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With the growing popularity and wide application of GIS in reality, performance has become a critical requirement, especially for mobile GIS services. To attack this challenge, this paper tries to optimize the performance of GIS services by deploying them into edge computing architecture which is an emerging computational model that enables efficient offloading of service requests to edge servers for reducing the communication latency between end-users and GIS servers deployed in the cloud. Stochastic models for describing the dynamics of GIS services with edge computing architecture are presented, and their corresponding quantitative analyses of performance attributes are provided. Furthermore, an optimization problem is formulated for service deployment in such architecture, and a heuristic approach to obtain the near-optimal performance is designed. 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