=Paper=
{{Paper
|id=Vol-2344/paper5
|storemode=property
|title=A model for estimating energy consumption seen when nodes of ubiquitous sensor networks communicate information to each other
|pdfUrl=https://ceur-ws.org/Vol-2344/paper5.pdf
|volume=Vol-2344
|authors=Tatyana Astakhova,Natalya Verzun,Mikhail Kolbanev,Aleksey Shamin
|dblpUrl=https://dblp.org/rec/conf/micsecs/AstakhovaVKS18
}}
==A model for estimating energy consumption seen when nodes of ubiquitous sensor networks communicate information to each other==
https://ceur-ws.org/Vol-2344/paper5.pdf
A model for estimating energy consumption seen
when nodes of ubiquitous sensor networks
communicate information to each other
Tatyana Astakhova1[0000−0002−7032−0697] , Natalya Verzun2[0000−0002−0126−2358] ,
Mikhail Kolbanev2[0000−0003−4825−6972] , and Aleksey
Shamin1[0000−0001−7690−8718]
1
Nizhny Novgorod State University of Engineering and Economics, Oktyabrskaya
Str. 22a, 606340 Knyaginino, Russia ctn af@mail.ru, ngiei-spo@mail.ru
2
St. Petersburg State Electrotechnical University “LETI”, Professor Popov Str. 5,
197376 St. Petersburg, Russia verzun.n@unecon.ru, mokolbanev@mail.ru
Abstract. A model for calculating the total energy consumption for the
implementation of information interaction processes of nodes via radio
networks, which allows to evaluate the ecological compatibility of the
network and manage its lifetime, is developed on the basis of data on
the distribution in space of sensor nodes organized in accordance with
the mesh topology. The probability distribution functions of the random
value of the power of the radiating antenna of the sensor device, sufficient
for transmitting the data block to the receiving side, and the total energy
consumption of this network during information interaction are obtained.
A mathematical model of the physical process of information interaction
in the sensor network in the case of a Poisson field of points and for differ-
ent variants of retransmissions – the first, second, fourth and n-th “neigh-
bor” is built. Numerical calculation and analysis of the influence of the
parameters of the considered ubiquitious sensor network and nodes on
the required radio signal power at the transmitting antenna of the object
are conducted. The presented material develops the results of modeling
the interaction process of Internet of Things devices by determining the
impact on energy consumption of probability-energy characteristics. The
study allowed to determine the interdependence of energy and informa-
tion parameters of the sensor network. The constructed model will allow
to estimate the lifetime of the sensor network. A possible development
of the presented research may be the development of routing protocols
that use the assessment of energy consumption by sensory devices.
Keywords: Distribution density · Energy costs · Energy efficiency · En-
vironmental friendliness of the network · Internet of Things · Poisson field
of points · Probability-energy characteristics · Sensor nodes · Ubiquitous
sensor network
1 Relevance
Information systems have an increasingly greater impact on the Earth’s envi-
ronment. It is already the case that roughly a third of electricity generated
2 T. Astakhova et al.
globally is consumed by back-end devices, routers, and infocommunication net-
works’ data processing centers, while electricity generation capacity of big cities
and smaller towns is becoming the main stumbling block to introducing digital
economy technologies [1, 2].
The fundamental principle that is recommended by the International Telecom-
munication Union to be followed when creating 5G networks or Future Networks
(FN) is the principle of environmental sustainability [3], according to which it
is required to implement technical solutions that reduce energy consumption in
order to make FN environmentally-friendly.
One of the most powerful consumers of electricity is the Internet of Things,
whose terminals are self-powered smart things (sensor-equipped devices) inter-
acting with each other via radio networks. Increased lifetime of this type of
network directly depends on saving battery power of sensor-equipped devices,
while battery power is mainly consumed by radio transmitters, which require
about a million times more energy to transmit one bit of information compared
to the power used when the bit is processed by a processor.
A need to make infocommunication networks more environmentally sustain-
able coupled with a need to increase the lifetime of sensor-equipped devices
by saving energy of their batteries have both determined the relevance of the
conducted study, whose results can be applied when developing methods for
managing energy consumption on the Internet of Things.
