Convergecast Algorithms for Wake-up Transceivers

Amir Bannoura

, Leonhard Reindl

and Christian Schindelhauer

Laboratory for Electrical Instrumentation, University of Freiburg,

Georges-Köhler-Allee 106, 79110 Freiburg, Germany

Department of Computer Networks and Telematics, University of Freiburg,

Georges-Köhler-Allee 51, 79110 Freiburg, Germany

Keywords:

Wake-up Receivers, Duty-cycling Backbone, Convergecast, Online-competitive Algorithms.

Abstract:

New transceiver and receiver hardware technology allow the usage of special wake-up signals, which are able

to awake neighbored sensor nodes from the sleep. However, such messages need more energy e

than those

standard message transmissions e

, when nodes are awake. Furthermore, the distance range r

is also smaller

than the distance range r

of standard messages. Therefore, it does not completely replace duty-cycling for the

convergecast problem in wireless sensor networks. We present a theoretical and practical discussion of energy-

efﬁcient algorithms for the convergecast problem. First, we present a model based on the current technology

and show that without constraints on the delivery times wake-up signals are obsolete, when arbitrary long

sleeping times are allowed. The wake-up graph G

and the message graph G

are modeled by planar r

and r

-disk-graphs. Then, we give a competitive analysis for the general case, where we discuss an online

∆-convergecast algorithms bounded by competitive energy ratios. Finally, we present simulation results for

these algorithmic ideas in the plane by considering the energy efﬁciency and the latency of data delivery.

1 INTRODUCTION

Energy is one of the most fundamental characteristics

to ensure the continuous operation of Wireless Sen-

sor Networks (WSNs). Most wireless nodes use duty

cycling to conserve energy through switching off and

on their wireless transceiver. The concept of wake-

up receivers (Gu and Stankovic, 2004) introduces a

new approach that allows the wireless transceiver to

be switched off for unlimited amount of time in order

to decrease the power consumption to the minimum.

The nodes switch their transceivers on when

a wake-up signal is received. Transmission of

data packets occurs upon activating the wireless

transceivers. Despite that the wake up technology

provides a solution for the energy consumption prob-

lem, transmitting a wake-up signal that is required to

wake up other nodes is energy expensive compared

to the data packets. As well, the wake-up distances

of these signals are limited compared to the normal

data communication distances. In this case, multi-hop

wake-up signals are required to cover the area of a sin-

gle hop of normal data communication. Since waking

up the nodes periodically is considered energy expen-

sive, a proper solution would be to maintain an ac-

tive path for a while to function as a backbone for the

nodes to deliver messages to the sink.

Previously, we presented several algorithms to

wake-up the network from a single source node (Ban-

noura et al., 2015). It focuses on how to cover the

network without considering any information about

the nodes and their positions. However, waking up

the nodes and construct a routing path from scratch

each time to deliver data to the sink is not a practical

approach, since this process consumes a lot of energy

each time a node has data to transmit. Instead, comb-

ing the wake-up approach with duty cycling for dense

networks reduce the need to transmit several wake-

up signals. Based on the available information about

the network, some active nodes perform duty cycle to

build virtual backbones. These backbones are acti-

vated for a limited time to reduce the need for wake-

up signals. In case a node has no direct communi-

cation with an active node in the backbone, wake-up

signals are used to wake-up nodes until one node has

a direct communication with the backbone or the sink.

Latency and energy are the two major challenges

for data gathering at the sink. Despite introducing the

wake-up technology to reduce energy, the end-to-end

delay for packet delivery increases signiﬁcantly due

to the time required to wake-up the nodes in the path

toward the sink. Thus, we study the problem of time

Bannoura, A., Reindl, L. and Schindelhauer, C.

Convergecast Algorithms for Wake-up Transceivers.

DOI: 10.5220/0005795601370143

In Proceedings of the 5th International Confererence on Sensor Networks (SENSORNETS 2016), pages 137-143

ISBN: 978-989-758-169-4

137

and energy for data gathering using wake-up receivers

at the sink.

2 RELATED WORK

Wake-up receivers, like the ones developed by Gamm

et al. (Gamm et al., 2010), give us an alternative to the

concept of duty cycling for communication in sensor

networks.

An optimal solution for data aggregation is to con-

struct a minimum connected dominating set (MCDS)

of nodes to get the data to a sink. But creating such

a MCDS for sensor networks is NP-hard in general

graphs as well as for unit disc graphs (Lichtenstein,

1982; Clark et al., 1991). Although a polynomial-

time approximation scheme (PTAS) is shown for the

unit-disc version of the problem in (Cheng et al.,

2003).

