**2. Fundamental concepts**

## **2.1. Network virtualization**

under the conditions stated in a service level agreement (SLA), having dynamic scaling of resources and transparent access to network services, unaware of the location and hardware/ software characteristics of the required resources [2]. Apart from high bandwidth, cloud computing applications require the following functionalities from the underlying physical

• Abstraction: The technology/implementation specific details of the physical network resources are hidden to the users, due to the "computing as a utility" philosophy.

• Isolation: Different cloud computing applications should not interfere with each other in

• Flexible resource granularity: The amount of resources (storage, processing power and bandwidth) required by different cloud computing applications might vary significantly. • On‐demand setup/tear down: For efficiency, network resources should be set‐up/torn down with a highly dynamic, rapidly reconfigurable and programmable network environment,

• Resiliency: Grid/cloud computing applications should continue running in spite of failures

Network virtualization, which extends the well‐known concepts of server and storage virtual‐ ization to networks, is envisaged as a key enabling technology for cloud computing services. As such, the benefits of running cloud applications on top of virtual networks (as opposed to on top of virtual servers alone, as usually done [4, 5]), was evidenced by several prelimi‐ nary studies on network virtualization for cloud computing. In Ref. [6], resource allocation of cloud‐based data centres services was proposed by abstracting the service requests as vir‐ tual network requests. In Ref. [7], a network virtualization platform that acts as a mediator between the cloud user requirements and the physical resources was proposed. In Ref. [8], a new network architecture based on network virtualization was proposed for cloud computing applications where the geographic location of servers is relevant. In Ref. [9], a network opera‐ tor perspective was given about the convenience of network virtualization as an enabler for cloud computing. Nowadays, the benefits of network virtualization for cloud services are

The underlying network over which network virtualization takes place is of fundamental importance to guarantee a good service. Arguably, the two most important requirements regarding the underlying network are the bandwidth capacity and the variety in the band‐ width granularity of connections, to allow for a high number of cloud computing applications with different bandwidth requirements. Both requirements would be naturally provided by flexible‐grid optical networks [13, 14]. By overcoming the rigid spectrum allocation of cur‐ rent fixed‐grid wavelength‐division multiplexing (WDM) networks, elastic optical networks would make better use of the band C by allocating each connection the bandwidth just required. Depending on the bit rate and the modulation format, a gain in bandwidth usage between 33 and 100% could be achieved by using flexible‐grid networks instead of a fixed one operating with a spectral width of 50 GHz [15]. Finally, flex grid would allow a wide band‐

width granularity of connections: bit rates from 10 Gbps to 1 Tbps are envisaged [13].

network [1]:

20 Optical Fiber and Wireless Communications

the access to common physical resources.

affecting the optical network.

something not possible with the current status of Internet [3].

well identified in terms of cost, agility, resilience and multi‐tenancy [10–12].

Network virtualization refers to the creation of different isolated virtual networks on top of a common physical substrate. The isolation feature means that the information transmitted through a particular virtual network cannot be retrieved or affected by other existing virtual networks and the operation of the different virtual networks cannot affect the operation of the physical substrate [16].

Among the main features of network virtualization environments, we found several of the requirements imposed by cloud computing applications, namely, coexistence of different virtual networks, isolation between coexisting virtual networks, programmability, dynamicity, flexibility and heterogeneity [17].

By implementing cloud applications on virtual networks (i.e. one virtual network for each different cloud computing application), several benefits can be identified:


Network virtualization has been envisaged as a very useful tool in network research and industry. In research, the test of new routing algorithms, network protocols or network controllers can be done by establishing a virtual network, without interrupting the normal operation of a physical network or deploying a physical network for tests. Thus, the pro‐ duction network may become the testbed [19]. An early example of this type of use was PlanetLab [20–22], established in 2002 for distributed systems and network research. Other efforts have been GENI in USA [23], FEDERICA and OneLab2 in Europe [24, 25], Akari in Japan [26] and FIBRE in a joint effort between Brazil and Europe [27]. For a review of several precursor experimental initiatives, see Ref. [17]. In an industry, network virtualization can offer separate networks for different units in a company, differentiation of services based on bandwidth usage (e.g. voice and video) or a rapid and flexible creation of sub‐networks for different projects [28, 29]. For example, in a data centre each client can have its own topology and control its traffic flows. Finally, different service providers can share the same network infrastructure being unaware of the others.

As a way of illustration, **Figure 1** shows a schematic of a network virtualization system. The lower part shows the physical substrate, made of five nodes and six bidirectional links. The available capacity of physical links, measured in capacity units (c.u.), is shown next to each link. The upper part shows two of the virtual networks (three‐node rings with three bidi‐ rectional links each) that have been established on the physical network. The capacity unit required by the virtual links are shown near to each link. Dotted lines represent the mapping between virtual and physical links. Both virtual networks can have virtual links established over the same physical link and a virtual link can require more than one physical link to be established. For the sake of clarity, the mapping of the nodes is not shown but it can be deduced by identifying the physical nodes at the extreme of the physical links associated to the virtual links. The decision about whether establishing a new virtual network is possible or not and what virtual link/node is established in what physical link/node is made by a virtual network allocation algorithm.

