The concept of multi-access edge computing (MEC) has been recently introduced to supplement cloud computing by deploying MEC servers to the network edge so as to reduce the network delay and alleviate the load on cloud data centers. However, compared to a resourceful cloud, an MEC server has limited resources. When each MEC server operates independently, it cannot handle all of the computational and big data demands stemming from the users devices. Consequently, the MEC server cannot provide significant gains in overhead reduction due to data exchange between users devices and remote cloud. Therefore, joint computing, caching, communication, and control (4C) at the edge with MEC server collaboration is strongly needed for big data applications. In order to address these challenges, in this paper, the problem of joint 4C in big data MEC is formulated as an optimization problem whose goal is to maximize the bandwidth saving while minimizing delay, subject to the local computation capability of user devices, computation deadline, and MEC resource constraints. However, the formulated problem is shown to be non-convex. To make this problem convex, a proximal upper bound problem of the original formulated problem that guarantees descent to the original problem is proposed. To solve the proximal upper bound problem, a block successive upper bound minimization (BSUM) method is applied. Simulation results show that the proposed approach increases bandwidth-saving and minimizes delay while satisfying the computation deadlines.