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Fairness Index

Fairness Index. Lee Cheng-Ta October 3, 2006. Jain’s Fairness Index. Fairness Index = where x i is the normalized throughput ( in Kbps ) of the i −th TCP flow and n is the number of connections.

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Fairness Index

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  1. Fairness Index Lee Cheng-Ta October 3, 2006

  2. Jain’s Fairness Index • Fairness Index = • where xiis the normalized throughput (in Kbps) of the i−th TCP flow and n is the number of connections. • Example: A scheme gives 50, 30, 50 Mbps (throughput, ti) when the optimal is 50, 10, 10 Mbps (fair throughput, oi) • Normalized Throughput: xi = ti/oi • 50/50, 30/10, 50/10  1, 3, 5 • Fairness Index =(1+3+5)2 / 3(12+32+52) =92 / 3(1+9+25)= 0.77 • 1, 4, 5  0.79 • 1, 2, 5  0.71

  3. Fairness Index: Properties • Scale independent • Standard deviation (Throughput) = 10 Mbps = 104 kbps • Bounded • between 0 and 1 or 0 and 100% variance, standard deviation, and relative distance are not bounded. • Direct relationship: • Higher index  More Fair • Higher variance  Less fair • Continuous • min/max is not continuous. • The index should be continuous. Any slight change in allocation should show up in the fairness index. In the above example, if the normalized throughput is 1, 4, and 5 respectively, the fairness should obviously be different, yet it is not reflected in the min-max ratio which remain at 1/5.

  4. References • R. Jain, W. Hawe, D. Chiu, “A Quantitative measure of fairness and discrimination for resource allocation in Shared Computer Systems,” DEC-TR-301, September 26, 1984, http://www.cis.ohio-state.edu/~jain/papers/fairness.htm • Yu, O.; Saric, E.; Li, A.; “Fairly adjusted multimode dynamic guard bandwidth admission control over CDMA systems ,” IEEE Journal on Selected Areas in Communications, Volume 24,  Issue 3,  March 2006 Page(s):579 - 592 (2005/2/21) • Krishnamachari, B.; Ordonez, F ,”Analysis of energy-efficient, fair routing in wireless sensor networks through non-linear optimization,” 2003 IEEE 58th Vehicular Technology Conference, 2003. VTC 2003-Fall. Volume 5,  6-9 Oct. 2003 Page(s):2844 - 2848 Vol.5 (2005/9/22) • Baochun Li, “End-to-End Fair Bandwidth Allocation in Multi-Hop Wireless Ad Hoc Networks,” 25th IEEE International Conference on Distributed Computing Systems, June 2005 Page(s):471 – 480 (2005/9/22)

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