Fairness Index

1
Fairness Index

• Lee Cheng-Ta
• October 3, 2006

2
Jains Fairness Index

• Fairness Index
• 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 (135)2 / 3(123252)
  92 / 3(1925) 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/fairnes
  s.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)