Complete data center failures may occur due to disastrous events such as earthquakes or fires. To attain robustness against such failures and reduce the probability of data loss, data must be replicated in another data center sufficiently geographically separated from the original data center. Implementing geo-replication is expensive as every data update operation in the original data center must be replicated in the backup. Running the application and the replication service in parallel is cost effective but creates a trade-off between potential replication consistency and data loss and reduced application performance due to network resource contention. We model this trade-off and provide a control-theoretical solution based on Model Predictive Control to dynamically allocate network bandwidth to accommodate the objectives of both replication and application data streams. We evaluate our control solution through simulations emulating the individual services, their traffic flows, and the shared network resource. The MPC solution is able to maintain a consistent performance over periods of persistent overload, and is quickly able to indiscriminately recover once the system return to a stable state. Additionally, the MPC balances the two objectives of consistency and performance according to the proportions specified in the objective function.