Fairness Index
Lee Cheng-Ta
October 3, 2006
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Jain’s Fairness Index
( i 1 xi )
n
Fairness 
Fairness Index =
2
n i 1 xi2
n
where xi is 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
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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.
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References
1.
2.
3.
4.
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 MultiHop 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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