Fault-tolerant Embedding Algorithm for Node Failure in Airborne Tactical Network Virtualization

Airborne tactical networks (ATNs) are driving the promising development of Internet of Battle things by enabling efficient information sharing, which is impeded by the network ossification problem that is deep-rooted in the tightly coupled network architecture. As a solution, network virtualization (NV) can break the tight coupling between applications and network infrastructure, providing a more flexible and scalable architecture for ATNs. With complex interference and malicious attacks, the application of NV is challenged by network failures when instantiating multiple virtual networks on a shared substrate network, which is known as survivable virtual network embedding (SVNE). However, existing SVNE algorithms, mostly designed for wired networks, are not necessarily optimal for the virtualization of ATNs due to the complex wireless interference. To this end, a fault-tolerant SVNE algorithm, termed SVNE-FT, is proposed to recover virtual networks from single node failure (end or switching node failure) under the wireless interference. To end node failure, SVNE-FT firstly adopts a novel node ranking approach to select reliable substrate nodes for virtual nodes and then remaps the failed virtual nodes, affected by node failure, by releasing part of the substrate paths to improve the resource utilization. In addition, to switching node failure, it adopts the improved pre-configured cycle (p-Cycle) technology to augment the reliable link mapping with differentiated p-Cycles that protect switching node from node failure and reduce the resource consumption of backups. Numerical simulation results reveal that SVNE-FT outperforms typical and latest heuristic SVNE algorithms under the complex interference of ATNs. For instance, average acceptance ratio of virtual networks improves at least 12%.

mission applications of ATNs. To implement NV, software defined networking (SDN) can provide an ideal platform in comparison with conventional methods since it offers global state view of the resource usage and strict quality of service (QoS) provisioning without tunnelling overhead [10]. Therefore, a viable platform can be provisioned for the virtualization of ATNs, called as airborne tactical network virtualization (ATNV).
To realize the benefits of ATNV, resource management challenges exist in mapping virtual nodes (VNodes) and links (VLinks) of VNs onto substrate nodes (SNodes) and links (SLinks), respectively. This is known as VN embedding (VNE) problem that is proved to be NP-hard [11]. VNE solutions are also requested to survive substrate failures to avoid degraded QoS, which is widely accepted as survivable VNE (SVNE) [12]. In NV, the survival of SNode failure is fairly challenging due to the shared nature of SN. To single node failure, there are two kinds of node failure, namely, end and switching node failure. End node failure is the failure of SNode that maps VNode, whereas, switching node failure is the failure of a switching SNode on the substrate path that maps VLinks. Thus, single node failure can cause the malfunction of multiple VNodes and VLinks, seriously degrading the service performance of VNs. SVNE has received significant attention from the research community [13][14][15][16][17]. The existing SVNE solutions are broadly classified into two categories: proactive [13,14] and reactive mechanisms [15][16][17]. The proactive mechanisms, with high resource expense, provision disjoint redundant resources as backups, offering fast recovery from failures. In addition, the reactive mechanisms, with lower resource expense, remap the failed VNodes and VLinks as failures happen. However, to our knowledge, there are no wireless SVNE algorithms that focus on single node failure. These wired SVNE algorithms against node failure do not account for wireless network dynamics (e.g., link quality instability). In addition, they do not achieve a performance balance between backup resources and recovery efficiency.
Based on these backgrounds, we focus on the wireless SVNE problem in the virtualization of ATNs and propose a fault-tolerant SVNE algorithm, termed SVNE-FT, that considers both reactive and proactive mechanisms to recover VNs from single node failure under the wireless environment. To end node failure, we propose a novel node ranking method to select reliable SNodes to map VNodes and adopt a reactive recovery strategy to efficiently remap failed VNodes. In addition, to switching node failure, we reliably construct differentiated p-Cycles to protect the vulnerable switching nodes of substrate paths that map VLinks. To further validate the strength of SVNE-FT, we conduct a comprehensive simulation. Numerical results reveal that SVNE-FT outperforms representative and latest SVNE algorithms in terms of acceptance ratio and revenue to cost ratio. Also, it greatly enhances the achievable recovery efficiency, decreasing recovery delay.
Main contributions of this paper are summarized as follows: 1) A heuristic SVNE scheme is proposed to recover from end or switching node failure for the virtualization of ATNs. To end node failure, SVNE-FT adopts a novel reactive approach to efficiently remap the affected virtual nodes. Then, to switching node failure, it constructs reliable and differentiated p-Cycles for unreliable switching SNodes of the affected VLinks by the improved p-Cycle technology.
2) To reliably map VNodes, node capacity, link bandwidth, wireless interference, recent failure time and node failure times are exploited when ranking SNodes. While in previous wireless mapping scheme [18,19], virtual node constraints only include node capacity and link bandwidth.
3) Comprehensive simulations are made to validate the advantage of SVNE-FT. We compare our heuristic algorithm not only with its reactive version without p-Cycle technology, but also with typical SVNE algorithms. In addition, simulation results are illustrated in order to highlight our proposed algorithm.
The rest of the paper is organized as follows. Section II is the related work. Then, Section III presents the SDN based model for ATNV and formulates the SVNE problem. Next, Section IV presents the details of SVNE-FT. The simulation work is implemented in Section V, along with parameters setting. Finally, Section VI concludes our findings.

