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Reliable design for virtual network requests with location constraints in edge-of-things computing


How to efficiently map virtual networks (VNs) onto a shared physical network is a challenging issue in the field of network virtualization in edge-of-things computing. Since an efficient VN mapping approach can reduce network resource consumption, lower latency, and enhance service reliability, it is important for both customers and network service providers. In this paper, we study the problem of mapping multiple VNs with geographic location constraints onto a physical network while considering the survivability and reliability requirements of each VN request in edge-of-things based data centers. We present the model of this problem and propose a Geographic-Guided Survivable Multiple VN Mapping (GG-SMVNM) algorithm to efficiently solve this problem, which simultaneously considers resource sharing and mapping VN links and nodes in edge-of-things computing. Furthermore, we conduct a large amount of simulations to validate and evaluate our proposed approach. The simulation results show that the proposed method is superior to the existing solution.


The emerging edge computing technologies [1,2,3], Internet of Things (IoT) [4, 5], and rich cloud services [6, 7] are used to create novel edge-of-things computing. In it, the data processing occurs in part at the network edge or between the cloud-to-end that can best meet customer necessities rather than entirely processing the data in a comparatively fewer number of massive clouds. Operators use the edge-of-things computing paradigm to provide network and computing services in a flexible and resource-efficient way [8,9,10,11]. Network virtualization is one of the main technologies and promoters of edge-of-things computing. Network virtualization allows multiple heterogeneous virtual networks (VNs) to share the same physical network in edge-of-things computing [12,13,14,15,16]. Due to the increasing popularity of edge-of-things computing, a great deal of research has been conducted on network virtualization and virtual network mapping technology [17,18,19,20,21,22,23,24].

A network virtualization environment (NVE) [25] is composed of shared resources (i.e., physical network with resource capacity) and virtual network (VN) requests in edge-of-things computing. A set of VN links and VN nodes makes up a VN request. Every VN node needs a fixed amount of nodal resources (i.e., storage resources, CPU and memory) to execute the edge-of-things computing services and applications, and each VN link that connects two VN nodes needs a great deal of communication bandwidth to exchange the data and information between the connected VN nodes. The progress of virtual network (VN) mapping is quite complicated because of the constraints of virtual links and nodes, despite knowing all VNs in advance. The VN mapping process is composed of two steps: the mapping of VN nodes and the mapping of VN links. Even if the mapping of all the virtual nodes is accomplished, the mapping of virtual links is still complicated. As a result, there are many VN mapping algorithms that can map as many VNs onto the physical network of edge-of-things computing as possible and minimize the VN mapping costs [26,27,28,29,30]. The VN mapping algorithm proposed in [26] maps the VNs under the guidance of minimizing mapping costs. However, it does not take the nodal survivability into consideration. The author comes up with the multiple VN mapping problems that consider survivability in [29], which introduces the VN mapping algorithm that considers the circumstance of physical network link failures. Research in [27] studies the VN mapping problem. It shares the backup resource among different VNs without considering the backup resource sharing of a single VN during the mapping process. The author in [28] researched the redeployment and migration problem of the dynamic VN. The authors in [29, 30] study the problem of VN mapping while considering the local failures of the physical network in edge-of-things computing.

Although many algorithms for VN mapping in edge-of-things computing have been designed, few of these algorithms take the effect of VN nodes’ geographic constraints into account. Moreover, no contribution has been made on the backup resource sharing among multiple VNs arriving simultaneously when node survivability is taken into consideration. For example, the 1-redundant method and the K-redundant method introduced in [31] can realize working and backup link resource sharing when mapping backup nodes and links, although they only apply for a single VN. Meanwhile, the working and backup link resource sharing can be achieved among multiple VNs arriving spontaneously when at most one physical node fails at a certain time. Moreover, nodal resource sharing can be realized thanks to the geographic constraint, which is left to further exploration and research.

