**Abstract**

The increasing demand of communication services have led to the increase in energy consumption. Energy sustainability is important and challenging research in current world. An energy aware nearest cell association algorithm is proposed to make the mesh routers (MRs) to sleep if they are in idle state. If the MRs have no associated clients, then the MR is considered to be idle. Any network device in idle state consumes power hence a sleep mechanism is introduced to place energy aware routers. A fuzzy differential evolution (FDE) is introduced to dynamically decide the state of the MR by gaining the knowledge from the fuzzy table for parameters like traffic load, minimum distance and transmission power. Transmission cost and failure rate of the deployed network is evaluated and their performance is analyzed.

**Keywords:** fuzzy differential evolution, mesh router, mesh client, energy consumption, failure rate, client association, transmission cost

### **1. Introduction**

Future wireless network will make use of more renewable energy sources like solar, wind and hydro. Developing a sustainable communication is one of the critical and challenging issues in order to sustain the ever-growing traffic demands while alleviating the need of increased energy consumption. Traditional solutions have assumed that mesh routers have consistent power supply through wired electricity. Increasing demand for green mesh networks that can harvest their energies via solar or wind power have reached greater attention. But the energy supplies of these rechargeable routers are not consistent but depend on many environmental conditions [1]. For each router, energy consumption is due to the traffic demand of its associated mesh client and the distance between them. The existing router placement algorithms such as, exhaustive search and greedy search [2] are easily running into local optima. To overcome this drawback fuzzy differential evolution (FDE) placement of nodes with Energy Aware Nearest Cell Association (EANCA) algorithm is proposed in this module.

### **2. System configuration**

System model: In this work, any renewable energy powered MRs is considered to be deployed in a grid scenario where the field is divided into grid cells of equal

area. The deployed MRs should provide wireless access for all the stationary MCs which are assumed to be distributed using normal probability distribution. The number of MCs associated with the MR changes periodically. Each MR deployed in the candidate location consumes more energy to guarantee QOS and ensure the traffic demands of the associated MCs [3–5].

Energy flow model: The renewable energy powered routers are equipped with battery storage. The continuous time line of energy stored is divided into consecutive slots of 't'. The energy charging and discharging of a router can be defined with a discrete time energy model as [6, 7]

$$E(t) = E(t-1) + H(t) - Ec(t) \tag{1}$$

*FR* ¼ ∑ *t*∈*K* ∑ *i* ∈*C*

*DOI: http://dx.doi.org/10.5772/intechopen.83747*

*Energy Aware Router Placements Using Fuzzy Differential Evolution*

*FR* must be less than a predefined failure threshold (Fth).

defined for two sets of input parameters respectively as follows:

**4. Fuzzy differential evolution**

1. DE control parameters

adaptive parameter controls.

feedback from the search.

offspring.

**137**

2. Network inputs

where *xij*ð Þ¼ k

storage.

1 � ∑ *j*∈*S xij t*ð Þ !�

1 *if a node is associated with the MR*

number of clients, |*K*| denotes the time slots and *S* denotes the set of candidate locations [8]. The renewable energy powered routers are equipped with battery

Eq. (5) ensures that the difference between the initial and residual energy must be greater or equal to the energy required to guarantee QOS between the mesh routers and clients. Eq. (6) ensures that the transmission power required for any mesh router to get associated with any client must be less than the maximum transmission power. Eq. (7) ensures that the energy consumed is less than the energy harvested. Eq. (8) ensures that the failure rate (FR) a parameter which is incurred from [8] measures the network performance. The constraint specifies that

According to the former literatures [9] the control parameters S,CR were kept fixed during the optimization process. The control parameters of DE is made adaptive using fuzzy logic. Here in this proposed optimization model fuzzy rules are

DE control parameters: In DE algorithm, usually empirical values are selected for

Deterministic parameter control: A rule strategy is defined to deterministically

Adaptive parameter control: This approach is handled when a feedback arises from the search and this feedback is used to determine the values to the parameters. Self-adaptive parameter control: Here in the evolutionary search encoded

crossover operation to produce effective individuals that could survive and produce

