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Optimization of green RNP problem for LTE networks using possibility theory

  • Soufiane DahmaniEmail author
  • Mohammed Gabli
  • El Bekkaye Mermri
  • Abdelhafid Serghini
Original Article
  • 16 Downloads

Abstract

At present, the demand for natural energy has been ever increasing, so energy has become a major concern for everyone. As Long Term Evolution Base Stations consume a large amount of the total energy expenditure in a cellular network, it is of keen interest to researchers to reduce the energy consumed by BSs when considering network planning. In this paper, we consider the green radio network planning problem for the LTE cellular networks. Our aim is to reduce energy consumption by reducing the number of active BSs, which will also reduce the production of carbon dioxide. Now BSs are currently operated and deployed for the worst traffic peak estimates. However, traffic fluctuates with time depending on the mobile stations behavior and their data needs. From our point of view, in order to investigate more realistic cases, we consider the situation where the traffic information is taken as imprecise and uncertain value. So, we introduce a model of problem where each traffic is a fuzzy variable, and then, we present a decision-making model based on possibility theory. To solve the problem, we propose a solution method using genetic algorithms and a dynamic Evolved Node B switching on/off strategy. The obtained results showed the efficiency of our approach and demonstrated considerable energy saving, through dynamic adaptation of the number of active BSs.

Keywords

Green LTE network planning BS switching Energy consumption Genetic algorithms Possibility theory 

1 Introduction

Long Term Evolution (LTE) was started as a project in 2004 by a telecommunication body known as the Third Generation Partnership Project (3GPP). LTE evolved from the universal mobile telecommunication system (UMTS), which in turn evolved from the Global System for Mobile communication (GSM). Rapid development of information technologies and their wide dissemination puts high requirements to telecommunication systems. During this period, there are many different approaches for LTE network planning. Some papers studied the radio part and its parameters optimization such as power allocation, radio resource scheduling, antenna down tilt and base station (BS) positioning (see, for instance, [1]) or even traffic capacity planning approach for LTE radio networks [2]. In general, LTE network planning involves several components such as antenna height, antenna inclination angle, base station (BS) transmit power, energy consumption and \(\hbox {CO}_{2}\) production from base station, BS capacity, BS position, transmission bandwidth, base station location. Energy is becoming a main concern, especially that it constitutes up to \(18\%\) of the operational cost in European countries; this is due to the increase in energy prices. Nowadays, the energy demand of major network operators is on the order of 3000 gigawatts (GW) per hour [3]. Mobile communications are increasingly contributing to global energy consumption and green house gas emissions which is very harmful to the environment since it traps heat inside the atmosphere. The global greenhouse gas emissions from information and communication technology (ICT) are comparable with those of the aviation industry. Wireless communications constitute approximately \(15\%\) of ICT [3]. Emissions of \(\hbox {CO}_{2}\) from the mobile network infrastructure were 64 Megatons in 2002 and are expected to reach 178 Megatons in 2020 [3].

Currently, several researches in different fields aim at finding solutions valuing green energy and environmental protection, see, for example, [4] and [5].

The area of cellular radio network planning (RNP) has been addressed in the literature using different models, assumptions and solution approaches. The authors in [6] proposed and evaluated a green RNP approach by jointly optimizing the number of active BSs and the BS on/off switching patterns based on the changing traffic conditions in the network in an effort to reduce the total energy consumption of the BSs. In [7], the authors proposed a multi-objective optimization framework aimed at minimizing the power consumption and the number of BS sleep mode switching in cellular networks, by jointly considering quality of service (QoS) requirements. In [8], the authors formulated an optimization problem that aims to maximize the profit of LTE cellular operators and to simultaneously minimize the \(\hbox {CO}_2\) emissions in green wireless cellular networks without affecting the desired quality of service (QoS). In [9], the authors have studied Evolved Node B (eNB) sleep modes to identify the traffic awareness in LTE networks and subsequently design a cooperative communication framework for energy consumption reduction. They calculated the percentage of energy which can be saved with eNB sleep modes, proving that it can be close to \(30\%\) of the total network energy consumption. The authors in [10] presented a MATLAB-based simulator to measure the network performance concerning LTE Advanced, in terms of throughput, energy efficiency and on-grid energy savings. In [11], the authors proposed a novel network model for the downlink LTE Advanced cellular networks with hybrid power supplies by deploying BSs having individual energy storages and on-site green energy harvester such as solar panel.

Only few works have explicitly taken into account uncertain parameters as part of the planning process. In [12], the authors developed optimization models and algorithms for joint stochastic approach for LTE RNP that optimizes the eNodeBs locations. For this, they presented a novel approach for cellular RNP that captures the uncertainty in signals and interference as part of the problem formulation leading directly to an optimized planning solution.

Because of the importance of load balancing and transfer optimization, the authors in [13] proposed a unified fuzzy-based self-management mechanism and reinforcement learning. In particular, they proposed an algorithm which modifies the transfer parameters to optimize the main key performance indicators related to load balancing and transfer optimization. In [14], the authors addressed the problem of planning the universal mobile telecommunication system base stations location for uplink direction using fuzzy logic. In this paper, we consider the green radio network planning (RNP) problem for LTE cellular networks. Our aim is to reduce energy consumption by reducing the number of active BSs in a given area while maintaining good coverage. In the classic model, when we do not use the dynamic eNodeB switching on or off strategy, the network operators deployed BSs at the peak hour or for the maximum load which determines the maximum required number of BSs. However, the set of deployed BSs remains active at all times even for low traffic states. Therefore, a loss of energy is made, at the moment when we can deactivate some BSs to save this energy. So, our first challenge is to determine the optimal set of BSs that should be turned on or off at a given traffic state. Thus, the operators can use these sets to optimally control the energy consumption of the network with the traffic variations.

