# An Optimized Load Balance Solution for Multi-homed Host in Heterogeneous Wireless Networks
## 3 Proposed System
### The Connection Utility Equation  
The connection utility equation provides the mathematical representation that is used to utilize the application data as a weighted round robin. In fact, there are several approaches to represent the relation between the application, connections, and device status. An approach is devised in the proposed model from which the connection utility equation is derived. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **AHP** & **TOPSIS** & **SAW** \\ \hline \multirow{2}{*}{Advantages} & Can include qualitative & & \\  & criteria & Simple to employ & Simple to employ \\ \hline \multirow{2}{*}{Disadvantages} & \multirow{2}{*}{With subjectivity} & Ranking abnormality, optimal the solution depends on the vector & Issues with weights, ranking identification \\  & & Position of alternatives & \\ \hline Consistency & Yes & No & No \\ \hline \multirow{2}{*}{Core Process} & \multirow{2}{*}{Hierarchy principle} & \multirow{2}{*}{Distance principle} & Weighted average principle \\ \cline{1-1} \cline{3-3} \cline{5-5}  & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: AHP, TOPSIS, and SAW algorithms illustration. Assume that the interface utility function is represented in a vector relation between \(U\) that is the satisfaction level of application \(j\) (\(U_{j}\)) and \(Q\) that is the battery consumption for application \(j\) using interface \(i\) represented in the vector (\(Qj\)) [78]. Then, the vector \(I_{j}\) is given by:  
\[\left[ \begin{array}{c}I_{1j}\\ \ldots\\ I_{nj}\end{array} \right]=\ a_{j}\left[ \begin{array}{c}U_{1j}\\ \ldots\\ U_{nj}\end{array} \right]+\ \beta_{j}\left[ \begin{array}{c}Q_{1j}\\ \ldots\\ Q_{nj}\end{array} \right] \tag{14}\]  
Interface utilization may also be achieved by distributing the application data traffic among available connections. The data traffic represented as \(W\) should be distributed over \(m\) interfaces for \(j\) iterations, starting from a single interface until the last \(m\) interface. This data traffic has unity distribution given by:  
\[\sum\
olimits_{j=1}^{m}w_{j}=\ 1 \tag{15}\]  
Actually, Equation (15) maintains the packet distribution using the equal cost load balance, which achieves the distribution in round robin format. If we assume unequal cost load balance to transmit application data among all connections, the constraint given in (15) would be modified to be:  
\[\sum\
olimits_{j=1}^{m}\alpha_{j}*w_{j}\leq 1 \tag{16}\]  
where \(\alpha_{j}\) is the connection utility factor (rate adaptation factor) that is used to adapt the interface bit rate, obtained by a suitable algorithm while calculating the weighting value as a cost. It has two values; either 0 in case of operating at low power transmission state; or a given value in accordance with the cost of the corresponding interface weight \(W_{j}\) being the amount of data transfer per \(J\) connection which will be sent based on the pre-calculated weight of that connection. In order to reformulate the constraint condition i.e. sum =1, then we add the term \(\beta*W_{low}\) thus, the connection utility equation is modified to:  
\[\beta*\text{Wlow }+\sum\
olimits_{j=1}^{m}\alpha j\ *\ wj=\ 1 \tag{17}\]  
where \(\beta\) is the transmission rate factor that is used under low power transmission state (assumed to be <15% of the system power). It has two values; which are either zero, in case of operating in good conditions i.e. system power >15%; or another value that represents the cost of the less power consuming connection under low power transmission state. \(W_{low}\) is the amount of the application data transmission per the less power consuming connection. In normal cases, i.e. running in a good state, the multiple transmissions are maintained by the aid of the good state connection utility equation as:  
\[\sum\
olimits_{j=1}^{4}\alpha\ *\ wj\ =\ 1 \tag{18}\]  
In case of running at low system power, the transmission is maintained over the less power consuming connection.