In this paper, we study the problem of resource efficiency and reliable VN mapping/deployment in edge-of-things computing. In our research, we take the geographic constraint of each VN node into consideration. We realize the resource sharing inside every VN and the resource sharing link among VNs while mapping multiple VNs arriving spontaneously on the premise that virtual nodes’ survivability is guaranteed in edge-of-things computing applications. The main contributions of this paper are as follows:

  • We study the problem of reliable mapping for VN requests with location constraints in edge-of-things computing.

  • We propose the model and design an efficient algorithm for the studied problem.

  • We conduct extensive simulations to evaluate the performance of our proposed algorithms.

The remainder of the paper is arranged as follows. Section 5 outlines the problem statements and is followed by the heuristic algorithms in Section 3. Section 4 gives the detailed simulation results. Finally, Section 5 gives the conclusion of this paper.

Problem statement and formulation

Virtual network request

In this work, we research the issue of mapping multiple VN requests that guarantees the nodes’ survivability while at most only one node of physical network (PN) fails at any time in edge-of-things computing and while considering the geographic location constraints of VN nodes.

Figure 1 gives an example of three VNs simultaneously arriving. Note that, in practice, the number of simultaneously arriving VNs is random. Every VN can be described as G v  = (N v , L v ), where N v represents the set of virtual nodes with resource requirements corresponding to each node (such as the CPU and the memory capacity of physical nodes) and L v represents the set of virtual links. Every link has a bandwidth requirement for physical links to guarantee the communication between two VN nodes connected by a virtual link. Additionally, every node of the VN request has a geographic coordinate constraint. For example, the coordinate (x, y) beside the virtual node v0 in the virtual network VN0 means the geographic position of virtual node v0, thus constraining the range of physical nodes that v0 can be mapped onto. Every virtual node of each VN has its own geographic position constraint in Fig. 1, while only the coordinate of v0 is labeled in Fig. 1.

Fig. 1

An example of VN mapping

Physical network in edge-of-things computing

The physical network of edge-of-things computing is composed of multiple data centers that are dispersed across multiple geographical locations interconnected by a network. Like the VN request, a physical network model can be represented as G S  = (N S , L S ), where N S represents the set of physical nodes of the physical network (every node of which provides a physical resource such as CPU and memory capacity with corresponding geographic coordinates) and L S represents the set of physical links of the physical network (with every physical link providing physical bandwidth resources to satisfy the communication demand between physical nodes). Furthermore, when a physical node fails, the corresponding physical links also fail. Hence, the virtual nodes mapped onto the failed physical node need to be migrated to another physical node that is not failed, and the corresponding virtual links also need to migrate. In this paper, there is at most only one physical node that fails at all times in the physical network of edge-of-things computing.

Reliable virtual network provisioning


A substrate edge-of-things computing physical network PN is represented as G S  = (N S , L S ), and several virtual network requests arrive simultaneously.

Mapping constraints

They include the geographical position constraints of virtual nodes, the resource demands of virtual links, and the resource demands of virtual nodes.


There is at most one physical node failure at any time, and if there is a virtual node mapped onto it, the virtual node and adjacent links need to be migrated and recovered.


Under the precondition above with the mapping constraints, the problem is how to design and realize a mapping algorithm that can map several VNs arriving simultaneously onto the physical network and guarantee the survivability of virtual nodes. It must realize the resource sharing in every VN and also the resource sharing among VNs to save the physical resources of edge-of-things computing, with the aim of minimizing the mapping costs and getting a generally comparatively good multiple VN mapping result.

Problem formulation

Residual resources

The residual resources include the residual bandwidth of every physical link and the residual node resource of every physical node in edge-of-things computing. The residual bandwidth capacity R l (l s ) of physical link l s represents the total amount of bandwidth available on link l s .

$$ {R}_l\left({l}_s\right)=\mathrm{Cap}\left({l}_s\right)-\sum \limits_{l_v\in {S}_{l_s}}\mathrm{req}\left({l}_v\right) $$

where Cap(l s ) denotes the resource capacity of physical link l s , req(l v )represents the amount of link resource requirements of VN link l v , and \( {S}_{l_s} \)indicates the set of VN links mapped on the physical link l s .

