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 different variants of retransmissions - the first, second, fourth and n-th “neighbor” 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 information 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.
globally is consumed by back-end devices, routers, and infocommunication
networks’ data processing centers, while electricity generation capacity of big cities
and smaller towns is becoming the main stumbling block to introducing digital
economy technologies [
The fundamental principle that is recommended by the International
Telecommunication Union to be followed when creating 5G networks or Future Networks
(FN) is the principle of environmental sustainability [
One of the most powerful consumers of electricity is the Internet of Things, whose terminals are self-powered smart things (sensor-equipped devices) interacting 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 sustainable 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
ITU-T Recommendation Y.3021 identifies three levels (for devices, equipment,
and the network as a whole), any of which requires specific energy-saving
technologies to be developed [
In this case, total expenditure of electricity in the network with the appropriate 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 between sensor network nodes that depends on spatial network parameters as well as technical parameters of sensor-equipped devices, since this indicator is the one 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 threedimensional, 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 [
All the other spatial characteristics depend on the size (the area or the volume) 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
According to the currently used routing protocols of the ubiquitous sensor network, there are various options for retransmitting data blocks when transmitting from a smart thing to base station: the first, second, and so on “neighbor” (Fig. 1).
We construct a mathematical model of the physical process of information interaction 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 on a sufficiently large circle of radius R. The distribution function of the distance between sensor nodes obeys the Poisson law (1) (2) (3) (4) 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 where does the distribution density of the random variable r Then the average distance to the nearest sensor node is calculated by the formula r = ∫ 1 0 r · f1(r)dr = r · 2
re ∫ 1 0 r2 dr =
1 2√ According to the Friis transmission equation, the radio signal power at the transmitting antenna of the object of the wireless sensor network is determined as follows:
Pt = 16Pr 2r2 where 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 f where c – speed of light (∼ 3 · 108[m=s]).
Substituting in the Friis equation, we obtain the radio signal power at the transmitting antenna in the form: The average power is found by substituting the average distance: The total transmission time of all data blocks is t = · , where is the activity time of a smart object when transmitting one block, is the total transmission intensity of all blocks.
The total intensity with regard to transits is = (k + 1) · , where k is the number of hopes, is the blocks transmission rate.
The channel speed at frequency f according to the Nyquist formula is 2f [bit=s], and then the activity time is calculated as = 2bf , where b is the length of the transmitted blocks (bit).
The number of transits (hopes) will be taken upwards to the nearest integer k = ⌈ R ⌉
2 · r t = ⌈R√ + 1⌉ b 2f Then the total time takes the form The average energy spent on the transfer of the block smart things e = Pt · t (6) (7) (8) (9) (10) The average energy spent on the transfer of the second block of the distance of a sensor node
Therefore, for transfer information to the nearest object is calculated as follows Fn(r) = 1 − n 1 ∑ ( r2 )k k=0 k!
e r2 Fn(r) = 1 − (n; r2 )
(n) (n + 21 ) fn(r) = √ √ (n) The average energy spent on the transfer of the block to the fourth sensory object Consider the case when information is transmitted to the n-th sensor node. In this case, the Rayleigh’s law will be as follows or where (n) = ∫01 e ttn 1dt, and (n; r2 ) = ∫r12 e ttn 1dt.
Distribution density of a random variable r and the average energy that is required to transfer b bits of information of the n-th is 8Pr (n + 21 )2f b (⌈ Rp(np+ 12 )(n) ⌉ + 1
) (n)2CrCtc2 en = 4
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) (12) (13) (14) (15) (16) (17) (18) (20) (21) 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 selecting routes in mesh networks according to the criterion of energy saving. 5
When communication networks created in the twentieth century had been
designed, correlations between their space-, time-, and energy-related
characterFig. 4: Dependence of energy consumption on the length of the transmitted
blocks.
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 [
Another kind of indicators are network reliability indicators [
In modern networks, such as FN or the Internet of Things, the mutual dependence 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 [
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 characteristics, 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.
The presented research may be followed up by an attempt to design routing protocols that use estimation of energy consumption by sensor-equipped devices.