Virtual network embedding (VNE) problem is a key issue in network virtualization technology, and much attention has been paid to the virtual network embedding. However, very little research work focuses on parallelized virtual network embedding problems which assumes that the substrate infrastructure supports parallel computing and allows one virtual node to be mapped to multiple substrate nodes. Based on the work of Liang and Zhang, we extend the well-known VNE to parallelizable virtual network embedding (PVNE) in this paper. Furthermore, to the best of our knowledge, we give the first formulation of the PVNE problem. A new heuristic algorithm named efficient parallelizable virtual network embedding (EPVNE) is proposed to reduce the cost of embedding the VN request and increase the VN request acceptance ratio. EPVNE is a two-stage mapping algorithm, which first performs node mapping and then performs link mapping. In the node mapping phase, we present a simple and efficient virtual node and physical node sorting formula and perform the virtual node mapping in order. When mapping virtual nodes, we map virtual nodes to physical nodes that just meet the CPU requirements. Substrate nodes with more CPU resources will be retained for subsequent virtual network mapping requests. In the link mapping phase, Dijkstra’s algorithm is used to find a substrate path for each virtual link. Finally, simulations are carried out and simulation results show that our algorithm performs better than the existing heuristic algorithms.

As we all know, the Internet has become one of the infrastructures of today’s social communications, information exchange, economic and commercial operations, and multimedia services [

In recent years, network virtualization technology has been widespread concern in industry and academia [

In the virtualization network environments, the virtualized network model divides the role of Internet service provider (ISP) into two separate entities: infrastructure provider (InP) and service provider (SP) [

The problem of allocating infrastructure network resources according to virtual network requests with node and link resource constraints is called virtual network embedding (VNE) problem [

Consider the example in Figure

Parallelizable virtual network embedding. (a) Virtual network request. (b) Substrate network. (c) Substrate network with parallelization.

In this paper, we study parallelizable virtual network embedding (PVNE) and propose an efficient parallelizable virtual network embedding (EPVNE) algorithm. We summarize the main contributions here as follows:

Based on optimization theory and resource integration technology, an optimized mathematical model for parallel virtual network embedding is proposed.

A new heuristic algorithm named EPVNE is proposed to reduce the cost of embedding the VN request and increase the VN request acceptance ratio. Firstly, the substrate nodes and virtual nodes need to be ordered by a metric proposed in this paper which is simple and can be calculated efficiently. Secondly, when mapping each virtual node

Extensive simulations have been performed to evaluate the performance of our new algorithm. The results demonstrate that our algorithm performs better than the existing heuristic algorithms.

This paper is organized as follows: the related work is introduced in Section

Researchers have conducted in-depth research on virtual network embedding algorithms from different perspectives, and a series of research results have emerged. Several papers [

Depending on whether the node and link resource constraints of the underlying network or virtual network are fully considered, the virtual network mapping algorithm is divided into a mapping algorithm that considers both node and link resource constraints and a mapping algorithm that ignores node or link resource constraints. For example, in the virtual network mapping process, the literature [

Depending on the underlying network resource allocation method, the virtual network embedding algorithm can be divided into static embedding algorithms [

According to the different processing methods for virtual network requests, the virtual network embedding algorithm can be divided into offline embedding algorithms [

Depending on the calculation method of virtual network mapping, the virtual network mapping algorithm can be divided into a centralized mapping algorithm and a distributed mapping algorithm. The centralized virtual network mapping algorithm allocates corresponding resources for virtual network requests according to the underlying network resource status by the central decision-making organization [

According to the mapping order of virtual nodes and virtual links, the virtual network mapping algorithm can be divided into one-stage mapping algorithm and two-stage mapping algorithm. The node mapping and link mapping of the one-stage mapping algorithm are completed in the same stage. In other words, the virtual link in the one-stage mapping algorithm maps when mapping virtual nodes [

In the real substrate network, various failures often occur. In a network virtualization environment, failure of a single physical network entity will affect all virtual networks mapped to that physical network entity. In order to solve the problem, a very realistic idea is to provide redundancy or backup. The redundant virtual network mapping refers to the provision of redundant resources in the virtual network mapping, including node resources and link resources, to deal with node failures. In contrast, the concise virtual network mapping algorithm does not provide redundant resources. The concise solution uses only as few substrate resources as possible to meet the needs of the proposed virtual network without leaving additional resources for any failures. This also means that virtual networks cannot be guaranteed to recover from accidental failures, although more substrate resources can be reserved to embed more virtual networks.

The redundant VNE methods [

Recently, Cao et al. divided the virtual network mapping algorithm into exact solution [

Virtual network mapping problems can be solved using the heuristic algorithm [

Some metaheuristic algorithms perform well in solving some problems, such as flowshop scheduling problems [

The above is a description of the classification of virtual network mapping algorithms. It should be noted that the different classifications are independent. That is, any selected VNE algorithm can be, for example, static, centralized, and concise. Let us discuss the results of recent research. As the research progressed, people came up with some novel ideas and were not able to classify them according to the previous classification. Ni et al. [

The paper mentioned above does not discuss the case where virtual nodes can be mapped to multiple physical nodes. The literature [

In this section, we will first model the substrate network of InPs and VN of SPs and give the VN embedding problem description, followed by the definition of objectives.

