# American Institute of Mathematical Sciences

2011, 1(4): 675-689. doi: 10.3934/naco.2011.1.675

## Analysis of the statistical time-access fairness index of one-bit feedback fair scheduler

 1 Department of Systems Design and Engineering, Nanzan University, 27 Seirei, Seto, Aichi 489-0863, Japan

Received  June 2011 Revised  September 2011 Published  November 2011

Recently various schedulers exploiting multiuser diversity in wireless networks have been proposed and studied. Although the utilization of multiuser diversity can increase the information theoretic capacity, there exists a tradeoff between the capacity and fairness. Among schedulers exploiting multiuser diversity, the one-bit feedback fair scheduler is considered as an attractive choice for the reduction of feedback overheads and the ease of implementation. In this paper, we study the short term fairness of the one-bit feedback fair scheduler. Since the short term fairness has a strong impact on the quality-of-service of each mobile station, it is important to examine the short term fairness properties of the scheduler. As a short term fairness index, we consider the statistical time-access fairness index (STAFI). We then develop two numerical methods to estimate the STAFI of the scheduler. The first method calculates the exact value of the STAFI by using the inverse discrete FFT method. The second method estimates the asymptotic decay rate of the STAFI by using the theory of large deviations. Numerical results show that the threshold value of the one-bit feedback fair scheduler greatly affects its short term fairness properties.
Citation: Fumio Ishizaki. Analysis of the statistical time-access fairness index of one-bit feedback fair scheduler. Numerical Algebra, Control and Optimization, 2011, 1 (4) : 675-689. doi: 10.3934/naco.2011.1.675
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##### References:
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