The wake-up receivers form an online version of

the MCDS problem. In our previous work (Bannoura

et al., 2015), we tried to create a technique for waking

up all nodes with no knowledge about the network

using a push-based epidemic rumor spreading algo-

rithm. However, a broadcast wake-up is considered

an energy expensive approach in order to construct a

path between a source and a destination. In a dense

network, it is better to combine the wake-up approach

with the traditional duty cycling.

The main task of sensor networks is to collect in-

formation about their environment. In general, the

information is gathered at the sink in a communica-

tion pattern known as convergecast. The converge-

cast problem focus on minimizing the required time

for message delivery through minimizing the sched-

ule time. However, Choi et al. (Choi et al., 2009)

proved that ﬁnding the minimum schedule time is NP-

hard for general graphs. They propose an optimal

scheduling of 3(n - 2) for a minimum scheduling for a

line or tree topology, where n is the number of nodes.

Gandham et al. (Gandham et al., 2006) propose a

distributed convergecast scheduling algorithm that re-

quires at most 3N time slots. Through extensive simu-

lation they showed that the actual time slot required is

1.5N. Similar result of 3N for routing in line topology

is achieved by Zhang et al. (Zhang et al., 2015). For

a tree routing graphs, the lower bound on the num-

ber of time slots required to complete convergecast is

max { 3n

+∆, N + 2 }, where they assume the nodes

> n

> .. > n

. ∆ = 1 if n

= n

, otherwise ∆ =

0. Lu et al. (Lu et al., 2005) studied how to minimize

the end-to-end delay communication. An approxima-

tion algorithm is proposed that achieves a bound of

d + O(k) for a tree and a grid topology. In arbitrary

graphs, a bound of O((d +k) logn) is achieved, where

d is the distance between two nodes and n is the total

number of nodes.

The purpose of minimizing scheduling is to re-

duce the energy required for data delivery to the sink.

Adjusting the communication ranges of the nodes by

controlling transmission power can reduce the con-

sumed energy. Kesselman and Kowalski (Kesselman

and Kowalski, 2005) suggested a random distributed

algorithm with a trade-off between latency and en-

ergy. Their approach has a latency bound of O(log n)

and a minimum energy consumption of O(nlog n),

where n is the total number of nodes and each node

can adapt to different communication ranges. Simi-

lar approach in (Yu et al., 2004) is to reduce energy

consumption based on latency constrains. They con-

sidered an on-line and off-line variant for data aggre-

gation with different communication ranges. Also,

Sheng et al. (Shang et al., 2010) propose an approx-

imation greedy algorithm for minimal convergecast

and it is bounded by a constant performance ratio.

3 THE PROBLEM

The convergecast main challenges are the limited en-

ergy supply and latency for delivering packets to the

sink. We consider a set of sensor nodes V is dis-

tributed in the plane. In our round model, a node is

either asleep or awake. At the end of each round, a

node can decide to go to sleep and set a counter to

wake up again after speciﬁc round. This process is

called duty-cycling. Another way to leave the sleep

state, is to receive a wake-up message.

In our model the sensor nodes are not moving and

the information about the neighbor nodes is known.

The model considers two types of transmissions:

First, every node can send a data message, which is a

unicast message that contains aggregated sensor data

to be forwarded to the sink. Second, each node can

generate a wake-up signal, which can wake up a spe-

ciﬁc neighbored node. Depending on the technology,

the energy and distances of these transmissions differ.

Therefore, the energy of transmitting and being awake

during a speciﬁc duration for a round is donated by

> 0, which also allows to transmit or receive data

messages. We assume a disk-communication model,

such that a node can be reach an awake neighbor in

distance r

> 0 with a data message. Furthermore,

in a round the sensor data is small compared to the

transmission overhead. So, we assume that in a round

only one message is necessary to transmit all col-

lected data, i.e. only the energy sum of a tree is nec-

essary to send all messages to the sink.

SENSORNETS 2016 - 5th International Conference on Sensor Networks

138

Then, we have the wake-up signals, which wake

up speciﬁc sensor nodes by carrying their addresses.

Because of a special modulation they have higher en-

ergy cost e

> e

, since all available technologies

need considerably higher cost, e.g. the range e

have a value of more than 50 times. Furthermore, the

transmission range r

of a wake-up call is considered

smaller, i.e. r

< r

. Current technology delimit the

ratio r

between 5 to 20 times depending on the

transmission power, antenna and wake-up circuit sen-

sitivity.

