Simulation Results of the Three Scenarios

We use the same 15 topologies with different revenues, as shown in Table 12, to deploy small cells. Figure 25 to Figure 27 show the performance in terms of profit of

Figure 25: Simulation results of scenario 1

Figure 26: Simulation results of scenario 2

Figure 27: Simulation results of scenario 3

The orange line represents the genetic algorithm and the blue line represents the greedy algorithm. The genetic algorithm outperforms the greedy algorithm in all scenarios. The result of scenario 1 shows a significant difference between the genetic algorithm and the greedy algorithm. The average absolute difference in profits is 47 and the average percentage difference in profit is 16%. For scenario 2, the performances of the two algorithms are relatively close. The average absolute difference is 16 and the average percentage difference is 4%. For scenario 3, the genetic algorithm also outperforms the greedy algorithm. However, the difference is not that great compared to scenario 1. The average absolute difference is 27 and the average percentage difference is 12%. The performance of the algorithms in different scenarios varies a lot. Table 13 lists the numerical results in different scenarios.

Table 13: Numerical comparison in different scenarios

In simulation, the performance of the two algorithms depends on the revenue of neutral host services and the properties of the algorithms. We give an explanation in an example.

Figure 28: Original configuration

Figure 28 is the original configuration of a simulation result. The users are distributed in an 800m * 800m region. The red dots are site-specific users and the black dots are neutral host users. The distribution and parameters of the users are described in Sector 2.1 and Section 2.6. In the beginning, the micro operator provides service to the site-specific users. Figure 29 is the configuration when the micro operator covers all the site-specific users with the greedy algorithm and the genetic algorithm, respectively.

Figure 29: Configuration when all the site-specific users are covered with (a) the greedy (b) the genetic

The blue dots are the covered site-specific users. The green dots are the covered neutral host users. The black dots are the unserved neutral host users. In the current stage, all the site-specific users are served so that there are no red dots in the figures. The red triangles

and the red crosses are the positions of micro and pico cells, respectively. After covering all the site-specific users, the micro operator provides service to the neutral host users to earn additional profit. Figure 30 to Figure 32 are the deployment results in different scenarios. It is worth noting that the small cells are deployed densely to serve neutral host users in scenario 1. In scenario 2, the number of extra small cells to serve neutral host users are much fewer than scenario 1. In scenario 3, the number of additional small cells are larger than scenario 2 but smaller than scenario 1. Table 14 lists the numerical results of profit in three scenarios. The disparity between the two algorithms is in proportion to the number of deployed small cells. The larger the number of small cells are deployed, the greater the gap of the performance is.

Figure 30: Scenario 1 with (a) the greedy algorithm (b) the genetic algorithm

Figure 31: Scenario 2 with (a) the greedy algorithm (b) the genetic algorithm

Figure 32: Scenario 3 with (a) the greedy algorithm (b) the genetic algorithm Table 14: Numerical results of the example

From Figure 30 to Figure 32, the number of small cells varies a lot. The number of small cells is affected by the revenue of neutral host services. For the revenue of site-specific services, the micro operator only earns the money when it covers all site-site-specific users. The micro operator can only take a fixed revenue from the site-specific owner.

Hence, the key point of the number of small cells is the revenue from neutral host services.

If the revenue from neutral host services is low, the micro operator needs to cover more neutral host users to make up the cost of deployed cells. If the revenue from neutral host services is high, the micro operator only needs to cover a few users so that it can have profit. In case the micro operator has profit, it would like to keep deploying small cells.

It is the reason that the revenue from neutral host service affects the number of deployed small cells. The more revenue from each neutral host user is, the more small cells are able to be deployed. Moreover, the number of small cells and the properties of the algorithms

affect the performance of the two algorithms. For the greedy algorithm, whenever it makes a decision, it chooses the best option (i.e. a position that covers most users) in the current condition. The decision will never be changed. In cell deployment, small cells will be affected by newly deployed cells. When the number of small cells is small as shown in Figure 31, the inter-cell interference is also slight. However, when the number of small cells becomes as large as Figure 30 and Figure 32, the inter-cell interference becomes significant. Although the cells are deployed in the best position at the time, it may no longer be the best position when small cells are continuously deployed. On the other hand, when the genetic algorithm wants to deploy small cells, it decides the position of all small cells at the same time with an iteration method. Compared with the greedy algorithm, it will not be affected severely by the number of small cells and can find suitable positions though the complexity is much higher than the greedy algorithm.

However, in long-term deployment, the complexity is not taken into account. To sum up, the revenue of neutral host services and the properties of the algorithms have a large influence on the performance.