An+m = S|An = S) = 1 p(1 m) (2)P (An+m = F|An = F) = p + (1 p)m (3)P (An+m = S|An = F) = 1 p (1 p)m. (4)

Hence only a pair of parameters is sufficient to representthe channel with the first order Markov assumption. For thepurpose of illustration, the conditional probabilities of failurefor p = 0.6 and = 0.8 are plotted in Fig. 2. The deferredtime slots represents the number, m, of time slots waitedbefore the next transmission attempt after an event S or F.

We can form an underlying Markov chain corresponding tothis wide-sense Markov process as follows. The Markov chainhas two states S (Good) and F (Bad) and the chain makesa transition between these states depending on An takingon an S or an F as shown in Figure 3. One can evaluatethe parameters p and for the associated Markov processgiven the transition probabilities, x and y for this Markovchain and vice versa as shown in Section III-B. The channelmodel is an HMM, since x and y are unknown initially andwe estimate them based on the observed values of An usinga maximum likelihood estimator. Based on these estimatedvalues, we calculate the two channel parameters and p,which is detailed in Section IV. Note that the reason forestimating x and y initially is due to the simplicity of thetask (based on observation of An). The reason why we pursueour analyses with and p afterwards, instead of x and y, isthat the performance metrics of the pushback algorithm aretied to and p more naturally.

In fact, HMMs have been used to model the channelbehavior previously by representing the (bit or packet level)error process in wireless communications [33][36]. Whilenot as simple as a Bernoulli or an independent loss channelmodel, Markov models are more capable of characterizingthe statistical dependencies which might occur in a wirelesschannel.

From the two curves in Fig. 2, one can see the reasoningbehind choosing a pushback duration conditional on an eventF only. If we schedule the next packet for immediate trans-mission (i.e., m = 1) after an S, we have the best chance ofobserving another S. Intuitively, we are taking advantage of thegood channel state. On the other hand, if we defer schedulingthe transmission (i.e., m > 1) of the next packet after anF, we lower the probability of failing in that transmission.The longer the deferral time, the higher the probability of anS in the next transmission. However, waiting indefinitely cancause the throughput to drop significantly. So we need to strikea balance between these two requirements, throughput andprobability of success. Hence, with the Markov channel model,the problem reduces to finding the appropriate pushback periodafter a failed transmission. In the next subsection, we will

5S F

x

y

1y

1x

Fig. 3. Markov chain representation of the channel.

derive the expressions for the throughput and packet successrate for this scheme using our channel model.

B. Channel ParametersTo find the channel parameters, packet success ratio and

throughput, we sketch the Markov chain associated with ourfirst order Markov process. Our main objective here is to findthe throughput as a function of the number of deferred timeslots, k, on a transmission failure2. Once we have this function,we can choose k according to the desired throughput basedon the incoming data rate. To validate this model using realdata, we also find the expression for the PSR.

Our Markov chain has two states, S and F as illustrated inFig. 3. The current state is S if the final packet transmissionis successful and F, otherwise. Note that a transition does notnecessarily occur every time slot, rather it occurs for everypacket transmission attempt. Since we schedule a transmissionimmediately after a successful event, the expression for x isobtained by substituting m = 1 in (1). Direct application of(3) with m = k gives the expression for y.

x = P (An+1 = F|An = S) = p(1 ) (5)y = P (An+k = F|An = F) = p + (1 p)k (6)

Notice that the transition probabilities at state F are functionsof k as well as p and . This is due to the effect of thepushback period of k time slots after the failed transmissionattempts. The associated steady state probabilities are thereforefunctions of k as well, and these probabilities for state S andstate F are respectively,

piS(k) =(1 p)(1 k)

p(1 ) + (1 p)(1 k)(7)

piF(k) = 1 piS(k).

We define the packet success ratio (PSR) as the total fractionof the packets that are successfully transmitted, i.e., it is equalto the steady state probability, piS(k) of state S.

Likewise, we define the throughput () as the number ofsuccessful packet transmissions in a unit time slot. To formu-late an expression for throughput, consider the following: ona transmission attempt, we wait for k time slots in state F and1 time slot in state S for the next transmission attempt. Thus,the average number of slots per attempt is piS(k) + kpiF (k).Consequently the number of packet transmissions per slot,

X(k) =1

piS(k) + kpiF (k)=

p(1 ) + (1 p)(1 k)

kp(1 ) + (1 p)(1 k).

(8)

2Upon a successful transmission, the deferral time is 1 (no deferral).

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Th

rou

gh

pu

t(

)

1

p = 0.2 = 0.8

1

p = 0.2 = 0.5

1

p = 0.8 = 0.8

1

p = 0.8 = 0.5

1

Fig. 4. Theoretical throughput () achieved by deferring transmission on apacket loss for different values of p and .

