The recent discovery of instability caused by the interaction of local routing policies of multiple ASes has led to extensive research on the subject. However, previous studies analyze stability under a specific route selection algorithm. In this paper, instead of studying a specific route selection algorithm, we study a general class of route selection algorithms which we call rational route selection algorithms. We present a sufficient condition to guarantee routing convergence in a heterogeneous network where each AS runs any rational route selection algorithm. Applying our general results, we study the potential instability of a network where the preference of an AS depends on not only its egress routes to the destinations but also its inbound traffic patterns (i.e., the distribution of incoming traffic from its neighbors). We show that there exist networks which will have persistent route oscillations even when the ASes strictly follow the constraints imposed by business considerations, and adopt any rational route selection algorithms.