Since the air–ground integrated network and the service function chaining have node attribution and link attribution that are remarkably similar to those of graphs in the mathematical model, they are modeled as different types of graphs according to their characteristics. Due to the diversity and heterogeneity of air–ground network resources, it is necessary to distinguish them according to their attribution when modeling.
2.1. Model Building
Air–ground physical network: We regarded the air–ground physical network as a strongly connected directed graph, which is represented by tuples , where is the set of network nodes and represents the set of physical links. The rich resources of the ground network can solve more complex tasks, but the base station is fixed and the coverage is limited. The air network composed of UAVs covers a wide range, but computing resources are scarce. In the air–ground integrated network, the most appropriate forwarding strategy can be selected according to the service requirements to flexibly access the air or ground network to meet the business requirements. Therefore, the resources and coverage of nodes in air–ground physical networks, namely, network connectivity and computing capacity, are different. Nodes in different networks need to be distinguished. In an air–ground network, physical network nodes are represented by , where is the set of air network nodes and is the set of ground network nodes. Similarly, physical links are represented by , where is the spatial link set, is the ground link set and is the air–ground link set. is used to represent all routing paths from the initial node to endpoint . Each node has the ability to handle specific functions, but each node can only handle one function at a time, and each physical node has fixed computing power . and represent the bandwidth consumption and latency consumption of the physical link, respectively.
Service request definition: We treated the service request as a directed acyclic graph, assuming that a batch of requests is processed with an interval . Of course, these requests may arrive at any time during the last processing interval. This study focused on batch processing within the time interval . Service request is represented by tuples , where represents the service request that arrives within time . The source and destination nodes of each service request are represented by and , respectively. The node of the service request is the VNF, and the link is the dependency among the VNFs. There are types of VNFs required by the service, including bandwidth requirements , computing power requirements and the delay deadline . Each service request consists of a set of VNFs , and the link between the VNFs needs to follow the dependencies between virtual network functions.
Consumption model: To visually express the SFC mapping and to make calculations more convenient, the model variables were defined in matrix form. The mapping of unknown vertices and the mapping of links were also represented by a binary matrix. Define as a virtual network function deployment variable for task , and when its value is 1, this means that the virtual network function is deployed on the physical node . represents the collection of all paths in the network nodes. Define the virtual link mapping variable , which has a value of 1 when the link between two adjacent virtual network functions and in task is mapped to the underlying physical link ; otherwise, has the value 0.
We defined a virtual network function mapping binary matrix
for all possible vertex mappings.
Similarly, we defined a binary matrix
of link mappings that represents all possible link mappings.
is the binary matrix of all possible link mappings.
For each successfully deployed SFC, the following constraints must be met:
Uniqueness constraint: a virtual network function of a task can only be embedded on one physical node, and a virtual link of a task can only be mapped to a unique physical link.
Bandwidth constraint: each path in the routing path must have enough bandwidth to meet the requirements of the virtual link.
Computing power constraint: the physical node needs to have enough computing resources to handle the data traffic carried by the SFC.
Compatibility constraints: Each virtual network function can only be mapped to a physical node capable of processing this function, and a virtual link can only be mapped to a physical link with sufficient bandwidth resources, that is, the bandwidth resources of the physical link must meet the bandwidth resources required by the service request.
The function determines the type of VNF and can only be mapped when the type of VNF and the type carried by the physical node are the same.
We used the load-balancing index
to measure the effect of network load balancing, where the formula is
where
represents the
-type resource occupancy rate of node
and
represents the average
-type resource occupancy rate of each physical node.
Since the computational consumption of the processing VNF is fixed, the resource consumption requested by the task in this article includes instantiation consumption and bandwidth consumption. However, air–ground integrated network nodes are different in terms of coverage and computing power. Therefore, their instantiation overhead and bandwidth consumption are different.
represents the instantiation overhead of mapping function to physical node in the air network, and represents the instantiation overhead of mapping function to physical node in the ground network. represents the actual bandwidth requirement for mapping virtual link to physical link in the air network, represents the actual bandwidth requirement for mapping virtual link to physical link in the ground network and represents the actual bandwidth requirement for mapping virtual link to physical link in the air–ground links.
