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Along with the growing popularity of 5G technology, providing flexible and personalized network services suitable for requirements of customers has also become a lucrative venture and business key for network service providers. Therefore, dynamic network provisioning is needed to help network service providers. Moreover, increasing user demand for network services meets specific requirements of users, including location, usage duration, and QoS. In this paper, a routing algorithm, which makes routing decisions using Reinforcement Learning (RL) based on the information about link stability, is proposed and called Link Stability aware Reinforcement Learning (LSRL) routing. To evaluate this algorithm, several mininet-based experiments with various network settings were conducted. As a result, it was observed that the proposed method accepts more requests through the evaluation than the past link annotated shorted path algorithm and it was demonstrated that the proposed approach is an appealing solution for dynamic network provisioning routing.