[ieee 2008 second international conference on sensor technologies and applications (sensorcomm 2008)...

Non-Uniform Entropy Compression for UniformEnergy Distribution in Wireless Sensor Networks

Xiaoming Lu∗, Matt Spear∗, Karl Levitt∗ and S. Felix Wu∗∗Department of Computer Science

UC Davis, Davis, CA 95616Email: {lu, spearmat, levitt, wu}@cs.ucdavis.edu

Abstract—Recently there has been an influx of work on extend-ing a wireless sensor networks lifetime by distributing sourcecompression and deploying non-homogeneous nodes to handlethe aggregation. Both of these mechanisms have been shown toincrease the network’s lifetime, but they each have requirementsthat might not be plausible. With distributed source compression,message distributions must be known a-priori, and the existingpractical schemes tend to require modification of a layer in thenetwork stack. In non-homogeneous node deployment, placementof more powerful nodes is a major factor in balancing networkenergy, but many scenarios exist where this is not reasonable. Wepropose non-uniform entropy compression wherein bottlenecknodes trade computation energy for transmission energy and domore aggressive compression, which induces a synthetic non-homogeneity across a network built from physically identicalnodes and extends network lifetime. Our method inserts acompression layer between Medium Access Control (MAC) andthe routing layers without modifying existing network layers,thus providing a general platform for message compression. Weperformed extensive simulations to show how our architectureaffects network energy and delay considering message size, queuesize, compression ratio and time, and network topology. Oursimulations show that a computationally inexpensive and effectivecompression algorithm (with high compression ratio) that takesless than 0.2 s/ kbytes time (including both compression anddecompression time) to execute will help extend network lifetimefor most motes; for some motes (such as Mica2 and Rene2)1 s/ kbytes or more will work also. This supports our theorythat synthetic-non-homogeneity is a viable and practical methodfor extending Wireless Sensor Networks (WSNs) lifetime.

I. INTRODUCTION

Wireless Sensor Networks (WSNs) have been shown to havea non-uniform energy drain in most topologies. Nodes that arecloser to the base station lose energy at a much higher rate thannodes farther away. Recently, [1] detailed the problem formallyand gave some bounds on the energy savings that could beachieved. Following [1], we assume a single base-station asthis is common in WSNs. This non-uniform energy loss occursbecause nodes closer to the base-station would likely processmore messages. These nodes also need to execute more carriersensing, as well as more Request to Send (RTS)/Clear toSend (CTS). A recent study shows that Carrier Sense MultipleAccess (CSMA) causes a large amount of delay/energy loss[2]. Therefore these bottleneck nodes have a longer hold-timefor their messages.

In most cases, the transmitting and receiving power aremuch higher than active or idle power. According to [3], interms of power consumption, transmitting a single bit of data

is equivalent to 800 instructions. For a network with frequentsensing events, the energy loss is directly proportional to thenumber of transmitted and received bits. To compensate for thenon-uniform energy loss in single base-station WSNs, a largernumber of nodes can be placed near the base station [1]. Otherpapers [4] have shown that energy usage can be lessened andnormalized via placing non-homogeneous, data-aggregationnodes throughout the network. That is, the nodes would eithercollect some data and transmit it via correlated compression,e.g. source coding [5], or would use a-priori knowledge of thedistribution of the messages to do the correlated compression,e.g. Slepian-Wolf [6]. Most existing solutions require carefulplacement of motes, modification of existing network stack,or prior knowledge of message distribution and might not beable to be adapted to mobile scenarios.

Our goal is to provide a simple, flexible solution to extendnetwork lifetime. We accomplishes this by utilizing sim-ple entropic compression algorithms wherein nodes, depen-dent on hop-count from the base-station, choose the queue-size/compression algorithm. This approach ueses spatial-temporal-correlation to create a greater amount of compressionas messages are funneled in toward the base-station. WSNsmessages have a lot of redundancy that can be exploited forcompression, such as repetition of a symbol, or repetition of asequence of symbols across messages. Our method improvesnot only individual sensor lifetime, but also overall networklifetime. We define WSN lifetime in this paper as the timefrom network initialization to when there is no longer a pathfor a sensing node to communicate with base-station.

