In this paper, we consider the server allocation problem for edge computing system deployment where each edge cloud is modeled as an M/M/c queue. Our goal is to minimize the overall average system response time of application requests generated by all mobile devices/users. We consider two approaches for edge cloud deployment: The flat deployment, where all edge clouds are co-located with the base stations, and the hierarchical deployment, where edge clouds can be co-located with other system components besides the base stations. In flat deployment, we demonstrate that the allocation of edge cloud servers should be balanced across all the base stations, if the application request arrival rates at the base stations are equal to each other; if the application request arrival rates are not the same, we propose a Largest Weighted Reduction Time First (LWRTF) algorithm to assign servers to edge clouds. Numerical comparisons of the proposed algorithm against several other reasonably designed heuristics verify that algorithm LWRTF has very good performances in terms of minimizing the average system response time. We also conduct preliminary study on hierarchical deployment for edge computing and show that the hierarchical deployment approach has great potentials in minimizing the overall average system response time.