The residual node resource capacity R n (n s ) of physical node n s can be computed as follows:

$$ {R}_n\left({n}_s\right)=\mathrm{Cap}\left({n}_s\right)-\sum \limits_{n_v\in {S}_{n_s}}\mathrm{req}\left({n}_v\right) $$

where Cap(n s ) shows the resource capacity of physical node n s , req(n v ) represents the amount of VN node n v ’s requirement for nodal resources, and \( {S}_{n_s} \) indicates the set of VN nodes that have been mapped onto physical node n s .


We define the costs C(G V ) of the mapping VN request G V as all of the costs of physical resources (i.e., physical link and nodal resources) in edge-of-things computing allocated to G V .

$$ C(Gv)=\sum \limits_{l_v\in {L}_V}\sum \limits_{l_s\in {L}_S}{b}_{l_v}^{l_s}p\left({l}_s\right)+\sum \limits_{n_v\in {N}_V}\sum \limits_{n_s\in {N}_S}{r}_{n_v}^{n_s}p\left({n}_s\right) $$

where \( {b}_{l_v}^{l_s} \) denotes the amount of resources that physical link l s assigned to virtual link l v and \( {r}_{n_v}^{n_s} \) denotes the amount of nodal resources that physical node n s assigned to virtual node n v . The symbols p(l s ) and p(n s ) respectively represent the costs of per unit of the physical link and nodal resources.

Our objective is to minimize the VN mapping costs:

$$ \operatorname{Minimize}C(Gv) $$

Algorithm design

To achieve the survivable VN mapping in a reasonable time, we design an effective heuristic to solve the problem that we researched in the paper. The Geographic-Guided Survivable Multiple VN Mapping (GG-SMVNM) algorithm is detailed in this section.

In spite of the fact that at most one physical node fails in the physical network of edge-of-things computing when multiple VNs simultaneously arrive, different from the K-redundant scheme, the GG-SMVNM algorithm first successively maps the spontaneously arriving VNs onto the physical network with the geographic location constraints with the objective of minimizing costs instead of enhancing each VN with additional backup nodes and links. During the successive mapping, virtual nodes from different VNs may be mapped to the same physical node. After mapping all these VNs, a new VN is generated based on the physical mapping topology of the physical network. Finally, similar to the K-redundant scheme, the GG-SMVNM algorithm enhances the new-generated VN with backup nodes and corresponding backup links. It maps the backup nodes and links to the physical network to ensure the survivability of virtual nodes while also realizing the nodal and link resource sharing among spontaneously arriving VNs and the resource sharing in VNs. The GG-SMVNM algorithm works with the following steps (Fig. 2).

Fig. 2

The framework of the GG-SMVNM algorithm

Step 1: successively map all the simultaneously arriving VNs onto the physical network of edge-of-things computing

When mapping the VN requests, we aim to map the virtual nodes of different VNs to the same substrate node to make the newly generated VN more concise. The mapping results satisfying the geographic location constraints of VN0, VN1, and VN2 are shown in Fig. 1. Figure 1 only depicts the mapping of virtual nodes, but the corresponding mappings of virtual links are not shown here. We map the virtual node v1 from VN0 and node v0 from VN1 to the same substrate node s4. Therefore, the capacity demand of the new virtual node generated based on s4 is the total amount of the resource demands of v1 from VN0 and v0 from VN1 when the new virtual network is generated from the physical mapping topology. Similarly, the resource demand of the new virtual node generated by physical node s2 is the total demand of the resource demands of v2 from VN0 and v2 from VN1. The corresponding links also satisfy this demand if two or more virtual links are mapped onto the same physical link. Then, the resource requirement of the new virtual link generated by the physical link is the sum of the resource requirements of these virtual links. If there are several mapping results of the virtual nodes belonging to different VNs due to the geographic constraint, then we need to choose the best one with the minimum mapping costs. For example, in Fig. 1, v1 from VN0 and v0 from VN1 can both be mapped onto the physical node s4, while node v1 of VN0 and v2 of VN1 can both be mapped onto s4 as well. Then, we chose the mapping solution with minimum mapping costs.