Similar to the papers of other scholars, the two parameters of CPU and bandwidth are mainly studied in this paper. The subscript s indicates the substrate network, and the subscript v indicates the virtual network. In the following, we will model the substrate network and the virtual network as undirected weighted graphs, where the vertices represent nodes and the edges represent links. Each vertex is associated with CPU capacity/constraint, and each edge is associated with bandwidth capacity/constraint.

We represent the substrate network as a weighted undirected graph

Similarly, the topology of the virtual network can also be represented by a weighted undirected graph

Each VN request may be represented by

Figure

Yu Liang and Sheng Zhang divided the parallelizable virtual network embedding into three components: master mapping, salve mapping, and link mapping. The master mapping _{ms} maps a virtual node _{v} to a substrate node, denoted by _{v} to a subset of the neighbors of

As shown in Figure

Based on the introduction of Section

Variables:

_{uv} is routed on physical link _{ij} and 0 otherwise.

_{i}^{u}: a real variable, such that _{i}^{u} > 0 if virtual node _{i}^{u} unit CPU resource of the substrate node _{i}^{u} = 0 if virtual node

Objective:

Constraints:

Capacity constraints:

Domain constraints:

Remarks:

The objective function tries to minimize the cost of embedding the VN request. The objective function consists of three parts. The first part is the cost of mapping the virtual links on the substrate links. The second part is the cost when the virtual node is mapping. The third is the cost of the links between the slave nodes and the master node.

Constraint set (

Constraint set (

Finally, constrain sets (_{i}^{u}, respectively.

The proposed heuristic EPVNE employs a greedy approach to deal with node mapping, and the link mapping utilizes Dijkstra’s algorithm to find the shortest path that meets the resource demands. EPVNE is shown in Algorithm

In the initialization phase (lines (1)–(3) in Algorithm _{v}). Similarly, all substrate nodes are sorted in the decreasing order of ACPU(_{v}) which can be derived from the following equation:_{nei}(_{s}) denotes the set of direct neighbors of node _{s} and _{s} which has not been used. There is a similar calculation formula (_{nei}(_{s}) whose function is similar to ACPU(_{s}) in this paper. The calculation formula (

//initialization phase

//node mapping phase

Mapping the virtual nodes in queue

Mapping

Else

Mapping

//link mapping phase

Dijkstra’s algorithm is used to find a substrate path for each virtual link.

Break

End if

End for

Map

Remove

_{nei}^{unused}(

Remove the node with the lowest CPU value from

End if

add

End if

Break;

End if

End for

Map

Remove the elements in

In the node mapping phase (lines (4)–(9) in Algorithm

In the link mapping phase (lines (10)-(11) in Algorithm

Mapping-one-to-one shown in Algorithm

Mapping-one-to-multi described in Algorithm

In the following, we analyze the computational complexity of Algorithms _{s}|) and _{s}| ∗ speed), respectively. The complexity of Algorithm _{s}| denotes the number of physical nodes, and |_{v}| is the number of virtual nodes.

In the initialization phase of Algorithm _{v}|^{2}) and the complexity of substrate nodes sorting is _{s}|^{2}). In the node mapping phase of Algorithm _{v}| multiplied by the complexity of Algorithm _{v}| ∗ _{s}| ∗ speed) = _{v}| ∗ |_{s}| ∗ speed). The complexity of the Dijkstra algorithm is _{s}|^{2}). In the link mapping phase of Algorithm _{v}| ∗ _{s}|^{2}), and |_{v}| is the number of virtual links. Finally, the complexity of Algorithm _{v}|^{2}) + _{s}|^{2}) + _{v}| ∗ |_{s}| ∗ speed) + |_{v}| ∗ _{s}|^{2}). The complexity of

In this section, we first introduce our simulation setup and then present performance comparison results. The substrate network topology is configured to have 20 nodes, and each pair of nodes is connected with probability 0.4. The CPU and bandwidth resources of the substrate nodes and links are real numbers uniformly distributed between 50 and 100. The number of virtual nodes in each virtual network follows a uniform distribution between 2 and 10. Each pair of virtual nodes is connected with probability 0.5. The bandwidth requirements at virtual links are generated randomly from the range [50, 70]. The CPU requirements of the virtual nodes are also randomly generated, and the ranges are [50, 90], [70, 110], [90, 130], [110, 150], [130, 170], [150, 190], and [170, 210]. The three parameters described in Section

The following metrics are used for performance comparison: (i) Acceptance ratio, which is the ratio of the number of accepted virtual network requests to all requests; (ii) CPU ratio, which is the ratio of the amount of occupied CPU resources in the substrate network to overall CPU resources in the virtual network; and (iii)

Figure

Acceptance ratio.

The comparison of the CPU ratio is depicted in Figure

CPU ratio.

Figure

Network virtualization technology allows multiple heterogeneous virtual networks to be built on top of a shared underlying physical network. Network virtualization technology enables network operators to deploy new network architectures or protocols without affecting the existing Internet, providing a viable path for evolution from the current network to the future network. As one of the main challenges facing network virtualization, the virtual network mapping problem is NP-hard. It has become a research hotspot in the field of network virtualization.

In this paper, we studied parallelizable virtual network embedding. Firstly, the formulation of

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.