**Figure 1.** Two virtual networks established on the same physical substrate.

#### **2.2. Mathematical modelling for network virtualization**

operation of a physical network or deploying a physical network for tests. Thus, the pro‐ duction network may become the testbed [19]. An early example of this type of use was PlanetLab [20–22], established in 2002 for distributed systems and network research. Other efforts have been GENI in USA [23], FEDERICA and OneLab2 in Europe [24, 25], Akari in Japan [26] and FIBRE in a joint effort between Brazil and Europe [27]. For a review of several precursor experimental initiatives, see Ref. [17]. In an industry, network virtualization can offer separate networks for different units in a company, differentiation of services based on bandwidth usage (e.g. voice and video) or a rapid and flexible creation of sub‐networks for different projects [28, 29]. For example, in a data centre each client can have its own topology and control its traffic flows. Finally, different service providers can share the same network

As a way of illustration, **Figure 1** shows a schematic of a network virtualization system. The lower part shows the physical substrate, made of five nodes and six bidirectional links. The available capacity of physical links, measured in capacity units (c.u.), is shown next to each link. The upper part shows two of the virtual networks (three‐node rings with three bidi‐ rectional links each) that have been established on the physical network. The capacity unit required by the virtual links are shown near to each link. Dotted lines represent the mapping between virtual and physical links. Both virtual networks can have virtual links established over the same physical link and a virtual link can require more than one physical link to be established. For the sake of clarity, the mapping of the nodes is not shown but it can be deduced by identifying the physical nodes at the extreme of the physical links associated to the virtual links. The decision about whether establishing a new virtual network is possible or not and what virtual link/node is established in what physical link/node is made by a virtual

infrastructure being unaware of the others.

22 Optical Fiber and Wireless Communications

network allocation algorithm.

**Figure 1.** Two virtual networks established on the same physical substrate.

The physical network is modelled by a directed graph = (*Np*, *Lp*, *R pt* , *Cp*), where *Np* and *Lp* are the sets of physical nodes and links, respectively; *R pt* is the set of resources of type *t* in the physical nodes (for example, storage and processing resources; *t* ∈ ℕ ) and *Cp* the set of resources at the physical links (optical bandwidth).

Analogously, the *i*‐th virtual network can be modelled by a directed graph *<sup>i</sup>* <sup>=</sup> (*<sup>N</sup> vi* , *L vi* , *R vi t* , *C vi* ), where *<sup>N</sup> vi* is the set of virtual nodes and *<sup>L</sup> vi* the set of virtual links; *<sup>R</sup> vi t* is the set of resources of type *t* required by each virtual node of the virtual network *<sup>i</sup>* (e.g. storage and processing resources) and *<sup>C</sup> vi* is the set of resources required by the virtual links (optical bandwidth).

The information required to execute the resource allocation algorithm is as follows:


Every time the resource allocation algorithm must process a new virtual network request, at least the following two constraints must be met to be able to accept such request:

$$r\_k^t \ge \sum\_{\forall \text{ av } \overline{\mathfrak{g}} \text{ s.tav}\_i} r\_{uv}^t \; ; \; \forall t \tag{1}$$

$$\mathbf{c}\_{m} \ge \sum\_{\forall \text{ by } \mathbf{g} \text{ s!} \mathbf{b}\_{\star}} \mathbf{c}\_{\text{l}v} \tag{2}$$

where *r k t* is the total number of resources of type *t* in physical node *k*, *r nv <sup>t</sup>* is the number of resources of type *t* allocated to virtual node *nv*, *c <sup>m</sup>* is the total number of resources in physical link *m* and *c lv* is the number of resources allocated to virtual link *lv*.

Eqs. (1) and (2) forbid that the number of resources allocated to the virtual nodes/links established in a particular physical node/link exceed the capacity of that node/link.

Additionally, depending on the type of physical network, extra constraints might appear on the allocation of resources to the virtual links. In the case of an optical network, fixed and flexible‐ grid networks impose different constraints. We review these two types of optical networks and their associated constraints in the following.

#### **2.3. Fixed‐grid optical network**

In a circuit‐switched optical network, each circuit is carried by an optical channel/carrier, based on the wavelength division multiplexing (WDM) technique. Currently, such optical channels operate in the range 1530–1565 nm, known as band C.

