**4. Taxonomy**

Much work is still needed in identifying the features of good performing heuristics to allocate

Under dynamic operation, as a result of the resource release from virtual network that depart from the network, voids in the spectrum are generated. A void is a set of contiguous available FSUs between portions of allocated FSUs (or between a portion of allocated FSUs and the

Due to the FSU contiguity constraint, the existence of these voids is problematic, as they frag‐ ment the spectrum. As a result, a virtual link could not be implemented due to the lack of enough contiguous FSUs, leading to a higher blocking ratio. For example, in the situation depicted in **Figure 4**, although three FSUs are available, a virtual link requiring three FSUs

virtual networks as well as evaluating the performance of meta‐heuristics.

**3.5. Spectrum fragmentation**

30 Optical Fiber and Wireless Communications

**Figure 4.** Spectrum fragmentation.

beginning/end of the band), as shown in **Figure 4**.

could not be established because of the contiguity constraint.

**Figure 5** shows a comprehensive classification of the resource allocation algorithms in the area of network virtualization over flexible‐grid optical networks. The taxonomy includes current proposals, but it is generic enough as to include algorithms not studied yet.

In the taxonomy, each possible algorithm is defined by three main dimensions: its perfor‐ mance metric, its operation conditions and the type of service offered to the user. In the fol‐ lowing each of these dimensions are described as well as the different choices available in each one of them.

### **4.1. Performance metric**

The most commonly used performance metric in the literature is the blocking ratio [46–56, 64]. Although the use of the same metric would facilitate comparison, due to the different assumptions made on the physical and virtual topologies, a direct comparison is not always possible.

The variant of blocking, first blocking, has been used in Refs. [48, 49]. Remaining metrics used in reported works are the traffic carried by the physical networks [54, 57–59] and cost‐related metrics [46, 56, 61, 62].

Although published works do not explicitly mention the performance metric of availability, few works make assumptions on the operation conditions of the network that allow guaran‐ teeing 100% availability. In Refs. [53, 59, 61, 62], only single link failures are assumed. Thus, the allocation of two link‐disjoint spectrum paths to implement each virtual link is enough to ensure the operation of every virtual network. In Ref. [49], single link/node failures are assumed and, then by allocating two node/link‐disjoint spectrum paths to each virtual link, a 100% availability is provided. Note that if the system violates the assumptions on the type of failure that can occur (e.g. a double link failure occurs in a system designed to tolerate single link failure), 100% availability cannot be guaranteed anymore.

**Figure 5.** Taxonomy of network virtualization algorithms over optical flexible‐grid networks.

Guaranteeing availability under any type of failure has not been researched in the area of network virtualization over flexible‐grid networks neither the combination of quality and cost performance metrics.

#### **4.2. Operation**

#### *4.2.1. Information management*

To date, all proposals implicitly assume centralized information management [46–59, 61, 62, 64]. That is, a central entity has global knowledge of the network status and the resource allocation algorithm is executed every time a new virtual network request is generated. In fact, the first proposals for architecture with a virtual network controller are based on a centralized scheme, as the one proposed in Ref. [74]. Centralized systems are suitable when the time between suc‐ cessive requests is long enough for the central controller to execute the resource allocation algorithm.

In Ref. [75], different distributed virtual network allocation approaches are discussed in the context of packet networks. Results show that a distributed operation reduces the delay in mapping a virtual network and the number of messages required to be exchange to coor‐ dinate the allocation. In Ref. [76], the impact of a distributed virtual network reconfigura‐ tion approach on the interruption time of the service is studied in the context of fixed‐grid networks. Although the distributed operation has advantages in terms of resilience against failures, lower computation times and network congestion due to message exchange, it has increased complexity in terms of control plane network (more controllers), synchronization of messages and a potential decreased performance due to the obsolescence of information. These aspects are yet to be studied in network virtualization systems over flexible‐grid networks.

#### *4.2.2. Resource allocation strategy*

Guaranteeing availability under any type of failure has not been researched in the area of network virtualization over flexible‐grid networks neither the combination of quality and cost

**Figure 5.** Taxonomy of network virtualization algorithms over optical flexible‐grid networks.

To date, all proposals implicitly assume centralized information management [46–59, 61, 62, 64]. That is, a central entity has global knowledge of the network status and the resource allocation algorithm is executed every time a new virtual network request is generated. In fact, the first proposals for architecture with a virtual network controller are based on a centralized scheme,

performance metrics.

*4.2.1. Information management*

32 Optical Fiber and Wireless Communications

**4.2. Operation**

The virtual network allocation strategy must consider two aspects: the method used to solve the problem of embedding the virtual network on the physical network and the model used to characterize the constraints of the physical substrate.