II RELATED WORK
ATNs are currently constructed on discrete data link systems (e.g., Link-16, TTNT, MADL) [6]. These communication systems have been a critical information sharing capability between both manned and unmanned military aircraft as well as surface and ground platforms for a number of decades. While these systems serve the immediate need, they fail to fulfil the actual desire to support an ever-increasing number of users and emerging applications, and then adapt to the network failures [3]. This is because of the ossification problem in the vertically integrated network architecture, which also exists in many public networks like unmanned aerial vehicles (UAVs) networks. The virtualization technology has been a promising solution in UAVs [20,21]. Therefore, NV can improve the resource allocation in recovering node failure during missions for ATNs by solving the SVNE problem.
The SVNE problem, proved to be NP-hard, has been accepted as one key research area to improve the survivability of VNs affected by network failures. Therefore, many efforts have been made in heuristic approaches. Rahman et al. in [12] firstly addressed the survivability of VNs. There are many significant aspects in the research literature such as single SNode failure, multiple SNode failures, single SLink failure and multiple SLink failures [22]. This paper focuses on the single SNode failure. After a VN is embedded into the SN, single node failure can have direct and bad influence in the normal operation of virtual nodes and links. Therefore, the approaches for ensuring survivability of VNs during a single substrate node failure can be broadly classified into two categories, namely, end node and switching node protection approaches. In the following subsections, we discuss the end node (Section II-A) and switching node (Section II-B) protection approaches from the SVNE literature.

A. PREVIOUS TYPICAL AND LATEST END NODE PROTECTION APPROACHES
To one embedded VN, VNodes are mapped onto qualified SNodes, called as end nodes for transmitting and receiving the data on the virtual links. End node protection approaches protect end nodes from single node failure. On the one hand, many proactive approaches (e.g., [13,23]) have been proposed. Liu et al. addressed the problem of selecting standby virtual routers that is provided by the SN to serve VNs under a single node failure. A node protection approach was proposed in this paper to dynamically reconfigure VNs back to original topologies right after a single substrate node failure. In addtion, for the multiple substrate node failures, Xiao et al. [23] proposed to use topology attributes, considering dedicated substrate backup scheme, to enhance the survivable VN. In these proactive protection approaches, resource utilization may be reduced due to the fact that backup resources remain unused during normal operations. On the other hand, reactive approaches (e.g., [17,24]) are also proposed to protect end nodes. Shahriar et al. [17] proposed a reactive protection scheme, solving the problem of recovering a batch of VNs affected by a substrate node failure. This scheme aims to achieve customized objectives such as fair treatment on the failed VNs, partial treatment based on priority, and so on. In contrast, Chang et al. [24] proposed a migration aware protection approach to recover from a single substrate node failure. The approach facilitates the re-mapping of the failed virtual nodes and virtual links by the migration of some active virtual nodes and links to free up some substrate resources. All of these reactive approaches may need a chain of migrations to converge and thus disrupting ongoing communication in the VN.
Most of these end node protection approaches are designed for wired networks. For the specific wireless environment in ATNs, it is definitely requested to reliably map virtual nodes, considering the complex electromagnetic interference. In addition, proactive approaches will cause high resource expense by prepare backups for both virtual nodes and their adjacent virtual links, which may be not proper for ATNs with limited resources. Thus, to improve the resource utilization, it is important to design reactive approaches to protect virtual node from single node failure.

