# 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
##### References:

show all references

##### References:
 [1] Gregory M. Zaverucha, Douglas R. Stinson. Short one-time signatures. Advances in Mathematics of Communications, 2011, 5 (3) : 473-488. doi: 10.3934/amc.2011.5.473 [2] Jiongmin Yong. Remarks on some short rate term structure models. Journal of Industrial and Management Optimization, 2006, 2 (2) : 119-134. doi: 10.3934/jimo.2006.2.119 [3] Massimo Barnabei, Alessandro Borri, Andrea De Gaetano, Costanzo Manes, Pasquale Palumbo, Jorge Guerra Pires. A short-term food intake model involving glucose, insulin and ghrelin. Discrete and Continuous Dynamical Systems - B, 2022, 27 (4) : 1913-1926. doi: 10.3934/dcdsb.2021114 [4] Bing Gao, Rui Gao. On fair entropy of the tent family. Discrete and Continuous Dynamical Systems, 2021, 41 (8) : 3797-3816. doi: 10.3934/dcds.2021017 [5] Semih Yalçındağ, Ettore Lanzarone. Merging short-term and long-term planning problems in home health care under continuity of care and patterns for visits. Journal of Industrial and Management Optimization, 2022, 18 (2) : 1487-1504. doi: 10.3934/jimo.2021029 [6] Yiju Wang, Wei Xing, Hengxia Gao. Optimal ordering policy for inventory mechanism with a stochastic short-term price discount. Journal of Industrial and Management Optimization, 2020, 16 (3) : 1187-1202. doi: 10.3934/jimo.2018199 [7] Bashar Khorbatly. Long, intermediate and short-term well-posedness of high precision shallow-water models with topography variations. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022068 [8] Wenjun Liu, Hefeng Zhuang. Global attractor for a suspension bridge problem with a nonlinear delay term in the internal feedback. Discrete and Continuous Dynamical Systems - B, 2021, 26 (2) : 907-942. doi: 10.3934/dcdsb.2020147 [9] Guofu Lu. Nonexistence and short time asymptotic behavior of source-type solution for porous medium equation with convection in one-dimension. Discrete and Continuous Dynamical Systems - B, 2016, 21 (5) : 1567-1586. doi: 10.3934/dcdsb.2016011 [10] Cătălin-George Lefter, Elena-Alexandra Melnig. Feedback stabilization with one simultaneous control for systems of parabolic equations. Mathematical Control and Related Fields, 2018, 8 (3&4) : 777-787. doi: 10.3934/mcrf.2018034 [11] Francesca Faraci, Alexandru Kristály. One-dimensional scalar field equations involving an oscillatory nonlinear term. Discrete and Continuous Dynamical Systems, 2007, 18 (1) : 107-120. doi: 10.3934/dcds.2007.18.107 [12] Qichun Wang, Chik How Tan, Pantelimon Stănică. Concatenations of the hidden weighted bit function and their cryptographic properties. Advances in Mathematics of Communications, 2014, 8 (2) : 153-165. doi: 10.3934/amc.2014.8.153 [13] Agnaldo José Ferrari, Tatiana Miguel Rodrigues de Souza. Rotated $A_n$-lattice codes of full diversity. Advances in Mathematics of Communications, 2020  doi: 10.3934/amc.2020118 [14] Ian Johnson, Evelyn Sander, Thomas Wanner. Branch interactions and long-term dynamics for the diblock copolymer model in one dimension. Discrete and Continuous Dynamical Systems, 2013, 33 (8) : 3671-3705. doi: 10.3934/dcds.2013.33.3671 [15] Lianzhang Bao, Zhengfang Zhou. Traveling wave solutions for a one dimensional model of cell-to-cell adhesion and diffusion with monostable reaction term. Discrete and Continuous Dynamical Systems - S, 2017, 10 (3) : 395-412. doi: 10.3934/dcdss.2017019 [16] Dilek Günneç, Ezgi Demir. Fair-fixture: Minimizing carry-over effects in football leagues. Journal of Industrial and Management Optimization, 2019, 15 (4) : 1565-1577. doi: 10.3934/jimo.2018110 [17] José Gómez-Torrecillas, F. J. Lobillo, Gabriel Navarro. Information--bit error rate and false positives in an MDS code. Advances in Mathematics of Communications, 2015, 9 (2) : 149-168. doi: 10.3934/amc.2015.9.149 [18] Shingo Iwami, Shinji Nakaoka, Yasuhiro Takeuchi. Mathematical analysis of a HIV model with frequency dependence and viral diversity. Mathematical Biosciences & Engineering, 2008, 5 (3) : 457-476. doi: 10.3934/mbe.2008.5.457 [19] Evariste Sanchez-Palencia, Jean-Pierre Françoise. Topological remarks and new examples of persistence of diversity in biological dynamics. Discrete and Continuous Dynamical Systems - S, 2019, 12 (6) : 1775-1789. doi: 10.3934/dcdss.2019117 [20] Onur Şimşek, O. Erhun Kundakcioglu. Cost of fairness in agent scheduling for contact centers. Journal of Industrial and Management Optimization, 2022, 18 (2) : 873-896. doi: 10.3934/jimo.2021001

Impact Factor: