The capacity assignment (CA) problem is one of the most essential yet important topics in packet communication networks. However, most reported CA models were established under the framework of Markovian queuing processes or, in general, renewal processes. The crucial properties such as selfsimilarity and correlations have usually been ignored. In the present work, we establish the CA model with the packetized generalized processor sharing (PGPS) discipline. The non-Markovian traffic is taken into account. The models is solved by the stochastic programming (SP) methodology.