This paper studies edge caching in fog computing networks, where a capacity-aware edge caching framework is proposed by considering both the limited fog cache capacity and the connectivity capacity of base stations (BSs). By allowing cooperation between fog nodes and cloud data center, the average-download-time (ADT) minimization problem is formulated as a multi-class processor queuing process. We prove the convexity of the formulated problem and propose an Alternating Direction Method of Multipliers (ADMM)-based algorithm that can achieve the minimum ADT and converge much faster than existing algorithms. Simulation results demonstrate that the allocation of fog cache capacity and connectivity capacity of BSs needs to be balanced according to the network status. While the maximization of the edge-cache-hit-ratio (ECHR) by utilizing all available fog cache capacity is helpful when the BS connectivity capacity is sufficient, it is preferable to keep a lower ECHR and allocate more traffic to the cloud when the BS connectivity capacity is deficient.