On the other hand, in the literature, to decide the traffic states, the control center should monitor the traffic variations across a day over a period of time such as a month. Then, he calculates the average traffic per hour (see, for instance, [6]). However, considering only the average does not concretely reflect the variations in the data. From our point of view, since traffic demands vary a lot during the day, the traffic information must be taken as imprecise and uncertain value. To solve this kind of decision-making problems, there are two typical approaches which are stochastic approach and fuzzy approach. Classical probability theory has been and continues to be employed with remarkable success in those fields in which the systems are mechanistic, and human reasoning, perceptions and emotions do not play a significant role (see Zadeh [15]). However, in this problem, human reasoning and perceptions play a very important role. So, our second challenge is to introduce a fuzzy model, where each traffic number is taken as fuzzy number, instead of a crisp value.

As a result, we consider a model based on possibility theory using a dynamic eNodeB switching on or off strategy. Indeed, we study both possibility and necessity measures using reactive and proactive approaches. To solve the problem, we propose a solution method using genetic algorithms.

The rest of the paper is organized as follows. Section 2 presents the problem formulation and both proactive and reactive approaches into LTE networks. In Sect. 3, we propose a model based on possibility theory. In Sect. 4, we develop the proposition metaheuristic to solve the problem. We give in Sect. 5 some applications of our approach; then, we present the numerical results obtained. Finally, Sect. 6 presents the main conclusions of the study.

2 Problem statement and model presentation

Consider a territory to be covered by an LTE service. Let \({\mathcal {B}}\) be a set of possible BS locations. Given a traffic distribution at different time intervals, the aim is to choose the minimum set of BS locations from \({\mathcal {B}}\) to meet coverage and capacity constraints while minimizing the energy consumption of the network.

2.1 Traffic states

Nowadays, BSs are operated and deployed for the worst traffic peak estimates. However, traffic fluctuates with time. Indeed, traffic demands vary a lot during the day depending on the mobile stations (MSs) behavior and their data needs. Figure 1 illustrates this variation. In this figure, traffic variations are divided into three different states \(s_1\), \(s_2\) and \(s_3\) where \(s_1=[0,600]\), \(s_2=[600,900]\) and \(s_3=[900,1200]\). The period from the hour 00 a.m. to 12 a.m. corresponds to the first traffic state \(s_1\). Then, from the hour 12 to 14, the traffic increases to be in the second traffic state \(s_2\). The traffic continues to increase in the period [14, 20]. In this period, we are in the third traffic state \(s_3\). After this, the traffic decreases in the periods [20, 22] and [22, 24] which correspond, respectively, to the second and first traffic states.
Fig. 1

Example of traffic variation

2.2 Reactive and proactive approaches

In the reactive approach, we choose from \({\mathcal {B}}\) the optimal set of BSs, at the highest traffic state. This set represents the largest set of BSs that can be active in the network for any traffic state. Then, as the traffic state decreases, several BSs can be turned off while meeting the capacity and coverage requirements. For example, in Fig. 1, we begin to choose the optimal set of BSs at the third traffic state \(s_3\), see Algorithm 1 which explains the principle.

In the proactive approach, we choose from \({\mathcal {B}}\) the optimal set of BSs, at the lowest traffic state. This set of BSs can be used at any time, in the network, for all traffic states. Then, additional BSs are turned on from a traffic state to another as the traffic increases to meet the increasing capacity and coverage requirements. In Fig. 1, if we use this method, we must start by the first traffic state \(s_1\), see Algorithm 2.

The aim in both cases is to determine the optimal set of BSs that should be turned on or off at a given traffic state. Thus, the operators can use these sets to optimally control the energy consumption of the network with the traffic variations.

2.3 Parameters and variables

The main parameters in the considered system model are presented in Table 1. The decision variables are:
$$x_{i} = \left\{ {\begin{array}{*{20}l} 1 \hfill & {{\text{if}}\;BS_{i} \;{\text{is}}\;{\text{selected}},} \hfill \\ 0 \hfill & {{\text{otherwise}}.} \hfill \\ \end{array} } \right.$$
(1)
$$y_{{k,i}} = \left\{ {\begin{array}{*{20}l} 1 \hfill & {{\text{if }}\;MS_{k} \;{\text{is}}\;{\text{served}}\;{\text{by}}\;{\text{BS}}_{i} ,} \hfill \\ 0 \hfill & {{\text{otherwise}}.} \hfill \\ \end{array} } \right.$$
(2)
Table 1

Parameters and variables

Parameter

Meaning

\({\mathcal {B}}\)

A set of possible BS locations

\(S := \lbrace s_{1},\ldots ,s_{n} \rbrace\)

A set of traffic states

\(N_{{\rm B}}\)

The total number of input candidate BS locations

\(I:= \lbrace 1,\ldots ,N_{{\rm B}}\rbrace\)

A candidate set of BSs

\(K_{{\rm s}}\)

The total number of mobile stations (MSs)

for a given traffic state s

\(J:= \lbrace 1,\ldots ,K_{{\rm s}}\rbrace\)

A set of MSs for the traffic state s

\(K_{{\rm BS}}\)

A maximum number of MSs that can be

served by each BS

\(P_{{\rm BS}}\)

A maximum BS transmit power

\(P_{k,i}\)

The received power for \({\text{MS}}_k\) by its serving \({\text{BS}}_i\)

