Convergecast Algorithms for Wake-up Transceivers
Amir Bannoura
1
, Leonhard Reindl
1
and Christian Schindelhauer
2
1
Laboratory for Electrical Instrumentation, University of Freiburg,
Georges-Köhler-Allee 106, 79110 Freiburg, Germany
2
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
w
than those
standard message transmissions e
m
, when nodes are awake. Furthermore, the distance range r
w
is also smaller
than the distance range r
m
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
w
and the message graph G
m
are modeled by planar r
w
-
and r
m
-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
Copyright
c
2016 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
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
1
+, N + 2 }, where they assume the nodes
n
1
> n
2
> .. > n
m
. = 1 if n
1
= n
2
, 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
e
m
> 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
m
> 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
w
> e
m
, since all available technologies
need considerably higher cost, e.g. the range e
w
/e
m
have a value of more than 50 times. Furthermore, the
transmission range r
w
of a wake-up call is considered
smaller, i.e. r
w
< r
m
. Current technology delimit the
ratio r
m
/r
w
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
m
, since otherwise
the communication network is disconnected. Now, if
two neighbored nodes have a distance of more than
r
w
, 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
i
be the wake-up messages and M
i
be
the data messages in round i. Then, the average total
energy per round is defined as
E
avg
=
1
T
T
i=1
|M
i
|e
m
+ |W
i
|e
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
m
, 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
2
. Then the energy
over all rounds is at most n
T e
m
, which results in an
average energy of
1
T
ne
m
, which converges towards
0.
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
m
/r
w
e nodes with
distance r
w
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
m
/ + 2e
m
.
r
m
r
w
wake-up
sink
r
m
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
m
. An algo-
rithm with wake-up signals could have woken up the
middle nodes with energy 2dr
m
/r
w
ee
w
.
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
0
,v
1
,.. ., v
k
= s) such that
|v
i
,v
i+1
| r
w
.
Theorem 2. Using wake-up signals there is an on-
line algorithm which achieves an online competitive
bound of at most 4n
e
w
e
m
. 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
T
0
n(e
w
+ e
m
), if T
0
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
T
0
2
e
m
, since sensor data of
two consecutive intervals could have been combined.
e
w
> e
m
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
T
0
ne
w
is necessary.
wake-up
sink
data
r
w
r
m
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
w
is much
sparser than the graph of possible communication
messages G
m
.
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
w
of the graph, i.e. O(sD
w
e
w
).
Duty-cycling Covering Backbone is the standard
approach without wake-up signals. It uses a backbone
tree T
b
of nodes, which is a tree in G
m
, where for every
node u V there exists a node in V
b
= V (T
b
), 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
b
|
T
e
m
+ se
m
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
r
w
and r
m
in Fig. 5. Therefore, a virtual backbone
can be built from the node u
1
to any node within the
range of r
m
. However, choosing the nodes that are
located in the outer coverage region u
2
, . . . ,u
5
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
1
uses the wake-up signals to wake-up
the nodes in the r
w
region, then it continues until a
node participating in the backbone is reached.
rw
rm
u1
u2
u3
u4
u5
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
m
. 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
r
w
Wake-up signal range
40 m
r
m
Data messages range
200 m
e
w
Wake-up signal energy 456 mW
e
m
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
0
100
200
300
400
500
600
700
800
900
1000
1
2
3
4
S
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
0
100
200
300
400
500
600
700
800
900
1000
1
2
3
4
S
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
0
20
40
60
80
100
120
140
Number of Events
Delay (Hops)
SP
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
0
10
20
30
40
50
60
Time (Rounds)
Power Consumption (W)
SP
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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