The resulting throughput, (k), is thus

(k) = piS(k)X(k)

=(1 p)(1 k)

kp(1 ) + (1 p)(1 k). (9)

The theoretical value of the throughput () is plotted asa function of the pushback period k in Fig. 4 for differentchannel parameters p and . In Fig. 4, by changing the valueof p (keeping constant), we can see that a channel with lowerp gives a better throughput performance. This trend is expectedas we have defined p as the probability of transmission failureand a channel with a smaller p will have a lower chance oftransmission failure which leads to a higher throughput. Forthe same value of p, larger implies a higher correlation inthe channel quality. Since pushback takes advantage of thecorrelation in channel quality to schedule transmissions, wecan see that the throughput performance of a channel withhigher correlation will be better with transmission pushbackthan a channel with lower correlation.

We tested the validity of our Markov model using anexperimental setup in the Kansei testbed [37] by setting upa wireless link between two sensor motes. This link wasencircled with seven sensor motes spread around the perimeterof a 20 m2 area. We measured the packet success rate betweentwo motes, while the rest of the motes acted as sources ofinterference. For this experiment, the wireless link transmitted36 byte packets at 100 ms interval. We programmed the nodescausing interference to transmit bursts of packets once everysecond. The burst size was selected according to a uniformdistribution between [0,15]. We estimated the two parameters, and p using the ACK-level data of the entire trace of 30mins. Note that the purpose of this experiment was to validatethe model. In our actual algorithm, the estimation of the twoparameters is much simpler and does not depend on a longtrace of data. The theoretical packet success rate based onthe estimated and its actual experimental value are plottedin Fig. 5 as a function of k. This plot gives credence to theMarkov model.

IV. THE PUSHBACK ALGORITHM

The objective of the pushback algorithm is to estimate theperiod for which the channel will remain in a poor state anddefer retransmissions accordingly in order to conserve energy.

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Act

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PSR

Actual PSRTheoretical PSR Fit

Fig. 5. Comparison of the actual PSR gain achieved by our pushbackalgorithm and the theoretical fit using (7).

In addition, the algorithm must provide similar throughput asCSMA for a reduced number of transmission attempts.

The proposed pushback algorithm is based on CSMA. If atransmission is successful, the next transmission is scheduledby CSMA. However, in case of a failed transmission, the nexttransmission is pushed back by k slots after which CSMAtakes effect. Note that a pushback slot is a packet slot, i.e.,the time it takes to transmit a packet. Therefore it is differentfrom the contention slot of CSMA. Also, even though thevalue of k is generated deterministically, the randomness of thebackoff period (in contention slots) of CSMA avoids persistentpushbacks caused by local synchronization of nodes due tosimilar channel conditions.

When nodes boot up, an initial value kinit is assigned tok, and then k is recalculated periodically each time the m-th (predefined) transmission failure happens using a simplemechanism based on the estimates of the channel parametersand throughput constraint. Our computation is both practical toimplement and is also shown to perform well using simulationsin Section V.

The proposed mechanism for computing k is based on theformulation presented in Section III. First, k is set to aninitial value kinit, and based on the ACK-level observations ofsuccess and failure in the recent past, a maximum likelihood(ML) estimation of parameters and p is made. In fact,estimating the transition probabilities of the Markov chain(parameters x and y in Fig. 3) is sufficient for the desired MLestimation. Indeed, given the ML estimates x and y (of x and yrespectively), we show in Appendix II that the solution (, p)to the system of Equations (5) and (6) gives the ML estimatesof and p which characterize the channel. In addition, toensure that a node can sustain the incoming rate of packets,the computation of k must take the incoming packet rate intoaccount. We use the running average of the incoming packetrate, new = /te + (1 )old, to represent the throughputconstraint. Here new (old) is the new (previous) estimateof the throughput requirement, te is the time elapsed sincethe last packet arrival and is smoothing factor. Using new(throughput constraint), and p, Equation (9) can be used tocompute the new value of k.

To avoid the complexity of direct computation of k, we

TABLE IILOOKUP TABLES USED IN THE PUSHBACK ALGORITHM.

Table Equations PurposeT(x, y, k) Eqns. (5), (6) To compute for given x, y and k.Tk(p, , ) Eqn. (9) To compute k for given p, and .

propose the use of look-up tables. The first table T(x, y, k)contains the values of corresponding to k and discretized xand y. The second table Tk(p, , ) contains the values of (k)corresponding to k and discretized and p. A brief descriptionof the various tables used is given in Table II. These tables willnot change during the operation of the node, so they can becomputed offline and uploaded. The available storage spaceson the nodes will determine the size of the tables. From ourexperimental experience, it should suffice to have a 102020table. For instance, this table can have 10 values of k (2 to11), 20 values of p (0 to 0.95 in increments of 0.05) and 20values of (0 to 0.95 in increments of 0.05). These numberscould be stored as integers between 0 and 100. Hence, the twotables would take 8K bytes.