There are three general methods to solve the problem of the virtual network embedding:


Normally, heuristics designed to solve complex problems, divide the original problem in sub‐ problems easier to solve separately. This approach is applied in this area as well. The original problem of mapping a virtual network is divided in node mapping (allocation of a physical node to a virtual node) and link mapping (allocation of a spectrum path to a virtual link). Most proposals map nodes first to then establish the virtual links connecting them [46–48, 50, 51, 53, 54, 56, 58, 62, 64].

To map the nodes and links, the heuristic must define the order in which the virtual and physical nodes/links are processed. To do so, a ranking is elaborated for each set of physical/ virtual nodes/links and the first element in the ranking of virtual nodes/links is attempted to be mapped in the first element of the ranking of the physical nodes/links. The most common criterion to build the physical node ranking is the amount of available resources [48, 49, 58]. A function of the computing capacity and the nodal degree [50], a function of the number of sub‐carriers of each transponder in the physical node and the slice capability of the physical node [46] and the node index [64] have also been used. Criteria to rank the virtual nodes are the amount of resources required [48, 58], the nodal degree [50] or the node index. The case where the virtual nodes must be established in specific physical nodes (defined in the virtual network establishment request), as in Ref. [47], is a particular case of a node/link mapping, as all virtual nodes are established in the specified physical nodes (if enough resources are avail‐ able) before establishing the virtual links.

Physical links can be ranked in terms of their distance [48, 50, 58], cost [64] or number of avail‐ able FSUs. Finally, virtual links are ranked in terms of their FSU requirements [47, 53, 58, 64].

Given that the solution found by solving the node/link mapping sub‐problems sequentially is expected to be of lower quality than solving the original problem, an attempt to solve both problems jointly was proposed in Refs. [53, 55, 57, 59]. In these works, a sub‐set of all possible mapping patterns for the nodes of a virtual network are evaluated and the one using the lowest slot layer (slot layer of a mapping pattern is the highest FSU used) [57], lowest cost [53] or best Hamming‐inspired distance [55] is selected.

Finally, the approach of alternating the allocation of virtual nodes and links (mixed) has also been studied in Refs. [48, 49, 52, 61, 62, 64]. For example, in Ref. [61], the virtual nodes at the ends of each virtual link are mapped to then map the virtual link, showing results close to the ILP approach in a static scenario.

Apart from the FSU continuity and contiguity constraints, the solution methods can use one of several models to characterize additional constraints of the physical substrate. To date, the following models have been used:


**d.** Optical reach and guard band, where the optical reach is determined by the modulation format and the bit rate. Since the optical reach can decrease due to effect of neighbouring signals, by adding (selectively or not) guard bands between channels [47, 52, 55, 64] such detrimental effect can be mitigated.

#### *4.2.3. Traffic management*

Normally, heuristics designed to solve complex problems, divide the original problem in sub‐ problems easier to solve separately. This approach is applied in this area as well. The original problem of mapping a virtual network is divided in node mapping (allocation of a physical node to a virtual node) and link mapping (allocation of a spectrum path to a virtual link). Most proposals map nodes first to then establish the virtual links connecting them [46–48, 50,

To map the nodes and links, the heuristic must define the order in which the virtual and physical nodes/links are processed. To do so, a ranking is elaborated for each set of physical/ virtual nodes/links and the first element in the ranking of virtual nodes/links is attempted to be mapped in the first element of the ranking of the physical nodes/links. The most common criterion to build the physical node ranking is the amount of available resources [48, 49, 58]. A function of the computing capacity and the nodal degree [50], a function of the number of sub‐carriers of each transponder in the physical node and the slice capability of the physical node [46] and the node index [64] have also been used. Criteria to rank the virtual nodes are the amount of resources required [48, 58], the nodal degree [50] or the node index. The case where the virtual nodes must be established in specific physical nodes (defined in the virtual network establishment request), as in Ref. [47], is a particular case of a node/link mapping, as all virtual nodes are established in the specified physical nodes (if enough resources are avail‐

Physical links can be ranked in terms of their distance [48, 50, 58], cost [64] or number of avail‐ able FSUs. Finally, virtual links are ranked in terms of their FSU requirements [47, 53, 58, 64]. Given that the solution found by solving the node/link mapping sub‐problems sequentially is expected to be of lower quality than solving the original problem, an attempt to solve both problems jointly was proposed in Refs. [53, 55, 57, 59]. In these works, a sub‐set of all possible mapping patterns for the nodes of a virtual network are evaluated and the one using the lowest slot layer (slot layer of a mapping pattern is the highest FSU used) [57], lowest cost [53] or best

Finally, the approach of alternating the allocation of virtual nodes and links (mixed) has also been studied in Refs. [48, 49, 52, 61, 62, 64]. For example, in Ref. [61], the virtual nodes at the ends of each virtual link are mapped to then map the virtual link, showing results close to the

Apart from the FSU continuity and contiguity constraints, the solution methods can use one of several models to characterize additional constraints of the physical substrate. To date, the

**b.** Optical‐reach‐based, this is the simplest model where the maximum distance covered by a spectrum path is determined solely by the modulation format and the bit rate, as in Refs.

