1. Introduction

Within the enterprise data centers, traffic patterns are found to change significantly. Both the explosion of mobile application and the advent of server virtualization are driving the elastic networking industry to reexamine the traditional optical network architecture. Cloud services claim the nework resources to be virtualized and to be shared on the common underlying substrate infrastructure. Optical network virtualization enables network operators to partition their physical infrastructures into virtual optical networks (VONs) based on the application requirements and simplifies optical-layer resource management. Data centers also become an efficient infrastructure for supporting data storage and provide the diversified network services and applications. In order to preferably suit for the application service requirements, we can converge flexible bandwidth optical networks and data centers as a network service infrastructure. Meanwhile, optical network virtualization supports flexible resources scheduling and optimizes network fuction configuration. However, there are some great challenges about the network resources virtualization over the optical networks with data centers, such as the energy efficiency of VON mapping and how to map a given set of VONs.

In previos studies, two important aspects about the VON mapping problems are disscussed as follows. For VON mapping problem, a mixed integer programming model is developed to improve the efficient utilization of networking resources by employing the traffic-matrix-based VON mapping [1]. In cloud computing environments, the authors in [2] address the role of high-performance dynamic optical networks. Also, the concept of the virtualized data centers is proposed to provide the excellent management flexibility at low cost and high energy efficiency [3]. The minimum-cost survivable virtual optical network mapping is developed to minimize the network cost in flexible bandwidth optical networks [4]. The VON mapping algorithms are also proposed to minimize power consumption in the converged data centers and elastic optical networks [5]. Also, several virtual network embedding algorithms with the coordinated node and link mapping are proposed to decrease the cost incurred in the substrate network [6]. The survivable impairment-aware virtual optical network mapping problem is investigated to minimize the total cost of transponders and regenerators [7]. The heuristic impairment-aware VON mapping algorithms are investigated to improve the cost efficiency in single-line-rate and mixed-line-rate WDM networks [8].

Virtual infrastructure planning problems are investigated to reduce the power consumption and to minimize the wavelength utilization in the converged optical networks and data centers [9]. A novel dynamic virtual infrastructure planning approach is proposed to reduce the blocking rate in the converged optical network and data centers [10]. Also, a mixed integer linear programming model is proposed to minimize the energy consumption over a converged physical infrastructure incorporating integrated optical network and IT resources [11]. In order to handle the increased communication bandwidth of emerging applications, the cost and the power consumption are discussed by surveying optical interconnects for data centers [12]. To minimize blocking probability of cloud service requests, a survivable algorithm with the spectrum-shared ability is proposed to address the above problems in flexible bandwidth optical networks with distributed data centers interconnection [13].

Differentiating the above studies, we consider the virtual link or virtual node priority mapping in this paper. Moreover, we develop the architecture of optical network virtualization that consists of the flexible bandwidth optical networks and data centers, address the VON-based energy efficiency problems, propose two different VON mapping approaches based on the priority of virtual nodes or virtual links, and introduce a lower bound. According to the proposed VON mapping approaches, the energy efficiency can be improved for a given set of VONs that are mapped to the converged flexible bandwidth optical networks and data centers.

The paper is organized as follows. Section 2 describes the network model and problem statement. Section 3 presents heuristic VON mapping approaches. The simulation results are discussed in Section 4, and the paper concludes in Section 5.

