**3. Research challenges in virvtual network allocation over flexible‐grid optical networks**

In the following, the main challenges in the research area of network virtualization over flexible‐ grid optical networks are discussed.

#### **3.1. Performance metrics**

A performance metric allows defining the quality of an algorithm to carry out its task. Thus, usually the (single) objective of an algorithm is the maximization or minimization of a perfor‐ mance metric. However, for a complex algorithm such as a virtual network allocation algorithm, there are several performance metrics that could be optimized.

Most published results have focused on minimizing the virtual network request rejection rate [46–56, 64]. The main advantage of using the performance metric is that it allows evaluating the ability of the algorithm to accommodate new virtual networks on the physical substrate. However, given that the blocking depends on many parameters (the physical and virtual network topologies, the capacity availability in physical nodes and links, the capacity require‐ ments of virtual nodes and links [50–52]), to identify the best algorithm is necessary knowing exactly the network configuration where the algorithm will operate (something difficult to achieve in dynamic scenarios) or running extensive simulation experiments with different network configurations (a time‐consuming task).

Instead of registering the blocking ratio, a computationally simpler metric consists on regis‐ tering the number of virtual network establishment requests received when the first blocking (rejection) occurs [48, 49]. A good algorithm would aim at registering such event at the latest possible instant. If used in conjunction with the blocking ratio, the first blocking metric can give information about the instant when the network starts saturating (when the first blocking occurs) and the dynamic of the system once such saturation state is reached.

Single‐carrier and multi‐carrier (super‐channel) can be used to create an optical connection. In the latter, the overall bit rate is achieved through lower‐rate sub‐carriers. Examples of these systems are Co‐WDM, Nyquist‐WDM and time frequency packing [34, 39, 40]. In general, multi‐carrier systems require a lower number of FSUs and exhibit a longer optical reach than

Regarding the modulation formats, there are bi‐level and multi‐level types. In a bi‐level mod‐ ulation format, as OOK and binary phase shift keying (BPSK) [42], the symbol rate equals the bit rate. In a multi‐level modulation format, as QPSK and x‐quadrature amplitude modula‐ tion (x‐QAM) [41, 42], the symbol rate is lower than the bit rate of the bi‐level type, leading to a lower requirement of FSUs. However, the optical reach of multi‐level modulation formats is lower than that of bi‐level [34, 36], highlighting a trade‐off between number of FSUs and

Once the number of FSUs required by a virtual link has been determined, the establishment of such link must meet at least two additional constraints: FSU continuity and FSU contiguity constraints. The FSU continuity constraint is analogous to the wavelength continuity constraint (exactly the same FSUs must be used in every physical link selected to establish a virtual link). The FSU contiguity constraint imposes that, if more than one FSU is required to establish a

The sequence of physical links used to establish a virtual link meeting the FSU continuity and

**3. Research challenges in virvtual network allocation over flexible‐grid** 

In the following, the main challenges in the research area of network virtualization over flexible‐

A performance metric allows defining the quality of an algorithm to carry out its task. Thus, usually the (single) objective of an algorithm is the maximization or minimization of a perfor‐ mance metric. However, for a complex algorithm such as a virtual network allocation algorithm,

Most published results have focused on minimizing the virtual network request rejection rate [46–56, 64]. The main advantage of using the performance metric is that it allows evaluating the ability of the algorithm to accommodate new virtual networks on the physical substrate. However, given that the blocking depends on many parameters (the physical and virtual network topologies, the capacity availability in physical nodes and links, the capacity require‐ ments of virtual nodes and links [50–52]), to identify the best algorithm is necessary knowing exactly the network configuration where the algorithm will operate (something difficult to achieve in dynamic scenarios) or running extensive simulation experiments with different

single‐carrier systems with the same total bit rate and modulation format [41, 42].

virtual link, then these FSU must be contiguous in the spectrum [45].

there are several performance metrics that could be optimized.

network configurations (a time‐consuming task).

contiguity constraints is known as a spectrum path.

optical reach [34, 43, 44].

26 Optical Fiber and Wireless Communications

**optical networks**

**3.1. Performance metrics**

grid optical networks are discussed.

Maximizing the traffic carried by the physical network due to the established virtual networks has also been the objective of some algorithms [54, 57–59]. As with the blocking ratio, the value of this performance metric depends on the topologies of the physical and virtual networks as well as the capacity of physical nodes/links and capacity requirements of virtual nodes/links, which makes difficult drawing general conclusions about the quality of different algorithms. Additionally, the lack of information about the number of virtual networks rejected does not allow measuring the quality of the service offered to the users. Thus, it should be used in con‐ junction with the blocking ratio.

