Spectrum Continuity Awareness for Virtual Network Construction
in Elastic Optical Networks
Badr Mochizuki
The Kyoto College of Graduate Studies for Informatics

Abstract
With network virtualization technology, network resources are managed efficiently because
multiple virtual networks (VNs) can be constructed over a shared physical network. On the other
hand, Elastic Optical Networks (EONs), with its variable spectrum grids, can use the spectrum
efficiently because the spectrum can be allocated at a subwavelength level. A VN can be constructed
over an EON if there are enough available network resources and if the spectrum contiguity
constraint is satisfied. In this paper, we consider the case where network operators do not use
network convertors in order to reduce network costs. In this situation, an additional constraint called
spectrum continuity has to be satisfied. Therefore, we propose a VN over EON construction algorithm
which satisfies both the spectrum continuity constraint and uses spectrum splitting if there are notenough link resources. We evaluate the effectiveness of the proposed method by simulation for the
NSFNET topology and discuss its results.

■ 1. Introduction

Union (ITU) [2].
However, having a grid that has a fixed size may

With network virtualization technology, network

result in inefficient spectrum utilization if theresources are managed efficiently because multiple

required bandwidth is not a multiple of 50 GHz

virtual networks (VNs) can be constructed over a[3], [4], [5]. As a cost-effective solution, elastic

shared physical network [1]. When a VN

optical networks (EON) have been proposed.

construction request arrives, node mapping andIn contrast to fixed grid optical networks, thelink mapping are performed. In node (link)

spectrum in EONs can be allocated at a

mapping, the requested virtual node (link)subwavelength level, where the spectrum unit isresources are mapped by allocating physical nodecalled frequency slot (FS). Furthermore, the size

(link) resources if there are enough availableof the spectrum grid is variable because opticalresources. Since, physical network resources aretransponders that allow transmitting, receiving

limited, it is important to design an efficient VN

and switching optical signals at multiples of FSs

construction algorithm in order to construct as

are used [6]. Therefore, EONs can use the spectrum

many VNs as possible.

more efficiently and flexibly without adding more

Optical networks are high speed networks

bandwidth. Hence, in this paper, we consider

where data is transmitted as an optical signal

elastic optical networks (EON) as the physicalthrough channels called spectrum grids. In fixed

network for VN construction.

grid optical networks, optical signals in the form

When constructing a VN over EON, nodeof wavelengths are transmitted through spectrum

mapping will succeeds the number of available

grids with a predefined size. Here, the size of aphysical CPU resource slots is larger than or equal

grid as been set to 50GHz as per the standards

to the requested virtual node resources [7], [8]. On

defined by the International Telecommunication

the other hand, in link mapping, FSs at physical

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links are allocated by establishing a connection

performance of the proposed method with Monte

called a lightpath, which is established between

Carlo simulation in NSFNET and investigate its

two physical nodes. Link mapping succeeds if theeffectiveness.

lightpaths between the mapped physical nodes

Next, we introduce background information inare established successfully. Here, a lightpath cansection 2 and summarize some related work on

be established if the number of available FSs isspectrum splitting in section 3. In Section 4, wegreater than or equal to the requested one [9],explain our system model and our proposed[10], [11]. In addition, the spectrum contiguity has

methodalso to be satisfied. In the spectrum contiguity
constraint, the available FSs have to be allocatedadjacently in the spectrum at each link of alightpath. In this paper, we consider the casewhere network operators do not use network
convertors in order to reduce network costs. In
this situation, an additional constraint called
spectrum continuity has to be satisfied. Here, thesame FSs have to be allocated at each link of the

Figure 1. Comparison of spectrum grids.

lightpath.
In the literature, several techniques for VN
construction over EON have been proposed. In

in section 5. Numerical results are shown in
Section[12], two algorithms have been proposed where(a) Fixed grid optical networks.

one algorithm maximizes the utilization of FSs(b) Elastic optical networks.

and the other minimizes the blocking rate of VN
requests. In [13], the proposed method constructs
VNs by minimizing the network cost in the casewhere the trafﬁc is known in advance. In [14], theauthors have presented a load-balancing algorithm
in order to resolve the fragmentation issue that

6, and conclusions are presented in Section 7.

