# A Mathematical Model for Efficient and Fair Resource Assignment in Multipath Transport
## 6 Conclusions  
The aim of this work was a rigorous analysis of fairness in multipath transport. Formal definitions for the different resources and participants in a network were given, based on which fairness definitions were specified. An optimum solution for the resource allocation in arbitrary networks considering both high network utilization as well as fairness was developed using mixed (non-)linear programming. The results were compared with an algorithmic solution which imitates the way resources would be assigned manually. It can be observed that the network utilization, measured by the aggregated allocation of all flows, is almost the same for all fairness methods, whereas network-fair allocation, according to the investigated fairness metrics, performs best if fairness is in focus. The achieved results  
Figure 23: [PERSON]’s fairness index, normalized by NFF, for different fair allocation methods, based on the numerical results in Tables 10–14. Figure 22: [PERSON]’s fairness index, normalized by NFF, for different fair allocation methods, based on the numerical results in Tables 10–14. Figure 24: Product of efficiency and [PERSON]’s fairness index, normalized by NFF, for different fair allocation methods, based on the numerical results in Tables 10–14. can serve as a benchmark to assess the performance and fairness of existing MPTCP implementations. Since the best fairness results can be achieved with the network-based solution and an individual (MP)TCP flow, this suggests that assistance of the network operator may be useful. MPTCP is an end-to-end solution; the protocol has only information about the end-to-end connection, but not about the entire network. The presented results show the optimum assignments of data flows in the case of perfect \"good-view\" network knowledge and an idealized view with constant data flows. They provide a benchmark for practical implementations of multipath transport whose congestion control only has a \"local\" view onto the network by analysing the performance of ongoing connections. In order to enhance the performance of the purely transport-layer based approach, it can be complemented by the network infrastructure in two ways: multipath routing which is aware of the internal network state can further optimize network utilization and fairness. Another possible approach could be that routers are equipped with intelligence to identify MPTCP data transfers. Using this data, packets could be selectively dropped in order to trigger the sender's congestion control with the target of shaping the traffic injected into the network. The results which are given for fairness should by interpreted with care for two reasons: on the one hand, as already mentioned in the Introduction, an idealistic view onto a network with perfect global knowledge is assumed. In practice, an endpoint running a practical transport protocol can only roughly estimate possible constraints which may apply to the data flow which it injects into the network. On the other hand, the fairness metrics available in the literature which are used in this paper are designed for single path transport. The investigations in this paper show that they cannot give a direct comparison independent from the observed scenario and fairness method, which is the reason why the normalization has to be brought in. This situation is not satisfying; it would be useful if dedicated fairness metrics for multipath transport were available, which is not the case to the best of the authors' knowledge. An important step therefore would be the extension of the fairness metrics for multipath transport, which allows direct comparison of multipath fairness for any scenario irrespective of the fairness method. **Author Contributions:** Conceptualization, A.K., M.S., A.S. and A.F. ; Data Curation, M.S. ; Formal Analysis, M.S. and A.S.; Funding Acquisition, A.F. ; Investigation, A.K., M.S. and A.S.; Methodology, A.K., M.S., A.S. and A.F. ; Project Administration, A.F. ; Software, M.S. ; Supervision, A.F. ; Visualization, A.K.