B. PREVIOUS TYPICAL AND LATEST SWITCHING NODE PROTECTION APPROACHES
To one embedded VN, VLinks are mapped onto the corresponding substrate paths including switching that forward the data of virtual links. A single substrate node failure on switching nodes may cause the operation disruption of multiple virtual links. However, switching nodes are not fully taken into consideration in the node protection for the survivability of VNs. Most of the previous SVNE algorithms deal with the switching node failure by remapping the virtual links affected by node failure, which will increase the recovery delay and probably cannot find the proper path if most of the network resources of SN have been used. Thus, there are proactive approaches [25,26] that protect VLinks from switching node failure, adopt p-Cycle technology. Jarray et al. [25] addressed the problem of single/multiple logical link failures caused by a single substrate node failure in switching substrate node. A two-step protection mechanism was proposed to recover a VN. The first step uses a large-scale optimization technique to embed VNs. And the second step adopts link p-Cycle based protection techniques to protect the switching substrate nodes while minimizing the backup resources. Also, the logical layer related to the VN topology is considered to guarantee a node failure independent path protection scheme. In [26], Jarray et al. extends the results to handle any single physical failure in the substrate by adopting p-cycle protection approach in physical layer. The switching node protection approaches are mostly designed for wired networks and thus cannot adapt well to ATNs due to the wireless environment.
In addition, p-Cycle technology also takes too much network resources to protect the switching node. Most of these switching node protection approaches are based on reactive schemes, which cannot efficiently protect switching node protection. However, proactive schemes, especially for p-Cycle based approaches, can offer high efficiency in recovering VNs from switching node failure for the virtualization of ATNs. In addition, it is vital to fully consider the complex interference while protecting switching nodes and the balance between backup resources and recovery efficiency due to the limited network resources.

C. BRIEF SUMMARY OF PREVIOUS WORKS
To summarize, the ossification problem of ATNs can be properly solved by NV. Also, SVNE problem has been accepted as a vital aspect of NV to improve the network reliability. Thus, it is significant to further study SVNE problem that is NP-hard for the virtualization of ATNs to protect mission applications from network failures. In virtualization environment, a single physical node failure can result into the operation disruption of both virtual nodes and multiple virtual links. Many efforts in the literature have been made to protect virtual nodes (Section II-A) and virtual links (Section II-B) against a single node failure. However, these heuristic node protection algorithms are designed for wired networks and may not adapt to the specific wireless environment in ATNs. In addition, these node protection algorithms do not consider the balance between backup resources and recovery efficiency which is important for the virtualization of ATNs with the limited network resources.
Our proposed SVNE-FT algorithm differs from previous heuristic SVNE algorithms in four main aspects. First of all, the SVNE-FT algorithm adopts a reliable embedding method to map VNs, decreasing the effects of a single substrate node failure on the VN layer. Second, for end node protection, we design a proactive mechanism that shortens the chain of migrations to converge. Next, a p-Cycle based method is adopted in switching node protection, considering the specific complex interference in air-combat field. Finally, a comprehensive simulation is implemented against typical node-protection heuristic SVNE algorithms under wireless interference.

III PRELIMINARIES
In this section, we firstly present the slice-based ATNV model. Then, we formally represent the SVNE problem model. Finally, main evaluation metrics and objective functions are defined.