In summary, upon the m-th transmission failure, functionPushback() (Algorithm 1) is called. In this algorithm, TheML estimates x and y are calculated in lines 3 and 4. A tablelookup is employed to find the value of corresponding to x, yand k, and then p can be calculated according to Equation (5).Finally the pushback period k is estimated using another tablelookup with the appropriate values of p, and .

Algorithm 1: Pushback()if (failureCount = m) then1

failureCount 0;2x Number of SF transitionsTotal number of stays in S states ;3y Number of FF transitionsTotal number of stays in F states ;4 T(x, y, k);5p x/(1 );6k Tk(p, , );7

end8Delay the retransmission for k slots;9

A. Remedial MechanismsThe pushback algorithm above can work well if the real

packet loss pattern is captured well by our channel model in-troduced earlier and the transition probabilities are accuratelymeasured. However, either of them may deviate from reality,in which case the throughput may not be maintained if k ischosen too aggressively. Hence, we introduce two remedialmechanisms to solve such problems.

1) Measuring Actual Pushback Amount: In our pushbackalgorithm, the delay amount, k slots, is calculated according tothe state transition probabilities and the throughput constraint.However, after delaying k slots, nodes may need to delaytheir retransmissions further due to contentions from othersenders. This could lead to the loss in throughput since thedelaying amount is longer than expected by the model. Hence,the running average of the difference between the calculated

7delay amount and the actual delay amount is maintained, andsubtracted from the newly calculated k.

2) Controlling the Pushback Amount at the InterfaceQueue: Once our channel model deviates from the actualchannel, simply adjusting the k as in Section IV-A.1 may stillnot work very well. To cope with such situations, we let theinterface queue impose a pushback control policy to speed upthe packet forwarding once the queue is excessively built up.This policy simply commands the pushback algorithm to fallback to CSMA (using k = 1) if the queue length is above acertain threshold. In our evaluations, this value is set to halfof the queue capacity.

V. SIMULATION EVALUATIONWe conduct simulations in ns2 [38] to compare the per-

formance of our pushback algorithm with plain CSMA withand without binary exponential backoff in wireless sensor net-works. Here the CSMA without exponential backoff (denotedas CSMA) simulates BMAC, the default MAC layer protocol,while CSMA with exponential backoff (denoted as CSMA/EB)represents other general CSMA protocols. We also studythe performance improvement when the pushback algorithmworks jointly with other congestion control mechanisms suchas based on rate control and back-pressure. In this section, theradio propagation model used in our simulations is introduced,followed by the simulation results.

A. Radio ModelThe CSMA (MAC and PHY) protocol simulated in ns2

has two shortcomings. First, it fails to consider interferencefrom nodes outside the carrier sensing range. However, thecumulative interference from more than one node sufficientlyfar away may still affect packet receptions. Second, it does notcalculate the packet loss probability according to the Signal-to-Noise Ratio (SNR). In our simulations, we extended thephysical layer of ns2 to combine all sources of noise andinterference to calculate the SNR and then use Equation (9)in [39] to calculate the packet success rate.

In our simulations, we use a radio propagation model basedon the shadowing model implemented in ns2. Consequently,the received power level at a receiver is determined by[

Prec(d)

P rec(d0)

]dB

= 10 log

(d

d0

)+ XdB,

where Prec(d) is the received power at this receiver whichis at a distance d away from the sender, is the path lossexponent, P rec(d0) is the average received power level at areference distance d0, and XdB is a Gaussian random variablewith mean 0 and standard deviation dB (called shadowingdeviation).

In standard ns2, XdB is independent for different packets.However, XdB usually varies according to some random pro-cess (see e.g., [39] [40]) and we use an order 1 autoregressivemodel (AR(1)) as follows.

XdB(t) = XdB(t 1) + Z(t),

where is called the channel coherence coefficient whichquantifies the memory in channel variations and Z(t), the

TABLE IIISIMULATION PARAMETERS

Packet Size 100 bytes Ack Size 5 bytesBandwidth 19.2 Kbps Transmit Power 0 dBmBackoff Slot 0.4167 s Pushback Slot 18.33 ms 4 [39] dB 4 0.8 Data Rate 0.1 packet/sec.Number of nodes 25 (5 5) Node separation 45 m

error term, is independently and identically distributed withnormal distributionN (0, 2Z). To make the variance of XdB(t)independent of , we choose Z = dB

1 2. In our

simulations, the time is discretized such that 1 slot is roughlyequal to the average time to transmit a packet, and the valueof XdB(t) is constant within a time slot. Note that in themodified shadowing model, if the autoregression coefficient = 0, then the model just falls back to the default shadowingmodel provided by ns2. In our evaluation we also study theimpact of different values of the channel coherence coefficient,.

