Through the detailed analysis of the previous two case studies, we are able to compute the expected revenue of the three QoS scenarios for every possible combination of the techno-economic parameters. Though this methodology provides a fine-grained view for each case, we need to extract general conclusions. Indeed, for a given set of techno-economic parameters, the ultimate challenge for the MNO is to choose the prices \(P_L\) and \(P_H\) so that its revenue will be maximised. Therefore, we can consider this fine-grained analysis as an internal process for the MNO to compute: (i) the value of \(P_L\) that maximises its revenue for the low QoS scenario, (ii) the value of \(P_H\), i.e., parameter *K* and \(P_L\), that maximises its revenue for the high QoS scenario, and (iii) the values of \(P_L\) and \(P_H\) that maximise its revenue for the mixed QoS scenario. Then, the MNO can choose which QoS scenario maximises globally its revenue.

Though the MNO controls the technical parameters and the price, the distribution of the users’ budgets as well as the users’ preferences for the two QoS classes are private information. The complementary problem of how to estimate this piece of information is not addressed in this paper. However, we present a broad number of scenarios for the parameters that each user controls, so as to estimate the revenue for the three QoS scenarios under different users’ behaviours. Having identified the most profitable QoS scenarios, the operator is then expected to mine the profiles of the users in order to match the general distribution of their budgets with the pricing policy that maximises its revenue.

Initially, we generalise the results of the previous section where we consider 36 budget scenarios for the distribution of the users’ budgets \(B_L\) and \(B_H\). The number of budget scenarios arises since the 4-tuple {\(\mu _L\), \(\sigma _L\), \(\mu _H\), \(\sigma _H\)} can get \(3\cdot 2\cdot 3\cdot 2=36\) possible values. Figure 5 represents the evolution of the budget distribution. We progressively update the elements of the 4-tuple in four loops, with the following order from the outermost loop to the innermost loop: (i) \(\mu _L\), (ii) \(\sigma _L\), (iii) \(\mu _H\), and (iv) \(\sigma _H\). Due to this, as we can see from Fig. 5a, \(\mu _L\), depicted as a red line, increases every 12 budget scenarios, remaining the same for scenarios 1–12, 13–24, and 25–36. Let us consider scenarios 1–12: due to a higher value of \(\sigma _L\), scenarios 7–12 have higher upper quartiles and whiskers than scenarios 1–6. For the case of \(B_H\) (Fig. 5b), we notice that every 6 scenarios where \(\mu _L\) and \(\sigma _L\) are fixed (i.e., scenarios 1–6, 7–12, etc.), the upper quartile increases. Moreover, the maximum upper whiskers correspond to scenarios 6, 12, etc., where \(B_H\) has the highest coefficients for \(\mu _H\) and \(\sigma _H\).

Figure 6 presents the maximum revenue and the corresponding values for \(P_L\) and \(P_H\) for the three QoS scenarios. As in Fig. 1, we consider the *non-strict* version for the choice of the QoS class and the results are obtained for the carrier frequency \(f=3800\) MHz and the indoor propagation environment. For all combinations of budgets \(B_L\) and \(B_H\) in Fig. 6a, the maximum revenue of the MNO is achieved for the high QoS scenario, followed by the mixed QoS scenario and then by the low QoS scenario. This result highlights the existence of a tussle for this market between the social welfare (i.e., supporting the maximum number of PMSE users) and the revenue maximisation. Focusing on the revenue from the high QoS scenario, we notice that, for budget scenarios 1-6, the maximum is for the last scenario (scenario 6) and this trend is repeated every six scenarios. The explanation is based on the previous analysis for the distribution of the budget \(B_H\). The same trend holds for the mixed QoS scenario, implying that the dominant component for the mixed QoS revenue is the revenue that arises from the users with \(Q_H\). Finally, for the low QoS scenario, there is a repeating trend for budget scenarios 1–12, 13–24, and 25–36. We recall from Fig. 5a that all budget scenarios of each of these cycles correspond to the same \(\mu _L\) of the budget distribution \(B_L\). Moreover, the revenue during each cycle slightly decreases, admitting three local maxima for budget scenarios 1, 13, 25, where \(\mu _H\) and \(\sigma _H\) have the lowest values (see Fig. 5b).

