## 3 Performance Analysis  
In this paper, a heterogeneous network architecture with a macro cell with overlaid small cells overlapped with each other is assumed for performance evaluation, as shown in Figure 8. Within a macro cell, small cells are densely distributed at a few hot spot areas, which are generated randomly. Small cells are sparsely distributed outside the hot spot areas. We note that we only consider a single macro cell in this paper, similar to the work in [63]. Work on multi-macro cell environment will be carried out in our future work. The mobility of a UE follows a random movement model with locality within hot spot areas and it follows a random movement outside hot spot areas. The speed of a UE follows a uniform distribution. Data traffic generated at a UE is defined as either low rate data traffic or high rate data traffic, depending on a predefined value of the ratio of high rate data traffic. In the proposed energy saving scheme, the main objective is to associate UEs with appropriate BSs with maximum energy efficiency. To this end, we define an optimization problem, where the total sum of the power consumption of BS is set as an objective function and the maximum power consumption  
Figure 8: Network configuration. Figure 7: Session management of user equipments (UEs). of BSs and the context information of BSs are set as constraints. The optimization problem in this paper is Non-Deterministic Polynomial-time hard (NP-hard) problem and thus the solution is obtained using the particle swarm optimization algorithm, which is one of the widely used bio-inspired optimization algorithms. This is because it is generally accepted that the particle swarm optimization has merit of easy implementation, very simple calculation, and fast calculation speed within a short time. Also, it is less dependent of initial points than other optimization algorithms and there exist techniques which ensure convergence. Therefore, it has been applied to network issues such as the resource allocation problem [64] and routing algorithms [65]. Table 2 shows the notations used in the development of the optimization problem. The objective function is the sum of power consumption by an MBS, \(P_{macro}\) and power consumption by SBSs under the coverage of an MBS, \(\sum_{j=0}^{m-1}P(j)_{small}\), and power consumption due to switching between different states, \(P_{switching}\) and it is denoted as \(P_{total}\) as in Equation (1):  
\[P_{total}=P_{macro}+\sum_{j=0}^{m-1}P(j)_{small}+P_{switching}, \tag{1}\]  
The connection between \(BSj\) and UE i is denoted as \(a_{j,i}\), and the value of it is defined as in Equation (2), where we note that \(BS_{m}\) corresponds to an MBS and \(BSj\) (\(0\leq j\leq m-1\)) corresponds to an SBS. We assume that all UEs under the coverage area of an MBS are associated with the MBS. \[a_{j,i}= \begin{cases}1,&\text{If $u_{i}$ is connected with $B_{j}$}\\ 0,&\text{otherwise}\end{cases} ,(0\leq j<m+1,\ 0\leq i<n), \tag{2}\]  
The data traffic demand of a UE \(i\) is denoted as \(d_{i}\), and the value of it is defined as in Equation (3):  
\[d_{i}= \begin{cases}1,&\text{If $u_{i}$ $required data service}\\ 0,&\text{otherwise}\end{cases} ,(0\leq i<n), \tag{3}\]