2 Methods
ITU-T Recommendation Y.3021 identifies three levels (for devices, equipment,
and the network as a whole), any of which requires specific energy-saving tech-
nologies to be developed [4]. At the network level, energy saving can be facilitated
not only by the rational choice of parameters for information flow control proto-
cols such as the length of transmitted blocks, a way to route packages through
the network, an algorithm for media access, a method for error-control coding of
transmitted blocks, data compression, data encryption, etc. but also by power
control of sensor-equipped device’s radio transmitter [5]. With the distance be-
tween the interacting sensors reduced, the power can be adjustably reduced;
conversely, with the distance between the interacting sensors increased, it can
be increased. Respective mechanisms have been implemented in a number of
existing radio networks.
In this case, total expenditure of electricity in the network with the appropri-
ate protocols does not only depend on how intensely information is transmitted
between the terminals, but also on how dense the sensory field is and which
criterion has been used for selecting the transit node.
The purpose of this paper is to develop a model for estimating the total
energy consumption required for organizing information-based interaction be-
tween sensor network nodes that depends on spatial network parameters as well
as technical parameters of sensor-equipped devices, since this indicator is the one
A model for estimating energy consumption 3
that characterizes ecological compatibility of the network during its operation
and gives insight into the network lifetime as a whole.
The subject under investigation is a ubiquitous sensor network, which is a
set of sensor-equipped smart things connected with each other and with a cloud,
where measurement of physical parameters of the environment is ensured by the
sensors.
It is assumed that the sensor network has a cellular (or mesh) topology
and, at the data link layer, provides direct communication between neighbors
within the radio range, whereas communication between the other elements is
ensured with relays. A coordinator can be used to communicate with the outside
environment.
The sensory network is characterized by the size of the sensory field and
the number of smart things located in this space. Unlike the coverage area of
infrastructure networks, the sensor field can change linear dimensions which
depend on random relocation of smart things; be two-dimensional and three-
dimensional, accommodate the changing number of smart things that require
integrated management.
Examples of the sensory field include but are not limited to the following:
the territory of a settlement, a monitoring system for aroma safety in a certain
area [6, 7], an agricultural farm, a body or part of a human body in medicine,
an oil rig in the extractive industry, etc.
All the other spatial characteristics depend on the size (the area or the vol-
ume) of the sensory field as well as the number of smart things put together.
The field of points which are randomly distributed in space is chosen as a
model of the sensory field, with the main characteristic being density of the
field measured by an average number of points per unit of the area (volume). A
sensory field consisting of homogeneous sensors is looked into, where:
– the probability of occurrence of any given number of points in any area of
the surface does not depend on how many points fall into any areas that do
not intersect with this one;
– the probability of hitting the elementary region of two or more points is
negligible compared to the probability of hitting a single point.
Such a sensory field can be described by a Poisson field of points.
These conditions have enabled us to obtain probability distribution functions
of the random power value of the radiating antenna on the sensor-equipped
device, sufficient for transmitting the data block to the receiving side, and the
total energy consumption of this network while communicating data.
3 Results
According to the currently used routing protocols of the ubiquitous sensor net-
work, there are various options for retransmitting data blocks when transmit-
ting from a smart thing to base station: the first, second, and so on “neighbor”
(Fig. 1).
4 T. Astakhova et al.
(a) (b)
(c)
Fig. 1: Possible options for hops: (a) retransmission to the nearest sensor node;
(b) retransmission to the second closest sensor node; (c) retransmission to the
third nearest sensor node.
We construct a mathematical model of the physical process of information in-
teraction in the sensor network in the case of a Poisson field of points (sensor
nodes) and for different versions of retransmissions of the data blocks to the
first, second, fourth and n-th neighbor.
The number of points (m) of a uniform Poisson field on a plane with density ν
on a sufficiently large circle of radius R. The distribution function of the distance
between sensor nodes obeys the Poisson law
am −a
Fm = e (1)
m!
where a is the mathematical expectation of the number of points falling into the
domain S [m2 ].