In each round, it is possible for a sensor node to

sense new data. This can trigger the sensor node to

send this data in this round. Also, due to the limited

storage space of the node, we don’t consider that the

nodes are capable of storing data. So, an awake node,

which has data to send, check if neighbor nodes are

awake at the beginning of the round by broadcasting

a status messages. Depending on this information, the

node can send data messages to a subset of the awake

sensors, or if no node is awake the awake node trans-

mits wake-up messages to wake-up neighbor nodes

similar to Fig 1. In the next round, the awake nodes

are not necessarily receiving data and may be put back

to sleep immediately. The main goal may be to wake

up some connected sensors which allows the trans-

mission of all data intended to reach the destination

in this round.

sink

round 2

sensor data

sleeping

nodes

sink

active

node

round 1

sink

round 3

wake-up

sink

round 1

sink

round 2

data

sink

round 3

duty-cycling

Figure 1: Duty cycling and wake-up signals.

4 THE SLEEPING BEAUTY

PARADOX

We assume that the maximum distance between two

neighbored nodes is bounded by r

, since otherwise

the communication network is disconnected. Now, if

two neighbored nodes have a distance of more than

, then it is necessary that two nodes on both sides

of this gap perform duty cycling.

Since our work focuses on reducing energy

through waking up and performing the duty cycle, we

deﬁne the average energy required per round as fol-

lows.

Deﬁnition 1. Given a communication scheme for T

rounds and let W

be the wake-up messages and M

the data messages in round i. Then, the average total

energy per round is deﬁned as

avg

∑

i=1

+ |W

Now the sleepy beauty paradox is that for grow-

ing T and any sensor data the average total energy

converges to 0 even without the use of wake-up mes-

sages. For this assume that all nodes wake up in

rounds f (1) < f (2) < f (3) < ... and buffer the sensor

data in all other rounds. Then, the energy cost of each

round is bounded by (n −1)e

, since we assume per-

fect data aggregation. Now, if f (i + 1) − f (i) grows

strictly monotone, then the average converges to 0 for

growing T.

Proposition 1 (Sleeping Beauty). A delay tolerant

sensor network with perfect data aggregation allows

a duty-cycling communication scheme where the av-

erage total energy converges towards 0 for growing

number of rounds T .

Proof. Consider waking up all nodes at times f (i) for

growing function f , e.g. f (i) = i

. Then the energy

over all rounds is at most n

√

T e

, which results in an

average energy of

√

, which converges towards

time

nodes

awake

nodes

sleep

energy

f(1) f(2) f(3) f(4) f(5) f(6)

Figure 2: Increased sleep cycles make wake-up signals ob-

solete.

So, all nodes sleep for longer and longer times and

the network becomes less and less reactive. Basically,

it slows down and becomes less reactive, which is not

a desirable solution for a sensor network.

In order to deal with this problem, we must set

a delivery bound for all data to some number of ∆

rounds. Such algorithms are called ∆-convergecast al-

gorithms. One can see this bound as a real-time con-

straint on sensor data. Another motivation is that the

clocks are drifting and ∆ is an upper bound for syn-

chronizing the nodes.

5 COMPETITIVE ANALYSIS

If one tries to perform a competitive analysis of this

problem one faces the following problem. For an of-

ﬂine algorithm with full knowledge of the sensor data,

Convergecast Algorithms for Wake-up Transceivers

139

the duty cycles can be set to the perfect timing that

a communication networks just appears at the right

time at the perfect place. In order to facilitate the

delivery of data at rounds 0,∆,2∆, .... No online al-

gorithm can provide a reasonable bound compared to

this clair-voyant solution using only duty-cycling.

Theorem 1. Sensor networks without wake-up sig-

nals do not allow online ∆-convergecast-algorithms

with bounded competitive energy ratios.

Proof. Consider a network with 2dr

e nodes with

distance r

on a line with the sink on one side, see

Fig. 3. Now, for T rounds only one sensor measure-

ments arrives at the other side round r. In order to

meet the delay bound ∆ at least one of the middle

nodes has to wake up at least T /∆ times to forward the

single measurement with total energy Te

/∆ + 2e

wake-up

sink

data

Figure 3: Wake-up signals are necessary if few sensor data

arrive.

For the ofﬂine algorithm a middle node wakes up

in round r which corresponds to energy 2e

. An algo-

rithm with wake-up signals could have woken up the

middle nodes with energy 2dr

Wake-up signals allow some solution. For this,

we assume from now on that there is always a wake-

up path from every node to the sink, i.e. for all u ∈V

there exists a path (u = v

,.. ., v

= s) such that

i+1

| ≤ r

Theorem 2. Using wake-up signals there is an on-

line algorithm which achieves an online competitive

bound of at most 4n

. This bound is tight up to a

constant factor.