Many existing protocols require modification of the existingnetwork stack [7], [8], but our approach simply inserts acompression layer to the stack for queuing, combining andcompressing relevant messages. Since only the hopcount ofeach node must be updated, the overhead required to facilitatecompression is minimal. It has been shown that the energyimprovement of the correlation aggregation tree over ShortestPath Tree (SPT), even in the case increasing delay tolerance,scales very slowly (logarithmically) with respect to nodedensity [9]. A simple SPT, built by such as hopcount withoutknowing the data correlation distribution, can be used fordata gathering in conjuction with our algorithm. Althoughwe mainly investigate entropy compression in this paper, theproposed compression layer is basically a queuing and com-pressing processor where entropy compression or correlated

The Second International Conference on Sensor Technologies and Applications

978-0-7695-3330-8/08 $25.00 © 2008 IEEE

DOI 10.1109/SENSORCOMM.2008.98

730

The Second International Conference on Sensor Technologies and Applications

978-0-7695-3330-8/08 $25.00 © 2008 IEEE

DOI 10.1109/SENSORCOMM.2008.98

723

compression can be used interchangibly.The main contributions of this paper can be summarized as

follows. We propose to add an entropy compression layer toinsert non-uniformity across network. A simple and practicalmethod that matches the compression aggressiveness withsensor positions and throughput in the network is provided toallow synthetic-non-homogeneity in the network. Nodes onlyneed to do some message queuing for aggregation purpose andno extra coordinating message is needed. As our architecturedoes not affect the network’s existing stack, it provides ageneral platform for message compression. We performed ex-tensive simulations to show how our non-uniform compressionalgorithm affect network energy and delay under various pa-rameters such as message size, queue size, compression ratio,compression time, and different topologies. Standard compres-sion algorithms such as LZW [10] might be computationallyexpensive for WSNs. However, if a compression algorithm isdesigned to cater to a specific sensor application data formatand is computationally inexpensive, then the savings can belarge. Our simulation shows that a computationally conserva-tive and effective compression algorithm (high compressionratio) that takes less than 0.2 s/ kbytes time (including bothcompression and decompression time) to execute will helpextend network lifetime for most motes; for some motes (suchas Mica2 and Rene2) 1 s/ kbytes or more will also work.

The rest of the paper is organized as follows: in SectionII, we show existing work and introduce the compressionalgorithms that were used in our protocol. Next, in SectionIII, we describe the design of the compression layer; then, inSection IV we explain the energy model that we employed.Finally, we give the results of the simulation in Section V andgive the conclusions and future work in Section VI.

II. RELATED WORK

Many papers have shown that communication demandsare non-uniformly distributed in WSNs [1], [11]–[13]. Nodeswhich lie closer in Euclidean space to the base station tendto have a higher demand on their radios due to a “funnelingeffect” [11]. That is, in a uniform distribution the number ofnodes is directly proportional to the distance form the basestation. Therefore, nodes which lie closer to the base-stationmust transport more traffic per unit time.

There are many proposed solutions to the “funneling effect”.Funneling-MAC [11] proposed to use TDMA for nodes closerto the base-station and CSMA/CA for nodes further out inorder to reduce contention, but this does not address theproblem that nodes closer to base station need to send a higheramount of traffic. Other papers have attempted to normalizethe energy distribution via data aggregation [4], [14], energyaware routing [15], [16], and data compression [5], [17]. Indata aggregation, data is collected by an aggregating-node,and an aggregate, e.g. min, max, median, etc., of the datais forwarded toward the base station [18]. Previous efficientaggregation methods tend to require utilization of clusters [14],[19], or modification of the routing layer [7], [8], [20], [21].In the former, a cluster head is elected at random and these

cluster heads aggregate the data and directly transmit it tothe base station. In the latter, routing layer is changed so thatthe bandwidth is shared fairly across the divergent areas ofthe network. With energy aware routing each node maintainsinformation about its and its neighbors’ energy levels, androutes are chosen such that they utilize those nodes whichhave the highest energy [15], [16], [22], [23].

Data compression can be achieved through entropy encod-ing or correlated coding. Entropic encoding [24] compressesa message by assigning short codewords to symbols whichoccur frequently and longer codewords to symbols whichoccur infrequently. There are a number of algorithms in thisarea, some are more computationally expensive such as LZW[10], [25], Arithmetic [26], [27]; some are cheaper to use, suchas Run Length Encoding (RLE). In this paper, we introducedanother cheap compression algorithm, called XorRLE, whichis a hybrid version of Xor and RLE, where messages are Xoredfirst and then compressed with RLE. LZW produces generallygood compression ratio for ASCII text, whereas XorRLE giveshigh compression ratio when data are similar in format andvalues.

