Markov decision theory has been successfully used in adaptive routing in traditional circuit-switched networks. When extending Markov decision-based routing algorithms to future Broadband Integrated Service Digital Networks (B-ISDNs), the required computational complexity becomes extremely high. In this paper, we propose an approach towards adaptive routing in multi-rate networks using a Markov decision theoretic framework which maintains low computational complexity while still providing quite good routing information. In this approach, each link, based on PASCAL distribution, is modeled as a one-dimensional birth-death process to reduce the state space size and a policy iteration method from Markov decision theory is iteratively applied to achieve better network performance. Our results show that routing algorithms based on this approach yield better performance than least-load path routing (LLP) without incurring any significant increase in computational complexity.