In this paper, the resource management problem in geographically distributed cloud systems is considered. The Follow Me Cloud concept which enables service migration across federated data centers (DCs) is adopted. Therefore, there are two types of service requests to the DC, i.e., new requests (NRs) initiated in the local service area and migration requests (MRs) generated when mobile users move across service areas. A novel resource management scheme is proposed to help the resource manager decide whether to accept the service requests (NRs or MRs) or not and determine how much resources should be allocated to each service (if accepted). The optimization objective is to maximize the average system reward and keep the rejection probability of service requests under a certain threshold. Numerical results indicate that the proposed scheme can significantly improve the overall system utility as well as the user experience compared with other resource management schemes.