Guaranteeing a given level of availability (e.g. 0.99999) to a virtual network has not been addressed by the proposed virtual network allocation algorithms to date, although availability (the fraction of time that a service is in operative state) is one of the most important quality of service metrics in a service level agreement (SLA). However, some efforts have been carried out in guaranteeing operation under specific failure conditions [49, 53, 59, 61, 62].

All previous performance metrics somehow aim to evaluate the capacity of the algorithm to offer a good quality of service. However, the main challenge in evaluating the performance of complex algorithms is selecting a performance metric that can capture the quality of the service offered to the user as well as the cost in achieving such quality.

To offer physical resources to a virtual network, the service provider incurs expenditure and operational costs due to the acquisition and maintenance of transponders, regenerators, optical cables, optical amplifiers and ROADMs (reconfigurable optical add drop multiplexer) [60]. Thus, algorithms aiming at minimizing the cost have also been studied. This metric has been mostly used in static scenarios [46, 56, 61, 62], and it is useful for the network planning stage. In dynamic scenarios, it can be used to determine the cost per virtual network, the total cost of providing the network virtualization service during a period of time or the cost incurred to achieve a given performance in terms of blocking ratio or traffic carried.

To date, quality‐of‐service‐related metrics and cost have been studied separately. The algorithm is designed to minimize/maximize one of them whilst the other one is just measured. Thus, a multi‐objective optimization approach that evaluates quality (as blocking or availability) and the cost incurred to achieve the required quality would deliver more realistic information about the best algorithm alternative from a network operator perspective.

#### **3.2. Network virtualization dynamics characterization**

To date there are no commercial network virtualization systems over flexible‐grid optical networks. In Ref. [63], an experimental system is reported, but traffic is artificially generated. Therefore there are no empirical statistics that help to model the structure (virtual topologies and their capacity requirements) and dynamic of such system. In terms of structure, it would be useful knowing how to model the virtual topologies and their capacity requirements. Such knowledge would facilitate the evaluation of allocation algorithms in terms of simulation, the only technique used so far to evaluate performance of dynamic systems.

In terms of structure, different works make different assumptions regarding the topologies of the virtual networks and their capacity requirements. **Table 1** summarises the main models used to characterize the virtual topologies. In it, the name of each physical and virtual topol‐ ogy is given along with its number of nodes (|*Np*|, |*Nv*|) and links (|*Lp*|, |*Lv*|). When a number lower than one is provided for |*Lv*|, it means that the probability interconnection between a node pair is given. The column 'Node/Link requirement' corresponds to the percentage of usage of the physical node and link by any virtual node and link, respectively. The symbol '‐' implies that such information is not found in the chapter.

As most works (15 of 17) use a medium‐sized physical network (NSFNet or DTNet) for evalu‐ ation, future works should consider at least one of these topologies as the physical substrate to facilitate comparison among different proposals. No pattern can be observed in terms of the vir‐ tual topologies, with most works using mesh topologies with different degrees of connectivity. Regarding resource requirements, all proposals require no more than 10% of the physical node/ link resources. The rest uses percentages of a few units.

Regarding dynamism, the most used distribution to model the virtual network request inter‐ arrival time is the exponential [46, 50–56, 64]. The holding time is usually modelled by an exponential distribution [52, 55], a deterministic value [64] or infinite (to model incremental traffic) [48, 49].

#### **3.3. Physical impairments**

It is expected that flexible‐grid optical networks can accommodate channels (used to imple‐ ment virtual links) at rates from 10 Gbps to 1 Tbps. Such channels, in the same way as fixed‐grid channels, will be affected by several physical impairments that degrade the qual‐ ity of the signal transmission. Additionally to typical physical impairments, as attenua‐ tion, chromatic dispersion, four‐wave mixing (FWM) and amplified spontaneous emission (ASE) noise [65], in elastic optical networks the non‐linear effect of cross phase modulation (XPM) takes relevance because of the existence of channels with different modulation for‐ mats in the same link. Due to the XPM effect, channels using intensity‐based modulation formats (e.g. OOK typically used in 10 Gbps channels) interfere negatively in the quality of the signal of phase‐modulated channels (e.g. BPSK and QPSK, used for higher bit rate channels) [66].

Most previous works have not considered this situation, with some of them assuming an ideal physical substrate [50, 54] whereas others have resorted to simplified models. For instance, in Refs. [48, 49, 51, 53, 57, 61, 62], the degradation is summarized in the figure of the maximum optical reach of signals, in Refs. [46, 56, 58, 59], the use of guard bands to all channels is used to simulate an ideal substrate, whereas in Refs. [47, 52, 55, 64], guard bands (to all channels or selectively added to channels most affected by the XPM degradation) are added to the limita‐ tion of the optical reach.