SINR

Signal-to-noise and interference ratio

\({\text{SINR}}_{{\rm thr}, k}\)

The minimum threshold value that SINR must exceed

in order that \({\text{MS}}_k\) to be served

\(\sigma ^{2}\)

The thermal noise power

\(\beta\)

A target outage probability

2.4 Problem formulation

The LTE RNP problem is formulated in [6] as follows:
$$\begin{aligned} \min _{x} \sum _{i=1}^{N_{{\rm B}}}x_{i} \end{aligned}$$
(3)
subject to:
$$\begin{aligned}&x_{i}P_{k,i}-{\text{SINR}}_{{{\rm thr}},k}\sum _{j=1,j\ne i}^{N_{{\rm B}}} x_{j} P_{k,j} - {\text{SINR}}_{{{\rm thr}},k} \sigma ^2 \ge \nonumber \\&\quad \left( -{\text{SINR}}_{{{\rm thr}},k}\sum _{j=1,j\ne i}^{N_{{\rm B}}} P_{k,j} -{\text{SINR}}_{{{\rm thr}},k} \sigma ^2\right) (1-y_{k,i}) \quad \forall k \in J ,\forall i \in I, \end{aligned}$$
(4)
$$\begin{aligned}&y_{k,i}\leqslant x_{i} \qquad \forall k \in J,\forall i \in I, \end{aligned}$$
(5)
$$\begin{aligned}&\sum _{i=1}^{N_{{\rm B}}} y_{k,i}\leqslant 1 \qquad \forall k \in J, \end{aligned}$$
(6)
$$\begin{aligned}&\sum _{k=1}^{K_{{\rm s}}} y_{k,i}\leqslant K_{{\rm BS}} \qquad \forall i \in I, \end{aligned}$$
(7)
$$\begin{aligned}&\sum _{k=1}^{K_{{\rm s}}}\sum _{i=1}^{N_{{\rm B}}} y_{k,i} \geqslant (1-\beta )K_{{\rm s}}, \end{aligned}$$
(8)
$$\begin{aligned}&y_{k,i} \in {\lbrace 0,1\rbrace } ,x_{i} \in {\lbrace 0,1\rbrace } \qquad \forall k \in J,\forall i \in I. \end{aligned}$$
(9)
The objective function  (3) minimizes the number of selected BSs.

Constraint (4) represents the quality of service of the mobile stations (MSs) in the network. It is feasible for both served and non-served MSs in the network.

Constraint (5) guarantees that we can not assign the mobile station number k (\(\hbox {MS}_k\)) to be served by the base station number i (\(\hbox {BS}_i\)) if \(\hbox {BS}_i\) is not selected to be on service in the network.

Constraint (6) forces each \(\hbox {MS}_k\) to be served by at most one BS.

Constraint (7) guarantees that each \(\hbox {BS}_i\) can serve at most \(K_{{\rm BS}}\) MSs.

Constraint (8) guarantees that the percentage of MSs in outage, i.e., unserved MSs are lower than the target outage probability \(\beta\).

Constraint (9) requires the variables \(x_i\) and \(y_ {k, i}\) to be binary in Eqs. (1) and (2).

3 Proposed model based on possibility theory

3.1 Possibility theory

Possibility theory is a mathematical theory for dealing with certain types of uncertainty and is an alternative to probability theory. Zadeh [16] first introduced possibility theory in 1978 as an extension of his theory of fuzzy sets and fuzzy logic. Dubois and Prade [17] further contributed to its development.

3.2 Proposed model based on possibility theory

A traffic state can represent an interval of traffic \(s_i=[b_i,c_i]\) such as those presented in Fig. 1 and described in Sect. 2.1. In the literature, to decide the traffic states, the control center should monitor the traffic variations across a day over a period of time (n) such as a month (in this case \(n=30\)). Then, he calculates the average traffic per hour (see, for instance, [6]). Let \(a_j\) and \(\bar{a}_j\) are, respectively, the traffic amount and the average traffic per the hour j; then,
$$\begin{aligned} \bar{a}_j = \frac{1}{n}\sum _{i=1}^{n}a_i. \end{aligned}$$
In this paper, this model is denoted by classic model (existing model).
From our point of view, in order to investigate more realistic cases, we consider the situation where the traffic information is taken as imprecise and uncertain value. So, to deal with this situation, we introduce a fuzzy logic model, where each traffic number \(a_i\) is taken as fuzzy number \(\tilde{a_i}\), instead of a crisp value. Therefore,
$$\begin{aligned} \tilde{\bar{a}}_j = \frac{1}{n}\sum _{i=1}^{n}\tilde{a}_i \end{aligned}$$
(10)
where each traffic \(\tilde{a_i}\), \(1\le i\le n\), is a fuzzy number with the following membership function:
$$\begin{aligned} \mu _{\tilde{a}_i}(t) = \left\{ \begin{array}{l l} {\text {max}} \displaystyle \left( 0,1-\frac{a_i-t}{\alpha _i}\right) \quad & {\text { if }}\; t\le a_i,\\ {\text {max}} \displaystyle \left( 0,1-\frac{t-a_i}{\beta _i}\right) &{\text { if \;}} t> a_i. \end{array} \right. \qquad \end{aligned}$$
(11)
where \(\alpha _i\) and \(\beta _i\) are positive constants expressing the left and right spreads of fuzzy numbers, respectively. In the case where \(t\le a_i\), we have two possibilities:
  • if \(a_i-t\ge \alpha _i\), then \({\text {max}}(0,1-\frac{a_i-t}{\alpha _i}) = 0\), and therefore, \(\mu _{\tilde{a}_i}(t) =0\);

  • otherwise, \({\text {max}}(0,1-\frac{a_i-t}{\alpha _i}) = 1-\frac{a_i-t}{\alpha _i}\), and therefore, \(\mu _{\tilde{a}_i}(t) =1-\frac{a_i-t}{\alpha _i}\).