A. SLICE-BASED ATNV MODEL
ATNs refer to large-scale wireless multi-hop networks, formed by manned and unmanned military aircrafts as well as surface and ground platforms. Existing ATNs can support a certain degree of operational coordination between aviation platforms in the existing aviation combat mode in terms of network transmission performance indicators such as transmission reliability, end-to-end delay, and transmission rate [27]. However, the ossification problem is impeding the revolution of ATNs to support the application requirements of future aviation swarm combat. The ossification problem lies in the network architecture, tightly coupled and vertically implemented to support users and applications. Therefore, it is vital to design a scalable and flexible infrastructure. A slice-based ATNV framework is designed in Fig. 1, inspired by the SDN-enabled ATN [27] and the virtualization scheme [18]. The framework is composed of the following layers: 1) Substrate network layer: Massive aircrafts are deployed in concomitant formation. Lead aircrafts in the formation form a wireless multi-hop network, abstracted as the shared airborne tactical substrate network (ATSN). These aircrafts, equipped with SDN-enabled devices, are the access points that access and transfer situation information and thus compose the data plane.
2) Virtualization layer: A hypervisor virtualizes the ATSN and performs as a slicing agent between data plane and SDN controllers. The cloud icon represents the tactical data centre that owns strong information processing capability to deal with the rapid changes of situation information and mission applications. The hypervisor can orchestrate and collaborate multiple applications in an overlapped way and thus adopts the SVNE algorithm. Also, the hypervisor can adopt the optimized link state routing (OLSR) protocol [28] to collect the dynamic link state information and support the resource requests of mission applications stably and timely.
3) Application layer: Various military mission applications are precisely abstracted into logical and self-contained airborne tactical virtual networks (ATVNs). Accordingly, each ATVN has arbitrary topology with customized QoS demands to fulfil specific tactical service demands. Also, a dedicated SDN controller is deployed to support the protocol reconfiguration and evolution of each ATVN.

FIGURE 1. Illustration of slice-based virtualization for ATN
In general, there are four main features in the virtualized ATNs. First of all, a platform is offered to accept and deploy military applications since each ATVN is allowed to run and evolve its own protocol. Therefore, network services are flexibly coupled with military airborne missions, solving the ossification problem of traditional ATNs [29]. Second, the hypervisor possesses global state view of the resource usage to make the global allocation possible. Third, the full isolation exists in the network configurations of different ATVNs [30], satisfying the efficiency and security demand of military missions. Finally, its high scalability and sustainability can decrease the overhead of extra devices for innovative mission applications. Thus, new network technologies can be deployed more quickly and easily [9].  3) Embedding process: Embedding any ATVN onto ATSN includes node and link mapping. To node mapping, v from the same ATVN is mapped onto a different n by mapping M N : There are two types of direct failures of ATVNs: VNode failure: The VNode

C. EVALUATION METRICS
The average acceptance ratio is an important metric that presents the efficiency of successfully accepting VN requests.
NUM t is the total number of ATVNs.  represents a constant infinitely close to 0.
The average revenue to cost ratio can present the ability in resource utilization, especially for link mapping. It is shown in Eq. (2) below.
t is the working ATVNs at time t. The revenue   , V R G t represents the total network resource requirement (node power and link bandwidth resource) of embedding accepted ATVNs at time t. Under the total network resource requirement, it is useful to calculate the amount of consumed network resource that is represented by (3) and (4) are the specifical definition where  and  are weighting coefficients that coordinate the relationship between node power and link bandwidth. In this paper, both  and  are set to be 1.   v n p n  is the power resource allocated by n to map is the bandwidth resource allocated by a SLink S l of S p to map V l . S p is the total link number of S p .
The average failure recovery ratio presents the ability in recovering the failed SNodes. It is shown in Eq. (5).
where ( ) f num t represents the total number of failures at time t.
_ ( ) f r num t denotes the number of failures that are successfully recovered at time t. Similar to  in Eq. (1),  represents a constant infinitely close to 0.