2. Network model and problem statement

2.1 Network model

An architecture of optical network virtualization is shown in Fig. 1, where the converged data centers and flexible bandwidth optical networks are depicted as a physical optical network, which is shown in Fig. 1(b). This physical optical network is represented as a directed graph $G^p(V^p,E^p,D^p)$, where$V^p$,$E^p$, and$D^p$represent a set of physical nodes, a set of physical links, a set of data centers. The n^th physical node $V_n^p\in V^p$corresponds to an optical switch node that contains optical transponders and optical regenerators, to which a data center is attached. The n^th physical link $E_n^p\in E^p$is an optical fiber cable with sufficient spectrum resources, where all optical fibers in an optical fiber cable support several line rates with different modulation formats and placing an in-line erbium-doped optical fiber amplifier (EDFA) after every 80 km in each fiber link. The n^th data center$D_n^p\in D^p$provides computing resources with the limited capacity. A set of VONs is represented by a directed graph $G^v(V^v,E^v)$in Fig. 1(a). The i^th VON is denoted as a directed graph$G_i^v(V_i^v,E_i^v)$, where$V_i^v$and$E_i^v$denote a set of virtual nodes and a set of virtual links. Suppose that the j^th virtual node$V_{i,j}^v\in V_i^v$ is a virtualized data center on the i^th VON. The j^th virtual node $V_{i,j}^v$on the i^th VON is mapped to a physical node $V_n^p$when the available computing resources on$V_n^p$are sufficient for the computing resources required by$V_{i,j}^v$. The j^th virtual link$E_{i,j}^v\in E_i^v$represents the bandwidth requirements between the virtualized data centers. This virtual link is also mapped to a physical path when the spectrum resources on this physical path are enough to support the spectrum resources required on this virtual link. In this study, we assume that there are sufficient spectrum resources on each physical link that represents an optical fiber cable in the converged flexible bandwidth optical networks and data centers. To evaluate the power consumption of the considered flexible bandwidth optical network, we sum up the power consumption of three different types of optical components that contain optical transponders, regenerators, and EDFAs for different line rates, since these types of optical components depend on the line rate and spectrum width.

 

Fig. 1 An architecture of optical network virtualization for two VON requests (a) and the converged flexible bandwidth optical networks and data centers (b).

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2.2 Problem statement

We consider a static traffic demand scenario, under which the number of the VON requests is given in advance. Our objective is to minimize the total power consumption for a given set of VONs that are mapped to the converged flexible bandwidth optical networks and data centers. The statement of the problem is as follows: given a flexible bandwidth optical network that converges data centers,$G^p(V^p,E^p,D^p)$, a set of VON requests,$G^v(V^v,E^v)$, a set of different line rates, R = {r₁, r₂,…, r_N}, where N is the total number of line rates, a set of modulation formats, M = {m₁, m₂,…, m_N}, a set of maximum reachability of optical signal corresponding to different line rates, B = {b₁, b₂,…, b_N}, a set of power consumption of transponders at the different line rates, Ψ = {ψ¹, ψ²,…, ψ^N}, a set of unit power of regenerators corresponding to several line rates, Φ = {Φ¹, Φ²,…, Φ^N}, and a set of unit power of EDFAs corresponding to several line rates, Ω = {ω¹, ω²,…, ω^N}.The reachability of an optical channel is determined by the line rate, spectrum channel width, and modulation format. An in-line EDFA is placed on a fiber link after every 80 km. For a VON, we need to find optimal virtual nodes mapping and virtual links mapping. Also, optical regenerators are placed along a path if this path length exceeds the reachability of the optical signal, where the reachability of a lightpath is determined by the line rate, spectrum width, and modulation format. Therefore, we propose two virtual optical network mapping approaches to improve the energy efficiency for a given set of VONs in the converged flexible bandwidth optical networks and data centers, and for comparsion we introduce a lower bound as the benchmark solutions.

3. Heuristic VON mapping approaches

The power consumption is determined by the number of network components used, where the network components include optical transponders, optical regenerators, and EDFAs. We can improve energy efficiency by attempting to reduce the usage of optical transponders, optical regenerators, and EDFAs on the converged flexible bandwidth optical networks and data centers. Both the number of regenerators and the number of EDFAs are related to the transmission distance along a physical path on the flexible bandwidth optical network and depend on the optical signal reachability of the different line rates and modulation formats. The energy efficiency is improved by reducing the transmission distance of a physical path that is mapped by a virtual link for a VON. Thus, in order to simplify mapping a set of VONs to the converged flexible bandwidth optical networks and data centers, we preconfigure all shortest paths for all node-pairs and calculate the total distance for an arbitrary physical node-pair (k, l) on physical optical network. Therefore, an auxiliary graph (AG) needs to be constructed by using the distance of two arbitrary nodes k and l as the weight of a link (k, l) on physical optical network. We develop two heuristic VON mapping approaches to optimize the power consumption in the converged flexible bandwidth optical networks and data centers. One is the virtual link priority mapping (LPM) approach that considers the granularity of bandwidth requirement for each virtual link on a VON. The other is the virtual node priority mapping (NPM) approach that considers computing resources requirements of each virtual node. For comparison with the LPM and NPM approaches, the VON-mapped lower bound is also developed and its power consumption is defined as the benchmark solutions. The heuristic VON mapping approaches are described as follows.