■ 2. Background

2.1 Elastic Optical Networks

occurs in EON because some FSs cannot be usedby VNs if the number of adjacents is too small for
VN requests.
In this paper, we propose a spectrum continuity
aware algorithm for VN construction, where theobjective is to decrease the blocking rate of VN
requests by performing spectrum splits. In thisalgorithm, a VN is constructed if node mapping
and link mapping succeed under the spectrum
contiguity and continuity constraints. If node
mapping fails, the VN request is blocked. If node
fails,

grid is utilized in EON. Figure 1 illustrates the

spectrum splitting is executed. Here, the required

differences between EON and fixed grid opticalFSs are allocated by establishing two lightpaths

networks in terms of the utilization of the opticalthrough different paths and a VN is constructed.

spectrum.

mapping

8

In this subsection, we explain how the spectrum

succeeds

and

link

mapping

If there are not enough available FSs at otherAs illustrated in Figure 1 (a), the size of thepaths, the VN request is blocked. We evaluate thespectrum grid for fixed grid optical networks is

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always 50 GHz, meaning that it is fixed. Therefore,

Step 1: Signaling

if the required bandwidth is not a multiple of 50

A ligthpath establishment request arrives at

GHz, the spectrum grid is not fully utilized. For

the source node with a required number of FSs

example, if the required bandwidth is 80 GHz

and a destination node. Next, a path between thethen two grids will be used. Here, one 50 GHz gridsource and destination node is computed. Then, ais fully utilized while in the other grid only 30

control packet is sent along the computed path

GHz are used. Therefore, in this example, 20 GHz

from source to destination. At each link along theof spectrum are wasted because it cannot be used

path, the control packet collects information on

by other users. In addition, a guard-band is needed

the number of idle FSs and its positions in the

between adjacent grids even when these grids arespectrum.

used by the same lightpath, hence, in fixed grid

Figure 3. VN construction over EON.

Figure 2. Lightpath establishment in EON.

Step 2: Reservation of FSs
When the control packet arrives at the

optical networks, the spectrum grid is not useddestination node, the number of idle andefficiently.

contiguous FSs are checked for each link, based on

On the other hand, as shown in Fig. 1 (b) for

the information included in the control packet. At

EON, the spectrum can be allocated per FS unit. In

this step, at each link, a number larger or equal toaddition, if a lightpath uses multiple grids, only

the requested FSs have to be:

two guard-bands are needed. As a result, the optical• Idlespectrum can be utilized more efﬁciently in EON.

• Contiguous (adjacent in the spectrum) to satisfy
the spectrum contiguity constraint.

2.2 Lightpath Establishment in EONIn EON, data is transmitted all optically. This

• Continuous (the same FSs have to be utilizedalong all links in the lightpath) to satisfy themeans that the optical signal remains in the

spectrum continuity constraint.

optical domain from source to destination, and the

If the above three conditions are true, the FSs

Optical/Electrical/Optical (O/E/O) conversion is

are reserved at each link and a lightpath isnot performed at intermediary nodes, hence

established. Otherwise, it is blocked.

providinganultra-fast

datatransmission.

Moreover, in EON, a connection, called a lightpath,

Step 3: Data Transmission

has to be established prior to data transmission.

At the end of step 2, if a lightpath has been

When a lightpath establishment request between

established, then data is transmitted continuously

a source and a destination node arrives, theand all optically from source to destination.

following four steps are performed (see Fig. 2):

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construction over EON because node resources

Step 4: Lightpath Termination
After all data is transmitted, all the reserved
FSs are freed and the lightpath is released.

have not been considered.
In [20], path splitting for VN construction over
EON has been proposed and numerical results

2.3 Virtual Network Construction over EON

show that the VN request blocking probability has

In this subsection, we explain how VNs are

been significantly reduced. Here, four schemes forconstructed over EON. Figure 3 illustrates how

node mapping have been considered. For link

multiple VNs are constructed over EON as a

mapping, the shortest path between the mappedshared physical network. A VN is constructed

nodes, is computed. If there are no available FSs,

based on the information in a VN construction

path splitting is performed. Here, part of therequest, which includes the number of required

requested FSs are assigned at links in the shortest

links, FSs (link resources) and CPU resource slots

path and the remaining FSs at links in alternative

resources (node resources). Here, the requested

paths. However, this method considers the casenode resources are allocated to available nodes inwhere spectrum conversion is allowed, hence VNs

