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This letter investigates the server deployment for a randomly deployed mobile edge computing (MEC) network. Under a given density of users, the theoretical analysis shows that there exists an optimal deployment density of MEC servers to maximize the network-wide resource utilization, and the optimum can be determined by bisection searching. In the analysis, a modified gamma distribution is introduced to deal with the inaccurate approximation of the existing methods. Moreover, we propose a workload migration scheme to tackle load imbalance and improve network resource utilization. Numerical simulations verify the analytical results and demonstrate the superior performance of the proposed scheme.