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Energy-Optimal Data Aggregation and Dissemination for the Internet of Things
Fitzgerald, Emma; Pioro, Michal; Tomaszewski, Artur
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IEEE Internet of Things Journal
DOI:
10.1109/JIOT.2018.2803792
2018
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Citation for published version (APA):
Fitzgerald, E., Pioro, M., & Tomaszewski, A. (2018). Energy-Optimal Data Aggregation and Dissemination for
the Internet of Things.
IEEE Internet of Things Journal
,
5
(2), 955-969.
https://doi.org/10.1109/JIOT.2018.2803792
Total number of authors:
3
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1
Energy-Optimal Data Aggregation and
Dissemination for the Internet of Things
Emma Fitzgerald
∗
emma.fitzgerald@eit.lth.se
Michał Pi
´
oro
∗†
michal.pioro@eit.lth.se
Artur Tomaszewski
†
artur@tele.pw.edu.pl
∗
Department of Electrical and Information
Technology
Lund University
SE-221 00 Lund
Sweden
†
Institute of Telecommunications
Warsaw University of Technology
Nowowiejska 15/19
00-665 Warsaw
Poland
Abstract—Established approaches to data aggregation in wire-
less sensor networks (WSNs) do not cover the variety of new use
cases developing with the advent of the Internet of Things. In par-
ticular, the current push towards fog computing, in which control,
computation, and storage are moved to nodes close to the network
edge, induces a need to collect data at multiple sinks, rather
than the single sink typically considered in WSN aggregation
algorithms. Moreover, for machine-to-machine communication
scenarios, actuators subscribing to sensor measurements may also
be present, in which case data should be not only aggregated and
processed in-network, but also disseminated to actuator nodes. In
this paper, we present mixed-integer programming formulations
and algorithms for the problem of energy-optimal routing and
multiple-sink aggregation, as well as joint aggregation and
dissemination, of sensor measurement data in IoT edge networks.
We consider optimisation of the network for both minimal total
energy usage, and min-max per-node energy usage. We also
provide a formulation and algorithm for throughput-optimal
scheduling of transmissions under the physical interference model
in the pure aggregation case. We have conducted a numerical
study to compare the energy required for the two use cases, as
well as the time to solve them, in generated network scenarios
with varying topologies and between 10 and 40 nodes. Although
aggregation only accounts for less than 15% of total energy
usage in all cases tested, it provides substantial energy savings.
Our results show more than 13 times greater energy usage for
40-node networks using direct, shortest-path flows from sensors
to actuators, compared with our aggregation and dissemination
solutions.
Index Terms—Internet of Things; fog computing; mixed-
integer programming; sensor networks; aggregation
I. INTRODUCTION
Data aggregation has been a vital ingredient in wireless
sensor network (WSN) design for some time, improving
energy efficiency as nodes collate data on its way towards
the sink, reducing the number of packets that need to be
transmitted. However, we are now seeing the development of
new architectures and use cases with the advent of the Internet
of Things (IoT) and machine-to-machine (M2M) communica-
tion. Monitoring applications are still prevalent in application
scenarios such as smart grids, vehicular communications,
and smart cities, but are increasingly being complemented
with actuation and in-network processing. The presence of
actuators in the edge network means that data must not only
be collected, but also disseminated to actuators that need it.
An example of such a use case could be a nuclear reactor
with temperature sensors distributed throughout and actuators
that can open valves to flood the reactor with water for
emergency cooling in case of overheating. Each actuator needs
to collect measurements from multiple temperature sensors,
and if any of them exceeds a threshold, the valve is opened.
In this case, the aggregation function would be to take the
maximum of the aggregated temperature measurements. With
the use of in-network processing, the functions to be executed
at intermediate nodes can range from simple aggregation
functions, such as the maximum function for the nuclear
reactor, to more complex computations like compress-and-
forward [1] or error correction, which may use an appreciable
amount of energy in their execution.
Even in cases where data does not need to reach in-network
actuators, but should simply be collected and transmitted to
a single server, the expanding use of fog computing [2],
[3] (also called network edge computing), and the increased
heterogeneity of IoT networks means that the assumption of
a single sink to collect this data is no longer valid. Rather,
there may be multiple gateways with backbone connections
located at the network edge and possibly operated by different
parties. Much of the existing literature on data aggregation in
WSNs has however focused on single-sink scenarios, and so
there is a need to develop solutions that combine both gateway
selection and routing for data aggregation for optimal energy
efficiency. Fog computing not only brings new challenges, but
also provides new opportunities. With more powerful nodes
present at the network edge, greater coordination based on
more complex, optimal algorithms becomes feasible in some
cases, potentially reducing energy usage even further than
existing approaches designed to be executed by resource-
constrained sensor nodes. Even where the optimal solutions are
Copyright
c
2018 IEEE. Personal use of this material is permitted. However,
permission to use this material for any other purposes must be obtained from
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2
not feasible to use in practice, for example in highly dynamic
networks, it is nonetheless valuable to develop them in order
to provide performance bounds for approximate solutions.
