This paper considers the support of grant-free massive access and solves the challenge of active user detection and channel estimation in the case of a massive number of users. By exploiting the sparsity of user activities, the concerned problems are formulated as a compressive sensing problem, whose solution is acquired by approximate message passing (AMP) algorithm. Considering the cooperation of multiple access points, for the deployment of AMP algorithm, we compare two processing paradigms, cloud computing and fog computing, in terms of their effectiveness in guaranteeing ultra reliable low-latency access. For cloud computing, the access points are connected in a cloud radio access network (C-RAN) manner, and the signals received at all access points are concentrated and jointly processed in the cloud baseband unit. While for fog computing, based on fog radio access network (F-RAN), the estimation of user activity and corresponding channels for the whole network is split, and the related processing tasks are performed at the access points and fog processing units in proximity to users. Compared to the cloud computing paradigm based on traditional C-RAN, simulation results demonstrate the superiority of the proposed fog computing deployment based on F-RAN.