In a fixed‐grid optical network, the optical carriers are determined by their central frequency and use a fixed amount of spectrum. According to the specification ITU‐T G.694.1 [30], the selectable spectrum widths are 12.5 GHz, 25 GHz, 50 GHz and 100 GHz. Once a spectrum width is selected, all optical channels in a link are established with such spectral width. Depending on the selected spectral width, the central frequency used by the *n*‐th optical channel is given by the following equation:

$$193.1 + \eta \times \mathbb{W}\,\text{THz} \tag{3}$$

where *W* ∈ {0.0125; 0.025; 0.05; 0.1} denotes the spectral width selected and *n* is an integer number whose range depends on the spectral width as follows: *n* ∈ [− 123 , 227] for *W* = 0.0125 ; *n* ∈ [− 61 , 113] for *W* = 0.025 ; *n* ∈ [− 30 , 56] for *W* = 0.05 ; *n* ∈ [− 15 , 28] for *W* = 0.1 .

**Figure 2** shows an example of the spectral usage of a fixed‐grid link where six optical chan‐ nels have been established: two optical channels at 10 Gbps using the on‐off keying (OOK) modulation format, three channels at 40 Gbps modulated with dual polarization‐quadrature phase shift keying (DP‐QPSK) and one channel at 100 Gbps, also modulated with DP‐QPSK. The spectral width of each channel is equal to 50 GHz and the central frequencies are deter‐ mined by Eq. (3). It is common practice to identify the channels by their equivalent wavelength as well. Thus, in **Figure 2**, the corresponding wavelength of each channel has been written between brackets under the central frequency.

**Figure 2.** Frequency allocation to different transmission rate optical channels in a fixed‐grid link.

In fixed‐grid optical networks (in the absence of wavelength converters), the wavelength con‐ tinuity constraint must be met. That is, the optical channel used by the virtual link must use the same central frequency and spectral width in all the physical links used. In networks oper‐ ating with multiple transmission rates (as shown in **Figure 3**), additional constraints to deal with the signal degradation of higher bit rates channels mainly due to cross‐phase modulation [31–33] may be required: for example, some channels should be left unused as guard bands or an optical reach (the maximum distance an optical signal can travel without exceeding a threshold on the bit error rate) be established.

The main drawback of fixed‐grid optical networks is the inefficient spectrum usage [34], as observed in **Figure 2**, where channels are allocated more spectrum than effectively required: both a 10 Gbps OOK‐modulated channel and a 40 Gbps channel modulated with DP‐QPSK require a bandwidth equal to 25 GHz [34, 35], whereas a 100 Gbps channel modulated with DP‐QPSK requires just 37.5 GHz [34]. To increase the spectrum usage, the flexible allocation of it has been proposed [14, 34]. This type of networks is known as flexible‐grid or elastic optical networks.

#### **2.4. Flexible‐grid optical networks**

spectrum widths are 12.5 GHz, 25 GHz, 50 GHz and 100 GHz. Once a spectrum width is selected, all optical channels in a link are established with such spectral width. Depending on the selected spectral width, the central frequency used by the *n*‐th optical channel is given by the following

 193.1 + *n* × *W T*Hz (3) where *W* ∈ {0.0125; 0.025; 0.05; 0.1} denotes the spectral width selected and *n* is an integer number whose range depends on the spectral width as follows: *n* ∈ [− 123 , 227] for *W* = 0.0125 ;

**Figure 2** shows an example of the spectral usage of a fixed‐grid link where six optical chan‐ nels have been established: two optical channels at 10 Gbps using the on‐off keying (OOK) modulation format, three channels at 40 Gbps modulated with dual polarization‐quadrature phase shift keying (DP‐QPSK) and one channel at 100 Gbps, also modulated with DP‐QPSK. The spectral width of each channel is equal to 50 GHz and the central frequencies are deter‐ mined by Eq. (3). It is common practice to identify the channels by their equivalent wavelength as well. Thus, in **Figure 2**, the corresponding wavelength of each channel has been written

*n* ∈ [− 61 , 113] for *W* = 0.025 ; *n* ∈ [− 30 , 56] for *W* = 0.05 ; *n* ∈ [− 15 , 28] for *W* = 0.1 .

**Figure 2.** Frequency allocation to different transmission rate optical channels in a fixed‐grid link.

between brackets under the central frequency.

equation:

24 Optical Fiber and Wireless Communications

In a flexible‐grid optical network, the spectral width of a channel can be varied depending on the data transmission requirements [36]. Thus, the spectrum is divided in small units, typically of 12.5 GHz, known as frequency slot units (FSU) [34]. By using a different number of contigu‐ ous FSUs, different spectral widths can be achieved [37, 38] depending on the transmission requirements of the signal, such as the modulation format and the bit rate.

As a way of illustration, **Figure 3** shows the same six channels of **Figure 2**, now operating in a flexible‐grid system. The numbers of 12.5 GHz FSUs required are 2, 2 and 3 for the 10, 40 and 100 Gbps channels, respectively. Thus, the flexible‐grid allocation uses just 54.2% of the spectrum originally required (162.5 GHz instead of 300 GHz).

**Figure 3.** Frequency allocation to different transmission rate optical channels in a flexible‐grid link.

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

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 optical reach [34, 43, 44].

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

The sequence of physical links used to establish a virtual link meeting the FSU continuity and contiguity constraints is known as a spectrum path.