Step 2: when all the virtual nodes are mapped, generate a new virtual network according to the mapping results

The new VN generated based on the mapping result of Fig. 1 is shown in Fig. 3. The virtual node v0 in Fig. 3 is reversely generated due to the physical node s0 in Fig. 1 with the same resource requirement as the resource requirement of v0 from VN0 mapped onto s0. The virtual node v1 in Fig. 3 is generated due to the physical node s4 in Fig. 1 with the resource requirement equal to the sum of resource requirements of v1 from the original VN0 and v0 from VN1 mapped onto s4. The other virtual nodes in Fig. 3 are generated in a similar way. The virtual links in Fig. 3 are also generated according to the mapped paths on the physical network such that if two or more virtual links are mapped onto the same physical path on the physical network, then the resource demand of the virtual link above is the sum of these virtual links’ resource requirements.

Fig. 3

New virtual network

Step 3: enhance the newly generated virtual network

This step is similar to the K-redundant scheme. The GG-SMVNM algorithm adds a backup node for each virtual node and adds the corresponding backup links as well. The enhanced newly generated virtual network with backup nodes and links is shown in Fig. 4. b0, b1, b2, b3, b4, and b5 are backup nodes, and the dashed lines represent the backup links.

Fig. 4

Enhanced new virtual network

Step 4: map the extra backup links and nodes

We apply the strategy similar with [31] to map backup links and nodes in order to decrease the costs of backup nodal mapping. Moreover, resource sharing of working links and backup links during the backup link and node mapping process leads to the resource sharing of links and nodes among original VNs, which will reduce the mapping costs as much as possible.

The detailed pseudo code of the GG-SMVNM algorithm is described in Table 1.

Table 1 Pseudo code of the GG-SMVNM algorithm

Next, we provide the GG-SVNM algorithm that does not consider the resource sharing among different VNs. The detailed pseudo code of the GG-SVNM is shown in Table 2.

Table 2 Pseudo code of GG-SVNM algorithm

In this, CMS i means the set of virtual nodes which physical node s i can host.

Simulations and results

We first introduce the environment of our simulation in the section, and then we give the results. Last, we analyze the results of simulation.

Simulation environment

Physical network

In the simulations, we use two different networks as the physical network of edge-of-things computing with 46 nodes and 55 nodes, respectively. Each node has a real geographic coordinate presented by a longitude and latitude. In the two different networks, we assume that the bandwidth capacities of each link follow a uniform distribution from 500 to 1000 and the resource capacities of each node are uniformly distributed from 200 and 400, respectively. The topologies of the physical networks used in our simulations are shown in Fig. 5.

Fig. 5

Physical networks used in our simulations. a Net-1: a network with 46 nodes. b Net-2: a network with 55 nodes

Virtual network configuration

In the case of multiple VNs mapping, the number of VNs simultaneously arriving is random in real applications. In our simulations, without the loss of generality, the number of arriving VNs is randomly distributed from 1 to 4, and each VN randomly consists of 3 or 4 nodes. The resource demand of each node is a variable that is randomly generated between 20 and 30, and its geographic coordinate is also generated randomly with the longitude and latitude whose values fall into a specific range. The possibility that there exists a virtual link between two virtual nodes is 50%. The bandwidth demand of the virtual link is randomly generated between 50 and 80.

Parameter g represents the ratio of the unit node resource overhead to the unit bandwidth overhead. Different values of g can compare the effects that different ratios of the unit node resource costs to unit bandwidth costs on VN mapping costs. We set the parameter g to 5 in the simulations.

