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In order to study the obstructive of the existing avionics network, the existing methods only consider the message transmission in network, but the effect of topology structure on message transmission is not considered. From network optimization and complex network theory, the topological complexity of avionics network based on complex network theory is systematically analyzed. Firstly, the topological complexity of avionics network is studied, then based on the consideration of the actual network topological characteristics, the relationship between the network topology and the obstructive is studied. The experiment shows that the proposed method is of reference value for the research on load and optimal topology of avionics network. Introduction In the process of studying the communication network congestion, the critical message package generation rate is usually used to measure the communication ability of the whole network. When the number of packets generated in the network is offset by the number of packets arriving at the destination, the network is in a free transmission state. But when the limited information processing capacity or the limited length of buffer queues of each node leads to the cumulative number of packets increasing with time, now, if not in time to control the system, the system will soon be in a state of congestion and even collapse. Any network structure has its maximum load, that is, the maximum capacity the network can carry. For the avionics network, the topology structure is closely related to the network maximum load and the network congestion. And because of the differences of different topology structure obstructions and their laws of spreading and dissipation, under the condition of considering the obstructive, it is very important to study which topology structure has the maximum load. It also helps to plan and design the avionics network scientifically from a long-term developmental perspective. Research on Avionics Network Load Capacity under Different Topologies Summary Recently, the research on different network maps shows that the network dynamic process is mainly dependent on the underlying topology structure. But the interdependence between the structure and function has not been completely revealed, such as the interrelation between the structure and the load as well as the optimal topology reflecting the network characteristics, the network traffic distribution, its statistical dynamics and the network topology and congestion. In fact, for many networks, in order to effectively improve the network efficiency, reduce the loss and alleviate the congestion degree, it is necessary to study the optimization relationship between structure and function. For the avionics network, the contradiction between the network bandwidth and the message transmission is becoming more and more serious, which brings great challenges to the network structure. The network load describes the network processing ability in a unit time. It is very important to study the network load capacity to the avionics network construction. Some scholars have done their research on the optimization of the network load. However, there is a lack of necessary and systematic 236 research on the relationship between network topology and load. In the actual network design, adding a switch will probably cause a greater congestion, which is the famous traffic strange phenomenon. However, in some cases, increasing the number of switches in the network can achieve the purpose of alleviating congestion. This chapter will consider the influence of avionics network topology on network congestion level, do not consider other properties (such as network availability and robustness), and provide a more comprehensive analysis method for the design of avionics network. Structure of Avionics Network Topology and Parameter Definition of the Network The network can be represented by an undirected, weighted graph G , ( , ) = G V K , Where V and K represent the set of nodes and the set of edges respectively. Weight is t [1-2]. In avionics network, t represents the impedance on the edge, which is defined by formula (1). If there are N nodes in the graph, then G can be represented as a × N N adjacency matrix . If there is a connection between any two nodes i and j , then 1 = ij e , otherwise 0 = ij e . We use random graph model, small world model and scale free model to generate three different network topologies respectively, and according to the betweenness of the edge a randomly allocate its ability a U (tolerance) [3]. Assume a certain edge is in normal state, its traffic a x should meet φ ≤ a a x U , otherwise the edge will be congested. Where φ is a parameter greater than 1. In the actual avionics network design, under the constraint of not violating the edge maximum load, through optimizing the nodes and increasing the number of nodes in the network two methods, it can usually make the demand OD [4] of the network can accommodate increasely. We say the demand for OD the network can accommodate after the optimization for the network is a load factor with a multiple edge of the demand for OD the network can accommodate before the comprehensive optimization for the network. Here, parameter φ can be approximated by the reserve capacity coefficient. Definition of Blockage Factor In the previous research on complex networks, the traditional traffic distribution is based on the degree or the betweenness without considering the crowding effect. But, due to the blockage effect of the avionics network, the network traffic distribution mechanism is different from other traditional complex networks. If all the messages select the path with the least time consumption, the impedance on the path will increase and the path will be congested. However, with the increase of the traffic on the path, it will no longer be the optimal path selection, and be replaced by other path with the minimum load impedance. The traffic is distributed in the network repeatedly, if each message selects the path with the least time consumption path to be sent, and finally reached the UE equilibrium state, that is, it satisfies the Wardrop principle [5-6]. Descriptions of the Wardrop principle: When path users are aware of the network traffic status and try to choose the shortest path, the network will reach a balanced state. In the network, considering the congestion effect on travel time, when the network reaches the equilibrium state, each path being used of each OD pair has equal and minimal travel time. The travel time of the paths not being used is equal to or greater than the minimum travel time. This definition is commonly referred to as Wardrop Equilibrium, in the actual network traffic distribution, it is also called User Equilibrium (UE). It can be easily seen, that when the equilibrium state is not reached, at least some of the side users will change the transformation line to shorten the transmission time until the equilibrium is reached. Therefore, the existence of network congestion is the condition for achieving equilibrium. The blockage effect can be expressed by the impedance function [7]. Due to the congestion, the impedance function should be an increasing function of the traffic. That is:

Research on Load and Optimal Topology of Avionics Network