## 3 System Model
### Preliminary Assumptions  
In the previous subsection, we introduced the transmission process of the considered ISTN; thus, here we focus on the leading culprits in transmission latency and network reliability. Assuming a controller or a gateway can be placed at the locations of switches separately, the ultimate goal is to place an appropriate number of gateways and controllers to maximize the network reliability with latency constraints. Distinguished from traditional networks, a significant feature of SDN is the separation between the control plane and the data plane. Specifically, the control plane consists of multiple dedicated  
Figure 1: An architecture for SDN-enabled integrated satellite-terrestrial networks. controllers, while the data plane is composed of multiple switches and gateways for forwarding packets. Thus, in the SDN-enabled integrated networks, the distributed controllers located on the ground facilitate network control and network services. We assumed that the satellite was also identified as an SDN switch to receive control instructions from the controllers. In pure SDN-enabled networks, we are mainly concerned with the placement of controllers and assignment with switches, while in SDN-enabled networks, the joint placement of gateway and controller affect many performance metrics. In other words, in addition to the controller-switch path, another two kinds of paths, i.e., gateway-switch and controller-gateway, should also be taken into consideration in SDN-enabled ISTNs. The relationship between the different kinds of paths and the performance metrics are illustrated in Table 1.  
Apparently, in pure SDN-enabled networks, there are only two kinds of nodes, the controller and the switch, in the network topology. Thus, the placement of the controllers and the assignment with switches determine the network reliability and the inter-plane latency. However, in SDN-enabled ISTNs, we mainly are concerned with the latency between the satellite and the user equipment on the ground through the gateways. Since the distance between the GEO satellite and the gateways on the surface of the Earth can be assumed as constant, while the distance between the gateways and the switches varies from according to the placement and the assignment between them, hence we focused on the process of transmission on the ground and defined the latency between the gateways and the switches as the network latency. That is to say, the gateway-switch paths determine the network latency, which is the difference between the pure SDN-enabled networks and the SDN-enabled ISTNs. The network latency between switches and the satellite consists mainly of two parts: propagation latency and forwarding latency. The former is mainly determined by the distance between switches and the satellite, while the latter is basically affected by the load of the nodes. Due to the huge coverage of the GEO satellite, the ground segment of the SDN-enabled ISTNs can be regarded as the Wide area Network (WAN), where numerous works have studied the controller placement problem. Here, we mainly study the effect of the propagation latency on the joint placement problem owing to the relative static assignment between gateways and switches in the architecture. Therefore, how to minimize the average propagation latency of the integrated networks is worthy of in-depth study, which depends on the number and locations of gateways. Since any node or link failure on occasion may disconnect the control plane and the data plane, invalid paths due to nodes' or links; failure may result in severe packet loss and performance degradation. Consequently, how to place properly gateways and controllers simultaneously to limit the impact of failed links and nodes on network reliability is of utmost importance. It should be noted that we here focused on the appropriate placement of various numbers of gateways and controllers; the optimum number of gateways and controllers and the traffic delivery between the control plane and the data plane are beyond the scope of this paper.