With correlated coding [5], [6], a node has a set of neighbors(N1, . . . , Nn), each sending a message (M1≤i≤n) and thenode wishes to forward these messages along with its ownmessage (M0) with the minimum energy. To accomplish thisthe node takes one message (Mi) and sends it unencoded; foreach of the other messages (Mj) the node uses conditionalentropy to create cosets, and sends the index into the coset thatcontains both Mj and Mi. Correlated coding is also used inour simulation for comparison with entropy coding.

Data can be compressed immediately and then sent alongthe shortest path to the base station [16], or a single com-pression algorithm can be utilized globally. In [28], it wasnoted that once a message is compressed it cannot be furthercompressed without decompression. Therefore once a messageis compressed it should be expedited to the base station, butthis ignores the funneling problem. Our algorithm compressesand decompresses data at each hop to reduce transmissions ondata’s path to BS.

III. ARCHITECTURE

In this section, we detail the architecture of the compressionlayer. The compression layer sits between the Medium AccessControl (MAC) and routing layers, and its job is to combineas many messages as possible and compress them. Ideally wewould like to use average throughput to determine the queuesize for the number of messages to be compressed. However,we use distance to approximate throughput as the probabilityof a message passing through a node is proportional to thatnode’s distance to BS. This is depicted by the equationbelow (directly from [13]). Let Pr(u) be the probability oftraffic passing throught node u; d(u) be the distance of Nu

to BS; ρ is the density of the network; r is the node’sradio communication range. According to [13], the followingequation holds:

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Pr(u) =1

π(2�d(u)r�+ 1)r2ρ

N − πd(u)2ρ

N(1)

A node’s distance to BS can be further approximated by itshopcount, which can be easily obtained by having BS broad-cast a beacon with hop-count of zero, which is incrementedby each node before rebroadcasting.

We concentrate solely on using hop-count as the basis ofdetermining the queue size for the number of messages tobe compressed, but there are other choices that would yieldgood (and possibly better) results, e.g. Euclidean distance, oraverage throughput. The latter would yield near-optimal resultsas it directly predicts the number of messages that will beforwarded through, but it makes determining which queue sizeto use more difficult.

Since the compression layer sits between the routing andMAC layers, MAC headers/messages will not be compressed.The reasoning for this is that MAC headers allow early abort,is i.e., nodes can turn off their radio when the message isnot destined for them. Furthermore, as entropic compressionalgorithms work better over many messages, the compressionlayer would hold messages for as long as possible and thiswould cause problems for RTS/CTS messages that should notbe delayed.

The compression layer has five parameters that determineits workings:

Di The hop-count from the base station for thisnode

Dmax The maximum hop-count from the base stationScomp The set of compression algorithms sorted by

increasing distance1

Squeue The set of queue sizes sorted by increasingdistance

Thold The set of maximum hold-times for a messageto remain in the queue2

Di can be computed based on routing information. Dmax caneither be set before deployment or the base station can sendout a short message with a hop count field. We used theformer method for reasons that it costs no energy and canbe bounded by

√N in most cases, where N is the number of

nodes in the sensor network. Having a tighter bound for Dmax

will give better results as nodes which are bottlenecks shouldhave as large a queue as possible. Thold determines the longesttime a message will remain in a node’s queue and affects themaximum end-to-end message delay in the network. Scomp,Squeue and Thold are configurable system parameters.

To determine what value should be used to index the set ofqueue sizes (Squeue), the node computes:

Indexi ←⌊

Di

Dmax − 1|Squeue|

⌋(2)

1In our work we keep |Scomp| = 1 so that every node uses the samecompression algorithm

2In our work we keep |Thold| = 1 so that every node has the same maximumhold-time

Fig. 1: The compression layer’s architecture and how it fitsinto the existing network stack; the figure shows node i.

The minimum hop-count to base station is trivially 1; if anode is mobile, it can recalculate Equation (2) based on itsnew neighbor’s hopcount.