D. OBJECTIVE FUNCTIONS
The major objective of the proposed algorithm is to maximize the average acceptance ratio under single node failure. The objective function is formulated as given below. Objection Constraints work when mapping VNodes and VLinks of ATVNs. First, the constraints of node mapping are included in Eq. (7) to (10). In Eq.

IV HEURISTIC SOLUTION: SVNE-FT
Due to the intractability of SVNE problem, we resort to a heuristic algorithm, SVNE-FT (Fig. 3), that is detailed in this section. Firstly, after one ATVN request arrives, SVNE-FT will adopt Algorithm 1 to map VNodes and VLinks. If the embedding process is successful, the node failure detection will start to check if there is a single node failure. Then, if single node failure happens, SVNE-FT will adopt Algorithm 2 to deal with the affected VNodes and VLinks. Next, in Algorithm 1, node and link mapping are coordinated in onestage. Meantime, it reliably maps VNodes (Procedure 1) and VLinks (Procedure 3) against end and switching node failure, respectively. Finally, in Algorithm 2, the recovery strategy is adopted to deal with end node (Procedure 2) or switching node (Procedure 4) failure.
To clarify the efficiency of the improved p-Cycle protection technology (Procedure 3), it is wise to make a simple reactive version of SVNE-FT, SVNE-FTs, that deletes Procedure 3 and Procedure 4 and only remaps failed switching SNodes and its adjacent SLinks.

1) RELIABLE NODE RANKING
To select the proper VNode, VNodes are ranked into a list based on ranking value that indicates the capacity demand. In this VNode list (VNo_List), the ranking value is expressed as where V v L denotes the set of VLinks adjacent to .

 
NoV v is the total requirement of transmission rate   V TR l for all adjacent VLinks of v . The VNode with highest ranking value will be selected and mapped.
To select the proper SNode, a SNode list (SNo_List) is formed based on SNode ranking value expressed as The specific procedures are shown in Procedure 1 below.

Procedure 1 Reliable node ranking
Input:     Fig. 2, not like u in Fig. 4, connects to more than one VLink. In this case, to decrease the time spending, the remapping of b needs to consider the distance between the selected SNode and extant SLinks of previous substrate paths. The distance can be expressed as   [32] is adopted, reliably mapping VLinks in consideration of complex interference. This subsection presents the recovery strategy, based on p-Cycles, against switching node failure.    and more than 2  , n can be protected by p-Cycle 1. In addition, it can be protected by p-Cycle 2 if   % NoV n is less than 2  or n has once failed. To construct a p-Cycle for n, we first find its two adjacent SNodes on the mapped path. In Fig. 5, A and E are adjacent SNodes of failed D. Then, the Dijkstra's algorithm is adopted to find a proper path that connects A and E. The influence weight of a SLink is expressed as

1) SWTICHING NODE PROTECTION APPROACH
where  is a constant set to 1 and   S ij TR l must be higher than   Keep n into a node list that is ready for protection in p-Cycle 1; 5. end if 6. end for 7. for each n in the protection list do Ready to construct a p-Cycle 2; 10. end if 11. if its adjacent nodes are in the node list do 12. Ready to construct a combined p-Cycle; 13

2) RECOVERY FROM SWITCHING NODE FAILURE
Procedure 4 presents an efficient and reliable recovery strategy that adopts p-Cycle protection techniques for vulnerable SNodes (step 2) and fast remapping for other switching SNodes (step 6). The complexity is mainly determined by step 2 or 6 which require at most

Procedure 4 Recovery from switching node failure
Input: l and S p , failed switching node n ; Output: V l recovered from switching node failure; 1. if is protected by one available p-Cycle do 2. Enable the p-Cycle and recover V l ; 3. else if 4. Hold the normal SLinks of S p ; 5. Find another proper SNode n  to replace ; 6. Find the shortest reliable path that connects n  and S p according to Eq. (21); 7. end if

C. ONE-STAGE EMBEDDING AND RECOVERY FROM SINGLE NODE FAILURE
A heuristic one-stage algorithm is first proposed, coordinating node and link mapping to improve embedding profits. Then, we propose a reliable recovery strategy against end or switching node failure.