The distribution function of the distance between points of a uniform Poisson
field of points on the plane obeys the Rayleigh law: for the nearest “neighbor”
(sensor node), the distribution law is
F1 (r) = 1 − e−πr ν
2
(2)
where does the distribution density of the random variable r
f1 (r) = 2πνre−πr ν
2
(3)
Then the average distance to the nearest sensor node is calculated by the formula
∫ ∞ ∫ ∞
1
r · 2πνre−πr ν dr = √
2
r= r · f1 (r)dr = (4)
0 0 2 ν
According to the Friis transmission equation, the radio signal power at the trans-
mitting antenna of the object of the wireless sensor network is determined as
follows:
16Pr π 2 r2
Pt = (5)
Cr Ct γ 2
A model for estimating energy consumption 5
where γ is the wavelength [m] of the transmitted radio signal, Ct is the isotropic
directivity of the transmitting antenna in the direction of the receiving antenna,
Cr is the isotropic directivity of the receiving antenna in the direction of the
transmitting antenna, Pt is the power delivered to the terminals of an isotropic
transmit antenna [W] (excluding losses), Pr is the power available at receiving
antenna [W] (excluding losses), r – distance between the antennas of sensor
network objects [m]. The required signal power at the transmitting antenna Pt ,
under the assumption that the radio signal power at the receiving antenna Pr is
constant, a random variable depending on the distance between the interacting
objects.
The wavelength is related to the frequency of the signal flow
c
γ= (6)
f
where c – speed of light (∼ 3 · 108 [m/s]).
Substituting γ in the Friis equation, we obtain the radio signal power at the
transmitting antenna in the form:
16Pr π 2 r2 f 2
Pt = (7)
Cr Ct c2
The average power is found by substituting the average distance:
4Pr π 2 f 2
Pt = (8)
νCr Ct c2
The total transmission time of all data blocks is t = Λ · τ , where τ is the activity
time of a smart object when transmitting one block, Λ is the total transmission
intensity of all blocks.
The total intensity with regard to transits is Λ = (k + 1) · λ, where k is the
number of hopes, λ is the blocks transmission rate.
The channel speed at frequency f according to the Nyquist formula is 2f [bit/s],
b
and then the activity time τ is calculated as τ = 2f , where b is the length of the
transmitted blocks (bit).
The number of transits (hopes) will be taken upwards to the nearest integer
⌈ ⌉
R
k= (9)
2·r
Then the total time takes the form
√
⌈R ν + 1⌉λb
t= (10)
2f
The average energy spent on the transfer of the block smart things
e = Pt · t (11)
6 T. Astakhova et al.
Therefore, for transfer information to the nearest object is calculated as follows
√
2Pr π 2 f λb (⌈R ν⌉ + 1)
e1 = (12)
νCr Ct c2
The average energy spent on the transfer of the second block of the distance of
a sensor node ( √ )
9Pr π 2 f λb ⌈ 23 R ν⌉ + 1
e2 = (13)
2νCr Ct c2
The average energy spent on the transfer of the block to the fourth sensory
object ( √ )
1225Pr π 2 f λb ⌈ 16
35 R ν⌉ + 1
e4 = (14)
128νCr Ct c2
Consider the case when information is transmitted to the n-th sensor node. In
this case, the Rayleigh’s law will be as follows
∑
n−1
(πr2 ν)k −πr2 ν
Fn (r) = 1 − e (15)
k!
k=0
or
Γ (n, r2 ν)
Fn (r) = 1 − (16)
Γ (n)
∫ ∞ −t n−1 ∫∞
where Γ (n) = 0 e t dt, and Γ (n, r2 ν) = r2 ν e−t tn−1 dt.
Distribution density of a random variable r
( )
Γ n + 21
fn (r) = √ √ (17)
π νΓ (n)
and the average energy that is required to transfer b bits of information of the
n-th is (⌈ √ √ ⌉ )
( )2 R π νΓ (n)
8Pr πΓ n + 12 f λb Γ (n+ 21 )
+ 1
en = 2 (18)
νΓ (n) Cr Ct c2
4 Numerical calculation
Using the above expressions, we carried out a numerical calculation and analyzed
the effects of the parameters of the considered wireless sensor network and sensor
nodes on the required radio signal power at the transmitting antenna of the
wireless sensor network object.