The same way is for the case where \(t> a_i\). The membership function \(\mu _{\tilde{a}_i}(t)\) is represented in Fig. 2.
Fig. 2

Membership function of the fuzzy traffic

Since each traffic is a triangular fuzzy variable, then the total traffic (\(\sum _{i=1}^{n}\tilde{a}_i\)) denoted by \(\tilde{A}\) becomes equivalent to the same type of fuzzy variable (see, for instance, [18, 19]). The fuzzy number \(\tilde{A}\) is represented by the following membership function and illustrated in Fig. 3:
$$\begin{aligned} \mu _{\tilde{A}}(t) = \left\{ \begin{array}{l l} {\text {max}} \displaystyle \left( 0,1-\frac{\sum _{i=1}^{n} a_i-t}{\sum _{i=1}^{n}\alpha _i}\right) \quad & {\text { if}}\; t\le \sum \nolimits _{i=1}^{n} a_i,\\ {\text {max}} \displaystyle \left( 0,1-\frac{t-\sum _{i=1}^{n} a_i}{\sum _{i=1}^{n} \beta _i}\right) &{\text { if}}\; t> \sum \nolimits _{i=1}^{n} a_i. \end{array} \right. \qquad \end{aligned}$$
(12)
The traffic state \(s_i=[b_i,c_i]\) becomes, therefore, \(\tilde{s}_i=[\tilde{b}_i,\tilde{c}_i]\). If we replace \(K_{{\rm s}}\) by \(K_{\tilde{s}}\) and \(J:= \lbrace 1,\ldots ,K_{{\rm s}}\rbrace\) by \(\tilde{J}\) in the model in Sect. 2.4, then we obtain the following fuzzy model:
$$\begin{aligned} \min _{x} \sum _{i=1}^{N_{{\rm B}}}x_{i} \end{aligned}$$
(13)
subject to:
$$\begin{aligned}&x_{i}P_{k,i}-{\text{SINR}}_{{{\rm thr}},k}\sum _{j=1,j\ne i}^{N_{{\rm B}}} x_{j} P_{k,j} - {\text{SINR}}_{{{\rm thr}},k} \sigma ^2 \ge \nonumber \\&\quad \left( -{\text{SINR}}_{{{\rm thr}},k}\sum _{j=1,j\ne i}^{N_{{\rm B}}} P_{k,j} -{\text{SINR}}_{{{\rm thr}},k} \sigma ^2\right) (1-y_{k,i}) \quad \forall k \in \tilde{J}, \forall i \in I, \end{aligned}$$
(14)
$$\begin{aligned}&y_{k,i}\leqslant x_{i} \qquad \forall k \in \tilde{J},\forall i \in I, \end{aligned}$$
(15)
$$\begin{aligned}&\sum _{i=1}^{N_{{\rm B}}} y_{k,i}\leqslant 1 \qquad \forall k \in \tilde{J}, \end{aligned}$$
(16)
$$\begin{aligned}&\sum _{k=1}^{K_{\tilde{s}}} y_{k,i}\leqslant K_{{\rm BS}} \qquad \forall i \in I, \end{aligned}$$
(17)
$$\begin{aligned}&\sum _{k=1}^{K_{\tilde{s}}}\sum _{i=1}^{N_{{\rm B}}} y_{k,i} \geqslant (1-\beta )K_{\tilde{s}}, \end{aligned}$$
(18)
$$\begin{aligned}&y_{k,i} \in {\lbrace 0,1\rbrace } ,x_{i} \in {\lbrace 0,1\rbrace } \qquad \forall k \in \tilde{J},\forall i \in I. \end{aligned}$$
(19)
In this model, we randomly generated the traffic across a day over one month. Then, we calculate the average fuzzy traffic \(\tilde{\bar{a}}_j\) according to Eq. (10). To decide the traffic states, we use both possibility and necessity measures.
Fig. 3

Membership function of the fuzzy total traffic

A possibility measure is useful when one tries to make a decision with an optimistic point of view. In this paper, for using possibility measure, we take \(\sum _{i=1}^{n}\beta _i=0\). Then, the membership function for the fuzzy total traffic \(\tilde{A}_p\) becomes:
$$\mu _{{\tilde{A}_{p} }} (t) = \left\{ {\begin{array}{*{20}l} {{\text{max}}\left( {0,1 - \frac{{\sum\limits_{{i = 1}}^{n} {a_{i} } - t}}{{\sum\limits_{{i = 1}}^{n} {\alpha _{i} } }}} \right)} \hfill & {{\text{if}}\;t \le \sum\nolimits_{{i = 1}}^{n} {a_{i} } } \hfill \\ 0 \hfill & {{\text{otherwise}}.} \hfill \\ \end{array} } \right.$$
(20)
However, in the case where the achievement of a goal is necessary or the decision maker has a pessimistic point of view to reduce the risk, a necessity measure is used. To achieve the necessity measure, we take \(\sum _{i=1}^{n}\alpha _i=0\).
Then, the fuzzy total traffic \(\tilde{A}_n\) can be represented by the following membership function:
$$\mu _{{\tilde{A}_{n} }} (t) = \left\{ {\begin{array}{*{20}l} {{\text{max}}\left( {0,1 - \frac{{t - \sum\limits_{{i = 1}}^{n} {a_{i} } }}{{\sum\limits_{{i = 1}}^{n} {\beta _{i} } }}} \right)} \hfill & {{\text{if}}\;t \ge \sum\nolimits_{{i = 1}}^{n} {a_{i} } ,} \hfill \\ 0 \hfill & {{\text{otherwise}}.} \hfill \\ \end{array} } \right.$$
(21)
For the defuzzification, there are many different methods such as mean of maxima, center of gravity, center of area, fuzzy goal. The center of gravity method (COG) is the most popular defuzzification technique and is widely utilized in actual applications. It takes into account the influence of all the values proposed by the fuzzy solution. In this paper, we use this method which consists of taking the abscissa corresponding to the center of gravity of the membership function. Formally, it is expressed as \(\displaystyle \frac{\int _{S}^ x\times \mu (x) \, {{\mathrm {d}}}x}{\int _{S}^ \mu (x) \, {{\mathrm {d}}}x}\), where S is the domain of the membership function.

