This paper proposes a novel and efficient real time network architecture, named RT-TelSurg, for one of the most appealing tactile Internet applications, i.e., Telesurgery. In telesurgery, the patient's vital signs and status and the required robotic commands during the surgery should be received on time. Otherwise, the life of the patient or the safety of the operation is endangered. Hence, transmitted packets should meet their respective relative deadlines. Software-defined networking is a relatively new architecture for computer and telecommunications networks in which the network control plane is separated from the data plane. One way to achieve real time telesurgery is to employ cloud and fog networks using SDN as infrastructure. By using a real time cloud controller in the SDN as the core and a fog controller on the edge of the network on the master (physician) side, one may satisfy the acceptable level of the timing constraints of the telesurgery. Accordingly, based on the presented architecture, we develop the statistical performance model of our proposed approach, RT-TelSurg. This statistical queuing theory model is designed for critical and non-critical states of the network. Based on these states, network resources are allocated to telesurgery data in both modes, and a computational bottleneck is detected. RT-TelSurg is evaluated according to real time and surgery efficiency parameters. The results show that the average deadline hit ratio is 98.2% in different conditions, which is quite acceptable for telesurgery applications.