A further challenge that must be met in conjunction with the
development of IoT systems is the rising density of networks,
with many nodes in close proximity nd multiple networks
often overlapping. This means that simple radio interference
models, such as the unit disk or protocol models, may not
be sufficient to capture the effects of second and higher order
interference. This refers to interference stemming from multi-
ple nodes transmitting simultaneously, even where any one of
these nodes’ transmissions would not be sufficient on its own
to prevent successful decoding of packets at a given receiver
node. Compatible sets (c-sets) [4] are capable of accounting
for physical interference — that is, based on received signal
strength — in a computationally efficient way, and have been
successfully applied to modelling and optimisation of wireless
mesh networks [5]–[9].
In this paper we present two new models for data ag-
gregation in IoT networks. The first model, which we call
1K, allows for collection of data at any of multiple, internet-
connected gateways. Meanwhile, the second model, nK, is
more applicable to scenarios with actuators present in the
network, and provides for joint data aggregation and dissemi-
nation to all, or some minimum number of, multiple destina-
tion nodes. In both of these models, it is possible to specify
a minimum number of sensor readings to be collected and
aggregated. We then formulate these models as optimisation
problems using mixed-integer programming (MIP), with the
objective of minimum total energy usage, taking into account
energy costs for both wireless transmissions and computation
of aggregation functions. While network lifetime is also often
a key performance metric, it requires a much more difficult
optimisation problem to achieve. In this work, we also make an
initial step towards network lifetime optimisation, by providing
formulations for min-max per-node energy optimisation, for
both the 1K and nK scenarios.
Using our models, sensor and gateway selection, as well as
the routing subgraphs for data aggregation and dissemination,
are jointly optimised. For the 1K case, we also present a
model and MIP formulation to optimise throughput of data
collection, while maintaining minimum energy usage. We have
performed numerical studies to investigate the minimum total
energy and min-max energy required for data aggregation and
dissemination, the maximum achievable throughput in the 1K
case, and the time to solve network scenarios with varying
numbers of nodes and topologies.
Our results show that aggregation constitutes a low energy
cost, disproportionately so when taking into consideration
the input energy costs for each transmission and aggregation
operation. However, it provides a large advantage, with, in the
most extreme case, 13.7 times higher energy usage using the
most efficient paths between individual sensors and actuators,
than using our nK aggregation and dissemination solutions.
Min-max energy optimisation provides overall less efficient
solutions, with less aggregation, but with energy usage more
fairly distributed amongst the nodes in the network.
The rest of this paper is organised as follows. In Section
II we provide an overview of the related work in this area.
Section III describes the network scenarios we consider, and
Sections IV–VII detail our system model and formulations.
In Section VIII we present the results of our numerical
study. Finally, Section IX concludes this paper and discusses
directions for future work.
II. RELATED WORK
The problem of energy-efficient data aggregation in wireless
sensor networks first began to receive substantial attention in
the 2000’s [10]. Given the constrained computation capacity of
sensor nodes and the distributed nature of such networks, much
of the focus was on approximation algorithms for practical
implementation, although some work has also been carried
out on finding optimal solutions [1], [11]–[18]. Approximation
algorithms for data aggregation can be mostly divided into
tree-based [19]–[23], clustered [24]–[29], and hybrid [30] ap-
proaches [10]. Two of the most influential protocols stemming
from such methods are LEACH [24], [25] and PEGASIS [20],
on which much other work is based [31]–[35]. More recently,
structure-free aggregation has been proposed [36], [37], which
does not rely on the formation of a routing tree or clusters and
is thus more suitable for highly mobile networks.
Most of this work assumes a single sink as the data
collection point, and only data aggregation is performed;
there is no dissemination to multiple actuators. Multiple sinks
are considered in [19], however here there is still only one
predetermined sink per data aggregation flow, making sink
selection unnecessary. In [21], data dissemination (but not
aggregation) is investigated, with multiple data sinks for each
source, but each sink can only receive data from a single
source. Optimal approaches with multiple sinks include [38],
however here only cluster formation is optimised, not the
overall routing tree, and cluster heads then transmit data
to a central collection point using single-hop transmissions.
In [17] multiple sinks were also used, giving an integer
linear programming formulation for an optimal data collection
schedule within each cluster such that at least one sensor
measurement of each type is collected in each frame. Again,
multihop transmission is not considered; sensor nodes transmit
directly to their nearest collection point. Another integer linear
programming solution, presented in [18], also has multiple
gateways, however the problem considered here is that of
gateway placement, rather than optimisation of a multihop
aggregation tree.