1) HEURISTIC ONE-STAGE EMBEDDING
The one-stage embedding includes Procedure 1 and Procedure 3, which is presented in Algorithm 1 below.

Algorithm 1 Embedding in One-Stage
Input: Output: Results of reliably embedding ATVN; Run Procedure 1 with as input; 4. Get the output u v with its SNo_List; 5.

2) RECOVERY STRATEGY AGAINST SINGLE NODE FAILURE
Algorithm 2 combines Procedure 2 and Procedure 4 to reliably recover from end and switching node failure. if n maps any VNode v of max Run Procedure 2 with v as input; 7. end if 8. if n is a switching SNode of max Run Procedure 4 with n as input; n n V n  This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and content may change prior to final publication. Each ATVN is assumed to have a predetermined working time according to practical requests of military missions. As single node failure happens, the influences will be worse if remaining working time is longer. To decrease the bad influence, we extract the failed ATVN with longest remaining working time by function EXTRACT-MAX in step 4. The time complexity of Algorithm 2 is mostly determined by step 6 and 9 which require at most O(( | |

V SIMULATION EVALUATION
SVNE-FT algorithm is evaluated through extensive simulations. Firstly, we present the simulation setup in detail. Then, we describe the compared algorithms and extensive simulations results.

A. SIMULATION SETTING AND PARAMETERS
We generate the network topology for ATSN and ATVN by an improved Salam network topology random generation algorithm [33]. The Salam network topology generation algorithm can randomly generate corresponding nodes and links that constitute ATSN and ATVN according to the network parameters in Table 1 and Table 2, respectively.
In Table 1, the unit of SNode power is W. The unit of SLink bandwidth is MHz. The power range is based on the practical power range of airborne radio station that includes HF station and VHF station. In Table 2, the unit of VLink transmission rate is Mbit/s.  We make some other simulation settings for ATSN and ATVN. Each SNode n is assumed to have enough basic power   b p n , used within one flight formation. And environmental noise is assumed to be white Gaussian noise with   6 10 Noise p n   W. Then, in air-combat field, the complicated link gain needs to consider some parameters (e.g., antenna gains, multipath models) which is not necessary for this paper. Thus, to simplify the analysis process, we set the link gain of a Slink as , where d is the Euclidean Distance between end nodes and k is the channel fading coefficient that is set to be 4. In ATVN, V  is set to be 100 km. In Eq. (20), 1  and 2  are set to be 20% and 10%, respectively. The intensity of general interference is denoted by AveI n nf n p  , which is described as 0dB ( ). Also, it is assumed that malicious attacks from enemy are not too intense. Finally, to simulate single node failure, normal SNodes are ranked into a list by failure value  Table 3 lists out all the heuristic SVNE algorithms with corresponding node protection strategies for experimental simulations. SVNE-FT adopts both reactive and proactive approaches. SVNE-FTs and Fast-ReNoVatE adopts reactive approach. SVNE-ORP adopts proactive approach. Especially, SVNE-ORP and Fast-ReNoVatE are the typical and latest node protection strategies in the literature. SVNE-ORP and Fast-ReNoVatE, designed for wired networks, may be not proper for SVNE simulations in wireless air-combat field. Thus, they are slightly modified to fit into simulations. Also, to evaluate the performance of p-Cycles, we adopt SVNE-FTs that remaps switching nodes and does not construct p-Cycles for vulnerable switching nodes as SVNE-FT does. End node protection allocates backups for key VNodes and their adjacent VLinks. Switching node protection is not taken into account. Fast-ReNoVatE [17] End node protection remaps the affected VNodes and adjacent VLinks by computing the maximum flow. Switching node protection remaps the whole affected VLinks by finding the shortest path.

SVNE-FTs
End node protection adopts the Procedure 1 proposed in this paper. Switching node protection remaps failed switching SNodes and its adjacent SLinks for the affected VLinks, which is proposed in this paper. SVNE-FT End node protection adopts Procedure 1 proposed in this paper. Switching node protection adopts Procedure 3 and 4 in this paper.

