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 edgeofthings 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.
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 GGSMVNM and GGSVNM 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.
The total VN mapping cost: the total expenses of using physical network resources to provide all VN requests. It can be calculated as follows:
$$ {M}_{\mathrm{cost}}^{\mathrm{total}}={\sum}_{i=1}^{\mid \mathrm{ArrivedVN}\mid }{M}_c^i, $$
(5)
where \( {M}_c^i \) represents the mapping cost of ith VN demand and ArrivedVN denotes the set of arrived VN demand.

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:
$$ {M}_{\mathrm{cost}}^{\mathrm{bakNode}}={\sum}_{i=1}^{\mid \mathrm{bakNode}\mid }{M}_{\mathrm{node}}^i, $$
(6)
where \( {M}_{\mathrm{node}}^i \) denotes the mapping cost of the ith backup virtual node and bakNode represents the set of backup virtual nodes.

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:
$$ {M}_{\mathrm{cost}}^{\mathrm{bakLink}}={\sum}_{i=1}^{\mid \mathrm{bakLink}\mid }{M}_{\mathrm{link}}^i, $$
(7)
where \( {M}_{\mathrm{link}}^i \) denotes the mapping costs of the ith 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 GGSMVNM and GGSVNM algorithms are lower than that of the existing EVPF approach [32]. Furthermore, the total mapping costs of multiple VNs of the GGSMVNM is less than the GGSVNM and that the advantage of the GGSMVNM 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 GGSMVNM 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 GGSMVNM 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 GGSVNM algorithm. Therefore, the mapping costs of multiple VNs achieved by using the GGSMVNM algorithm are less than that of the GGSVNM algorithm.
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.
Figure 8 depicts the backup nodes’ mapping costs in the GGSVNM, GGSMVNM, and EVPF algorithms for multiple VNs. Figure 9 shows the physical resource costs for mapping the backup links of VNs using the EVPF, GGSVNM, and GGSMVNM algorithms, respectively. We can see from Figs. 8 and 9 that the GGSMVNM 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 GGSMVNM 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 GGSMVNM algorithm than in the GGSVNM algorithm, which leads to lower mapping costs.
Figure 10 shows the simulation results on the average deployment time of the GGSVNM, GGSMVNM, 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 GGSMVNM 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.
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.