3.3 Illustration with an example

Suppose we did the calculations for a week (\(n=7\)) at the period of time from 8 a.m. to 9 a.m., and we found the following values (traffics): 220, 230, 220, 240, 250, 220 and 230. So for classic model, we get 230 as the average value.

For our approach, let \(\alpha _i=1\) for each i, \(1\le i\le 7\) and \(\beta _i=2\) for each i, \(1\le i\le 7\), for example. After calculation, we have \(\sum _{i=1}^{7}a_i = 1610\), \(\sum _{i=1}^{7}\alpha _i = 7\) and \(\sum _{i=1}^{7}\beta _i = 14\).
  • In the case of possibility measure, according to Eq. (20), the fuzzy total traffic \(\tilde{A}_p\) is represented in Fig. 4a.

    For the defuzzification,
    $$\begin{aligned} \displaystyle \frac{\int _{1603}^{1610} x\times (x/7-229) \, {{\mathrm {d}}}x}{\int _{1603}^{1610} (x/7-229) \, {{\mathrm {d}}}x} = 1607.66. \end{aligned}$$
    So, the average value for possibility measure is 229.66.
  • In the case of necessity measure, according to Eq. (21), the fuzzy total traffic \(\tilde{A}_n\) is represented in Fig. 4b.

    For the defuzzification,
    $$\begin{aligned} \displaystyle \frac{\int _{1610}^{1624} x\times (-x/14+116) \, {{\mathrm {d}}}x}{\int _{1610}^{1624} (-x/14+116) \, {{\mathrm {d}}}x} = 1614.66. \end{aligned}$$
    So, the average value for possibility measure is 230.66.
Fig. 4

Membership function of the fuzzy total traffic for the illustration example

4 Proposed metaheuristic to solve the problem

Since the problem (13) formulated in Sect. 3.2 is NP-hard (see [6], for instance), it is necessary to propose approximate algorithm to solve it. We find in the literature a number of relevant methods to solve this kind of problem such as tabu search, simulated annealing, genetic algorithm, ant colony optimization, neural network, particle swarm optimization, firefly algorithm. We chose the genetic algorithms (GAs) method for three reasons. Firstly, it is better to find a set of solutions rather than a single solution, so that the decision maker can choose the solution that suits them the most. Secondly, in this problem we have an explicit formula for the objective function and large numbers of constraints. GAs have proved particularly useful for problems where there are large numbers of constraints and where traditional gradient-based optimization methods are not applicable [20]. Thirdly, GAs are naturally suited to situations where a numerical simulation can be used to determine the outcome of a particular choice of control parameters. In this paper, we use genetic algorithms (GAs) as they are described in [21, 22]. In GA terminology, a solution vector x is called an individual or a chromosome. Chromosomes are made of discrete units called genes. Each gene controls one or more features of the chromosome. The main components of a GA are: selection, crossover and mutation.

4.1 Chromosome representation

For encoding the base stations (BSs) and mobile stations (MSs), we used an integer encoding. For \(N_{{\rm B}}\) base stations and \(K_{{\rm s}}\) MSs, we used a sequence of \(K_{{\rm s}}\) digits, where each digit is an integer taking values between 0 and \(N_{{\rm B}}\). If the digit in a position j takes a value k, \(d_j=k\), that means the \(MS_j\) is assigned to the \({\text{BS}}_k\) and \({\text{BS}}_k\) is installed; if \(k=0\) the \(MS_j\) is not assigned to any base station. For example, if \(K_{{\rm s}}=7\) and \(N_{{\rm B}}=4\), the code 2;3;1;0;2;4;4 means that the \(MS_1\) is assigned to the \({\text{BS}}_2\), \(\ldots\), the \(MS_{7}\) to the \({\text{BS}}_4\) and that BSs numbers 1,2,3 and 4 are installed. We see that the \(MS_{4}\) is not assigned to any BS; this means that the \(MS_{4}\) is not covered.

4.2 Initial population, crossover and mutation

  • Initial population Suppose we have \(K_{{\rm s}}\) MSs and \(N_{{\rm B}}\) BSs. To define each chromosome of the population, we generate \(K_{{\rm s}}\) random genes as integers in the set \(\{0,\dots ,N_{{\rm B}}\}\). A population is a set of chromosomes.

  • Crossover We use the usual crossover. Figure 5 illustrates this operation.

  • Mutation We use the usual mutation. Once the gene to mutate is chosen, we replace it by an integer chosen randomly from the set \(\{1,2,\dots ,N_{{\rm B}}\}\). Figure 6 shows that the \(MS_{6}\) was assigned to the \({\text{BS}}_{9}\), but after the mutation, it will be assigned to the \({\text{BS}}_{2}\).

