With the increase of data traffic in global mobile network, data computing close to the edge is going more and more memorandum to deal with the resources limitations. This paper, addresses Cloud Radio Access Network (C-RAN) architecture and proposes to provide extra computing and storage resources in the edge in order to allow the offloading of a set of mobile users services from the remote cloud computing infrastructure to a cloud computing infrastructure deployed in the edge next to Remote Radio Heads (RRHs). This approach raises many challenges. One of the challenges is the scheduling strategy of the offloading. Therefore, the main contribution described in this paper is a novel cost based service scheduling (CBSS) mechanism which takes into account deployment cost, deadline and available resources in order to make offloading decisions more efficient and to increase user experience. The solution was implemented in a simulator to highlight the benefit of the approach compared to existing approach.