**c.** Guard‐band‐based, where a given number of FSUs might be left unused between channels

51, 53, 54, 56, 58, 62, 64].

34 Optical Fiber and Wireless Communications

able) before establishing the virtual links.

Hamming‐inspired distance [55] is selected.

ILP approach in a static scenario.

following models have been used:

[48, 49, 51, 53, 57, 61, 62].

**a.** Ideal, where no signal degradation is assumed [50, 54].

of different bit rate, as in Refs. [46, 56, 58, 59].

In the context of packet networks, the split of traffic of a virtual link into several paths in the physical substrate has been proposed as a way of increasing the probability of accepting a virtual network establishment request [79]. In a flexible‐grid optical network where a virtual link requiring *M* contiguous FSUs must be established but no path has more than *x* < *M* contiguous FSUs, such situation could be solved by establishing the virtual link along several spectrum paths in such a way that the total number of FSUs used along all the paths equal *M* . Such mechanism could be enabled by recently introduced sliceable or multi‐flow transpon‐ ders [80, 81]. This approach has not been explored in the area of network virtualization over flexible‐grid networks.

#### **4.3. Type of service**

#### *4.3.1. Service nature*

The service provider can offer a static or dynamic service. In the former case, the virtual net‐ work demands are known *a priori* and they are established permanently, whether they are used to transmit information or not [58, 59, 61, 62, 64]. In the latter case, virtual networks are established and released on demand.

In a dynamic service, spectrum experiences fragmentation. As a result, even when there is an enough number of FSUs to accommodate a new virtual network, these FSUs might not meet the contiguity constraint, leading to the rejection of requests. To decrease spectrum fragmen‐ tation, some dynamic systems reconfigure the established connections. Several works have evaluated the impact of reconfiguration on point‐to‐point connections on flexible‐grid opti‐ cal networks [68–72]. As expected, reconfiguration decreases blocking [54] at the expense of higher complexity of the control plane.

There are two types of reconfiguration techniques: proactive or reactive [82]. The former re‐allocate resources before a blocking condition occurs, either in a synchronous or asynchro‐ nous way. In Refs. [69–71], pro‐active reconfiguration algorithms are presented for point‐to‐ point connections over flexible‐grid optical networks. Reconfiguration may take place every time a given number of virtual networks request has been received. No proactive systems have been reported in network virtualization over flexible‐grid networks. Reactive recon‐ figuration techniques re‐allocate resources only when a new request cannot be accepted. In Ref. [54], a reactive reconfiguration method to re‐allocate virtual networks over fixed‐grid networks is presented, getting lower rejection rates than not reconfiguring at low‐medium loads.

Reconfiguration can be applied at two different levels: re‐allocation of complete virtual networks or re‐allocation of a sub‐set of virtual links/nodes, as in Ref. [54] in flexible‐grid networks or [83] in fixed‐grid networks. None of these cases has been studied in network virtualization systems over flexible‐grid optical networks.

#### *4.3.2. Fault tolerance*

A network virtualization service can offer different levels of fault tolerance: zero, specific or guaranteed. Most works reported to date have studied systems without fault tolerance at all [46–48, 50–52, 54–58, 64]. In that case, the occurrence of any type of failure interrupts the oper‐ ation of the virtual networks operating over the physical component affected by the failure. A specific survivability system is capable of continuing operation in spite of the occurrence of specific types of failures. Normally, these systems are designed to survive the most common failure events (e.g. a cable cut) and remain unprepared for unlikely events (as a node failure). In the area of network virtualization over flexible‐grid networks, the algorithm proposed in Refs. [53, 59, 61, 62] can survive only to single link failures, whereas Ref. [49] can survive single link or node failure. Finally, a guaranteed survivability system ensures that limits on downtime are not exceed, no matter what the type of failure, as done in Refs. [84, 85] in a con‐ text different from network virtualization. If such condition is violated, the service provider is enforced to pay an economic compensation to the user. Such approach has not been explored in the area of network virtualization over flexible‐grid networks.

