Proportional Fair Scheduling: Analytical Insight under Rayleigh Fading Environment

This paper provides analytical expressions to evaluate the performance of a random access wireless network in terms of user throughput and network throughput, subject to the constraint of proportional fairness amongst users. The proportional fair scheduling (PFS) algorithm is considered an attractive bandwidth allocation criterion in wireless networks for supporting high resource utilization while maintaining good fairness among network flows. The most challenge of a PFS problem is the lack of analytic expression. Though the PFS algorithm has been a research focus for some time, the results are mainly obtained from computer simulations. It is known that a PFS problem is NP-hard and, until recently, there are very few papers which give analytic insights into the PFS algorithm. Typically, existing works use simplified form of the PF preference metric and assume simple linear model, or the given analytic expression is valid only for very limited cases. In this research, we give analytical results of the PFS algorithm by providing closed-form expressions for the throughput in Rayleigh fading networks. We use Gaussian approximation method to model the feasible data rate in Rayleigh fading environments. Results obtained from the simulation and numerical analysis verifies the high accuracy of the closed-form expressions given in the paper. In particular, the analytic expressions given here will provide great help for the system design of a PFS-enable network, not only in that it is obtained from more realistic rate model, but also it applies to various kinds of network scenarios.