C. SIMULATION RESULTS
In this sub-section, we discuss the simulation results in terms of average acceptance ratio, average revenue to cost ratio, average execution time, average failure recovery ratio and average failure recovery delay. Fig. 6 shows two conclusions. Firstly, average acceptance ratios decrease quickly in the beginning simulation stage and reach stable states in the post simulation stage. This is because there is a balance between the available network resource of ATSN and the number of accepted ATVNs that cost resources. Also, the available network resource will decrease as SNodes and SLinks fail. Secondly, SVNE-FT has the highest average acceptance ratio about 0.65 as simulation time extends. In SVNE-FT, Procedure 2 is adopted to efficiently protect VNodes against end node failure, decreasing resource cost. Procedure 3 and 4 are adopted to protect VLinks against switching node failure, increasing recovery efficiency. In comparison with SVNE-FT, SVNE-FTs does not construct p-Cycles for vulnerable switching SNodes and thus may not recover more VLinks from switching node failure. Fast-ReNoVatE remaps failed VLinks, by releasing the whole substrate path, decreasing recovery efficiency. SVNE-ORP allocates backups for VNodes and VLinks that may be affected by end node failure, costing more network resource. Also, it does not consider the recovery of failed VLinks affected by switching node failure.   7 illustrates the comparison results of longterm average revenue to cost ratios. As simulation time extends, longterm average revenue to cost ratios will decrease to stable states. SVNE-ORP has the lowest ratio because it allocates backups for key VNodes and VLinks, increasing resource cost and the average length of paths mapping VLinks. In comparison with SVNE-ORP, Fast-ReNoVatE remaps failed VNodes and VLinks, saving extra network resource and increasing embedding revenue. However, SVNE-FT and SVNE-FTs behave better due to the recovery strategy against single node failure, adopting Procedure 2.