Network inputs: In the deployed network the distance between the client and the mesh router in each grid cell is calculated and formulated as a matrix called the distance matrix. The minimum distance value is returned from the matrix which is denoted as Dmin. The Traffic Load (TL) is calculated from the number of clients

change the parameters. It strategically changes the values without getting any

parameters are used in the chromosomes to perform the mutation and

its search process. Using fuzzy rules the system is made adaptive to search the parameters for mutation and crossover operation. The setting of parameter values can be done in two ways through parameter tuning and parameter control. Parameter tuning is one of the common methods used to find out good values before running the algorithm. Using the best result the algorithm is made to run. In parameter control approach the values are changed while the algorithm is running [10, 11]. This later approach is further divided into deterministic, adaptive and self-

<sup>0</sup> *otherwise* � �, |*C*| stands for total

j j *C* ∗j j *K* (9)

where *E t*ð Þ is the residual energy of the router after the *t*th slot. If *t* ¼ 0, *E*ð Þ 0 is the initial stored energy in the router. The harvested energy is denoted as *H t*ð Þ and the energy consumed is denoted as *Ec t*ð Þ.*H t*ð Þ is a dynamic function since it purely depends on the nature. Let the maximum charging power of renewable energy powered routers is 100 mW. Here two cases can be analyzed, and the connection failures are adjudged.

$$\text{Case } (\mathbf{1}): \text{If } H(t) > Ec(t) \text{ and } E(t) = \mathbf{1}; \text{failure rate is less} \tag{2}$$

$$\text{Case (2)}: \text{If } H(t) < Ec(t) \text{and } E(t) = 0; \text{failure rate is more} \tag{3}$$

### **3. Problem definition**

The objective is to place minimum number of energy aware routers such that user's traffic demand is satisfied to minimize energy consumption. Here energy consumption is referred as function of a cost metric called transmission cost (TC). The objective function is given by

$$\text{Minimize } \text{TC} = f(\text{D}\_{\text{min}}, \text{TL}, \text{P}\_t) \tag{4}$$

where *TC* is the transmission cost, *Dmin* is the minimum distance between the mesh routers and clients,*TL* is the traffic load and *Pt* is transmission power. Subject to:

$$E\_{in} - E\_r \ge E\_{i,j} \tag{5}$$

where *Ein* is the initial energy, *Er* is the residual energy and *Ei, j* is the energy required to guarantee QOS between the mesh routers and clients.

$$P\_{t(i,j)} \le P\_{t(max)}\tag{6}$$

where *Pt i*ð Þ*;<sup>j</sup>* is the transmission power required for any ith mesh router to associate with the *j*th mesh client and *Pt max* ð Þ denotes the maximum transmission power.

$$E\_c \le E\_{h+} \tag{7}$$

where *EC* is the energy consumed and *Eh*<sup>þ</sup> is the energy harvested.

$$FR \le F\_{\text{th}} \tag{8}$$

where *FR* indicates the failure rate and *Fth* denotes the failure threshold. The *FR* is expressed as

*Energy Aware Router Placements Using Fuzzy Differential Evolution DOI: http://dx.doi.org/10.5772/intechopen.83747*

$$FR = \sum\_{t \in K} \sum\_{i \in C} \left( \mathbf{1} - \sum\_{j \in \mathcal{S}} \mathbf{x}j(t) \right) \Big/ |C| \* |K| \tag{9}$$

where *xij*ð Þ¼ k 1 *if a node is associated with the MR* <sup>0</sup> *otherwise* � �, |*C*| stands for total number of clients, |*K*| denotes the time slots and *S* denotes the set of candidate

locations [8]. The renewable energy powered routers are equipped with battery storage.

Eq. (5) ensures that the difference between the initial and residual energy must be greater or equal to the energy required to guarantee QOS between the mesh routers and clients. Eq. (6) ensures that the transmission power required for any mesh router to get associated with any client must be less than the maximum transmission power. Eq. (7) ensures that the energy consumed is less than the energy harvested. Eq. (8) ensures that the failure rate (FR) a parameter which is incurred from [8] measures the network performance. The constraint specifies that *FR* must be less than a predefined failure threshold (Fth).

