Mobile Edge Computing (MEC) architecture is composed of geographically distributed edge servers, in which computing capabilities are provisioned at the boundary of the network, which is in close proximity to the end users to provide network services with low latency. The planning of MEC edge servers at appropriate locations is the fundamental first step towards the deployment of the MEC system. In the literature, edge servers planning is based on deterministic resource requirements. This assumption largely neglects the pragmatic complexities imposed by the real dynamic world, in which base station (BS) resource demands are stochastic variables with arbitrary pattern. In view of this fact, we formulate the MEC planning problem as a joint optimization problem of MEC edge servers placement and resource allocation with uncertain BS demands through an uncertain programming formulation. Due to the complexity of this jointuncertain problem, a learning based framework is utilized to practically solve this problem, and the relevance of applying this mechanism in practical usage with sampled arbitrary BS demands data is also discussed. Finally, we conducted intensive real-data driven simulations to evaluate the performance of our proposed mechanism. The results show the effectiveness of our approach with arbitrary BS demands. INDEX TERMS Mobile edge computing, edge server planning, uncertain programming, learning-based framework, resource optimization