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:
[1]

J. A. Bucklew, "Large Deviation Techniques in Decision, Simulation and Estimation," Wiley-Interscience, 1990.

[2]

C. S. Chang, "Performance Guarantees in Communication Networks," Springer-Verlag, 2000. doi: 10.1007/978-1-4471-0459-9.

[3]

J. Diaz, O. Simeone and Y. Bar-Ness, Sum-rate of MIMO broadcast channels with one bit feedback, in ''Proc. of IEEE International Symposium on Information Theory (ISIT '06)," (2006), 1944-1948.

[4]

F. Florén, O. Edfors and B. A. Molin, The effect of feedback quantization on the throughput of a multiuser diversity scheme, in ''Proc. of IEEE GLOBECOM 2003," (2003), 497-501.

[5]

D. Gesbert and M. S. Alouini, How much feedback is multi-user diversity really worth?, in ''Proc. of IEEE ICC '04," (2004), 234-238.

[6]

G. U. Hwang and F. Ishizaki, Design of a fair scheduling exploiting multiuser diversity with feedback reduction, IEEE Communications Letters, 12 (2008), 124-126. doi: 10.1109/LCOMM.2008.071547.

[7]

G. U. Hwang and F. Ishizaki, Analysis of short term fairness and its impact on packet level performance, Performance Evaluation, 67 (2010), 1340-1352. doi: 10.1016/j.peva.2010.08.021.

[8]

F. Ishizaki and G. U. Hwang, Queuing delay analysis for packet schedulers with/without multiuser diversity over a fading channel, IEEE Trans. Veh. Technol., 56 (2007), 3220-3227. doi: 10.1109/TVT.2007.900523.

[9]

F. Ishizaki and G. U. Hwang, Throughput performance of quantized proportional fair scheduling with adaptive modulation and coding, in ''Proc. of Wireless Telecommunications Symposium (WTS) 2009," (2009).

[10]

H. Kim and Y. Han, An opportunistic channel quality feedback scheme for proportional fair scheduling, IEEE Communications Letters, 11 (2007), 501-503. doi: 10.1109/LCOMM.2007.070106.

[11]

R. Knopp and P. A. Humblet, Information capacity and power control in single-cell multiuser communications, in ''Proc. of IEEE ICC '95," (1995), 331-335. doi: 10.1109/ICC.1995.525188.

[12]

Q. Liu, S. Zhou and G. B. Giannakis, Queuing with adaptive modulation and coding over wireless links: cross-layer analysis and design, IEEE Trans. Wireless Commun., 4 (2005), 1142-1153. doi: 10.1109/TWC.2005.847005.

[13]

Y. Liu, S. Gruhl and E. W. Knightly, WCFQ: an opportunistic wireless scheduler with statistical fairness bounds, IEEE Trans. Wireless Commun., 2 (2003) 1017-1028. doi: 10.1109/TWC.2003.816777.

[14]

X. Qin and R. Berry, Exploiting multiuser diversity for medium access control in wireless networks, in ''Proc. of IEEE INFOCOM '03," (2003), 1084-1094.

[15]

S. Sanayei and A. Nosratinia, Opportunistic downlink transmission with limited feedback, IEEE Trans. Infor. Theory, 53 (2007), 4363-4372. doi: 10.1109/TIT.2007.899529.

[16]

O. Somekh, A. M. Haimovich and Y. Bar-Ness, Sum-rate analysis of downlink channels with 1-bit feedback, IEEE Communications Letters, 11 (2007), 137-139. doi: 10.1109/LCOMM.2007.061464.

[17]

H. C. Tijms, "A First Course in Stochastic Models," John Wiley & Sons, 2003. doi: 10.1002/047001363X.

[18]

B. Tan, L. Ying and R. Srikant, Short-term fairness and long-term QoS, in ''Proc. of Conference on Information Science and Systems (CISS)," (2008), 1201-1204.

[19]

D. Wu and R. Negi, Utilizing multiuser diversity for efficient support of quality of service over a fading channel, IEEE Trans. Veh. Technol., 54 (2005), 1198-1206. doi: 10.1109/TVT.2005.844671.

[20]

Y. Xue and T. Kaiser, Exploiting multiuser diversity with imperfect one-bit channel state feedback, IEEE Trans. Veh. Technol., 56 (2007), 183-193. doi: 10.1109/TVT.2006.883784.

[21]

M. D. Yacoub, "Foundation of Mobile Radio Engineering," CRC-Press, 1993.

[22]

L. Yang, M. Kang and M.-S. Alouini, On the capacity-fairness tradeoff in multiuser diversity systems, IEEE Trans. Veh. Technol., 56 (2007), 1901-1907. doi: 10.1109/TVT.2007.897229.

