# SDN-Based Routing for Backhauling in Ultra-Dense Networks
## 7 Results  
This section provides numerical results to validate the effectiveness of the proposed SDN-based routing approach. As stated in Section 5, the aim of our paper is to minimize the total amount of UTDs, which is the requested capacity that the backhaul network is unable to support due to links overloading. As a consequence, we are interested in evaluating the total amount of UTDs achieved with the proposed method. We define different macro-scenarios where network parameters are random variables with a certain probability distribution as reported in Table 1. We have averaged numerical results over several realizations of a given scenario. In that way results depend on the macro-scenario but not on a specific distribution of cells and traffic-loads. Macro-scenarios differ in the mean values of the probability distributions. In particular, macro-scenarios are characterized by edges capacity and the network degree of connectivity. Edges' capacity depends on the link type, and we distinguish among three cases: high-, low-, and medium-capacity network as reported in Table 1. Low- and medium-capacity networks have been set so that not always there is sufficient capacity to satisfy all data-traffic demands, while the high-capacity network is always able to support all control and data-traffic demands. Also for what concerns the degree of connectivity of the network (i.e., the mean number of edges per cell) we consider three cases: (i) 2 edges - low-connected, 3 edges medium-connected, 5 edges highly connected. In particular, the number of edges per cell is derived as an integer value uniformly distributed in the intervals defined in Table 1. Finally, cells are randomly distributed in the considered area, \(A\), and the number of cells is selected according to a homogeneous spatial Poisson point process, with intensity \(\lambda_{s}\). Numerical results are given as a function of the mean number of cells, which is \(S=\lambda_{s}A\). Moreover,  
Figure 4: Reconfiguration example using the proposed SDN-routing scheme. data-traffic demands are uniformly distributed on given intervals that are different for each kind of cell as reported in Table 1. The control traffic is a percentage of the data traffic, in particular, in simulations we have assumed 1%. We want to underline that varying the network capacity while maintaining the traffic load constant leads to the same considerations as fixing the network capacity and varying the network load. Since the control traffic is bandwidth-constrained, the control-traffic demands are always satisfied. Moreover, in high-capacity network scenarios, all traffic demands are satisfied (i.e., UTD is zero). For these reasons when we show results in terms of UTDs, we refer only to data traffic in low- and medium-capacity networks. The high-capacity network is considered for delay evaluations. Figure 5 reports the total amount of UTDs for the data traffic as a function of the mean number of cells in the area when the network has medium (a) and low (b) capacity. Figures report the behavior of the proposed algorithm (FUDM) and the two benchmarks (MNH, HC). We can see that the proposed algorithm always outperforms the two benchmarks. In particular, the effectiveness of FUDM algorithm is more evident when the network has low capacity (or similarly, is overloaded), indeed in this case the gain in terms of UTDs increases. This means that the proposed method is more able to distribute the traffic among the available paths, thus reducing the links' congestion. In all cases we can observe that increasing the number of cells introduces only a slight increase of the UTDs value because also the number of possible paths in the network increases accordingly.