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To meet the need of computation-sensitive (CS) and high-rate (HR) communications, the framework of mobile edge computing and caching has been widely regarded as a promising solution. When such a framework is implemented in small-cell IoT (Internet of Tings) networks, it is a key and open topic how to assign mobile edge computing and caching servers to mobile devices (MDs) with CS and HR communications. Since these servers are integrated into small base stations (BSs), the assignment of them refers to not only the BS selection (i.e., MD association), but also the selection of computing and caching modes. To mitigate the network interference and thus enhance the system performance, some highly-effective resource partitioning mechanisms are introduced for access and backhaul links firstly. After that a problem with minimizing the sum of MDs' weighted delays is formulated to attain a goal of joint MD association and resource allocation under limited resources. Considering that the MD association and resource allocation parameters are coupling in such a formulated problem, we develop an alternating optimization algorithm according to the coalitional game and convex optimization theorems. To ensure that the designed algorithm begins from a feasible initial solution, we develop an initiation algorithm according to the conventional best channel association, which is used for comparison and the input of coalition game in the simulation. Simulation results show that the algorithm designed for minimizing the sum of MDs' weighted delays may achieve a better performance than the initiation (best channel association) algorithm in general.