[23]

W. Zhang and K. B. Letaief, MIMO broadcast scheduling with limited feedback, IEEE J. Sel. Areas Commun., 25 (2007), 1457-1467. doi: 10.1109/JSAC.2007.070918.

show all references

References:
[1]

J. A. Bucklew, "Large Deviation Techniques in Decision, Simulation and Estimation," Wiley-Interscience, 1990.

[2]

C. S. Chang, "Performance Guarantees in Communication Networks," Springer-Verlag, 2000. doi: 10.1007/978-1-4471-0459-9.

[3]

J. Diaz, O. Simeone and Y. Bar-Ness, Sum-rate of MIMO broadcast channels with one bit feedback, in ''Proc. of IEEE International Symposium on Information Theory (ISIT '06)," (2006), 1944-1948.

[4]

F. Florén, O. Edfors and B. A. Molin, The effect of feedback quantization on the throughput of a multiuser diversity scheme, in ''Proc. of IEEE GLOBECOM 2003," (2003), 497-501.

[5]

D. Gesbert and M. S. Alouini, How much feedback is multi-user diversity really worth?, in ''Proc. of IEEE ICC '04," (2004), 234-238.

[6]

G. U. Hwang and F. Ishizaki, Design of a fair scheduling exploiting multiuser diversity with feedback reduction, IEEE Communications Letters, 12 (2008), 124-126. doi: 10.1109/LCOMM.2008.071547.

[7]

G. U. Hwang and F. Ishizaki, Analysis of short term fairness and its impact on packet level performance, Performance Evaluation, 67 (2010), 1340-1352. doi: 10.1016/j.peva.2010.08.021.

[8]

F. Ishizaki and G. U. Hwang, Queuing delay analysis for packet schedulers with/without multiuser diversity over a fading channel, IEEE Trans. Veh. Technol., 56 (2007), 3220-3227. doi: 10.1109/TVT.2007.900523.

[9]

F. Ishizaki and G. U. Hwang, Throughput performance of quantized proportional fair scheduling with adaptive modulation and coding, in ''Proc. of Wireless Telecommunications Symposium (WTS) 2009," (2009).

[10]

H. Kim and Y. Han, An opportunistic channel quality feedback scheme for proportional fair scheduling, IEEE Communications Letters, 11 (2007), 501-503. doi: 10.1109/LCOMM.2007.070106.

[11]

R. Knopp and P. A. Humblet, Information capacity and power control in single-cell multiuser communications, in ''Proc. of IEEE ICC '95," (1995), 331-335. doi: 10.1109/ICC.1995.525188.

[12]

Q. Liu, S. Zhou and G. B. Giannakis, Queuing with adaptive modulation and coding over wireless links: cross-layer analysis and design, IEEE Trans. Wireless Commun., 4 (2005), 1142-1153. doi: 10.1109/TWC.2005.847005.

[13]

Y. Liu, S. Gruhl and E. W. Knightly, WCFQ: an opportunistic wireless scheduler with statistical fairness bounds, IEEE Trans. Wireless Commun., 2 (2003) 1017-1028. doi: 10.1109/TWC.2003.816777.

[14]

X. Qin and R. Berry, Exploiting multiuser diversity for medium access control in wireless networks, in ''Proc. of IEEE INFOCOM '03," (2003), 1084-1094.

[15]

S. Sanayei and A. Nosratinia, Opportunistic downlink transmission with limited feedback, IEEE Trans. Infor. Theory, 53 (2007), 4363-4372. doi: 10.1109/TIT.2007.899529.

[16]

O. Somekh, A. M. Haimovich and Y. Bar-Ness, Sum-rate analysis of downlink channels with 1-bit feedback, IEEE Communications Letters, 11 (2007), 137-139. doi: 10.1109/LCOMM.2007.061464.

[17]

H. C. Tijms, "A First Course in Stochastic Models," John Wiley & Sons, 2003. doi: 10.1002/047001363X.

[18]

B. Tan, L. Ying and R. Srikant, Short-term fairness and long-term QoS, in ''Proc. of Conference on Information Science and Systems (CISS)," (2008), 1201-1204.

[19]

D. Wu and R. Negi, Utilizing multiuser diversity for efficient support of quality of service over a fading channel, IEEE Trans. Veh. Technol., 54 (2005), 1198-1206. doi: 10.1109/TVT.2005.844671.

[20]

Y. Xue and T. Kaiser, Exploiting multiuser diversity with imperfect one-bit channel state feedback, IEEE Trans. Veh. Technol., 56 (2007), 183-193. doi: 10.1109/TVT.2006.883784.

[21]

M. D. Yacoub, "Foundation of Mobile Radio Engineering," CRC-Press, 1993.

[22]

L. Yang, M. Kang and M.-S. Alouini, On the capacity-fairness tradeoff in multiuser diversity systems, IEEE Trans. Veh. Technol., 56 (2007), 1901-1907. doi: 10.1109/TVT.2007.897229.

[23]

W. Zhang and K. B. Letaief, MIMO broadcast scheduling with limited feedback, IEEE J. Sel. Areas Commun., 25 (2007), 1457-1467. doi: 10.1109/JSAC.2007.070918.

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