A scenario with multiple gateways motivates the work in
[1], but only a single sink is used in the actual optimisation
formulation. This work is however interesting from another
perspective, as it uses compress-and-forward to reduce the size
of a node’s transmission after it has overheard correlated mea-
surements from other nodes. In this paper, we consider fixed
packet sizes, and thus fixed transmission costs, however in
M2M communications, it is common for measurements to be
correlated, for example temporally, spatially, or semantically.
The use of compress-and-forward would thus be a worthwhile
direction to pursue in future iterations of our models.
In our 1K model, we address the optimisation of a multihop
routing tree for data aggregation of at least some given min-
3
imum number of sensor measurements, and their propagation
to any subset of multiple data collection nodes. As such, this
constitutes joint gateway selection and routing. Moreover, if
the total number of sensors in the network is larger than
the number of required measurements, sensor selection is
also included. In our nK model, rather than routing data
aggregates to any gateway, each destination node must receive
measurements from a minimum number of sensors. To the
best of the authors’ knowledge, ours is the first work that
considers such a joint aggregation and dissemination problem.
Such models are necessary, since use cases for networks
containing not only sensors producing data, but also actuators
consuming this data, will become increasingly common in
M2M communication scenarios [39].
We also provide throughput optimisation for the 1K case
using a physical interference model based on compatible sets.
Most existing work on data aggregation optimisation uses
either a unit disk or protocol interference model, in which
nodes have a larger interference range than their transmission
ranges, but still only first order interferences from individual
nodes are considered. Work that uses a more realistic physical
interference model includes [11], [13], [14], [16], though
with only a single sink and without joint aggregation and
dissemination.
III. SYSTEM OVERVIEW
For our use case, we consider an Internet of Things network,
with four types of nodes: sensor nodes, which produce data
by taking measurements and can also transit and aggregate
other sensors’ measurements; aggregator nodes, which act as
multihop relays and aggregators but do not take measurements;
actuator nodes, which require sensor data in order to perform
tasks; and gateways, which are fog nodes with backhaul
connections. Fog nodes are thus capable of reaching a central
server, such as a cloud service, via the Internet, and do not have
the same energy constraints as other nodes. Sensors, actuators,
and aggregators are battery-powered, and suffer energy costs
for both wireless transmission and the computation required
for data aggregation.
We thus have a wireless multihop network in which there is
a set of data streams S, representing different types of sensor
measurement. In each stream, there are a number of origin
nodes (sensors) O(s) producing data (one measurement from
each sensor per frame), and a number of destination nodes
(gateways or actuators) that wish to receive this data. Data
may be aggregated by nodes during transmission such that a
node receiving multiple packets belonging to a given stream
can combine them according to some function (e.g., average,
sum, count) and the node then only transmits a single packet
representing this aggregate. Data from different streams is not
aggregated; a stream is thus defined in a data-centric way as
consisting of information that is subject to aggregation.
How the destination nodes receive the data depends on the
application. In the simpler case, which we name 1K, we wish
to collect a certain number K of (aggregated) measurements
at some central server. In this case, the destination nodes
represent fog gateways, and it is not important which gateway
Fig. 1: An example 1K scenario, with K = 12. Sensors nodes
are shown in red, aggregator nodes in white, and gateway
nodes in blue. The central server is shown in yellow. Transit
nodes and links belonging to the minimum-energy aggregation
tree are highlighted in green.
collects any given measurement (Figure 1). In the figure, the
transmission links between the gateways and the central server
go over the Internet and thus do not incur energy costs.
The second use case, nK, is where the destination nodes
themselves wish to use the data, that is, the destination nodes
are actuators that must perform some action based on the
sensor measurements, and thus need to each collect a sufficient
number of measurements (Figure 2). These measurements
must originally come from different origin nodes, but multiple
destination nodes may receive the same set of measurements.
The performance metrics of interest will also in general
depend on the application, however here we will consider two
objective functions: minimum total energy usage, and min-max
energy usage. Energy is used both to transmit each packet,
and to aggregate packets. This means there is an inherent
trade-off in performing aggregation; each packet that must be
aggregated costs energy, but this aggregation saves energy by
reducing the number of packets to be transmitted.
