Statistical Time-Access Fairness Index of One-Bit Feedback Fair Scheduler

Since the utilization of multiuser diversity in wireless networks can increase the information theoretic capacity, much attention has been paid to schedulers exploiting multiuser diversity. It is known that there exists a tradeoff between the capacity and fairness achieved by schedulers exploiting multiuser diversity. Due to its good balance between the capacity and fairness, the one-bit feedback fair scheduler is considered as an attractive choice. The fairness is classified into short term fairness and long term fairness. It is known that the one-bit feedback fair scheduler has an ideal long term fairness property. However, the short term fairness properties of the scheduler have not been sufficiently explored yet. Since packet level performances of individual MSs (Mobile Stations) are strongly affected by short term fairness, it is also important to examine the short term fairness of the schedulers. In this paper, we focus on the short term fairness of the one-bit feedback fair scheduler. As a short term fairness index, we consider the statistical time-access fairness index (STAFI). We then develop two numerical methods to understand the transient properties of the STAFI of the one-bit feedback fair 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.