In this paper, we study the call admission control (CAC) and routing issue in multi-service networks. Two categories of calls are considered: a narrow-band with blocked calls cleared and a wide-band with blocked calls delayed. The optimisation is subject to several quality of service (QoS) constraints, either on the packet or call level. The objective function is formulated as reward maximisation with penalty for delay. A suboptimal solution is achieved by applying Markov decision process (MDP) theory together with a three-level approximation. First, the network is decomposed into a set of links assumed to have independent Markov and reward processes respectively. Second, the dimensions of the link Markov and reward processes are reduced by aggregation of the call classes into call categories. Third, by applying decomposition of the link Markov process, the link MDP tasks are simplified considerably. The CAC and routing policy is computed by the policy iteration algorithm from MDP theory. The numerical results show that the proposed CAC and routing method, based on the approximate link MDP framework, is able to find an efficient trade-off between reward loss and average call set-up delay, outperforming conventional methods such as least loaded routing (LLR).