In our simulations, we presume that zero or one substrate node fails at any time and several VNs arrive simultaneously. For evaluating our proposed algorithm, we compare the mapping performances of our GG-SMVNM and GG-SVNM algorithms with the EVPF approach proposed in [32] and consider the geographic location constraints of virtual nodes. Furthermore, we vary the number of simultaneously arriving VNs (the number of nodes on each VN is 3 or 4) on the premise that the physical resources are abundant and compare the total mapping costs, backup node mapping costs, and backup link mapping costs of these two algorithms.

We used Microsoft Visual Studio 2008 and C++ programming language to implement the compared algorithms.

Performance metrics

We define some metrics for evaluating the performance of our proposed algorithm in the simulation.

  1. 1.

    The total VN mapping cost: the total expenses of using physical network resources to provide all VN requests. It can be calculated as follows:

$$ {M}_{\mathrm{cost}}^{\mathrm{total}}={\sum}_{i=1}^{\mid \mathrm{ArrivedVN}\mid }{M}_c^i, $$

where \( {M}_c^i \) represents the mapping cost of i-th VN demand and ArrivedVN denotes the set of arrived VN demand.

  1. 2.

    The backup node mapping cost: the total expenses of using physical node resources to host the backup virtual nodes. It can be calculated as follows:

$$ {M}_{\mathrm{cost}}^{\mathrm{bakNode}}={\sum}_{i=1}^{\mid \mathrm{bakNode}\mid }{M}_{\mathrm{node}}^i, $$

where \( {M}_{\mathrm{node}}^i \) denotes the mapping cost of the i-th backup virtual node and bakNode represents the set of backup virtual nodes.

  1. 3.

    The backup link mapping cost: the total expenses of using physical link resources to host the backup links. It can be defined as follows:

$$ {M}_{\mathrm{cost}}^{\mathrm{bakLink}}={\sum}_{i=1}^{\mid \mathrm{bakLink}\mid }{M}_{\mathrm{link}}^i, $$

where \( {M}_{\mathrm{link}}^i \) denotes the mapping costs of the i-th backup virtual link and bakLink represents the set of backup virtual links.

Simulation results and analysis

We can see from Fig. 6 that the total mapping costs of our proposed GG-SMVNM and GG-SVNM algorithms are lower than that of the existing EVPF approach [32]. Furthermore, the total mapping costs of multiple VNs of the GG-SMVNM is less than the GG-SVNM and that the advantage of the GG-SMVNM on mapping costs gets more obvious with the increase in the number of simultaneously arriving VNs. This is because when there are several VNs simultaneously arriving, one physical node may host more than one virtual node because of the geographic location constraints of virtual nodes. Therefore, while using the GG-SMVNM for mapping the multiple arrived VNs, the new VN generated according to the mapping solutions for mapping multiple VNs onto the physical network is simpler than the multiple original VNs. Furthermore, the resource sharing in every VN and the node and link resource sharing across VNs can be realized when the GG-SMVNM performs the mapping of backup nodes and links while at most one node fails in the physical network, whereas the node and link resource sharing only occurs in each VN in the GG-SVNM algorithm. Therefore, the mapping costs of multiple VNs achieved by using the GG-SMVNM algorithm are less than that of the GG-SVNM algorithm.

Fig. 6

Mapping costs vs. number of VNs. a Simulation results on Net-1. b Simulation results on Net-2

Furthermore, Fig. 7 shows the simulation results on total mapping costs under various reliability requirements. For a specific reliability requirement, our proposed algorithms have lower total mapping costs than the existing approach since our approaches can efficiently deploy the arrived virtual network requests and thus consume less physical network resources. Moreover, the mapping costs of the compared algorithms increase with the increasing reliability requirements since it is necessary to allocate greater and more expensive resources for a VN request with higher reliability demand to guarantee the reliability.