B. Simulation EvaluationsWe conduct simulation evaluations on our pushback algo-

rithm in data gathering networks. The node located at onecorner of the area serves as the sink, while all other nodesgenerate data periodically to be sent to the sink. We evaluatethe performance of all three protocols (CSMA, CSMA/EB andCSMA/EB with Pushback) under different data rates, channelcoherence coefficients , shadowing deviations, network sizes,node densities in grid and random topology, and packet sizes.The metrics focused on in this study include the followingfour.

Throughput: number of packets received at the sink in500 seconds.

Packet success rate (PSR): average success rate for eachtransmission attempt in the network.

Transmission tax: average number of transmissions (in-cluding retransmissions) in the network required to de-liver one packet to the sink.

Normalized delay: average delay per hop.Each set of simulations is carried out for 10 times with dif-ferent random seeds, and the error bar denoting the minimumand maximum values of each simulation set is also plotted.In all simulations, the default parameter values simulating theXSM nodes [41] are summarized in Table III. In this paper,we show some relevant graphs. A more elaborate set of graphscan be found in the technical report [42].

1) Data Rates: The pushback algorithm takes advantage ofthe flexibility provided by nodes that can afford to delay theretransmissions (e.g., the ones away from the sink) withoutreducing the throughput. On the other hand, some nodes (e.g.,those close to the sink) may have very small room for push-back (i.e., k 1) since they need to accommodate higher datarates. In this section, we evaluate the pushback algorithm fordata generation rate at each non-sink node varying from 0.01packets/second (pps) to 0.2 pps. Fig. 6 shows the simulationresults, from which it can be observed that when data rateis low (< 0.15 pps in this case), the pushback algorithm

8 0

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0

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60

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Nor

mal

ized

Del

ay

Data Rate (Packets/Second)

PushbackCSMA/EBCSMA

(d) Normalized Delay

Fig. 6. Simulation results for various data rates.

0

0.1

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

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PushbackCSMA/EB

CSMA

(a) Packet Success Rate

0

200

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600

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1000

1200

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Thro

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PushbackCSMA/EB

CSMA

(b) Throughput

Fig. 7. Simulation results for various channel coherence coefficients in a 5 5 network.

9can improve the PSR by 51% and 71% when compared toCSMA/EB and CSMA respectively. Observe that the networkthroughput is saturated beyond 0.15 pps data rate. For evenhigher data rates, the improvement in PSR is smaller, but thethroughput is higher than the CSMA protocols. This impliesthat with pushbacks the queue drop rates are reduced. Similarimprovement in transmission tax can also be observed. Notethat for data rates higher than 0.18 pps the queuing delaycaused by the pushback algorithm results in higher normalizeddelay. The queuing delay is also caused due to the higherthroughput provided by pushback. In this region, the networkscapacity is reached, as depicted by the throughput curve. Ifapplications can tolerate delay then even at data rates beyondthe networks capacity, pushback is preferable over CSMAprotocols.

The peak throughput point is the critical point beyondwhich all protocols start to experience packet losses due toqueue overflows. In such an event of congestion, many ofthe lost packets are lost either at the intermediate nodesor at nodes closer to the sink. Consequently, the overallthroughput decreases, since the lost packets consume resources(e.g., queue occupancy, spectrum) along the path, withoutan ultimate positive contribution to the throughput. In otherwords, the resources consumed by lost packets can be viewedas wasted opportunities for other packets and thus the end-to-end throughput decreases at the point we start to observepacket losses. On the other hand, as the arrival rate is furtherincreased, the throughput increases slightly. This is because, inthe event of heavy congestion, packets tend to be lost closerto their sources before they consume much of the networkresources.

2) Channel Coherence Coefficient: The pushback algo-rithm is very effective in the presence of temporal correla-tion in channel losses. Such correlations may be caused bychannel coherence or correlated interference. In this section,we evaluate the performance of the pushback algorithm underchannel coherence coefficient ranging from 0 to 0.8. Fig. 7shows the simulation results. It can be seen that by utilizing thepushback algorithm, the improvement in PSR over CSMA/EBis between 46% to 63%, and it increases with . Meanwhile,the throughput is maintained. As expected, the pushback algo-rithm is more effective when the channel is more coherent. Theresults also show that even in case of low channel coherence,our pushback algorithm can bring significant benefit in PSR.

3) Shadowing Deviation: In our simulations, the shadowingdeviation dB is a major factor besides the interference thataffects packet receptions. According to the shadowing radiopropagation model, larger shadowing deviation causes morepacket losses. In this section, we evaluate the performance ofthe pushback algorithm for dB values as suggested in [40].Fig. 8 shows the results for the two evaluation metrics. Theresults show that the PSR for all three protocols decreases withdB, but the pushback algorithm can provide improvement ofup to 91% compared to CSMA/EB. For dB = 0 in which casethe shadowing model does not directly cause packet losses, ourpushback algorithm can still improve the PSR from 66% to76% (or 15% improvement). For throughput, we can observethat the channel capacity is reached for larger dB with the

pushback algorithm, which brings steady improvement of upto 27% than CSMA and CSMA/EB. It can observed that forlarge dB, CSMA/EB has lower throughput than CSMA dueto the inefficiency of the exponential backoff mechanism.