The overall architecture is displayed in Figure 1. Thecompression layer segregates messages based upon type, e.g.routing and agent, and then upon the next-hop address. Thereasoning for this is two-fold: (1) messages of differenttypes have vastly different distributions and grouping themtogether would adversely affect some compression algorithms,e.g. arithmetic compression, and (2) combining the messagesdestined for divergent next-hops would require the receivingnodes to do a decompression for a message that wasn’tsupposed to be received. As shown in Figure 1, a message(Mj) is tested to determine which queue it matches, and thenis inserted into that queue.

When a message has remained in the queue for a timegreater than Thold, it is removed from the queue and sent.Otherwise, when the cardinality of the queue is greater thanor equal to Squeue[Indexi], the messages are combined, com-pressed and sent. In Figure 1 all messages are given a timerthat counts down from Thold and are passed to the compressionalgorithm either when the timer expires or the queue becomesfull. In the next section we describe the energy model that weutilized, and how the compression layer saves energy.

IV. FORMAL MODEL

In this section we describe the formal energy model andgive some basic results. In Table I, we show energy model ofdifferent sensors [29].

As shown in Table I, energy is spent with every messagebit transmitted, received, or processed. The total energy spenton a message without compression is:

EM = (PTx+ PRx

) · |M| (3)

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PTxPRx

Pidle Pactive Data RateMica2 755

nJbit 1001

nJbit 3

nJbit 8 mW 38.4 kbpss

Telos 140nJbit 14

nJbit 3

nJbit 3 mW 250 kbpss

Rene2 900nJbit 3600

nJbit 15

nJbit 15 mW 10 kbpss

TABLE I: The energy model of different sensors.

whereM is the message and |M| is the length of this message.Equation (3) is constant given a fixed size message and aconstant decibel transmission rate (throughout the paper weassume a constant data rate as noted in Table I).

Our approach saves transmission energy by reducing amessage’s size via compression, but this introduces energyloss due to time spent in the active mode during compression.The goal is then to provide:

(PTx+PRx

)· |M|·CR−1+Pactive ·2Tcomp < (PTx+PRx

)· |M|(4)

where CR is the compression ratio (uncompressed messagesize over compressed), and Tcomp is the time taken to compressthe message. The reception energy loss equation is similar,merely replacing the transmitting power PTx

with receivingpower PRx

. The inequality in Equation (4) does not hold ifcompression time Tcomp is too large or CR is too low. A factorof 2 accounts for compression and decompression time. In thispaper, when we talk about compression time, we refer onlyto compression without decompression, unless we specificallystate that it includes both. The decompression time is assumedto be same as compression time and is accounted for in allour analysis and simulation.

Equation 5 defines space saving ratio (SS).

SS = 1− CR−1 (5)

Replacing CR by spacing saving SS in Equation 4 andsolve for SS, we get Equation 6 which shows what spacesaving is needed from compression under a given compressiontime for a mote to gain energy saving.

SS > 1− (PTx+ PRx

) · |M| − Pactive · 2Tcomp

(PTx+ PRx

) · |M| (6)

In Figure 2, we show the minimum spacing saving ratio re-quired under different compression time to gain energy savingfor three popular motes. We assume the compression queuehas 5000bytes of data to compress (e.g. 500bytes messagesize with queue size of 10). This figure shows that underthe same compression time, Rene2 requires least compressionspace saving to win over non-compression in energy saving.Telos performs the worst and loses to non-compression whencompression time 0.2 s/ kbytes; whereas the losing point foris about 0.5 s/ kbytes for Mica2 and 0.75 s/ kbytes for Rene2.Due to limited ratio between transmission/reception energyvs computation, Telos performs the worst; it actually losesto non-compression when compression time per 1000bytes ismore than 0.2 second.

As can be seen even with a large message and a decentcompression ratio, the energy loss could be worse if the

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

T˙comp(s/kbytes)

Space

Savin

g R

ati

o

Telos Mica2Rene2

Fig. 2: Under various compression time, the minimum spacesaving ratio required to gain energy saving for three popularmotes.

compression time is too long. In Section V we run a series ofsimulations and show the tradeoff of energy/delay.

The other issue that arises while using compression ismessage delay. At each hop, a message might be held foras long as Thold, which implies the maximum delay overa network can be bounded (ignoring MAC layer accessingproblems, which should be reduced further with our scheme asthe total number of messages in the network is being reduced):

Dend-to-end = H · (Thold + TTx+ TRx

+ 2Tcomp) (7)

where H is the number of hops from the sender to the basestation and TTx

is the time it takes to transmit the message.Thold should be chosen such that it maximizes the numberof full queues, while allowing messages to be received in areasonable time.

