u- rates, thus wasting resources. This is most marked in case (b) for the fixed slices where there is a smaller number of lower bitrate users requiring service SO that Slice 1 is underused. The effect of this waste is shown in Figure 8.12 by considering the QUR: there is a sig- nificant benefit to the total number of users served by allocating resources from the whole block of spectrum rather than as fixed slices. Fairness between service classes is shown in Figure 8.13 using the well-known Raj Jain index [46] for the overall QUR: the fairness obtained with sharing the whole spectrum is essentially 1 (i.e. maximum) for both cases, but for the fixed slice approach the fairness becomes quite low. Clearly these results show the benefit of sharing the spectrum using dynamic network slicing, particularly under uneven load; what the results do not show is whether isolation 1 The results are from [32] and reprinted under the author copyright agreement of the IEEE. 8 Network Slicing with Spectrum Sharing Number of users overall Fixed slice (a) Fixed slice (b) Spectrum shared (a) Spectrum shared (b) Figure 8.11 Comparison between fixed slices and overall sharing (uneven load) ©IEEE 2017. Spectrum shared (a) Spectrum shared (b) Fixed slices (a) Fixed slices (b) Number of users overall Figure 8.12 Overall results for qualified user ratio ©IEEE 2017. 8.4 Radio Resource Allocation that Considers Spectrum Sharing Spectrum shared (a) Spectrum shared (b) Fixed slices (a) Fixed slices (b) Number of users overall Figure 8.13 Raj Jain fairness index ©IEEE 2017. is maintained between slices. Since that is a very important aspect of network slicing, it is considered in detail in Section 8.6. 8.4.2 Other Considerations Since the use of game theory in the example is to implement an optimization process for resource allocation, it is possible to add different constraints to that optimization. As an example, consider adding in the need to keep transmitted power to a minimum, compared with the previous example where each RB had the same t