Figure 6b presents the corresponding value of \(P_L\) for which the maximum revenue for each QoS scenario is achieved. It is interesting that for the high QoS scenario, \(P_L\) is always equal to \(\$120\), i.e., the maximum that the MNO can set throughout the study. For the mixed QoS scenario, \(P_L\) is higher than the corresponding price for the low QoS scenario. This is expected, since in the mixed QoS scenario, the MNO can admit at most 13 users with \(Q_L\), instead of 37 users for the low QoS scenario (see Table 2). We also notice that the evolution of \(P_L\) is similar for both low and mixed QoS scenarios, with the highest values being for budget scenarios 31–36, where \(\mu _L\) and \(\sigma _L\) get the highest values (see Fig. 5a).

Then, we show in Fig. 6c the corresponding value of \(P_H\). As expected, it is higher for the mixed QoS scenario where at most 2 users with \(Q_H\) can be supported than for the high QoS scenario where \(N_H=4\). Moreover, the curves follow the same trend with the revenue. Finally, Fig. 6d depicts the evolution of parameter \(K=\frac{P_H}{P_L}\), where the trends are similar with the trends for \(P_H\). Clearly, there is room for the MNO to apply higher price differentiation for the case of the mixed QoS scenario compared to the high QoS scenario. Our analysis suggests that in budget scenarios where \(\mu _H\) and \(\sigma _H\) get the highest values, the MNO has motivation to charge the mixed QoS users with \(Q_H\) at the maximum level of price differentiation, i.e., 30 times more than the users with \(Q_L\).

We repeat the same analysis for the *strict* preference of the QoS class, where each user has a single choice for the QoS class. Figure 7a compares the maximum revenue for the non-strict and the strict version. The conclusion that arises is that, for all QoS scenarios and all budget scenarios, the revenue is higher for the non-strict version. This is justified due to the fact that the set of revenues for the MNO for the non-strict version is a superset of the strict version: it additionally includes the revenue that each user can bring for its second QoS preference in case it has not been admitted for its first QoS preference. We identify the factors that can justify the difference in the revenue between the non-strict and the strict version, as follows.

The first one is that the number of PMSE users for the non-strict version can be higher than for the strict version. This is clearly the case for the low QoS scenario where, as we can see from Fig. 7b, there is a significant drop in the number of users with \(Q_L\) for the strict version. However, it is worth mentioning that even in the case of the non-strict version, the maximum revenue for the low QoS scenario does not coincide with the theoretical maximum of PMSE users that can be supported, which is 37. This means that either some users do not have the necessary budget \(B_L\) to pay for a particular price \(P_L\), or it is more profitable for the MNO to support fewer users with \(Q_L\) but at a higher price. Furthermore, it is interesting to notice that, e.g., budget scenarios 1–6 correspond to a higher number of users with \(Q_L\) than scenarios 7–12. Given that these scenarios have the same mean \(\mu _L\), we conclude that the standard deviation \(\sigma _L\) for scenarios 1–6, which is smaller than for scenarios 7–12, is the reason for the difference in the number of users. Indeed, for the users with \(Q_L\), it is more profitable for the MNO if the standard deviation \(\sigma _L\) is smaller, since, for prices \(P_L\) that are close to \(\mu _L\), more users can afford to pay for it.

The second factor is that, in the non-strict version, the MNO may have motivation to support fewer users provided that it can charge them more. This is the case with the mixed QoS scenario, where, for some budget parameters (budget scenarios 26-28), the MNO in the non-strict version prefers to support fewer users with \(Q_L\) (dark blue solid line) than in the strict version (dark blue dashed line).

We finally proceed with the results for the other two technical cases, i.e., carrier frequency \(f=800\) MHz and indoor/outdoor propagation environment. We present the maximum revenue and the corresponding number of users for the three QoS scenarios in Fig. 7c–f. As in Fig. 7a, the high QoS scenario generates always the highest revenue. This is a strong result independent of the technical parameters and the distribution of the budgets. Regarding the corresponding number of users, the two key conclusions that we extracted from Fig. 7b still hold. First, the number of users that maximises the revenue for the low QoS scenario does not coincide with the maximum number of users (i.e., 65 users for indoor and 7 users for outdoor). Second, the number of users with \(Q_L\) for the mixed QoS scenario is in general lower for the non-strict version compared to the strict version, since the MNO has motivation to support fewer users with \(Q_L\) in order to admit more users with \(Q_H\) and charge them with high values of *K*. This trend becomes clearer in Fig. 7f, where the non-strict version of the mixed QoS scenario depicted as a dark blue solid line is almost always below the strict version of the mixed QoS scenario depicted as a dark blue dashed line.