3.1 LPM approach

For the LPM approach, we first construct an auxiliary graph of all physical node-pairs based on the shortest path algorithm in the converged flexible bandwidth optical networks and data centers. Second, all virtual links$\{E_1^v,E_2^v,\mathrm{...},E_N^v\}$ on the n^th VON $G_n^v(V_n^v,E_n^v)$are sorted in a descending order based on the amount of their bandwidth requirements, where N is the total number of virtual links on this VON. All virtual links on the n^th VON are mapped to the physical links according to the principle of mapping the virtual links with the highest bandwidth requirements to the physical links with the shortest distance on the constructed auxiliary graph of the converged flexible bandwidth optical networks and data centers. Note that one virtual node is mapped to one physical node if and only if the required computing resources are fewer than the computing resources provided on the physical node, and no two virtual nodes are mapped to the same physical node for the n^th VON. One virtual node with the largest computing resource requirements is mapped to one physical node with the largest available computing resource provisioning if two virtual nodes i and j are mapped to the physical optical network at the same time. Third, considering both the descending order of the bandwidth requirements and the topological connectivity of the n^th VON, we map the virtual links that are not yet mapped by extending a physical link from the already mapping physical nodes to the non-mapping physical nodes, which ensures the chosen physical link on the constructed auxiliary graph is the shortest distance. Finally, we select proper line rates$\chi =\left\{r_1,r_2,\dots ,r_{\left|R\right|}\right\}$to carry the bandwidth requirements of one virtual link (i, j) on the n^th VON, where |R| is the number of line rates. We compute the total power consumption based on the number of transponders, the number of regenerators, and the number of EDFAs, after that all virtual links on the i^th VON are mapped to the physical links on the constructed auxiliary graph. The LPM approach is described as Table 1.

Table 1. The LPM approach

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An example of the LPM approach shows how to map a VON to a physical optical network in Fig. 2. For a VON request in Fig. 2(a), the numbers on red octagons and the numbers on virtual links denote the required computing resources of virtual nodes and the bandwidth requirements. An auxiliary graph in Fig. 2(b), is constructed by using the converged flexible bandwidth optical networks and data centers in Fig. 1(b), where the number on green cycles are the available computing resources of data centers and the numbers on physical links denote the total distance (km) of a path between a physical node k and physical node l. The mapping orders of virtual links, (A, B) with 400 Gbps, (A, C) with 100 Gbps, and (B, C) with 40 Gbps, are according to descending order of bandwidth requirements. The virtual link (A, B) with 400 Gbps is first mapped to the physical link (3, 4) with 700 km, and virtual nodes A and B are mapped to the physical nodes 3 and 4 according to the principle of virtual node A with the largest computing resource requirement (8 unit computing resources)is mapped to physical node 3 with the largest available computing resource (17 unit computing resources) in Fig. 2(c). The second mapping order is the virtual link (A, C) with 100 Gbps, where virtual node A has been mapped to physical node 3 and virtual node C is not been mapped yet. In order to map virtual link (A, C), a physical link with the shortest distance is found from the physical node 3 to one of physical nodes that are not been mapped by any virtual node (1 and 2), to which this virtual link is mapped, since virtual node A has been mapped to physical node 3. We select the physical link (3, 2) as the mapping physical link of virtual link (A, C) because its distance is shortest from node 3 to node 2 or from node 3 to node 1 on the constructed auxiliary graph in Fig. 2(d). Thus the virtual node C is mapped to the physical node 2. Finally, the physical link (4, 2) is used for the mapping virtual link (B, C) based on the topological connectivity of this VON in Fig. 2(e). Therefore, the total power consumption of this VON is calculated according to employ proper line rates and modulation formats to carry the bandwidth requirements of virtual links.

 

Fig. 2 A VON request (a), an auxiliary graph of the converged flexible bandwidth optical network and data centers (b), the LPM approach (c)-(e).