4) Network Size: In a large network, even though the rateof data generated at each node may be low, the cumulativedata rates at nodes close to the sink may still be high. Hence,we evaluate the pushback algorithm for various network sizesin this section. We vary the number of rows and columns ina grid network from 2 to 10 (i.e., the network size variesfrom 4 to 100 nodes) while keeping other parameters fixed asin Table III. The results are shown Fig. 9. One can observethat the pushback algorithm can bring the most benefit inPSR when the network size is smaller than 64. For largernetworks, the pushback algorithm can still provide overallimprovement due to the relatively lower data rates at nodesnot in the hot-spots. Throughput for large network sizes canalso be improved.

5) Node Density in Random Topology: We evaluate theperformance of the pushback algorithm with nodes randomlyplaced in a 150 m 150 m area. We vary the numberof nodes from 25 to 100 with other parameters fixed as inTable III. As shown by the results in Fig. 10, even though theabsolute improvement in PSR decreases with the increase ofnode density, steady improvement of about 33% is maintainedexcept for the case of 100 nodes which represents quite highnode density and thus high data rates at nodes in hot-spots. Thepushback algorithm can lead to higher throughput comparedto CSMA.

6) Packet Size: Larger packet size implies smaller controloverhead of header size and acknowledgment. But using largerpacket size usually also means the transmission is morevulnerable to errors. Hence, we evaluate the performance ofthe three protocols with various payload sizes in this sectionand the results are summarized in Fig. 11. It can be seenthat with the increase in packet size, the PSR decreases forCSMA and CSMA/EB. But for the pushback algorithm, thePSR is steady, except for packet sizes as large as 250 bytes,and the improvement is more significant for medium packetsizes. For the packet size of 250 bytes, the SNR with fixednode separation is not sufficient to sustain a high success rate,which leaves smaller room for improvement.

7) Bandwidth: In this section, we evaluate the performanceof the pushback algorithm with different bandwidths rangingfrom 19.2 kbps provided by XSM nodes [41] to 250 kbpssupported by IEEE 802.15.4. The results plotted in Fig. 12show that the pushback algorithm can provide improvement inPSR, but the improvement is smaller for higher rates. However,for radios with higher rates, if the packet size is proportionallyincreased, we can still observe similar improvement as smallpacket sizes in Fig. 12.

8) Cooperation with Rate Control and Back Pressure:Many link layer protocols [14][17] use packet rate controland back-pressure techniques to mitigate the congestion in thenetwork. These techniques can work in conjunction with andbenefit from the pushback algorithm. To show this, we imple-ment and test the rate limiting and back-pressure mechanisms(denoted as RC/BP) proposed in [15] along with the pushback

10

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

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CSMA

(a) Packet Success Rate

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0 2 4 6 8 10 12

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ughp

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Shadowing Deviation

PushbackCSMA/EBCSMA

(b) Throughput

Fig. 8. Simulation results for various shadowing deviations dB in a 5 5 network.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0 10 20 30 40 50 60 70 80 90 100

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(a) Packet Success Rate

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1000 1200 1400 1600

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CSMA

(b) Throughput

Fig. 9. Simulation results for various network sizes.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

100 81 64 49 36 25

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(a) Packet Success Rate

0

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2000

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CSMA

(b) Throughput

Fig. 10. Simulation results for various node densities in a random topology.

11

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Fig. 11. Simulation results for various packet sizes.

0

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(b) Throughput

Fig. 12. Simulation results for various bandwidth.

algorithm. Fig. 13(a) shows the PSR when CSMA/EB andRC/BP are used with and without the pushback algorithmunder different data rates. It can be seen that the two metricshave similar variation trends as in Fig. 6, which shows thatthe pushback algorithm can still bring significant benefit whenother congestion control mechanisms are used in conjunction.The results for throughput (Fig. 13(b)) also show similar trendsas in Fig. 6.

VI. CONCLUSIONS AND FUTURE RESEARCHThis paper introduces a channel aware transmission push-

back mechanism to optimize energy efficiency. Using a simplebut effective packet loss model, this approach does not incurhigh computational overhead on the sensor nodes. Using simu-lations we show that the pushback algorithm can significantlyimprove the packet success rate and the energy tax withoutdegrading the throughput. In addition, this algorithm is easy toimplement over existing MAC and link layer protocols. Hence,we conclude that the pushback algorithm is highly suitable forenergy constrained wireless sensor networks.

Future research directions based on the concepts introducedin this paper are described below.

Push-Backs in Other Networks: This paper has focusedon the application of the novel concept of pushbacks in thecontext of sensor networks. However, the concept of pushbackswhen applied to other networking scenarios such as ad-hocnetworks and mesh networks, can be used to optimize otherparameters such as the number of transmissions. In thesenetworks, reduced interference due to reduction in number oftransmission is expected to result in increased throughput.