Proof. If sensor data occurs at a node it will be

stored to the rounds 0,∆,2∆, .. .. Then, it wakes up

and wakes up all nodes on the shortest path to the

sink. Then, the data is sent along the resulting short-

est path tree. The overall energy cost is therefore

∆

n(e

+ e

), if T

denotes the sum of all time in-

tervals, where sensor data has occurred in an interval

of length ∆.

The minimum ofﬂine energy needed to send data

along one hop. It is at least

2∆

, since sensor data of

two consecutive intervals could have been combined.

> e

implies the upper bound.

For the lower bound, consider a network, where

every wake-up path uses all nodes of the network

and the communication network is only one hop, see

Fig. 4. As soon as duty cycling is used, no data oc-

curs.

So, duty-cycling cannot be used and an overall

cost of

∆

is necessary.

wake-up

sink

data

sink

data

Figure 4: A worst case situation for a wake-up strategies.

Clearly such bounds are not fair, and therefore we

consider a plane with densely placed sensor nodes

and a fairer comparative ratio for online ratio, with-

out a clairvoyant ofﬂine strategy. Also, these bounds

are valid for sensor nodes in general positions, e.g.

where the graph of possible wake-up calls G

is much

sparser than the graph of possible communication

messages G

6 ALGORITHMS

The theoretical analysis of the wake-up algorithms

combining duty cycling needs to be throughly stud-

ied. Thus, we’ll focus on the practical implementation

of the algorithms. The following basic strategies for

convergecast are optimal if a very high or a very small

number of sensor messages needs to be handled.

Greedy Shortest Wake-up Path. Here, all sensor

nodes use only wake-up calls to communicate with

the sink. For this, they send wake-up calls on the

shortest path towards the sink, a subset of these nodes

take care of the sensor data and then all nodes go back

to sleep. The sensor nodes don’t consider performing

duty-cycling. Thus, the energy is dominated by the

number of messages s to be sent on the average and

the wake-up diameter D

of the graph, i.e. O(sD

Duty-cycling Covering Backbone is the standard

approach without wake-up signals. It uses a backbone

tree T

of nodes, which is a tree in G

, where for every

node u ∈V there exists a node in V

= V (T

), which

can be reached within one hop. This set of node sleeps

∆ −1 rounds and synchronously wakes up. Since, the

nodes cover the full graph, all sensor data can be sent

to the sink within ∆ rounds.

Computing such a backbone is not an easy task,

and it has been discussed here (Ghosh and Das, 2008;

SENSORNETS 2016 - 5th International Conference on Sensor Networks

140

Cardei and Wu, 2006). The average energy consump-

tion is clearly at most |V

∆

+ se

where s denotes

the average number sensor data occurring at the sen-

sor nodes.

Hierarchical Cut Decomposition uses the concept

proposed in (Fakcharoenphol et al., 2004) to create a

tree structure, where the root of the tree is the sink.

The algorithm uses different radius r-cut decomposi-

tions to create several clusters. In addition, between

any two nodes the algorithm achieves a stretch factor

of O(log(n)).

We can apply this concept to create a virtual back-

bone depending on the different ranges between the

nodes, which were created using the decomposition

r-cut algorithm. The most important two r-cuts are

and r

in Fig. 5. Therefore, a virtual backbone

can be built from the node u

to any node within the

range of r

. However, choosing the nodes that are

located in the outer coverage region u

, . . . ,u

will in-

crease the coverage of the network and reduces the

required number of nodes participating in the duty-

cycling backbone. When the backbone network is not

active, node u

uses the wake-up signals to wake-up

the nodes in the r

region, then it continues until a

node participating in the backbone is reached.

Figure 5: A hierarchical cut decomposition algorithm to

create a duty-cycling backbone.

7 SIMULATIONS

We have simulated the greedy shortest wake-up path

(SP) and the embedding tree (ET) algorithm to deliver

messages from a source to a sink. The embedding tree

algorithm uses the hierarchical cut decomposition to

create a duty-cycling backbone. Although, the back-

bone communication range can be chosen to be any

r −cut < r

. Our aim is to maximize the coverage and

reduce the number of participating nodes in the duty-

cycling backbone. The nodes are randomly deployed

in the network and the following parameters are used

to implement the algorithms and measure their per-

formances. These parameters are based on real world

measurements.

Table 1: Simulation parameters.

Symbol Description Value

n Number of deployed nodes 2000

l Square area edge length 1000 m

Wake-up signal range

40 m

Data messages range

200 m

Wake-up signal energy 456 mW

Wake-up signal energy 51 mW

In Fig. 6, the wake-up algorithm constructs a

path using the shortest path from each source to the

sink. The nodes go back directly to sleep after wak-

ing a node located nearer to the sink location based on

wake-up hops.