V. SIMULATION

Our simulation studies show how non-uniform aggregationand compression impact on network energy level and distri-bution and traffic delay under a number of parameters suchas queue size, compression ratio, compression time, messagesize and topologies.

The simulations were run with ns2 using a CBR interval of5 s between messages. Each message is a simple XML file con-taining the current weather for the Sacramento InternationalAirport for one day obtained from [30], scaled to the messagesize as required. These weather messages were originallycollected 30 min apart. The XML files were downloaded once.Each file is assigned a unique increasing index and used as datafor the ns2 messages. Given this set of data, temporal locality

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was implanted by having each node access every messageonce with an increasing index. Spatial locality was inserted bygiving nodes which are close geometrically file indices whichare close temporally. XML data was chosen as many sensorapplications are moving to that format for its simplicity andeasy management.

The aggregation/compression algorithms considered are: (1)simple message concatenation, (2) XorRLE, (3) LZW, (4)correlated. We use XorRLE to model inexpensive compressionalgorithms and standard LZW to model relatively computa-tionally expensive compression. For XorRLE, we always sendthe first message unencoded and then Xor the next messagewith the previous message to enforce spatial and temporalcorrelation and achieve maximum compression. This methodis very effective for messages with static fields, such as XMLstyle data, since Xor will zero-out static fields which remainin alignment and RLE will represent long string of zeros withminimum length. We also simulate correlated compressionto compare with entropy coding, under the assumption thatall messages can be represented at the optimal conditionalentropy, as our focus is on non-uniform compression, not justcompression.

Due to space limitations, we selectively present some sim-ulation results based on Telos, Mica2 and Rene2 using energymodel described in Table I on a few topologies.

Every node is initialized with 100 J of energy. The routinglayer was Dynamic Source Distance Vector [31] which usesSPT algorithm, and the MAC layer was 802.11. The trafficmodel is constant traffic (every 5 second) from network edgetowards BS. The set of queue sizes we used are (1, 5, 10, 20)and these queue sizes are evenly distributed to nodes basedon node’s distance in relation to BS. Each node is initializedwith a queue size choosen from this set, with nodes closer toBS having queue size of 20 and nodes farthest out at networkedge having queue size 1.

The topologies considered are:

Linear Nodes are exactly one communication radiusaway from each other, i.e. Ni can only com-municate with Ni−1 and Ni+1

Grid Nodes are arranged in an evenly spaced gridwith each node only being able to talk toadjacent nodes horizontally or vertically

Disk A number of circles are created (5 in oursimulations) with nodes equidistant along thecircumference, and each increasing circle dou-bles the number of nodes for the circle.

Nodes are placed into the above topologies with a range of(0, 0) → (xmax, ymax), with the base station (N0) placed at(xmax/2, ymax/2) (except for linear case where it is placed at(0, 0)). Any node which satisfies:

√(xi − xmax

2

)2

+(yi − ymax

2

)2

>(r

4

)2

where r is the communication radius (240 m), is a sensingnode that transmits weather data.

A. Topology, distance, throughput, queue holdtime study

We present in Figure 3 a comparison of energy consumptionand distribution using contour map for applying the sameXorRLE compression on three different topologies.

Nodes are represented by a black circles and labeled withtheir IDs. Since the sensor battery life depends on the sim-ulation time length, we normalize the energy remaining insensor network between 0 − 100% in our contour map. Thelight yellow regions represent a small amount of energy loss,the darker red represents a large amount of energy loss, andintermediary values are interpolated in hue-space.

Figures 3(a), 3(e), and 3(i) (the first column of Figure 3)represent the base case with no compression.

Figures 3(b), 3(f), and 3(j) (the second column of Figure 3)uses XorRLE compression and the compression time (includ-ing compression and decompression) is approximated to be0.2 s/ kbytes. The set queue sizes are Squeue = {1, 5, 10, 20}.We bucketize nodes according to Equation 2 by dividing thedistance range (max distance - min distance) by cardinalityof queue size sets, with nodes close to BS to have largerqueue size. We refer to the method of assigning queue sizeby distance as distance compression.

Figure 3(c), 3(g), and 3(k) (the third column of Figure 3)are the same as the second column save Thold =∞.

