As the 5G network promises to provide ultra-low latency services, mobile edge computing (MEC) is drawing attentions. MEC in satellite networks will be able to provide lower latency service with the advantage of a global coverage, and make satellite network virtualization feasible. In this paper, an analytic study of the overall satellite server MEC network architecture is presented. A satellite constellation model with the undirected graph representation is proposed for simulations. Propagation delays for constellation topologies and queueing delays with uplink and downlink packet error rate (PER) are considered for performance analysis. The average total latency and jitter are analyzed according to the ground distance between transmitters and receivers with respect to the offloading rate and satellite altitude. In conclusion, a guideline for the efficient satellite MEC architecture is proposed in terms of the MEC satellite parameters.