Our first objective function aims to simply reduce the energy
used by the network as a whole, while our second function
targets network lifetime. Whether total energy usage or net-
work lifetime is of greater interest depends on the specific
application scenario. Where nodes are easily accessible for
battery changes, or are connected to mains power (as in, for
example, smart grids), total energy may be more important,
whereas when nodes rely on a single battery or on energy har-
vesting, network lifetime may take precedence. To determine
total energy usage requires a relatively simple additive function
of the energy used by all nodes in the network. However,
4
Fig. 2: An example nK scenario., with K = 12, for the
same network as in Figure 1. Sensor nodes are shown in red,
aggregator nodes in white, and actuator nodes in blue. The
central server, shown in yellow, is not used for the nK case.
Transit nodes and links belonging to the minimum-energy
aggregation and dissemination subgraph are highlighted in
green.
using network lifetime as the objective leads to much more
complicated optimisation. This is because in this case we must
consider which nodes are depleted of energy first, and how this
affects the routing of the data streams. As such, the min-max
energy optimisation we contribute in this work does not fully
characterise network lifetime, but nonetheless provides the first
step towards this goal.
The performance of data aggregation will also depend on
the aggregation policy. For example, data may be aggregated
based on temporal or geographical locality, or on data sim-
ilarity. In our modelling, we take an agnostic approach to
the aggregation policy. Different aggregation policies may be
applied by selecting appropriate eligible origin, destination,
and aggregator nodes, and this topology can then be supplied
to our formulations. Our model allows for different sets of
origin, destination and aggregator nodes for each data stream,
giving fine-grained control over the data aggregation policy.
In the following sections, we present mixed-integer pro-
gramming formulations for minimum total energy and min-
max energy routing for both the 1K and nK cases, as well
as a formulation for minimum frame (maximum throughput)
transmission for the 1K case.
IV. 1K TOTAL ENERGY MINIMISATION
The method we employ for 1K aggregation is to use reverse
arborescences (called r-arborescences in the following), that is,
directed trees in which the arcs point towards the root node
V set of nodes (vertices) in the network
E set of arcs (v, w), v, w ∈ V indicating node w is within
transmission range of node v (barring any interference)
S set of data aggregation streams
V(s) set of nodes belonging to the subgraph for stream s ∈ S
E(s) set of arcs belonging to the subgraph for stream s ∈ S
K(s) number of packets that need to be collected to satisfy stream
s ∈ S
O(s) set of origin nodes for stream s ∈ S
N (s) set of aggregator nodes for stream s ∈ S
D(s) set of destination nodes for stream s ∈ S
W central server (sink node)
δ
−
(v) set of incoming arcs to node v
δ
+
(v) set of outgoing arcs from node v
P total transmission energy cost incurred by all nodes
Q total processing energy cost incurred by all nodes
x
o
s
whether or not the packet in stream s ∈ S from node o ∈ O(s)
is collected by the sink node W
y
se
whether or not arc e ∈ E is used for stream s ∈ S
z
o
se
flow in stream s ∈ S from node o ∈ O(s) on arc e ∈ E
g
sv
number of (aggregated) measurements in stream s ∈ S aggre-
gated at node v minus 1 (and 0 if there is no aggregation at
v)
B transmission energy cost
C processing energy cost for aggregation
A(s) optimal reverse arborescence for stream s ∈ S
C set of all compatible sets (c-sets) for the network (V, E)
T
c
number of time slots to be used by c-set c ∈ C
n(e) number of stream arborescences that use arc e ∈ A
π
e
dual variables for frame minimisation
π
∗
e
optimal values of dual variables for frame minimisation
Y
e
whether or not arc e is present in the c-set generated by the
pricing problem
X
v
whether or not node v is present in the c-set generated by the
pricing problem
B set of binary numbers{0, 1}
R set of real numbers
R
+
set of non-negative real numbers
TABLE I: Summary of notation for 1K formulations.
such that all leaf nodes have exactly one path to the root node.
Using r-arborescences ensures that no packet from an origin
node in a given stream is counted twice, since it can only
reach the central server along a single path. For a complete
r-arborescence, each destination node for a stream should have
an arc connecting it to the central server (the root node),
however transmissions along these arcs are omitted from our
energy model, and so they do not induce energy costs and are
only used to ensure correct flows from origin to destination
nodes. The notation used in the following formulations is
summarised in Table I.
A. Assumptions
For the 1K use case, a total of K(s) measurements must
be collected at destination nodes for each stream s ∈ S. We
assume that:
1) The network graph G = (V, E) is composed of the set of
nodes V and the set of (directed) arcs E ⊆ V
2
\ {(v, v) :
v ∈ V}. The set of arcs incoming to and the set of
arcs outgoing from a given node v ∈ V (the so-called
incoming and outgoing stars) are denoted by δ
−
(v) and
δ
+
(v), respectively.
2) The set of nodes V is composed of three mutually
disjoint subsets: the set of sensor nodes O, the set of
aggregator nodes N , and the set of destination nodes