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3.2 NPM approach

For the NPM approach, there are three steps to achieve the n^th VON mapping. First, all virtual nodes on the n^th VON$G_n^v(V_n^v,E_n^v)$ are recorded by a descending order$\{V_{n,1}^v,V_{n,2}^v,\mathrm{...},V_{n,\left|V_n^v\right|}^v\}$ based on the amount of their computing resource requirements, and the physical nodes are also sorted in a descending order$\{V_1^p,V_2^p,\mathrm{...},V_{\left|V^p\right|}^p\}$ with the available computing resources provisioning on the converged flexible bandwidth optical networks and data centers. Second, the i^th virtual node $V_{n,i}^v$on the n^th VON is one-by-one mapped to the u^th physical node on the constructed an auxiliary graph by the mapping principle $\{V_{n,i}^v\to V_u^p\}$when the computing resources provisioning by a physical node $V_u^p$exceed the computing resource requirements of the i^th virtual node$V_{n,i}^v$on the n^th VON. Finally, all virtual links on the n^th VON are mapped to the physical links based on the topological connectivity of this VON on the constructed an auxiliary graph. After all virtual nodes and all virtual links are mapped to the physical nodes and physical links on the constructed an auxiliary graph, we employ the proper line rates, modulation formats, and spectrum width to carry the bandwidth requirement of virtual links. The total power consumption is calculated by the number of transponders, the number of regenerators, and the number of EDFAs. The NPM approach is described as Table 2.

Table 2. The NPM approach

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An example of the NPM approach is show in Fig. 3. We record the descending order based on the computing resource requirements of virtual nodes {C, A, B} in Fig. 2(a), since their computing resource requirements are 10 units, 8 units, and 5 units. In Fig. 2(b), the descending order of physical nodes is also sorted by {1, 3, 2, 4} based on their available computing resources provided that are 20 units, 17 units, 15 units, and 10 units, respectively. Thus virtual nodes C, A, and B are first mapped to the physical nodes 1, 3, and 5 one by one in Fig. 3(a). After that, all virtual links (A, B), (A, C), and (B, C) based on the topological connectivity of this VON are mapped to the physical links (3, 2), (3, 1), and (2, 1) on the constructed an auxiliary graph in Fig. 3(b). We employ the proper line rates, modulation formats, and spectrum width to carry the bandwidth requirements of virtual links (A, B) with 400 Gbps, (A, C) with 100 Gbps, and (B, C) with 40 Gbps.

 

Fig. 3 Example of the NPM approach.

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3.3 Lower bound

In order to evaluate the LPM approach and the NPM approach, we derive a lower bound of power consumption for a given set of VONs that are mapped to the physical network, which is found as follows. (1) We relax the constraint that one virtual node is only mapped to one physical node for a VON, and we also relax no capacity constraint on computing resources at physical nodes, i.e., an arbitrarily virtual node can be mapped to all physical nodes. (2) The virtual links with descending bandwidth requirement are recorded for a VON. They are one-by-one mapped to one physical link without deleting already mapped physical nodes and physical links on AG, where each line rates are checked, and the total power consumption is then obtained. Note that the lower bound of power consumption may not be achievable for a VON that is mapped to a physical network, since it allows multiple virtual nodes to be mapped to the same physical node, a virtual node to be mapped to multiple physical nodes, or different virtual links to be mapped to the same physical link.

4. Simulation results

We evaluate the performance of the LPM approach, the NPM approach, and lower bound on the NSFNET topology in Fig. 4. Each frequency slot corresponds to a 12.5 GHz spectrum width. The network profiles are given in Table 3. The power consumption of each EDFA is assumed as 100 watts (W) that including the normal working power with 30 watts for each fiber and overhead power consumption with 70 watts per amplifier location [14]. Suppose that there are 40 optical channels on each fiber link and each optical channel has 50 GHz spectrum width. By employing the basic idea of the hardware resource virtualization in [15], the power consumption for sliceable EDFAs of DP-QPSK with 25 GHz spectrum width, DP-QPSK with 37.5 GHz spectrum width, and DP-16-QAM with 125 GHz spectrum width is 1.3 W, 1.9 W, and 6.3 W, respectively. For each VON, the number of virtual links, on which the required bandwidths are uniformly distributed within [200, 500] Gbps, is seven and the number virtual nodes is five. Each virtual node requires the computing resources within [5, 10] units. Each of the data centers provides 200 units of computing resources. For each test point, we apply the NPM approach, the LPM approach, and the lower bound to 10 sets of VON demands, and average their results. Note that we only consider the single line rate for the VON mapping approaches in the simulation, such as 40 Gbps, 100 Gbps, and 400 Gbps.

