Traffic classification is an essential task for network management. Many researchers have paid attention to initial sub-flow features based classifiers for traffic classification. However, the existing classifiers cannot classify traffic effectively in mobile IP networks. The classifiers depend on initial sub-flows, but they cannot always capture the sub-flows at a point of attachment for a variety of elements because of seamless mobility. Thus the ideal classifier should be capable of traffic classification based on not only initial sub-flows but also various types of sub-flows. In this paper, we propose a classifiable sub-flow selection method to realize the ideal classifier. The experimental results are so far promising for this research direction, even though they are derived from a reduced set of general applications and under relatively simplifying assumptions. Altogether, the significant contribution is indicating the feasibility of the ideal classifier by selecting not only initial sub-flows but also transition sub-flows.