Hence, we propose two orthogonal snap-stabilizing algorithms, each satisfying 2-phase discussion, and either maximal concurrency or fairness.
The total throughput of the proposed scheme is close to the maximal one, while significantly improving fairness compared to the existing solutions.
The simulation results show that the proposed algorithms acquire a good tradeoff between the overall system throughout and fairness, compared to maximal rate and max-min schemes.
Moreover, we proved that our developed resource allocation scheme can achieve maximal transmission rate with proportional fairness for two-way relay transmission system, and this conclusion also holds in both the source phase transmission and the relay phase transmission.
In general, the SABG scheme is adaptive and can be adjusted to reach two extreme states (i.e., maximal-rate and max-min fairness) by manipulating the budget allocated to each user.
From Figure 5, it is observed that the overall complexity of the SABG increases linearly with K and N. Though the order of complexity of the SABG is similar to that of the maximal-rate and max-min fairness schemes, the overall complexity of the SABG is slightly higher because of the iterative PA and BA algorithms.
So we can state that, although we explore the resource allocation schemes towards minimal transmission completion time, our proposed schemes also can be used to achieve maximal average transmission rate with proportional fairness for two-way relay OFDM transmission systems.
Figure 4 Comparison of total throughput and fairness index for the maximal-rate, max-min, NBS and SABG schemes in uncorrelated and correlated OFDM channels.
We also provide a comprehensive comparison of SG+ and several well-known fairness notions and their minimal and maximal completions.
Based on those premises, the authors propose coloring algorithms with an objective of maximal cumulative reward, maximal minimal reward, and maximal proportional fairness.