Fig. 5

Crossover operator

Fig. 6

Mutation operator

5 Application

In this section, we will:
  • describe the simulation data used in our application;

  • present the results of the existing model that is named here classical model, using booth proactive and reactive approaches;

  • present the results of our model which contains both possibility and necessity measures;

  • analyze \(\hbox {CO}_2\) emission for each model;

  • and finally, make a comparison between the existing model and our model and finish with a general discussion.

5.1 Data description

In this section, we consider a large network to be covered. The size of this network is 10 km \(\times\) 10 km. To evaluate the performance of our proposed approach, we consider the general simulation parameters presented in Table 2 (see [6]). The number of mobile stations (MSs) to be served is 1200, and the number of input base stations (BSs) is 70. Figure 7 presents the input BSs locations generated using uniform distribution.
Table 2

Simulation parameters [6]

Parameter

Value

\(P_{{\rm BS}}\)

20 W

\(\sigma ^{2}\)

\(5.97 \times 10^{-15}\) W

\(\beta\)

0.05

Carrier frequency

2000 MHz

\(K_{{\rm BS}}\)

50

\({\text{SINR}}_{{\rm thr}}\)

\(-\) 5 dB

Transmitter and receiver gain

0 dBi

Fig. 7

Input BSs locations

We generate the traffic across a day over one month.

In the existing model (classical model), authors calculated only the average traffic per hour; then, they have chosen the traffic states using these averages.

In our model, each traffic becomes a fuzzy number as described in Sect. 3.2. We generated randomly \(\alpha\) and \(\beta\) (positive constants expressing the left and right spreads of fuzzy numbers, see Sect. 3.2) between 1 and 10 for each traffic, and we decide to take three traffic states \(s_1\), \(s_2\) and \(s_3\).

5.2 Computational results

The algorithms were coded in JAVA programming language and implemented on a machine of Central Processing Unit (CPU) Intel Core2Duo-2GHz, and the memory RAM (Random Access Memory) is equal to 2 GigaBytes(GB). The parameters of GA are set as follows:
  • crossover probability \(p_{{\rm c}} = 0.5\);

  • mutation probability \(p_{{\rm m}} = 0.01\);

  • for proactive approach, population size is \(p_{{\rm s}} = 30\), \(p_{{\rm s}} = 35\) and \(p_{{\rm s}} = 40\) for the first, second and third traffic states, respectively;

  • maximum number of generations is, respectively, 500, 800 and 1000;

  • for the reactive approach, parameters are the reverse of the proactive approach.

5.2.1 Results of the traffic states

Using the previous data, we got three traffic states as follows:
  • For classic model (existing model), \(s_1=[0,450]\), \(s_2=[450,900]\) and \(s_3=[900,1200]\).

  • For our model :

  • in the case of possibility model where we try to make a decision with an optimistic point of view, we obtain \(s_1=[0,400]\), \(s_2=[400,800]\) and \(s_3=[800,1200]\).

  • and in the case of necessity model where we have a pessimistic point of view, we obtain \(s_1=[0,550]\), \(s_2=[550,1000]\) and \(s_3=[1000,1200]\).

Table 3 and Fig. 8 present the traffic states corresponding to classic, possibility and necessity models, respectively.
Table 3

Traffic states corresponding to classic, possibility and necessity models

 

Approach

Traffic state

Traffic state

Traffic state

 

\(s_1\)

\(s_2\)

\(s_3\)

Existing model

Classic

[0–450]

[450–900]

[900–1200]

Our model

Possibility

[0–400]

[400–800]

[800–1200]

Necessity

[0–550]

[550–1000]

[1000–1200]

Fig. 8

Traffic states for classic, possibility and necessity models

5.2.2 Results of the proactive approach

We start solving our problem by considering the traffic state \(s_1\); then, as the traffic state increases, we consider the traffic state \(s_2\) and finally the traffic state \(s_3\) (see Sect. 2.2). Table 4 presents the number of active base stations corresponding to classic, possibility and necessity models, respectively, using proactive approach.
Table 4

Proactive approach results corresponding to classic, possibility and necessity models

 

Approach

Traffic state

Traffic state

Traffic state

 

\(s_1\)

\(s_2\)

\(s_3\)

Existing model

Classic

BSs = 10

BSs = 21

BSs = 29

Our model

Possibility

BSs = 10

BSs = 19

BSs = 28

Necessity

BSs = 12

BSs = 22

BSs = 30

  • In classic model (existing model), we see that the optimal solution chooses 10 BSs to serve the traffic state \(s_1\), see Fig. 9a. As the traffic states \(s_2\) increase, 11 new BSs are turned on, making a total of 21 BSs which are essential to serve the increased demand. The additional BSs are presented by circles in Fig. 9b. In the same way for the traffic state \(s_3\), 8 new BSs are turned on, making a total of 29 BSs which are essential to serve \(s_3\). The additional BSs are presented by triangles in Fig. 9c.

  • In our model:
    • in the case of possibility measures, the number of BSs to serve \(s_1\) is 10; then, when traffic demand increases in \(s_2\), 9 new BSs are turned on, making a total of 19 BSs which are essential to serve \(s_2\). When we go from \(s_2\) to \(s_3\), 9 new BSs are turned on, making a total of 28 BSs to serve the increased demand. In Fig. 10b, the additional BSs for \(s_2\) are presented by circles, and those for \(s_3\) are presented by triangles. To note that in the objective of the readability of the figure, we did not add the sub-figure presenting \(s_2\). In fact, we clearly see in Fig. 10b the additional BSs for \(s_2\) and for \(s_3\).

