On some properties of the proportional fair scheduling policy

Abstract

The proportionalfair (PF) scheduling algorithm has been proposed as a technique to improve the throughput of multiple packet-data users sharing a wireless downlink channel while preserving fairness. It exploits the fact that the propagation channels between the base station (BS) and the mobile stations (MS) fade independently giving rise to "multi-user diversity". The gain offered is significant when the allowed packet delay exceeds the de-correlation time of the fading channels and the number of users is high. In this paper we investigate analytically the "time allocation" property and the multi-user diversity gain of the PF algorithm under certain conditions in the context of the HSDPA standard. Since in practical systems a certain latency is unavoidable, we have studied the use of a "backoff factor to reduce the probability that when the transmission takes place, the channel will not be able to support it.

Fair resource allocation under Rayleigh and/or Rician fading environments

“…It is easy to prove that the average throughput given by (6) lies between the upper and lower bounds given by (4) and (5), respectively. Now we have the closed-form expressions (4)-(6) for the PFS throughput.…”

“…To simplify the problem, most existing analytic results are assuming some kind of i.i.d relationship among users [5][6][7][8][9]11]. For example, [6,7] assume the SINR of each user is an i.i.d Exponential distribution; [8] takes the assumption similar to [6] that user k's SINR S k =c k ×C (∀k), where c k is a user-related constant and C is an i.i.d Exponential distribution random variable independent of all users, and [11] On the other hand, linear rate model and logarithm rate model are the two rate models commonly used for analyzing the performance of PFS.…”

“…For example, [6,7] assume the SINR of each user is an i.i.d Exponential distribution; [8] takes the assumption similar to [6] that user k's SINR S k =c k ×C (∀k), where c k is a user-related constant and C is an i.i.d Exponential distribution random variable independent of all users, and [11] On the other hand, linear rate model and logarithm rate model are the two rate models commonly used for analyzing the performance of PFS. For example, [5,6,11] use the linear rate model, while [8] uses the logarithm rate model. In the linear rate model, the instantaneous data rate R of a user is linearly proportional to the received SINR, i.e, R i = β×SINR i for any user i; while in the logarithm rate model, there is a logarithmic relationship between the received SINR and the instantaneous data rate, i.e., R i ∝Log 2 (1+β×SINR i ).…”

“…Though the PFS algorithm has got so much attention and currently implemented in 3G wireless network for high data rate delay-tolerant services [4], one can only see very limited analysis results on PFS [5][6][7][8][9][10][11], whose derivations typically assume a simple linear rate model or logarithm rate model and/or use a simplified form of the original PFS preference metric. The linear rate model is only valid for networks where the signal to interference-plus-noise ratio (SINR) is very small [5], while the logarithm rate model can only be used for singleinput-single-output (SISO) communications [8].…”

“…However, when examining throughput performance, it does not seem satisfactory to assume such simplified rate models. Moreover, all existing researches are assuming some kind of independent identically distributed (i.i.d) relationship among users in their derivations [5][6][7][8][9]11]. Undoubtedly, these assumptions limit the use of existing theoretical results on PFS.…”