Suppose that when a block is transmitted along a route, when choosing a
transit smart thing, the nearest “neighbor” is selected with probability p and
the fourth neighbor with probability (1 − p). Then the energy expended on the
transfer unit
egen = e1 · p + e4 (1 − p) (19)
A model for estimating energy consumption 7
√ ( √ )
2Pr π 2 f λb (⌈R ν⌉ + 1) 1225Pr π 2 f λb ⌈ 16
35 R ν⌉ + 1
egen = p + e 4 = (1 − p)
νCr Ct c2 128νCr Ct c2
(20)
At values c = 3 · 108 m/s, Ct = 1,Cr = 1, Pr = 0.1 · 10−3 W, R = 56m,
f = 13.56 · 106 Hz, b = 64 bits, λ = 1 block/s, ν = 0.01 m12 (see Fig. 2):
egen = −1.17 · 107 p + 2 · 107 [J] (21)
Fig. 2: The dependence of energy consumption on the probability of choosing a
transit option.
The influence on the energy consumption of a sensor node of the following param-
eters of ubiquitious sensor network: the density of distribution of smart things
in the network (ν), length (b) and intensity (λ) of transmitted blocks, radio
frequency (f ), transit option is also considered in the article.
The dependence of energy consumption on the distribution density of sensor
nodes on a plane with different transmission options for different signal frequency
values is presented in Figure 3.
Figure 4 shows the dependence of energy consumption on the length of the
transmitted blocks with the signal frequency f = 13.56 · 106 Hz, the intensity
of the transmitted blocks λ = 1 block/s, and the density of the distribution
ν = 0.01 m12 .
The dependences of energy consumption on the intensity of the message
appearance and on different values of the frequency with the length of the trans-
mitted blocks b = 64 bits and the distribution density ν = 0.01 m12 are presented
in Figures 5 and 6, respectively.
Thus, in the paper, the probability distribution function of the random power
values of the radiating antenna on the sensor-equipped device, which provides
the possibility of a stable information communication, has been obtained.
8 T. Astakhova et al.
(a) (b)
(c) (d)
Fig. 3: Dependence of energy consumption on the density of sensor nodes at
signal frequencies:
(a) f = 13.56 · 106 Hz, (b) f = 40 · 106 Hz,
(c) f = 2.4 · 109 Hz, (d) f = 5.8 · 109 Hz.
Influence of the spatial parameters of the sensor network on its total energy
consumption for various frequency ranges has been evaluated.
Recommendations are made regarding development of procedures for select-
ing routes in mesh networks according to the criterion of energy saving.
5 Discussion
When communication networks created in the twentieth century had been de-
signed, correlations between their space-, time-, and energy-related character-
A model for estimating energy consumption 9
Fig. 4: Dependence of energy consumption on the length of the transmitted
blocks.
Fig. 5: The dependence of energy consumption on the intensity of the blocks
appearance.
istics were not taken into account, while performance quality indicators were
described using probabilistic-temporal characteristics such as the probability
distribution functions of data transfer times from the information source to the
communication channel, transmission of the signal via channels between network
centers, control of signal moving in network centers or their components [8].
10 T. Astakhova et al.
Fig. 6: The dependence of energy consumption on the frequency of the radio
signal.
Another kind of indicators are network reliability indicators [9]. An example
of research where a redundant distribution of requests is proposed in order to
improve reliability of transmission in a network with additional energy expen-
diture for such interaction not having been taken into account, can be found in
the article [10].
In modern networks, such as FN or the Internet of Things, the mutual depen-
dence of physical parameters can no longer be neglected. The results obtained
in this paper confirm this statement and allow us to quantitatively compare the
correlation between the quality of service measured using the probability-time
characteristics with the energy consumption that ensures this quality.
The presented material specifies the results of the study [11], in which a
general approach to selection of information technologies has been worked out
for the first time. In addition to the quality of information interaction in a
particular subject area, the approach also takes into account the amount of
physical resources required. Moreover, the paper elaborates on the results of
work [12], where simulation of the interaction process between IoT devices has
been carried out with the impact of the physical and data link layer protocols
on the power consumption taken into account.
6 Conclusion
This study looks into probabilistic and energy characteristics, which also depend
on the network parameters of the network layer protocol apart from physical and
data link layer ones. It is proposed to add probabilistic and energy characteris-
tics, which depend on the spatial parameters of the network as well as technical
characteristics of sensor-equipped devices, to the previously used indicators for
network performance assessment.
A model for estimating energy consumption 11
The presented research may be followed up by an attempt to design routing
protocols that use estimation of energy consumption by sensor-equipped devices.
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