In this work, a solution of the multirate MDP routing problem for the minimization of call blocking probabilities has been derived. This solution is based on the well known separability assumption and on a specific averaging technique of MDP costs. The result is a new closed-form MDP link-cost function, called ATM-FLR cost function, which can be computed with little computational effort. The ATM-FLR link cost function represents a generalisation of a quotient formula expression for the MDP link cost to the multirate MDP problem. Furthermore, the work concentrates on the applicability of MDP routing and of the derived link-cost function in ATM networks.