A two-class MAP/PH/1 weighted fair queueing system and its application to telecommunications

The service discipline of weighted fair queueing (WFQ) has been practically used in many telecommunication systems. The development of analytically tractable models with WFQ discipline to determine their performances is vitally important. Motivated by a practical project on routers’ optimization from the Huawei Company, this paper deals with a two-class single server MAP/PH/1 queue with a finite capacity under the WFQ discipline, which is little investigated in the literature. To capture the most generality of stochastic factors in traffic traces, we assume that the arrive process is a Markovian arrival process (MAP) and the service time obeys a phase-type (PH) distribution. This paper focuses on the performance analysis of our proposed queueing system and its application to traffic flow performances. We model this system as a five-dimensional Markov chain and use the matrix-geometric method to derive its stationary probabilities and performance measures, such as the average queue length and sojourn time of each class of customers. In order to validate our analysis results, we further develop a simulator to evaluate the system performance with a real data of Internet packet traces. Experiment comparison demonstrates the effectiveness and applicability of our theoretical model.