Figure 3(d), 3(h), and 3(l) (the third column of Figure 3)assign each node queue size based on throughput, instead ofdistance. We refer to this throughput compression. Throughputis determined by message count of data messages as our datamessage size is fixed. For simplicity, we assume that thereis an oracle which knows all the throughputs of each nodeduring the entire simulation. We bucketize nodes according toEquation 2 by dividing the throughput range (max throughput- min throughput) by cardinality of queue size sets, with nodesof higher traffic to have larger queue size.

These simulations further confirms the theory that nodescloser to the base station die earlier, and non-uniform compres-sions (either distance compression or throughput compression)succeed in both reducing (graph become lighter color) andnormalizing network energy (graph becomes more even incolor transition).

For linear topology, throughput compression performedbetter than distance compression, as throughput in this caseis not proportional to distance. For example, nodes 1 - 6 inthis case all has the same traffic throughput, but only nodes1-2 are assigned with queue size 20 according to distancecompression algorithm.

For grid and disk topologies, both distance and throughputcompression perform similarly when Thold = ∞. This confirmsEquation 1’s assumptions that distance compression is a goodpredictor for throughput, as throughput distributions in thesenetworks are proportional to distance to BS.

Given the same distance compression algorithm, the longerthe nodes wait for queue to be full (such as the case hold time(Thold) is inifinty), the more energy reduction and normaliza-tion can be achieved. For example performance in Thold = ∞column is better than Thold = 1 (hold time is 1 second) column.

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However small hold time (Thold = 1) seems to be long enoughfor results to be close to ∞ hold time.

We indicate the normalized average (μ) and standard de-viation (σ) energy for each graph in Figure 3 to show theimprovement.

Our simulation results for distance and throughput algo-rihms can be summarized as follows:

1) Distance tends to be a good predictor of throughputin most topologies, although throughput methods areusually more reliable for normalizing network energy.

2) The longer the nodes wait for queue to be full, the moreenergy reduction and normalization can be achieved. Ifthere is enough traffic, a node does not have to wait forlong for queue to be full.

3) Both distance and throughput algorithms increase net-work energy and reduce variance (σ2).

B. Compression Ratio and Compression Time Study

We compare the energy and delay tradeoff of our algo-rithm for fixed compression ratio (using compression spacesaving matrix described in Section IV) and fixed compressiontime in Figure 4. The queue size Squeue is one for non-coompression/concatenation case and (1, 5, 10, 20) for com-pression/concatenation case.

Figure 4(a) – Figure 4(b) show that when the compressiontime (Tcomp) is fixed (in this case Tcomp = 0) and increasecompression space saving (SS, the percentage of bits savingfrom compression), the average (μ) energy saving increases byup to 15% and standard deviation (σ) decreases by 15% (lowerσ indicates desired better network-wise energy normalization).When SS=0, there is only concatenation of messages but nocompression. It is interesting that larger saving occurs with justconcatenation and even larger saving can be achieved whenmessage size is large or queue has many messages.

Figure 4(c) – Figure 4(d) show that when the compressionspace saving is fixed (in this case SS = 0.5) and increasecompression time from 0 to 0.5 second, the remaining energydecreases by up to 15% and σ increases by 15%. The de-compression time is assumed to be the same as compressiontime. When compression time is too long, the non-uniformcompression might use-up more network energy.

While comparing the impact of compression ratio andcompression time, we found that longer compression timeincreases energy consumption faster than higher compressionratio which reduces energy consumption. Therefore, a cheapcompression algorithm is desired for non-uniform compressionto reduce and balance network energy.

C. Energy Saving and Delay with Real Compression Algo-rithms

A comparison of energy saving and traffic delay whileapplying our algorithms on the same topology but differentcompression algorithms is presented in Figure 5. For energysaving, we consider both average remaining energy and vari-ance in the network. Our traffic delay simulatin includes delayfrom media access contention, transmission delay, message

queueing delay, and compression/decompression delay. Therelative compression ratio order for our data set is LZW >Correlated > XorRLE > Identity (compression ratio is zero).

In this figure, we plot the normalized remaining energy ofthe network vs message size, variance of network energy vsmessage size, and actual end to end delay vs message size forgrid topology. We show the results under the same evaluationmatrix with and without setting the data queuing threshold.

