## 5 Simulation Results
For example, in the configuration of seven users per cell, our proposed algorithm achieves 100% for a rate requirement of 150 kbps, while a reduction of 60% is observed when the condition is of 300 kbps. Furthermore, the pricing-based solution has a better performance than greedy algorithms in terms of feasibility. For instance, taking Figure 3b as a basis, our proposed approach has a feasibility of 90% when there are seven devices per cell, while the Max-SINR and Min-PL algorithms achieve a 0% feasibility; this is because, in both algorithms, the resource capacity at BSs is exceeded. Figure 4 shows the percentage of feasible BS assignment solutions under the variation of the backhaul capacity of BSs. A solution is assumed to be feasible when all of the system's resource constraints are satisfied. It is noted in the results that, for \(R_{c}^{\min}\)=250 Kbps, the percentage of feasible solutions is reduced for the three algorithms as the backhaul capacity is more limited. In the case of the six devices per cell and a backhaul capacity of 12 Mbps, our proposed approach has a percentage of 85%. In contrast, for a more restrictive scenario with a backhaul capacity of 4 Mbps, it has 0% feasibility. Even when there are available radio resources, the backhaul imposes a hard constraint on the assignment solution. From the results, even when the minimum required data rate is low,  
Figure 3: Feasible solutions (%) found by each algorithm under a backhaul capacity of 12 Mbps and different data rate requirements of human-type communication devices (HTC) devices: (**a**) 150 Kbps, (**b**) 200 Kbps, (**c**) 250 Kbps, and (**d**) 300 Kbps. the reason for the excess in the backhaul resource constraints is that the assignment between a device \(i\) and a BS \(j\) implies a data rate transmission that is associated to the perceived SINR. More specifically, given the SINR value in the association device to BS, the assigned data rate is computed according to a modulation and coding method, which varies from 1.5 Mbps to 46.1 Mbps. Figure 5 shows the cumulative distribution function (CDF) of the achieved throughput for the assignment solutions found by each algorithm. The number of HTC and MTC devices per cell is set to 10 and 20, respectively, which results in a total number of devices of 570 in the system. It is shown that the proposed pricing-based algorithm outperforms the two benchmark algorithms in terms of system's throughput. For instance, for the pricing-based algorithm, 50% of devices achieved an efficiency of 9.5 Mbps, while, for the Max-SINR and Min-PL algorithms, the achieved throughput is about 7 Mbps. That is because the assignment found by Max-SINR and Min-PL algorithms exceed the BSs capacity, and the assigned devices experience a reduction in the achievable data rate. Furthermore, in terms of the average sum cost at BS, there is a significant difference between the greedy algorithms and our proposed approach. The price-based algorithm's average sum cost is always below the maximum allowable cost of BSs, as illustrated in Figure 6. For instance, in eight devices, the average cost observed for the price-based algorithm is around to 1, while for the Max-SINR and the Min-PL algorithms, there is an average cost of 5.8. That is because the backhaul and radio capacity constraints steer the assignment process in the pricing-based approach. At the same time, the other algorithms do the assignment without considering such constraints. In this sense, the average sum costs of the greedy approaches reflect the number of resources that would be needed to support the provided BS assignment solution. We observe that such unfeasible BS assignment solutions lead to a user rate degradation situation, as presented in Figure 7. To be specific, we quantify data rate  
Figure 4: Feasible solutions (%) found by each algorithm under different backhaul capacity configurations (**a**) 4 Mbps, (**b**) 12 Mbps, and (**c**) 21 Mbps.