2.2. Selection Method of VNFs to Be Aggregated Based on Task Similarity
If each VNF is instantiated for each SFC, it will cause a huge instantiation overhead and waste of resources when deploying the service function chain. VNF aggregation effectively solves this problem. However, the existing function aggregation methods only focus on reducing the instantiation overhead and ignoring the load balancing problem caused by VNF aggregation. To solve the problem of load balance, Refs. [
9,
10,
12,
13] adopted VNF migration and solved it using SFC reconstruction, which seriously affected the stability of the link.
As shown in
Figure 1a, when airship 3 communicates with ship 1, the link indicated by the dashed line is selected to complete the communication. When airship 1 also receives the task of communicating with ship 1, due to the independence of the tasks, it chooses the link represented by the solid line to communicate. This not only causes a waste of network resources but also makes the links between nodes repeatedly disconnected, causing a network server instability. If the routing path of airship 1 can be shown as the solid line linked in
Figure 1b according to the similarity of the tasks, this problem will be solved.
In response to the above problems, this study proposed a VNF selection method to aggregate tasks based on task similarity.
The core idea of the method is as follows:
- (1)
For tasks that arrive in time interval T, the virtual network functions required by the task and the access to task resources that are more similar are placed into the same category. Tasks within the same class share the same type of physical node.
- (2)
In the same category, the same VNF is selected for functional aggregation under the condition of satisfying bandwidth and computing constraints.
- (3)
By adjusting the similarity threshold, there is a trade-off between resource consumption and load balancing.
The specific implementation is as follows:
Task similarity is divided into functional similarity and resource similarity. Task similarity within the time interval T is considered in order to divide similar tasks into the same class to share physical network nodes with the same functionality. On the one hand, this can reduce the instantiation overhead of the same virtual network function for similar tasks, reduce the global waiting time and maintain network stability. On the other hand, it can reduce the uneven load caused by all tasks sharing the same physical node for the same virtual network function. However, the task similarity division according to the time interval T cannot completely solve the problem of an uneven load, and thus, the task similarity threshold can be adjusted to balance the resource consumption and load balancing to meet the task requirements in different scenarios.
The definition of task similarity in the time interval T is given here, which includes virtual network function similarity and resource similarity.
Virtual network function similarity refers to the similarity of VNFs by different tasks.
is the similarity of the virtual network functions of the two tasks and . is the number of virtual network functions of the same type contained in tasks and . is the total number of virtual network functions in service request and is the proportion of the number of virtual network functions of the same virtual network functions in task to the total number of virtual network functions.
When tasks arrive, the system first calculates the similarity of the pairwise tasks and then divides it by the number of pairwise permutations and combinations to obtain the task similarity between tasks.
When
tasks arrive, the virtual network function similarity of the tasks is
Resource similarity refers to the similarity of the actual demand for the same virtual network function resources.
where
represents the resources that task
contains for virtual network function
that needs to be accessed.
represents the similarity of resources required for the same virtual network function in tasks and . and are the actual demand for the lth resource of the same virtual network function for tasks and , respectively.
When
tasks arrive, the resource similarity is
The task similarity is
where
and
are weights.
After classification according to task similarity, the system judges whether the aggregation can be performed by whether the bandwidth and computing resources meet the physical network constraints. The aggregation can be performed when the constraints are met; otherwise, it is achieved by adjusting the similarity. Each time, the network resource status is updated after a division by task similarity. For load balancing, this study took an approach to determine task classification by presetting similarity thresholds. While ensuring that the resource consumption is reduced, load balancing is achieved by adjusting the similarity threshold to avoid too many tasks waiting for the same physical node to meet the requirements of the tasks.