EON (node mapping) if the number of idle node

are constructed without satisfying the spectrum

resources is larger than that of the VN request.

continuity constraint. Therefore, it cannot be used

On the other hand, in link mapping, the requested

in cases where the spectrum continuity is required.

link resources are mapped to available links in

From the above, we conclude that spectrum

EON by establishing lightpaths between the

splitting has been proposed in cases of VN

mapped nodes if the three conditions mentioned

construction over fixed grid optical, for lightpath

in subsection 2.2 Step 2 are true.

establishment in EON, and for VN construction

If both node mapping and link mapping succeed,

over EONs that do not require spectrum continuity.

then a VN is constructed. Otherwise the VN

It is important to consider spectrum continuity

construction request is blocked.

■

because it provides an important cost saving for
network operators. Therefore, in this paper, we
propose a VN construction algorithm over EON

3. Related Workthat uses a continuity aware spectrum splitting.

Next, we introduce some related work on

spectrum splitting. In [15], the authors propose
spectrum splitting for constructing VNs over fixed
grid optical networks. Here, spectrum splitting is■ 4. Spectrum Continuity Aware Spectrum Splitting

In this section, we propose a spectrum continuity

utilized to split a virtual link into multiple paths

aware algorithm for VN construction, where thefor embedding many VNs, if the available amountobjective is to decrease the blocking rate of VN

of link resources is smaller than the amount ofrequests. In this algorithm, a VN is constructed if

requested link resources. However, the proposed

node mapping and link mapping succeed underalgorithm cannot be used for constructing VNs

the spectrum contiguity and continuity constraints.

over EON because the spectrum contiguity
constraint has not been considered.

4.1 Network Model

For lightpath establishment in EON, spectrum
splitting algorithms have been proposed in [16],model for the construction of VNs over EON.

[17], [18] and [19]. Here, spectrum splitting is

We consider our physical network (EON)

used to split a single trafﬁc demand into multiple

denoted as a graph Gp (Np, Lp) where Np is the set oflightpaths along the same link. However, these

physical nodes and Lp is the set of physical links.

lightpath

The maximum number of physical nodes is N andestablishment and cannot be used for VN

the maximum number of physical links is L. The ith

proposed10

In this subsection, we explain our network

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algorithms

are

for

(i=1, …, N) physical node is denoted as nip ∈ Np andthe number of CPU resource slots for n p is denotedias C. We define the j CPU slot at node n p as c n(j),
th

i

i

of CPU resource slots for each requested node, andthe number mv of FSs at each link. Based on the

VN request information, CPU resource slots arewhich is equal to 0, if the j CPU slot at node n p isallocated at all the mapped nodes. Furthermore,

In addition, the i (i=1, …, L) physical link ismapped nodes with mv FSs at each link of thethiidle, and 1 if it is used.
thdenoted as l p ∈ Lp, and the total number of FSs forilink l p is denoted as M. Here, we define the j FS atithlink l p as m n(j), which is equal to 0, if the j FS at
i

i

th

link l p is idle, and 1 if it is used.

lightpaths are established between each pair oflightpath.

A VN is constructed according to the following
steps (see Fig. 4).

i

In this network, a VN is constructed based on

Step 1: A new VN request arrives with the required

the information of a VN request. Let us represent

number of nodes k, CPU resource slots cv,

a VN as a graph Gv (Nv, Lv) where Nv is the set ofand mv FSs enough.

virtual nodes and Lv is the set of virtual links. The
vth virtual node is denoted as nv ∈ Nv, and the vthvirtual link is lv ∈ Lv. A VN request contains

information about the required number of nodes k,number of CPU resource slots cv, and number of
FSs mv. We assume that k ≤ N. In terms of node

resources, cv (cv ≤ C) is the number of required CPU

resource slots for virtual node nv ∈ Nv. For link

resources, mv (mv ≤ M) denotes the number ofrequired FSs for virtual link lv ∈ Lv.

