Maximum Throughput and Fair Bandwidth Allocation in Multi ...

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This means that when S ≠ S 1, ′ we can always identify atleast one node v ∈ S (β v > 0) such that v ∉ S 1 ′ and moveit out of S. Clearly,inatmostN −|S 1| ′ iterations, we willhave S = S 1. ′ This shows that we have computed S 1 ′ and thebandwidth value for S 1 ′ (α 1 ) correctly.For general k, 1
1210MBAMMBALMMBA400350300Bandwidth864Throughput2502001501005020MBA MMBA LMMBA01 5 10 15 20 25 30Sorted Node IndexFig. 8. Network throughput (n =25,N =20,C =12,CAP =53.9)Fig. 5. Bandwidth allocation (n =35,N =30,C =3,CAP =10.9)Throughput1101009080706050Bandwidth5550454035302520MBAMMBALMMBA403020100MBA MMBA LMMBA1510501 5 10 15 20 25 30Sorted Node IndexFig. 6. Network throughput (n =35,N =30,C =3,CAP =10.9)Fig. 9. Bandwidth allocation (n =35,N =30,C =12,CAP =53.9)55504540MBAMMBALMMBA500450400350Bandwidth3530252015105Throughput300250200150100500MBA MMBA LMMBA01 5 10 15 20Sorted Node IndexFig. 10. Network throughput (n =35,N =30,C =12,CAP =53.9)Fig. 7. Bandwidth allocation (n =25,N =20,C =12,CAP =53.9)That is to say, based on the MBA scheme, some of users willnot be able to access the network at all, which is definitelynot desirable. Compared with the MBA scheme, the MMBAscheme improves the fairness somehow, without sacrificingthe network throughput too much. It guarantees every nodebe allocated some reasonable amount of bandwidth. For thecases in which the network resources are relatively sparse(C = 3,CAP = 10.9), the throughput provided by theMMBA scheme is very close to the maximum throughput,which can be seen from Fig. 4 and 6. As expected, amongthe three bandwidth allocation schemes, the LMMBA schemeachieves fairest bandwidth allocation. If the bandwidth isallocated using the LMMBA scheme, we observe from theresults that the nodes are partitioned to several groups (usuallythe number of groups is very small) and within each group,all nodes are allocate exactly the same amount of bandwidth.The throughput provided by the LMMBA scheme is alwayssmaller than that provided by the other two schemes, especiallyThis full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the Proceedings IEEE Infocom.
Page 4 and 5: specifies the amount of flow routed
Page 6 and 7: subject to∑f vw − ∑w≠v u≠
Page 10: for cases in which the network reso

Maximum Throughput and Fair Bandwidth Allocation in Multi ...

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