Joint Optimization of Transmission Parameters: In thiswork we have used channel quality prediction to appropriatelydelay transmissions. However, channel quality prediction canbe used to adjust other parameters such as physical layer datarate, transmission power, and carrier-sense threshold, some ofwhich are inter-related.

VII. ACKNOWLEDGMENTSThis material is based upon work partially supported by

the National Science Foundation under Grants CNS-0546630

12

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(b) Throughput

Fig. 13. Simulation results for the cooperation of the pushback algorithm and RC/BP.

(CAREER Award), CNS-0721434, CNS-0721817 and CNS-0403342. Any opinions, findings, and conclusions or recom-mendations expressed in this material are those of the author(s)and do not necessarily reflect the views of the National ScienceFoundation.

APPENDIX IDERIVATION OF THE CONDITIONAL PROBABILITIES

In this section we derive the conditional probabilities ofa wide-sense Markov process given in Eqns. (1)(4). Awide-sense Markov process has an exponential autocovariancefunction. In our analysis, we assume that the autocovariancefunction is of the form KA(m) = p(1 p)|m| and theunconditioned probability of failure (P (An = F)) and success(P (An = S)) are p and 1 p respectively.

First, we derive the probabilities conditioned on failure,i.e., Eqns. (3) and (4). To facilitate the evaluation of theexpectation, we code the event of Failure (F) as 1 and theevent of Success (S) as 0. Covariance is defined as,

KA(m) = E[An+mAn] E[An+m]E[An]=

x{0,1}

y{0,1}

xyP (An+m = x|An = y) P (An = y)

x{0,1}

xP (An+m = x)

y{0,1}

yP (An = y)

= P (An+m = 1|An = 1) p p2. (10)

For m 0, we can compare Eqn. (10) to the autocovariancefunction for a wide-sense Markov process,

KA(m) = p(1 p)m = P (An+m = 1|An = 1) p p2,

to get Eqn. (3) or P (An+m = 1|An = 1) = p +(1 p)m. Using the fact, P (An+m = 0|An = 1) =1 P (An+m = 1|An = 1), we get Eqn. (4) orP (An+m = 0|An = 1) = 1 p (1 p)m.

To derive the probabilities conditioned on success, i.e.,Eqns. (1) and (2), we follow the same steps with minormodifications. In this case, we code the event of Success (S)

as 1 and the event of Failure (F) as 0. From the definitionof Covariance, we get,

KA(m) = p(1 p)m

= P (An+m = 1|An = 1) (1 p) (1 p)2. (11)

On simplification of Eqn. (11), we get Eqn. (2) orP (An+m = 1|An = 1) = 1 p(1 m). Finally,P (An+m = 0|An = 1) = 1 P (An+m = 1|An = 1) givesEqn. (1) or P (An+m = 0|An = 1) = p(1 m).

APPENDIX IIMAXIMUM LIKELIHOOD ESTIMATION OF THE CHANNEL

PARAMETERS

In this section we consider the ML Estimation of theMarkov channel parameters, , p, based on the binary errorrealization sequence. We assume that the initial state of thechain is picked according to its steady state distribution.

Suppose a transmitter transmits n 1 packets and observesthe associated ACK sequence. Let the number of successfultransmissions be Ns (i.e., the number of failed transmissions isNf = nNs), the number of successive successful transmis-sions be Nss and the number of successive failed transmissionsbe Nff . First we find the estimates of the Markov chaintransition probabilities x, y based on the observations Ns =ns, Nss = nss and Nff = nff . For notational simplicity,we drop the random variables and use P (nss) instead of

13

P (Nss = nss) for instance. The ML estimate for the pair

(xML, yML) = arg max(x,y)(0,1)

P (ns, nss, nff | x, y)

= arg max(x,y)(0,1)

P (nss, nff | ns, x, y) P (ns|x, y)

= arg max(x,y)(0,1)

(nsnss

)(1 x)nssxnsnss

(I)

(n nsnff

)(1 x)nssynff (1 y)nnsnff

(II)

P (ns | x, y) (III)

. (12)

The value of x (0, 1) that maximizes Term (I) is xm = 1nssns

and the value of y that maximizes Term (II) is ym = nffnns .If we show

(xm, ym) = argmax(x,y)

P (ns | x, y) , (13)

then (xML, yML) = (xm, ym). For n 1, P (Ns = ns | x, y)is maximized for ns = npis = n 1yx+1y . Thus, if we verify

nsn

=1 ym

xm + 1 ym,

then (13) is proved. Note that the number of transitions fromstate S to state F is nsf = ns nss and the number oftransitions from state F to state S is nfs = nf nff .Since nsf = nfs 1, nsfnfs 1 as n (x, y (0, 1),therefore nsf , nfs ). Consequently

1 ymxm + 1 ym

=1

nffnns

1 nssns

+ 1nf f

nns

=nfs/nf

nsf/ns + nfs/nf

=1/nf

1/ns + 1/nf=

nsn

Since p, is deterministic given x, y, the ML estimatespML, ML can be found by solving the system of equations

1nssns

= pML(1 ML)

nffns

= pML + (1 pML)kML.