### **4. Fuzzy differential evolution**

According to the former literatures [9] the control parameters S,CR were kept fixed during the optimization process. The control parameters of DE is made adaptive using fuzzy logic. Here in this proposed optimization model fuzzy rules are defined for two sets of input parameters respectively as follows:

### 1. DE control parameters

### 2. Network inputs

area. The deployed MRs should provide wireless access for all the stationary MCs which are assumed to be distributed using normal probability distribution. The number of MCs associated with the MR changes periodically. Each MR deployed in the candidate location consumes more energy to guarantee QOS and ensure the

Energy flow model: The renewable energy powered routers are equipped with battery storage. The continuous time line of energy stored is divided into consecutive slots of 't'. The energy charging and discharging of a router can be defined with

where *E t*ð Þ is the residual energy of the router after the *t*th slot. If *t* ¼ 0, *E*ð Þ 0 is the initial stored energy in the router. The harvested energy is denoted as *H t*ð Þ and the energy consumed is denoted as *Ec t*ð Þ.*H t*ð Þ is a dynamic function since it purely depends on the nature. Let the maximum charging power of renewable energy powered routers is 100 mW. Here two cases can be analyzed, and the connection

The objective is to place minimum number of energy aware routers such that user's traffic demand is satisfied to minimize energy consumption. Here energy consumption is referred as function of a cost metric called transmission cost (TC).

where *TC* is the transmission cost, *Dmin* is the minimum distance between the

where *Ein* is the initial energy, *Er* is the residual energy and *Ei, j* is the energy

where *Pt i*ð Þ*;<sup>j</sup>* is the transmission power required for any ith mesh router to associate with the *j*th mesh client and *Pt max* ð Þ denotes the maximum transmission power.

mesh routers and clients,*TL* is the traffic load and *Pt* is transmission power.

required to guarantee QOS between the mesh routers and clients.

where *EC* is the energy consumed and *Eh*<sup>þ</sup> is the energy harvested.

where *FR* indicates the failure rate and *Fth* denotes the failure threshold.

Case 1ð Þ : If *H t*ð Þ . *Ec t*ð Þ and *E t*ðÞ¼ 1*;*failure rate is less (2) Case 2ð Þ : If *H t*ð Þ , *Ec t*ð Þand *E t*ðÞ¼ 0*;*failure rate is more (3)

*E t*ðÞ¼ *E t*ð Þþ � 1 *H t*ðÞ� *Ec t*ð Þ (1)

*Minimize TC* ¼ *f D*ð Þ *min; TL; Pt* (4)

*Ein* � *Er* ≥*Ei,j* (5)

*Pt i*ð Þ*;<sup>j</sup>* ≤ *Pt max* ð Þ (6)

*Ec* ≤ *Eh*<sup>þ</sup> (7)

*FR*≤ *F*th (8)

traffic demands of the associated MCs [3–5].

*Wireless Mesh Networks - Security, Architectures and Protocols*

a discrete time energy model as [6, 7]

failures are adjudged.

**3. Problem definition**

Subject to:

The objective function is given by

The *FR* is expressed as

**136**

DE control parameters: In DE algorithm, usually empirical values are selected for its search process. Using fuzzy rules the system is made adaptive to search the parameters for mutation and crossover operation. The setting of parameter values can be done in two ways through parameter tuning and parameter control. Parameter tuning is one of the common methods used to find out good values before running the algorithm. Using the best result the algorithm is made to run. In parameter control approach the values are changed while the algorithm is running [10, 11]. This later approach is further divided into deterministic, adaptive and selfadaptive parameter controls.

Deterministic parameter control: A rule strategy is defined to deterministically change the parameters. It strategically changes the values without getting any feedback from the search.

Adaptive parameter control: This approach is handled when a feedback arises from the search and this feedback is used to determine the values to the parameters.

Self-adaptive parameter control: Here in the evolutionary search encoded parameters are used in the chromosomes to perform the mutation and crossover operation to produce effective individuals that could survive and produce offspring.

Network inputs: In the deployed network the distance between the client and the mesh router in each grid cell is calculated and formulated as a matrix called the distance matrix. The minimum distance value is returned from the matrix which is denoted as Dmin. The Traffic Load (TL) is calculated from the number of clients

which are associated with the MRs. The Transmission Power (Pt) needed to associate a MC with MR also varies between low and high.