 

Fig. 4 A NSFNET topology with 14 nodes and 21 links.

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Table 3. Network profiles

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In Fig. 5, we compare the power consumption of the NPM approach, the LPM approach, and lower bound. We can see that the LPM approach reduces 50%, 48%, and 48% power consumption than the NPM approach under 40 Gbps, 100 Gbps, and 400 Gbps line rates, respectively. The LPM approach also consumes much less the power consumption than the NPM approach, since the LPM approach considers the bandwidth requirements of virtual links when mapping the virtual links to the physical optical network, which ensures that the mapping physical path is the shortest distance and which uses fewer numbers of regenerators and EDFAs. Also, the power consumption of the LPM approach for 400 Gbps line rate is the lowest among all simulation results, since a higher line rate can reduce the number of the spectrum channels when splitting the bandwidth requirements of virtual link. Furthermore, the gap of power consumption between the LPM approach and a lower bound is gradually small when the bandwidth requirements are carried by high line rate, such as 400 Gbps line rate, since the lower bound may not be achievable when we map VONs to the physical network.

 

Fig. 5 Power consumption for the NPM approach, the LPM approach, and the lower bound versus the number of VONs.

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Figure 6 shows the energy efficiency of the NPM approach, the LPM approach, and lower bound versus the number of VONs under 40 Gbps, 100 Gbps, and 400 Gbps line rates. The energy efficiency of the LPM approach is very close to the results of the lower bound as the line rate increases, such as 400 Gbps line rate. Compared to the NPM approach, the energy efficiency reduces 52.1%, 50.3%, and 50.4% under 40 Gbps, 100 Gbps, and 400 Gbps line rates. The energy efficiency of the LPM approach outperforms that of the NPM approach at the same line rate. Furthermore, the energy efficiency of the NPM approach, the LPM approach, and lower bound does not change with the number of VONs, which is not sensitive to the number of VONs but which relates to line rates. Both the NPM and LPM approaches at 400 Gbps line rate have better energy efficiency than the line rates of 40 Gbps and 100 Gbps.

 

Fig. 6 Energy efficiency for the NPM approach, the LPM approach, and the lower bound versus the number of VONs.

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In Fig. 7, we compare spectrum usage for the NPM approach, the LPM approach, and lower bound in terms of the number of frequency slots. The number of frequency slots of the LPM approach reduces 40% compared to the NPM approach at 40 Gbps, 100 Gbps, and 400 Gbps line rates. Obviously, compared to the NPM approach, the LPM approach not only reduces power consumption but also consumes the fewer number of frequency slots. Figure 8 shows the effect of number of VONs on the number of regenerators. We observe that the LPM approach greatly reduces the number of regenerators compared to the NPM approach. Generally, compared to the NPM approach, the number of regenerators of the LPM approach saves 88.0%, 87.8%, and 84.5% for 40 Gbps, 100 Gbps, and 400 Gbps line rates. The reason is that the LPM approach finds the shortest distance on the physical optical network for each virtual link and employs the mapping principle of the largest bandwidth requirements of onevirtual link that is mapped to the path with the shortest distance on the constructed auxiliary graph. However, the number of the regenerators is the same for the lower bound, which does not change with the number of VONs, since all virtual links may be mapped to the physical links that are no need to be configured regenerators on these physical links.

 

Fig. 7 Spectrum usage for the NPM approach, the LPM approach, and the lower bound versus the number of VONs.

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Fig. 8 The number of regenerators for the NPM approach, the LPM approach, and the lower bound versus the number of VONs.

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5. Conclusions

In this paper, in order to improve the energy efficiency, we address the minimum power consumption problems over the converged flexible bandwidth optical networks and data centers. To simplify the VON mapping, an auxiliary graph of physical optical network is constructed by preconfigured the converged flexible bandwidth optical networks and data centers. We develop the LPM approach, the NPM approach, and the lower bound to minimize power consumption for a given set of VONs that are mapped to the constructed an auxiliary graph of physical optical network. Simulation results show that the LPM approach outperforms the NPM approach in the aspects of power consumption, energy efficiency, spectrum usage, and the number of regenerators. Also, the LPM approach becomes close to the lower bound when 400 Gbps line rate is used for carrying a given set of VONs.