1) APPARENT BASIC PERFORMANCE ADVANTAGE
To end node failure, they just release part of the path and thus increase the embedding revenue of ATVNs. To switching node failure, SVNE-FTs remaps the failed VLinks according to Eq. (21). SVNE-FT adopts Procedure 3 and 4 to protect failed VLinks, increasing the recovery efficiency and embedding revenue. Through the simulation, SVNE-FT further ensures the efficiency of substrate network resource in the long run. Thus, it has the highest longterm average revenue to cost ratio about 0.52.  As simulation time extends, the limited available network resource may cause the increase of average execution time. But it will increase to a stable state due to the balance between available network resource and accepted ATVNs. Firstly, to SVNE-ORP, it has the highest average execution time during the simulation process. The reason is that SVNE-ORP requires to find backups for most of VNodes and corresponding VLinks, which may spend more time embedding ATVNs. Then, to SVNE-FT, it only requires to construct p-Cycles for part of SNodes on the substrate path that maps corresponding VLinks, spending less time embedding ATVNs. Finally, to SVNE-FTs and Fast-ReNoVatE, the two reactive heuristic SVNE algorithms don't require to prepare backups for any VNode or VLink and have less average execution time. 2) RECOVERY PERFORMANCE IMPROVEMENT Fig. 9 depicts the average failure recovery ratio as a function of time. As the simulation time extends, the ratio will consistently decrease due to the fact that there is less available network resource to protect ATVNs against single node failure. Firstly, SVNE-ORP has a higher ratio in the beginning simulation stage with enough resources to allocate backups against single node failure. However, it has the lowest ratio in the post simulation stage with less resources to allocate backups. It also pays no attention to the protection of failed VLinks from switching node failure. In contrast, Fast-ReNoVatE performs better because it accounts for the switching node failure and remaps the failed VNodes and VLinks, decreasing the resource cost in the post simulation stage. Obviously, SVNE-FT and SVNE-FTs have an apparent advantage in the post simulation stage. To end node failure, they adopt Procedure 2 to find more proper SNodes and SLinks for failed VNodes. Also, to switching node failure, they release part of the substrate path and can find reliable SNodes and SLinks. Thus, more failed ATVNs can be recovered from single node failure. Compared with SVNE-FTs, SVNE-FT adopts Procedure 3 and 4, constructing p-Cycles to protect vulnerable SNodes against switching node failure. Therefore, SVNE-FT has the highest average failure recovery ratio as time extends. Fig. 10 shows the average failure recovery delay of the compare algorithms as a function of time. As the simulation time extends, the average failure recovery delay increases to a stable state, which is probably due to all the embedding algorithms need to take time to find enough network reosurces to remap VNodes or VLinks after single node failure happens. In addition, SVNE-ORP has the lowest average failure recovery delay about 12.5ms due to its backups prepared for all key VNodes. To our proposed SVNE-FT, it has the average failure recovery delay about 13.3ms that is lower than both SVNE-FTs and Fast-ReNoVatE because it prepares backups for unreliable switching nodes. SVNE-ORP has a delay that is just about 6% lower than that of SVNE-FT. However, SVNE-FT has an average failure recovery ratio that is about 20% higher than that of SVNE-ORP. Thus, SVNE-FT has better recovery performance.    Fig. 6. As shown in Fig. 10, the average acceptance ratio increases as the node failure interval increases, which is probably due to the fact that there may be less node failures as the node failure interval is bigger. In case of our proposed SVNE-FT algorithm, the average acceptance ratio increases from 0.21 to nearly 0.71 as the node failure interval increases This article has been accepted for publication in IEEE Access. This is the author's version which has not been fully edited and content may change prior to final publication. from 500 to 2500 time units. In addition, the average acceptance ratios of other three algorithms are lower than SVNE-FT as the interval increases. The major reason of the higher ratio in case of SVNE-FT is due to the better protection against end node or switching node failure.   12 shows the stable states of average acceptance ratios under different 1  and 2  in SVNE-FT. The average acceptance ratio under 1  denotes the stable state of average acceptance ratio under the condition that a switching node is protected only by p-Cycle 1 if its   % NoV n is less than 1  . Similarly, the average acceptance ratio under 2  denotes the stable state of average acceptance ratio with switching node protected only by p-Cycle 2 if its   % NoV n is less than 2  . As shown in Fig. 10, the average acceptance ratios under different 1  and 2  are graphs of concave functions. This is probably due to fact there is resource balance between resources used by back-up p-Cycles and resources used by embedding new VNs. In addition, the average acceptance ratio under different 2  will reach a maximum about 0.63 as 2  is equal to be about 10% while the ratio under different 1  will reach a maximum about 0.62 as 1  is equal to be about 20%. Thus, we set 2 10%   and 1 20%   to get comparably higher average acceptance ratio of the proposed SVNE-FT algorithm as shown in Fig. 6.

VI CONCLUSION
In this paper, we have addressed the problem of recovering failed ATVNs from a single substrate node failure (end and switching node failure) in the wireless airborne field.
To tackle the computational complexity, we have presented a heuristic algorithm, SVNE-FT. To end node failure, SVNE-FT is able to remap the failed VNodes and adjacent VLinks by releasing part of substrate paths. To switching node failure, SVNE-FT efficiently constructs p-Cycles to protect the affected VLinks. To decrease the resource cost, it selects the vulnerable SNodes of the path and constructs two types of p-Cycles. Different simulation results validate that SVNE-FT algorithm outperforms typical and latest heuristic SVNE algorithms in the wireless environment of ATNs. Main performance metrics are plotted, such as average acceptance ratio, longterm average revenue to cost ratio, average failure recovery ratio and average execution time.
In the future, there are still a number of issues to be done. First of all, this work is extended to recover from SLink failures, resulting from over-subscribed bandwidth allocation. Next, it is to study the problem in a real testbed environment and evaluate the SVNE-FT algorithm through a prototype implementation.
XIANG WANG received the B.S., M.S., and Ph.D. degrees in communication and information system from Air Force Engineering University, Xi'an, China, in 2006China, in , 2009, and 2013, respectively, where he is currently a Lecturer.
His research interests include airborne networks, wireless network virtualization and software-defined networking.