Mobile edge computing (MEC) has recently risen as a promising paradigm to meet the increasing resource requirements of the terminal devices. Meanwhile, small cell network (SCN) with MEC has been emerging to handle the exponentially increasing data traffic and improve the network coverage, and is recognized as one key component of the next generation wireless networks. However, with the growing number of terminal devices requiring computation offloading to the edge servers, the network would be heavily congested and thus the performance would be degraded and unbalanced among multiple devices. In this paper, we propose the joint admission control and computation resource allocation in the MEC enabled SCN, and formulate it as a stochastic optimization problem. The goal is to maximize the system utility combining the throughput and fairness while bounding the queue. We decouple the original problem into three independent subproblems, which can be solved in a distributed manner without requiring the system statistical information. An admission control and computation resource allocation (ACCRA) algorithm is designed to obtain the optimal solutions of the subproblems. Theoretical analysis proves that the ACCRA algorithm can achieve the close-to-optimal system utility and reach the arbitrary tradeoff between the utility and the queue length. Experiments are conducted to validate the derived analytical results and evaluate the performance of the ACCRA algorithm.