Fault tolerance mechanisms can also be classified as proactive (protected systems) or reac‐ tive (restored systems). Protected systems allocate backup resources when the primary resources for the virtual network are allocated [49, 53, 59, 61, 62]. Therefore, upon failure occurrence, the time to recover from failure is shorter than reactive systems. Protected sys‐ tems can allocate a complete backup virtual network (total protection) [49] or backup to some components (partial protection, e.g. only virtual links have backup resources) [53, 59, 61, 62]. Protected systems can also be classified as dedicated or shared. In the former, backup resources are dedicated to the corresponding primary resource. In the latter, a backup resource is shared among several primary resources. No research has been reported on the area of shared protection for virtual networks over flexible‐grid networks. Restored systems allocate resources to the virtual networks affected by a failure only once the failure has occurred; as a result, the recovery time is longer, but a lower amount of backup resources are required. Restoration can be carried out for complete virtual networks or only for the part of them affected by the failure. Restoration on virtual networks over flexible‐grid networks has not been researched yet.

#### *4.3.3. Revisitation*

Revisitation allows the establishment of two virtual nodes from the same virtual network in the same physical node [16]. Revisitation has been proposed in the context of overlay networks [86] as a way of emulating larger networks on small testbeds. In virtual network systems over flexible‐grid networks, revisitation has been used in Ref. [64] and the impact of it on blocking was studied in Ref. [52] showing a decrease of blocking ratio of two orders of magnitude with respect to the same algorithm without revisitation.

Revisitation has been little researched in the literature, probably because a real application for it has not been found yet. For example, for research on new Internet protocols, delay and bandwidth utilization are two key metrics that could not be measured if two virtual nodes are hosted in the same physical node. For cloud replication services would not be useful either, as the replicas must be allocated to geographically different sites. However, it is mentioned as one of the four key architectural principles of network virtualization in Ref. [16], where it would be useful to help the service providers to manage highly complex tasks and facilitate virtual networks management.

networks or [83] in fixed‐grid networks. None of these cases has been studied in network

A network virtualization service can offer different levels of fault tolerance: zero, specific or guaranteed. Most works reported to date have studied systems without fault tolerance at all [46–48, 50–52, 54–58, 64]. In that case, the occurrence of any type of failure interrupts the oper‐ ation of the virtual networks operating over the physical component affected by the failure. A specific survivability system is capable of continuing operation in spite of the occurrence of specific types of failures. Normally, these systems are designed to survive the most common failure events (e.g. a cable cut) and remain unprepared for unlikely events (as a node failure). In the area of network virtualization over flexible‐grid networks, the algorithm proposed in Refs. [53, 59, 61, 62] can survive only to single link failures, whereas Ref. [49] can survive single link or node failure. Finally, a guaranteed survivability system ensures that limits on downtime are not exceed, no matter what the type of failure, as done in Refs. [84, 85] in a con‐ text different from network virtualization. If such condition is violated, the service provider is enforced to pay an economic compensation to the user. Such approach has not been explored

Fault tolerance mechanisms can also be classified as proactive (protected systems) or reac‐ tive (restored systems). Protected systems allocate backup resources when the primary resources for the virtual network are allocated [49, 53, 59, 61, 62]. Therefore, upon failure occurrence, the time to recover from failure is shorter than reactive systems. Protected sys‐ tems can allocate a complete backup virtual network (total protection) [49] or backup to some components (partial protection, e.g. only virtual links have backup resources) [53, 59, 61, 62]. Protected systems can also be classified as dedicated or shared. In the former, backup resources are dedicated to the corresponding primary resource. In the latter, a backup resource is shared among several primary resources. No research has been reported on the area of shared protection for virtual networks over flexible‐grid networks. Restored systems allocate resources to the virtual networks affected by a failure only once the failure has occurred; as a result, the recovery time is longer, but a lower amount of backup resources are required. Restoration can be carried out for complete virtual networks or only for the part of them affected by the failure. Restoration on virtual networks over flexible‐grid networks

Revisitation allows the establishment of two virtual nodes from the same virtual network in the same physical node [16]. Revisitation has been proposed in the context of overlay networks [86] as a way of emulating larger networks on small testbeds. In virtual network systems over flexible‐grid networks, revisitation has been used in Ref. [64] and the impact of it on blocking was studied in Ref. [52] showing a decrease of blocking ratio of two orders of magnitude with

virtualization systems over flexible‐grid optical networks.

in the area of network virtualization over flexible‐grid networks.

*4.3.2. Fault tolerance*

36 Optical Fiber and Wireless Communications

has not been researched yet.

respect to the same algorithm without revisitation.

*4.3.3. Revisitation*

In **Table 2**, a summary of the virtual network resource allocation proposed to date is presented. For each algorithm, all the dimensions presented in the taxonomy of **Figure 5** are specified.



**Table 2.** Summary of the characteristics of the algorithms reviewed.
