Output queueing is the optimal switch of fast packet switching in performance. In this paper

the queueing performance of output queueing with arbitrary priority classes is studied. We derive the statistical characteristics

such as average queue length of any priority packet in independent and dependent packet arrival cases. It is found that for an N xN output queueing switch

the queueing performance of both cases tends to be the same if N is large enough. A numerical iteration is presented to get the stationary queue length distribution of high and low priority packets with queueing equation in two dimensional Markov process. The analyses are proved correct by computer simulation.