## 1 Introduction
### Related Works  
[PERSON] et al. [14] studied CPP in SDNs based on classical control theory. They defined the control delay as the number of time slots required to drive the network from one state to another, and proposed two complementary heuristic algorithms: a controller-minimization approach optimizing propagation latency under resource constraints, and  
Figure 1: Energy consumption node relationship network diagram. a delay-constrained optimization strategy achieving minimal controller deployment while satisfying predefined latency thresholds. Another aspect of CPP has aroused great interest in the industry, that is, the use of graph theory, game theory, queuing theory, and other concepts to model CPP. In general, the location problem exists in many scientific problems, such as virtual machine placement [15] and sensor placement in wireless sensor networks [16]. These exemplify problem configurations that share conceptual similarities with the Controller Placement Problem (CPP) in software-defined networking architectures, because their core is the classic facility location problem [17]. In all, CPP problems based on different optimization objectives cover a wide range of scientific problems. In the existing research, in order to obtain a suitable CPP solution, various methods are studied, including optimal strategy, heuristic strategy, and classical control theory. With the popularity of SDN in an array of sectors, such as data centers, wide-area networks, and mobile networks, CPP has been developed in emerging applications. Several aspects of CPP are worth noting, which can be considered from the perspective of different goals such as network responsiveness, fault tolerance, and load balancing. In previous CPP research, the optimization of a single target was the most important; for the multi-objective CPP problem, it is usually necessary to consider the weight between multiple conflicting targets. For example, in order to optimize the switch controller delay, the controller needs to be evenly distributed over the network, but this will increase the number of controllers in the network. The Internet of Vehicles is essentially a (VANET) composed of vehicle OBUs and fixed road infrastructure such as RSUs and base stations. In the existing research of vehicle networking, [PERSON] et al. [18] introduced a converged architecture for vehicle-to-everything (V2X) networks that synergistically integrates edge caching and distributed computing paradigms, employing deep reinforcement learning frameworks to co-optimize multidimensional parameter spaces within the system model. For a multi-area vehicle network with multiple controllers, each controller is responsible for processing most of the information in its area. Therefore, this section first proposes a delay-optimized SDVN system architecture model, which is composed of a two-layer distributed control plane architecture and refers to the HyperFlow distributed controller architecture [19] to reduce the delay caused by system/operation, as shown in Figure 2:  
As shown in Figure 2, in SDVN, different RSUs are connected through a broadband link, and the controllers synchronize the network state through an east-west interface. The controller is selected from a number of RSUs interconnected by wired links. The controller RSU is actually a combination of ordinary RSUs and SDN controllers. In addition, different regions of SDVN often have different traffic characteristics, and some global information flows may need to be forwarded between multiple regions. As traffic occurs in different areas that may belong to different service providers, it is necessary to use multiple controllers, at least one of which controls a single area. The controller of each region is responsible for its own region, but inter-domain communication should be performed to provide reliable data transmission [20]. The data plane consists of On-Board Units (OBUs) and conventional Road-Side Units (RSUs), with each OBU equipped with both a DSRC interface and a 4G/5G interface.