Mobile micro-cloud is an emerging technology in distributed computing, which is aimed at providing seamless computing/data access to the edge of the network when a centralized service may suffer from poor connectivity and long latency. Different from the traditional cloud, a mobile micro-cloud is smaller and deployed closer to users, typically attached to a cellular base station or wireless network access point. Due to the relatively small coverage area of each base station or access point, when a user moves across areas covered by different base stations or access points which are attached to different micro-clouds, issues of service performance and service migration become important. In this paper, we consider such migration issues. We model the general problem as a Markov decision process (MDP), and show that, in the special case where the mobile user follows a one-dimensional asymmetric random walk mobility model, the optimal policy for service migration is a threshold policy. We obtain the analytical solution for the cost resulting from arbitrary thresholds, and then propose an algorithm for finding the optimal thresholds. The proposed algorithm is more efficient than standard mechanisms for solving MDPs.