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This paper analyses the weighted fair queueing (WFQ) system subject to three classes of network applications. The arrival traffic flows follow Poisson processes. The service times is exponentially distributed. The system is modelled as a two-dimensional Markov chain and use matrix geometric technique to solve its stationary probabilities. The determination of the steady state probabilities can be used to compute the performance measures of the system, such as the mean queue length, the throughput and the mean response time. Numerical experiments corroborate the theoretical results are offered and make the developed model as an effective tool for examining the performance of WFQ systems.