REFERENCES[1] A. Woo, T. Tong, and D. Culler, Taming the underlying challenges of

reliable multihop routing in sensor networks, in Proc. of ACM SenSys,Oct. 2003, pp. 1427.

[2] J. Zhao and R. Govindan, Understanding Packet Delivery Performancein Dense Wireless Sensor Networks, in Proc. of ACM SenSys, Oct.2003, pp. 113.

[3] A. Willig, M. Kubisch, H. Christian, and A. Wolisz, Measurements of aWireless Link in an Industrial Environment Using an 802.11-CompilantPhysical Layer, IEEE Trans. Ind. Electron., vol. 49, no. 6, pp. 12651282, Dec. 2002.

[4] A. Kamerman and L. Monteban, WaveLAN II: A High-performanceWireless LAN for the Unlicensed Band, in Bell Labs Technical Journal,vol. 2, no. 3, 1997, pp. 118133.

[5] G. Holland, N. Vaidya, and P. Bahl, A Rate-Adaptive MAC Protocolfor Multi-Hop Wireless Networks, in Proc. of ACM MOBICOM, Jul.2001, pp. 236251.

[6] B. Sadeghi, V. Kanodia, A. Sabharwal, and E. Knightly, OpportunisticMedia Access for Multirate Ad Hoc Networks, in Proc. of ACMMOBICOM, Jul. 2002, pp. 2435.

[7] S. H. Y. Wong, H. Yang, S. Lu, and V. Bharghavan, Robust RateAdaptation for 802.11 Wireless Networks, in Proc. of ACM MOBICOM,Sept. 2006, pp. 146157.

[8] M. Buettner, G. V. Yee, E. Anderson, and R. Han, X-MAC: A ShortPreamble MAC Protocol for Duty-Cycled Wireless Sensor Networks,in Proc. of ACM SenSys, Nov. 2006, pp. 307320.

[9] S. Liu, K.-W. Fan, and P. Sinha, CMAC: An Energy Efficient MACLayer Protocol Using Convergent Packet Forwarding for Wireless SensorNetworks, in Proc. of IEEE SECON, Jun. 2007.

[10] W. Ye, J. Heidemann, and D. Estrin, Medium Access Control with Co-ordinated Adaptive Sleeping for Wireless Sensor Networks, IEEE/ACMTrans. Networking, vol. 12, no. 3, pp. 493506, Jun. 2004.

[11] G. Lu, B. Krishnamachari, and C. S. Raghavendra, An AdaptiveEnergy-Efficient and Low-Latency MAC for Data Gathering in WirelessSensor Networks, in Proc. of IPDPS, Apr. 2004, pp. 224231.

[12] M. Zorzi and R. R. Rao, Error Control and Energy Consumptionin Communications for Nomadic Computing, IEEE Trans. Comput.,vol. 46, no. 3, pp. 279289, Mar. 1997.

[13] C.-F. Chiasserini and M. Meo, Impact of ARQ Protocols on QoS in3GPP Systems, IEEE Trans. Veh. Technol., vol. 52, no. 1, pp. 205215,Jan. 2003.

[14] C.-Y. Wan, S. B. Eisenman, and A. T. Campbell, CODA: CongestionDetection and Avoidance in Sensor Networks, in Proc. of ACM SenSys,Oct. 2003, pp. 266279.

[15] B. Hull, K. Jamieson, and H. Balakrishnan, Mitigating Congestion inWireless Sensor Networks, in Proc. of ACM SenSys, Nov. 2004, pp.134147.

[16] S. Rangwala, R. Gummadi, R. Govindan, and K. Psounis, Interference-aware Fair Rate Control in Wireless Sensor Networks, in Proc. of ACMSIGCOMM, Sept. 2006, pp. 6374.

[17] C. Lim, H. Luo, and C.-H. Choi, RAIN: A Reliable Wireless NetworkArchitecture, in Proc. of IEEE ICNP, Nov. 2006, pp. 228237.

[18] M. Heusse, F. Rousseau, R. Guillier, and A. Duda, Idle Sense: AnOptimal Access Method for High Throughput and Fairness in RateDiverse Wireless LANs, in ACM SIGCOMM, Nov. 2005, pp. 134147.

[19] B. Prabhakar, E. U. Biyikoglu, and A. E. Gamal, Energy-EfficientTransmission over a Wireless Link via Lazy Packet Scheduling, in Proc.of IEEE INFOCOM, Apr. 2001, pp. 386394.

