Mobile phones and tablets are becoming the primary platform of choice. However, these systems still suffer from limited battery and computation resources. A popular technique in mobile edge systems is computing outsourcing that augments the capabilities of mobile systems by migrating heavy workloads to resourceful clouds located at the edges of cellular networks. In the multi-site scenario, it is possible for mobile devices to save more time and energy by offloading to several cloud service providers. One of the most important challenges is how to choose servers to offload the jobs. In this paper, we consider a multi-site decision problem. We present a scheme to determine the proper assignment probabilities in a two-site mobile-edge computing system. We propose an open queueing network model for an offloading system with two servers and put forward performance metrics used for evaluating the system. Then in the specific scenario of a mobile chess game, where the data transmission is small but the computation jobs are relatively heavy, we conduct offloading experiments to obtain the model parameters. Given the parameters as arrival rates and service rates, we calculate the optimal probability to assign jobs to offload or locally execute and the optimal probabilities to choose different cloud servers. The analysis results confirm that our multi-site offloading scheme is beneficial in terms of response time and energy usage. In addition, sensitivity analysis has been conducted with respect to the system arrival rate to investigate wider implications of the change of parameter values.