Fig. 7

Mapping costs vs. different reliability requirements. a Simulation results on Net-1. b Simulation results on Net-2

Figure 8 depicts the backup nodes’ mapping costs in the GG-SVNM, GG-SMVNM, and EVPF algorithms for multiple VNs. Figure 9 shows the physical resource costs for mapping the backup links of VNs using the EVPF, GG-SVNM, and GG-SMVNM algorithms, respectively. We can see from Figs. 8 and 9 that the GG-SMVNM algorithm achieves the lowest costs as the number of VNs increases. Furthermore, compared with the advantage in backup node mapping costs, the advantage in backup link mapping costs is more obvious. By analyzing the reason for this simulation result, as we said before, the resource sharing is in each VN, and the node and link resource sharing occurs across VNs while using the GG-SMVNM algorithm. Since the geographic location constraints and virtual nodes from different VNs may be abstracted to a new virtual node, the backup node resource sharing in VNs can be realized. In comparison, the backup link mapping is much more complicated and the probability of sharing resources among backup links of different VNs is much higher. Therefore, more resource sharing opportunities exist in the GG-SMVNM algorithm than in the GG-SVNM algorithm, which leads to lower mapping costs.

Fig. 8

Mapping costs for backup nodes. a Simulation results on Net-1. b Simulation results on Net-2

Fig. 9

Mapping costs for backup links. a Simulation results on Net-1. b Simulation results on Net-2

Figure 10 shows the simulation results on the average deployment time of the GG-SVNM, GG-SMVNM, and EVPF algorithms for multiple VN requests. In this set of simulations, we evaluate the performance of the compared algorithms under different numbers of VN requests and calculate the average value to eliminate the randomness and output it as the result. From the figure, we can see that our proposed GG-SMVNM algorithm has the lowest time complexity, whereas the EVPF has the worst time efficiency. Since an efficient routing strategy is used in our proposed algorithm, it can be used to quickly map a VN link onto a feasible physical path.

Fig. 10

Simulation results for deployment time. a Simulation results on Net-1. b Simulation results on Net-2

The simulation results shown in Fig. 11 evaluate the blocking ratios of the compared algorithms in different scenarios. The blocking ratio is defined as the number of blocked/rejected virtual network requests to the number of total arrived VN requests. The blocking ratios increase with the growth of the number of arrived VNs, since more VN requests means more resource consumption. However, the blocking ratios remain stable when the number of arrived VN requests is more than 4000. The blocking ratio of our proposed algorithm is lower than that of the existing approach EVPF, since our approaches consume less physical network resources while guaranteeing the same level of reliability of VN requests, thus lowering the blocking ratio.

Fig. 11

Simulation results on blocking ratio. a Simulation results on Net-1. b Simulation results on Net-2


In this paper, we propose a survivable VN mapping algorithm (GG-SMVNM) that considers the geographic location constraints of virtual nodes for efficiently mapping multiple VNs in edge-of-things computing. We introduce the resource sharing strategy in VNs and also across multiple VNs to save the physical resources of edge-of-things computing and reduce the mapping costs. Furthermore, the geographic location constraints are considered in both original virtual nodes mapping and backup node mapping, which makes significant sense in real edge-of-things computing applications. We conduct extensive simulations on different networks to evaluate our proposed algorithms. The simulation results show that our proposed algorithm has better performance than existing approaches.

In this research, we mainly focus on the problem of provisioning VN requests with location constraints in an autonomous domain network in edge-of-things computing. However, in practical applications, there are some VNs need to be deployed onto multiple autonomous domain networks. Therefore, in our future research, we are going to study and solve the problem of reliable VN mapping in multiple domains while considering the quality of service (QoS) requirements.


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This research was partially supported by the Fundamental Research Funds of China West Normal University (No.17D075).

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SZ is in charge of the major theoretical analysis, algorithm design, and numerical simulations. AKS is in charge of part of the theoretical analysis and algorithm design. Both authors read and approved the final manuscript.

Correspondence to San-mei Zhang.

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  • Network virtualization
  • Reliability
  • Mapping
  • Edge-of-things computing