[20] M. Zorzi and R. R. Rao, Lateness Probability of a RetransmissionScheme for Error Control on a Two-State Markov Channel, IEEE Trans.Commun., vol. 47, no. 10, pp. 15371548, Oct. 1999.

[21] C.-F. Chiasserini and M. Meo, Energy Efficiency of Radio LinkProtocols in 3GPP Systems, in Proc. of IEEE VTC01-Spring, May2001, pp. 26152619.

[22] S. Geirhofer, L. Tong, and B. M. Sadler, Cognitive Medium Access:Constraining Interference Based on Experimental Models, IEEE J.Select. Areas Commun., vol. 26, no. 1, pp. 95105, Jan. 2008.

[23] T. van Dam and K. Langendoen, An Adaptive Energy-Efficient MACProcotol for Wireless Sensor Networks, in Proc. of ACM SenSys, Nov.2003, pp. 171180.

[24] J. Polastre, J. Hill, and D. Culler, Versatile Low Power Media Accessfor Wireless Sensor Networks, in Proc. of ACM SenSys, Nov. 2004, pp.95107.

[25] J. Polastre, J. Hui, P. Levis, J. Zhao, D. Culler, S. Shenker, and I. Stoica,A Unifying Link Abstraction for Wireless Sensor Networks, in Proc.of ACM SenSys, Nov. 2005, pp. 7689.

[26] M. Zorzi and R. R. Rao, Geographic Random Forwarding (GeRaF)for Ad Hoc and Sensor Networks: Multihop Performance, IEEE Trans.Mobile Comput., vol. 2, no. 4, pp. 337348, Oct. 2003.

[27] , Geographic Random Forwarding (GeRaF) for Ad Hoc and SensorNetworks: Energy and Latency Performance, IEEE Trans. MobileComput., vol. 2, no. 4, pp. 349365, Oct. 2003.

[28] S. Jain and S. R. Das, Exploiting Path Diversity in the Link Layerin Wireless Ad Hoc Networks, in Proc. of WoWMoM, Jun. 2005, pp.2230.

[29] R. R. Choudhury and N. H. Vaidya, MAC-Layer Anycasting in AdHoc Networks, SIGCOMM Computer Communication Review, vol. 34,no. 1, pp. 7580, Jan. 2004.

[30] J.-G. Choi and S. Bahk, Channel aware MAC scheme based onCSMA/CA, in Proc. of IEEE VTC04-Spring, May 2004, pp. 15591563.

[31] L. Bononi, M. Conti, and L. Donatiello, A Distributed Mechanism forPower Saving in IEEE 802.11 Wireless LANs, Mobile Networks andApplications, vol. 6, pp. 211222, Jun. 2001.

14

[32] P. Papadimitratos, A. Mishra, and D. Rosenburgh, A cross-layer designapproach to enhance 802.15.4, in Proc. of IEEE MILCOM, Oct. 2005,pp. 17191726.

[33] E. N. Gilbert, Capacity of a burst-noise channel, Bell Syst. Tech. J.,vol. 39, pp. 12531266, Sept. 1960.

[34] B. D. Fritchman, A Binary Characterization Using Partitioned MarkovChains, IEEE Trans. Inform. Theory, vol. 13, no. 2, pp. 221227, Apr.1967.

[35] W. Turin and M. M. Sondhi, Modeling Error Sources in DigitalChannels, IEEE J. Select. Areas Commun., vol. 11, no. 3, pp. 340347, Apr. 1993.

[36] M. Zorzi, R. R. Rao, and L. B. Milstein, On the accuracy of a first-orderMarkov channel for data transmission on fading channels, in Proc. ofIEEE ICUPC95, Nov. 1995, pp. 211215.

[37] A. Arora, E. Ertin, R. Ramnath, W. Leal, and M. Nesterenko, Kansei:A High-Fidelity Sensing Testbed, IEEE Internet Computing, vol. 10,no. 2, pp. 3547, Mar. 2006.

[38] The Network Simulator ns-2, http://www.isi.edu/nsnam/ns/.[39] M. Zuniga and B. Krishnamachari, Analyzing the Transitional Region

in Low Power Wireless Links, in Proc. of IEEE SECON, Oct. 2004,pp. 517526.

[40] T. S. Rappaport, Wireless Communications: Principles and Practice,2nd ed. Prentice Hall, 2001.

[41] P. Dutta, M. Grimmer, A. Arora, S. Bibyk, and D. Culler, Design ofa Wireless Sensor Network Platform for Detecting Rare, Random, andEphemeral Events, in Proc. of IPSN, Apr. 2005, pp. 497502.

[42] S. Liu, R. Srivastava, C. E. Koksal, and P. Sinha, Optimizing EnergyConsumption with Transmission Pushbacks in Sensor Networks,Technical Report, Department of Computer Science and Engineering,Ohio State University, Feb. 2008. [Online]. Available: http://www.cse.ohio-state.edu/prasun/publications/tr/pushback.pdf