0 100 200 300 400 500 600 700 800 900 1000

100

200

300

400

500

600

700

800

900

1000

Figure 6: Shortest wake-up Algorithm.

In Fig. 7, a hierarchical cut decomposition parti-

tions the network into clusters where the green nodes

are located in the data message transmission range of

other nodes. A virtual backbone is created to con-

nect these nodes to perform a duty cycling when they

are active. Nodes participating in the backbones don’t

go directly to sleep after transmitting data messages.

In case a node sense new data, the node transmits

wake-up signal to wake-up near by node or if it is

Convergecast Algorithms for Wake-up Transceivers

141

located in the range of a nodes that is performing

duty-cycling data messages are transmitted without

the need to wake-up a chain of nodes to reach the

backbone. Therefore, we can see in Fig. 7 that the

source nodes transmit wake-up signals depicted in the

blue continuous line until they are in the range of the

backbone, then data messages are transmitted which

are depicted in a black dashed line.

0 100 200 300 400 500 600 700 800 900 1000

100

200

300

400

500

600

700

800

900

1000

Figure 7: Embedding Tree Algorithm.

We measured the performance of the algorithms

according to message delivery delay and power con-

sumption. Fig 8 shows the delay needed to transmit

a message from a source to the sink. In an inactive

and slow networks where events happen infrequently,

the delay is limited to waking the nodes on the short-

est path to the sink. When the density of events in-

creases, message delivery will occur on the backbone

which reduces the need to transmit wake-up mes-

sages. The message delay is measured based on the

number of hops to reach the sink. Thus, the delay in

the shortest wake-up algorithm depends on the diam-

eter of the network, whereas the delay in the embed-

ding tree depends on the number of active nodes. The

delay achieved for the embedding tree (duty 50%) has

a better performance than the shortest wake-up and

other embedding tree with different duty-cycles since

the nodes stay longer period active and cover higher

transmission ranges.

For power consumption in Fig 9, we randomly

generated 10 events in the network in different rounds

to measure the power needed to deliver messages to

the sink. Power consumption using the shortest path

grows linearly according to the number of messages

and the wake-up diameter described in section 6. The

shortest wake-up algorithm performs efﬁciently com-

pared to the embedding tree algorithm due to the fact

that the nodes go directly to sleep and don’t waste

time in idle listening in the network. However, upon

increasing the events and the network become more

0 1 2 3 4 5 6 7 8 9 10

100

120

140

Number of Events

Delay (Hops)

ET, duty 10%

ET, duty 25%

ET, duty 50%

Figure 8: Message delivery delay.

0 10 20 30 40 50 60 70 80 90 100

Time (Rounds)

Power Consumption (W)

ET, duty 10%

ET, duty 25%

ET, duty 50%

Figure 9: Network power consumption.

active, the nodes will use the backbone network to de-

liver data messages which reduces the need to trans-

mit wake-up signals. Since idle listing in an active

network consumes less energy than waking-up the

path to the sink. Therefore, the shortest wake-up al-

gorithm can’t compete with embedding tree algorithm

on the long run for a dense active network.

8 CONCLUSIONS AND FUTURE

WORK

The development of wake-up receivers is an alterna-

tive approach for sensor networks. Using wake-up

receivers decreases energy consumption to the min-

imum, where the transceiver is activated only on de-

mand by receiving wake-up signals or through sens-

ing new data.

In this work, we study the problem of converge-

cast for wake-up transceivers, where all the nodes try

to deliver messages to the sink. The challenge is to

decrease the latency for delivering messages because

SENSORNETS 2016 - 5th International Conference on Sensor Networks

142

using the wake-up transceivers will keep the network

for longer periods in sleep, which makes the network

less reactive. Thus, the convergecast algorithms have

to set a delivery bound of ∆ rounds to deliver mes-

sages to the sink in order to maintain an active net-

work.

We proposed a greedy shortest wake-up path and

embedding tree duty cycle covering backbone. The

performance for combing both the wake-up and duty-

cycle for a dense network lowers the energy and re-

duces the delay compared to the greedy wake-up al-

gorithm.

Furthermore, the behavior of the wake-up

transceiver increases the time required to wake-up the

nodes, which increases the latency of message de-

livery. A theoretical analysis for combining duty-

cycling with the wake-up transceiver has to be ex-

tensively studied. Since, the competitive ratio of the

algorithms has to be compared with the competitive

ratio of the ofﬂine algorithms.

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