We assume that no-compression (“1 Identity” line, queuesize is set to one) or identity compression (“1’5’10’20 Iden-tity” line, data message are simplily concatenated beforebeing sent) takes no compression time; XorRLE compressiontime is 0.2 s/ kbytes (“1’5’10’20 XorRLE line); both LZW(“1’5’10’20 LZW” line) and correlated compression time(“1’5’10’20 Correlated” line) takes 0.2 s/ kbytes. Since wesimulate optimal correlated compression ratio, we assume thecompression algorithm as expensive as LZW. The X-axis ofall graphs shows the original data message size.

For the energy μ graphs, the Y-axis shows the remainingenergy of the network normalized with respect to the leastenergy node. For the energy σ graphs, the Y-axis shows thestd of each node’s remaining energy normalized with respectto the lowest remaining energy node. For the delay graphs, theY-axis shows the actual average end to end message delay inseconds.

Our simulation results match the performance theoreticalprediction in Figure 2 , which is Rene2 performs betterthan Mica2 and Mica2 performs better than Telos. For Telosmote, cheap compression algorithm that executes 0.2 s/ kbytes(including both compression and decompression) messagesize is a viable approach to minimize and normalize energy.Expensive compression algorithms such as LZW and idealcorrelated compression lose to no-compression case (increasedenergy loss and variance), even though their compressionratio is higher for variety of data formats. For Mica2 andRene2, compression outperforms non-compression in energyin all cases even though some compression algorithms arecomputationally expensive (in this case, approximated to be1 s/ kbytes, including compression and decompression time),as these motes’ transmission rate is low and transmission isexpensive.

Due to lower transmission rate, Mica2’s delay is slightlylonger (less than 1 second) than Telos and Rene2’s delayis longer than Mica2. However, this difference is hardlynoticeable on both Thold = ∞ and Thold = 1 graphs, as thequeuing delay is a dominate factor over transmission time.

Interestingly, with or without one second queuing threshold,the remaining average energy and standard deviation do notdiffer much (therefore we only present the one second thresh-old case for Telos). However the delay reduces significantly(by a factor of ten) when one second threshold is imposed.This shows that we can achieve energy reduction and normal-ization throughout the network using message queuing anddelay threshold with moderate increasing delay, as long asthroughput is relative high to queue size.

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VI. CONCLUSION

To help solve the problem of non-uniform energy loss insensor networks, non-homogeneity provides a very promisingmechanism. Existing techniques require a-priori knowledgeand controlled distributions; our scheme, on the other hand,adapts dynamically to any network condition–even with ambu-lation. We provided a formal model to show possible savingsand the delay costs, and finally we supported the theory viasimulation. Our algorithm achieved both energy normalizationand savings over a variety of topologies and sensor motes, butdoes increase the delay of messages (with a configurable upperbound controlled by holdtime in the queue and compressiontime).

Our work provides a general framework for achievingenergy reduction and normalization, and can be implementedon existing motes without modifying the network stack. Itis computationally inexpensive and practical to adopt ourscheme to actual sensor deployment when using a compressionalgorithm that is designed in mind with the specific sensorapplication data format. In future work, we plan to implementour scheme on real motes, evaluate optimal queue sizes forcompression using real-time throughput. Quality Of Service(QoS) guarantees should also be investigated, wherein theTTL field of the IP header is used to determine how muchtime a message can remain in the queue, and the TTL isdecremented by the amount of time in the queue. Finally,inputting synthetic-non-homogeneity at software layer for sen-sor networks allows ease of deployment and is a viable andpractical solution to extending the lifetime of sensor networks.

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Fig. 3: Energy distributions with synthetic-non-homogeneity compression in different network topologies. Column 1: nocompression. Column 2: distance compression, XorRLE, Squeue = {1, 5, 10, 20}, Thold = 1. Column 3: distance compression,XorRLE, Squeue = {1, 5, 10, 20}, Thold = ∞. Column 4: throughput compression, XorRLE, Squeue = {1, 5, 10, 20}, Thold = ∞.

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(d) vary Tcomp, energy σ

Fig. 4: General energy and delay tradeoff study: (a)–(b) Fix Tcomp = 0, vary SS. (c)–(d) Fix SS = 0.5, vary Tcomp.

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Fig. 5: Remaining average energy (μ) and σ, and delay using non-uniform compression: Grid Topology, (a)-(f) Telos (g)-(j)Mica2 (k)-(m) Rene2

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