## 5 Simulation Results  
This section evaluates the performance of the proposed distributed price-based BS assignment algorithm. We consider a system that is composed of 19 hexagonal cells distributed in three tiers (one centric cell in first tier and two concentric tiers). The HTC devices and MTC devices are uniformly distributed over the coverage area. It is worth noting that the simulation results are presented in terms of the density of users per cell, where the total number of users in the system ranges from 190 to around 700 devices. Each device computes its candidate set when considering a PLM value of 6 dB, which implies that each BS whose path loss falls within such a range is considered as candidate BS. The BSs are configured with a maximum transmit power of 43 dBm. Furthermore, a bandwidth of 10 MHz is considered with a frequency reuse pattern of 3. The HTC devices and MTC devices have different downlink data rate requirements, which are defined as \(R_{c}^{min}\) and \(R_{d}^{min}\), respectively. The propagation losses are computed while using the Okumura-Hata model with the parameters given in Table 2. The log-normal shadowing is modeled with a standard deviation equal to 8 dB, and a noise figure of 5 dB is also considered. Based on the SINR, the modulation and coding scheme (MCS) and, consequently the achievable rate is taken from the look-up table provided in [8]. The cell's radius has been computed while taking into account that the minimum SNR requirement of the MCS 1 is assured at the cell edge. The main simulation parameters are presented in Table 2. In our simulations, we evaluate the performance of the following algorithms: (a) Max-SINR, a greedy approach that assigns the devices with the BS that provides the highest SINR value [14]; (b) Min-PL, which assigns each device with the BS that provides the minimum path-loss [35], and (c) Price-based algorithm, which is the proposed approach in this paper. Given a snapshot of the system with a distribution of devices over the coverage area, the algorithms are used to find a BS assignment solution. Subsequently, for each obtained solution, the following performance metrics are obtained:  
* Feasibility. This experiment allows for us to measure the percentage of feasible solutions found by each algorithm. A solution is assumed to be feasible when the system's constraints (i.e., radio and/or backhaul resources) are not exceeded. * Throughput. Given a BS assignment solution, we compute the total system's throughput as the sum of the data rate achieved by each device being served by a given BS. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Total number of cells \(N\) & 19 \\ Max. BS transmit power, \(P_{j}^{\text{max}}\) & 43 dBm \\ Cell radius & 0.293 km \\ Operating frequency & 2000 MHz \\ Reuse factor & 3 \\ Channel bandwidth & 10 MHz \\ Number of data subchannels & 1024 \\ OFDM symbol duration & 102.9 us \\ Path loss model & \(69.55+26.16\ \times\ \log_{10}(fc)-13.82\ \times\ \log_{10}(hb)-\) \\ \(\text{{\small{\small{\small{\small{\small{\small{\small{\small{\small{ \small{\small{\small{\small{\small{\small{\small{\small{\small{\,{\,}}}}}} {{\left[{{\small{\small{  
* Resource costs. We compute each BS's average sum cost to analyze if the algorithms violate the cost constraint. * Rate degradation. This metric shows the data rate reduction experienced by devices when they are assigned to overloaded BS. Figure 3 depicts the percentage of feasible solutions under the variation of the number of HTC devices per cell and a minimum rate requirement \(R_{c}^{\min}=\{150,200,250,300\}\) Kbps, and assuming a minimum rate requirement of MTC devices of \(R_{d}^{\min}=25\) Kbps. A solution is assumed to be feasible when the system's resource constraints are not exceeded. It can be seen that, when the minimum rate requirement has increased, the percentage of feasible solutions is reduced for the three algorithms.