    • in the same way in the case of necessity measures, the numbers of BSs to serve \(s_1\), \(s_2\) and \(s_3\), respectively, are 12, 22 and 30 BSs, see Fig. 11. The increase in the number of BSs is normal, since in this case the decision maker has a pessimistic point of view to reduce the risk.

Fig. 9

Proactive approach with classic model

Fig. 10

Proactive approach with possibility model

Fig. 11

Proactive approach with necessity model

5.2.3 Results of the reactive approach

In the reactive approach, the RNP is initially performed according to the highest traffic state \(s_3\) that determines the largest possible set of BSs, denoted by \({\text{BS}}_3\), that can be active at any time, as shown in Fig.12a. Then, when the traffic state decreases, some BSs from \({\text{BS}}_3\) are turned off. Output results for traffic states \(s_2\) and \(s_1\), corresponding to classic model, are shown in Fig. 12b, c, respectively. Table 5 presents the number of active base stations corresponding to the three models using reactive approach. In classic model, we see that the optimal solution chooses 32, 21 and 10 BSs to serve traffic states \(s_3\), \(s_2\) and \(s_1\), respectively. In possibility model, the numbers of BSs to serve \(s_3\), \(s_2\) and \(s_1\) decrease, respectively, to 30, 18 and 10 BSs, which present the optimistic vision of this model. If this vision is pessimistic (necessity model), these numbers increase to 32, 23 and 11 BSs. Figures 13 and 14 show the output BS locations for the various traffic states using reactive approach corresponding to possibility and necessity models, respectively.
Fig. 12

Reactive approach with classic model

Table 5

Reactive approach results corresponding to classic, possibility and necessity models

 

Approach

Traffic state

Traffic state

Traffic state

 

\(s_3\)

\(s_2\)

\(s_1\)

Existing model

Classic

BSs = 32

BSs = 21

BSs = 10

Our model

Possibility

BSs = 30

BSs = 18

BSs = 10

Necessity

BSs = 32

BSs = 23

BSs = 11

Fig. 13

Reactive approach with possibility model

Fig. 14

Reactive approach with necessity model

5.3 Green optimization: analysis of \(\hbox {CO}_2\) emissions

The \(\hbox {CO}_2\) emissions expression for the different traffic states can be written as follows (see [6], for instance):
$$\begin{aligned} {\text{CO}}_{2}(s_i)\,=\,\dfrac{N_{{\rm s}_i} \times P_{{\rm BS}} \times T_{{\rm s}_i} \times 620}{10^{6}}, \end{aligned}$$
(22)
where
  • \(\hbox {CO}_{2}(s_i)\) in [\(\hbox {kg\; CO}_{2}/\hbox {day}\)] is the quantity emitted of \(\hbox {CO}_{2}\) in one day from the traffic state \(s_i\), \(i \in \{1,2,3\}\);

  • \(N_{{\rm s}_i}\) is the number of BSs selected from the traffic state \(s_i\), \(i \in \{1,2,3\}\);

  • \(P_{{\rm BS}}\) in Watt (W) is the total consumption of the BS. It equals to 140 W when transmitting with a maximum transmit power of 20 W (see [6, 23]);

  • \(T_{{\rm s}_i}\) in hour is the duration of the traffic state \(s_i\), \(i \in \{1,2,3\}\);

  • In this expression, we assume that electricity energy is derived from fuel oil where each 1 KWh represents 620 g of CO\(_2\) [24].

For example, for the proactive approach in classic model, the \(\hbox {CO}_2\) emissions for each traffic state are calculated as follows:
  1. 1.

    \(\hbox {CO}_2(s_1) = \dfrac{10 \times 140 \times 10 \times 620}{10^{6}} = 8.68\)

     
  2. 2.

    \(\hbox {CO}_2(s_2) = \dfrac{21 \times 140 \times 8 \times 620}{10^{6}} = 14.58\)

     
  3. 3.

    \(\hbox {CO}_2(s_3) = \dfrac{29 \times 140 \times 6 \times 620}{10^{6}} = 15.1\)

     
Then, the total \(\hbox {CO}_2\) emission, in \(\hbox {Kg CO}_{2}/\hbox {day}\), for the proactive approach in classic model is
$$\begin{aligned} 8.68+14.58+15.1 =38.36. \end{aligned}$$
If we do not use the proactive approach, all the 29 BSs are always active; then, the total \(\hbox {CO}_2\) emission, in \(\hbox {Kg CO}_{2}/\hbox {day}\), is
$$\begin{aligned} \dfrac{29 \times 140 \times 24 \times 620}{10^{6}} = 60.41. \end{aligned}$$
Therefore, the \(\hbox {CO}_2\) emission is decreased by \(36.5 \%\).
Tables 6 and 7 present the results of \(\hbox {CO}_{2}\) emissions for different approaches and models. The word “green” in these two tables denotes that we used proactive and reactive approach. However, the word “traditional” denotes the model without proactive and reactive approaches. We note by existing model (classic approach), the model where we considered the traffic as constant. We see that using our model, the \(\hbox {CO}_2\) emissions are decreased by a value between 32.5 and \(43.5\%\) for proactive approach, and between 34.5 and \(43\%\) for reactive approach.
Table 6

\(\hbox {CO}_2\) emissions for the proactive approach

 

Aproach

\(\hbox {CO}_2\) emissions in Kg/day (Green)

\(\hbox {CO}_2\) emissions in Kg/day (traditional)

Decrease percentage (%)

Existing model

Classic

38.36

60.41

36.5

Our model

Possiblity

39.57

58.32

32.5

Necessity

35.4

62.49

43.5

Table 7

\(\hbox {CO}_2\) emissions for the reactive approach

 

Aproach

\(\hbox {CO}_2\) emissions in Kg/day (Green)

\(\hbox {CO}_2\) emissions in Kg/day (traditional)

Decrease percentage (%)

Existing model

Classic

39.92

66.66

40.5

Our model

Possibility

40.96

62.49

34.5

Necessity

38

66.66

43

5.4 Comparison and discussion

According to our approach, one of the main objectives of the network operators while deploying a new network is to reduce the energy consumed by base stations (BSs).

