Flow Level Performance Analysis of Wireless Data Networks: A Case Study

We give an example of flow level performance analysis of data traffic in wireless networks by studying a scenario where two base stations with link adaptation serve in a coordinated fashion downloading users on a road or street between the stations. Due to the dynamic nature of such systems, a detailed flow level analysis is challenging and conventional methods run into computational difficulties. We motivate the detailed analysis by studying the system under different operational goals such as maximum throughput, max-min fairness and balanced fairness, concluding that the performance under these dynamic policies differ significantly from the performance under more tractable static policies. We discuss how the corresponding numerical analyses can be facilitated by applying the notion of balanced fairness and, in particular, introduce a novel approximation method referred to as value extrapolation. Value extrapolation can be applied to approximate any performance measure expressed as the expected value of a random variable which is a function of the system state. The idea of the value extrapolation is to consider the system in the MDP (Markov Decision Processes) setting and to solve the expected value from the Howard equations written for a truncated state space. Instead of a simple truncation, the relative values of states just outside the truncated state space are estimated using a polynomial extrapolation based on the states inside. This leads to a closed system and, unless the system is heavily loaded, allows one to obtain accurate results with remarkably small truncated state spaces.