Performance of weighted fair queuing systems with long range dependent traffic inputs

This paper provides an analytical technique for estimating the queue length distributions for a weighted fair queue (WFQ) system fed with long range dependent (LRD) traffic input. The analysis considers the coupling between the queues of the WFQ system due to the dependency of the queue length on the weights and input traffic of other queues. It is also applicable to short range dependent (SRD) traffic sources. With aggregate LRD traffic streams represented by multi-scale wavelet models (MWM), the analysis starts by modeling each queue of a WFQ system as an MWM/D/1 queue and multi-scale queuing (MSQ) is used to estimate the queue length distribution. Each queue unused capacity is evaluated and an extension of our previous work on priority queuing of LRD traffic is used to provide an MWM model for the service rate of each queue and decompose the WFQ queues into MWM/MWM/1 queues. Subsequently, this MWM/MWM/1 decomposition is used to examine the queue length distribution. The accuracy of the proposed analytical technique is examined by comparing queue survivor functions obtained analytically to those directly measured from event-driven simulations for various traffic conditions and WFQ weight configurations. The analysis shows the effect of both weight variation and traffic self-similarity on the queue length distribution of each queue. Analytical and simulation results show that the proposed analytical technique can provide an accurate estimation of queue length distribution, and can be useful in optimal choices of WFQ weights.