In the traditional model, when we do not use the reactive approach or the proactive approach, the network operators deployed BSs at the peak hour or for the maximum load which determines the maximum required number of BSs. However, the set of deployed BSs remains active at all times even for low traffic states. Therefore, a loss of energy is made, at the moment when we can deactivate some BSs to save this energy. In the previous section, we saw that when we did not use the proactive approach, all the 29 BSs (deployed at the peak hour) are always active, increasing the total \(\hbox {CO}_2\) emission by \(36.5 \%\).

On the other hand, when reactive and proactive approaches are used without considering traffic information as imprecise and uncertain value, we can fall into a non-realistic case (context). Using the average does not solve the problem. In fact, suppose that the data collected during a given period are dispersed (the standard deviation is considerable) and that we plan according to the obtained average. During the time when the traffic is maximal, one can fall in the case where the percentage of unserved MSs is greater than the target outage probability \(\beta\). And during the time when the traffic is minimal, we will have more BS than necessary.

From our point of view, in order to investigate more realistic cases, we consider the situation where the traffic information is taken as imprecise and uncertain value. And as a result, we consider a model based on possibility theory using reactive and proactive approaches. This model has given to decision makers a feasible choice.

Indeed, if the network operator (decision maker) tries to make a decision with an optimistic point of view (possibility measure) using reactive approach, then he must use 30 BSs to serve the highest traffic state \(s_3\). Then, when the traffic state decreases, 12 BSs are turned off. The remaining 18 BSs are sufficient to serve the traffic state \(s_2\). When the traffic state continues to decrease leading to \(s_1\), 8 other BSs are turned off. This strategy leads to considerable energy savings and lower \(\hbox {CO}_2\) emissions. In our application, the \(\hbox {CO}_2\) emission is decreased by \(34.5\%\).

In the case where the network operator uses proactive approach, he must use 10 BSs to serve the lowest traffic state \(s_1\). Then, when the traffic state increases, 9 new BSs are turned on making a total of 19 BSs which are essential to serve the traffic state \(s_2\). When the traffic state continues to increase leading to \(s_3\), 9 other new BSs are turned on making a total of 28 BSs which are essential to serve the traffic state \(s_3\). In this case, the \(\hbox {CO}_2\) emission is decreased by \(32.5\%\).

On the other hand, if the decision maker has a pessimistic point of view to reduce the risk and he uses reactive approach, then he must use 32 BSs to serve the traffic state \(s_3\). Then, 9 BSs are turned off. The remaining 23 BSs are sufficient to serve \(s_2\). Next, 12 BSs are turned off. The remaining 11 BSs are sufficient to serve \(s_1\). In this case, the \(\hbox {CO}_2\) emission is decreased by \(43\%\). In the same way, if the network operator uses proactive approach, the \(\hbox {CO}_2\) emission is decreased by \(43.5\%\).

In summary, the minimal required number of active BSs is chosen by switching on or off the necessary BSs. This strategy reduces the overall energy consumption of the network compared to the case where all BSs are kept active for all traffic states. Furthermore, traffic information is often uncertain and imprecise, so the use of possibility logic becomes interesting for good and realistic planning.

6 Conclusion

In this paper, we have presented the green radio network planning (RNP) problem for LTE cellular networks. The main objective is to reduce energy consumption by reducing the number of active BSs in a given area which will also reduce the production of \(\hbox {CO}_2\). For this, we generated the BS on/off switching patterns based on the changing traffic conditions and we used both proactive and reactive approaches.

From our point of view, traffic informations are uncertain and imprecise, so to remedy this, we introduce an approach based on possibility theory. For this, we have studied both possibility and necessity measures. Possibility model is used when we try to make a decision with an optimistic point of view. However, necessity model is employed when the achievement of a goal is necessary or the decision maker has a pessimistic point of view to reduce the risk.

In order to solve the problem, we have proposed a solution method using genetic algorithms. For application, we have considered a large network to be covered. Then, we have applied our model and both proactive and reactive approaches. Moreover, we evaluated \(\hbox {CO}_2\) emissions for each model and approach. The obtained results show the efficiency of our model from quantifying the gain in terms of number of BSs and reduction in \(\hbox {CO}_{2}\) emissions.

This study is limited to a single objective which is the minimization of the number of base stations in order to minimize \(\hbox {CO}_2\) emissions. In fact, there are other objectives to achieve, such as reducing the total installation cost and maximizing the total traffic covered. Future research in this field can focus on the inclusion of these two objectives, so we will have a multi-objective problem instead of a mono-objective one. Another challenge to be addressed in the future is to try to apply these results on real data in a real context instead of data simulation.

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.LANO Laboratory, ESTO-FSOUniversity Mohammed PremierOujdaMorocco
  2. 2.Department of Computer Science, LARI Laboratory, Faculty of ScienceUniversity Mohammed PremierOujdaMorocco
  3. 3.Department of Mathematics, Faculty of ScienceUniversity Mohammed PremierOujdaMorocco

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