**Table 1.** Characteristics of virtual network requests used in the literature.

#### **3.4. Resource allocation to virtual networks**

be useful knowing how to model the virtual topologies and their capacity requirements. Such knowledge would facilitate the evaluation of allocation algorithms in terms of simulation, the

In terms of structure, different works make different assumptions regarding the topologies of the virtual networks and their capacity requirements. **Table 1** summarises the main models used to characterize the virtual topologies. In it, the name of each physical and virtual topol‐ ogy is given along with its number of nodes (|*Np*|, |*Nv*|) and links (|*Lp*|, |*Lv*|). When a number lower than one is provided for |*Lv*|, it means that the probability interconnection between a node pair is given. The column 'Node/Link requirement' corresponds to the percentage of usage of the physical node and link by any virtual node and link, respectively. The symbol '‐'

As most works (15 of 17) use a medium‐sized physical network (NSFNet or DTNet) for evalu‐ ation, future works should consider at least one of these topologies as the physical substrate to facilitate comparison among different proposals. No pattern can be observed in terms of the vir‐ tual topologies, with most works using mesh topologies with different degrees of connectivity. Regarding resource requirements, all proposals require no more than 10% of the physical node/

Regarding dynamism, the most used distribution to model the virtual network request inter‐ arrival time is the exponential [46, 50–56, 64]. The holding time is usually modelled by an exponential distribution [52, 55], a deterministic value [64] or infinite (to model incremental

It is expected that flexible‐grid optical networks can accommodate channels (used to imple‐ ment virtual links) at rates from 10 Gbps to 1 Tbps. Such channels, in the same way as fixed‐grid channels, will be affected by several physical impairments that degrade the qual‐ ity of the signal transmission. Additionally to typical physical impairments, as attenua‐ tion, chromatic dispersion, four‐wave mixing (FWM) and amplified spontaneous emission (ASE) noise [65], in elastic optical networks the non‐linear effect of cross phase modulation (XPM) takes relevance because of the existence of channels with different modulation for‐ mats in the same link. Due to the XPM effect, channels using intensity‐based modulation formats (e.g. OOK typically used in 10 Gbps channels) interfere negatively in the quality of the signal of phase‐modulated channels (e.g. BPSK and QPSK, used for higher bit rate

Most previous works have not considered this situation, with some of them assuming an ideal physical substrate [50, 54] whereas others have resorted to simplified models. For instance, in Refs. [48, 49, 51, 53, 57, 61, 62], the degradation is summarized in the figure of the maximum optical reach of signals, in Refs. [46, 56, 58, 59], the use of guard bands to all channels is used to simulate an ideal substrate, whereas in Refs. [47, 52, 55, 64], guard bands (to all channels or selectively added to channels most affected by the XPM degradation) are added to the limita‐

only technique used so far to evaluate performance of dynamic systems.

implies that such information is not found in the chapter.

link resources. The rest uses percentages of a few units.

traffic) [48, 49].

channels) [66].

tion of the optical reach.

**3.3. Physical impairments**

28 Optical Fiber and Wireless Communications

The selection of the physical nodes and links to be allocated to a virtual network is a ‐Hard problem [67]. Thus, most proposals solving this problem over flexible‐grid optical networks have resorted to heuristics [46–59, 61, 62, 64] and a few of them have proposed integer linear models [51, 58, 59, 61, 64], but mostly in the context of a static scenario where the random nature of the virtual network requests is not a problem.

Much work is still needed in identifying the features of good performing heuristics to allocate virtual networks as well as evaluating the performance of meta‐heuristics.

#### **3.5. Spectrum fragmentation**

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

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 could not be established because of the contiguity constraint.

**Figure 4.** Spectrum fragmentation.

To decrease the spectrum fragmentation, the re‐allocation of FSUs to the different channels in a link has been proposed in the area of flexible‐grid networks by Refs. [68–72]. In Ref. [73], the impact of avoiding fragmentation on the blocking ratio can be seen.

In Ref. [54], a technique of spectrum defragmentation in the area of virtual networks over flexible‐grid optical networks is reported, showing that the blocking ratio decreases with respect to an algorithm without defragmentation. However, defragmentation is costly as computation time and additional resources must be used to apply it. This highlights a trade‐off between the blocking ratio decrease and the frequency of defragmentation. Further research on the interplay of allocation algorithms and defragmentation techniques is required.