A VN is constructed if the requested virtual

nodes can be mapped to the physical nodes (nodemapping) and virtual links to the physical links(1),(link mapping). We denote node mapping asfollows:
Here, a virtual node is mapped to only one
physical node, if there are enough available CPU

Figure 4. Flow chart of the proposed method

resource slots at the physical node.
On the other hand, link mapping is denoted as:,(2)

A virtual link may be mapped to one or more

Step 2: In this step, k nodes which have the highest
number of idle CPU resource slots are
selected. These nodes are denoted as(N1,…,Ni,…,Nk).

physical links if there are enough idle FSs, which
are contiguous and continuous at each link.
4.2 Overview

Step 3: If the number of idle CPU slots is larger or
equal to cv at each selected node, go to Step
4. Otherwise, go to Step 9.

In this subsection, we give an overview of the
proposed method. We assume that a VN request
arrives at an EON with information about theStep 4: Compute the shortest path between Ni andNi+1.

required number k of virtual nodes, the number cv

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Step 5: 
If the number of idle, contiguous and(3)

continuous FSs is larger than or equal to
mv at all link of the shortest path between

At first, all possible paths between Ni and Ni+1 are

Ni and Ni+1, go to Step 6. Otherwise, go tocomputed. Then, a path which has the smallest

Step 7.

number of common links with the shortest path isselected as the alternative path. If there are

Step 6: If i+1=k, go to Step 10. Otherwise,

multiple candidate paths, the paths with theincrement i by 1 and go to Step 4.

smallest number of hops is selected. Next, as
explained in Step 8, the FS availability at each

Step 7: Spectrum splitting is executed because

link along the alternative path is checked. Here,

there are not enough idle, contiguous andspectrum splitting succeeds if the number of idle,

continuous FSs at each link of the shortest

contiguous and continuous FSs at each link along

path. Therefore, an alternative path withthe shortest path between Ni and Ni+1 is larger than

the fewest common links with the shortest
path is computed between Ni and Ni+1.
Step 8: If there are enough idle, contiguous andcontinuous FSs at each link of thealternative, go to Step 6. Otherwise, go to
Step 9.
Step 9: The VN request is blocked.

Figure 5. The NSFNET Topology.

Step 10: The VN request is accepted. Here, cv CPUor equal to m val. The VN request is accepted if

resource slots will be allocated at each ofthere are enough idle CPU resource slots andthe selected k nodes, and mv FSs will beallocated at all link for each establishedenough available FSs over both the shortest pathand the alternative path. Finally, cv CPU resource

lightpath.

slots are allocated at N i and N i+1 , and twolightpaths (one for the shortest path and another4.3 Spectrum Splitting
In this subsection, we explain Step 7. As
explained in subsection 4.2, Step 7 is performed if
there are enough idle CPU resource slots but notenough available FSs. Here, spectrum splitting is
executed because the number of idle, contiguous
and continuous FSs at each link along the shortest
path between N and N

satisfied, the VN requested is blocked.

■ 5. Numerical Results

In this section, we evaluate the performance ofis smaller than mv which

our proposed method by Monte Carlo simulationis the number of requested FSs. In this step, an

for the NSFNET topology shown in Fig. 5. In thisalternative path is computed in order to perform

topology, the number N of nodes is 14 and thespectrum splitting. Let us denote mv as thenumber L of links is 21. The number M of FSs at a

i

i+1

sp

maximum

numberandlink is 64, and the number C of CPU resource slots

continuous FSs that is common to all links of theis set to 64 at each node. We assume that VN

shortest path. Therefore, the remaining number ofrequests arrive at an EON according to a Poisson

FSs to be reserved at each link of the alternative

process with rate λ [Requests/ms], and thepath, denoted as mv , is defined as:

utilization time of a VN follows an exponentialal

12

for the alternative path) are established between
N i and N i+1 . If the above conditions are not

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of

idle,

contiguousdistribution with rate 1.0.

of the proposed method and that of the conventional

We compare the performance of our proposed

methods denoted as “EON” and “EON SS”. Note

method with two conventional VN construction

that, “EON” and “EON SS” perform spectrum

methods under spectrum contiguity and continuity

splitting if there are enough CPU resource slots

constraints. In the node mapping of bothbut not enough available FSs. The main difference

conventional methods, all required nodes of a VN

between these two methods and the proposedrequest are selected at random. The first method

method is that the proposed method implements

denoted as “EON” constructs VNs over EON

node mapping by selecting nodes with the most

without performing spectrum splitting, hence if

available CPU resource slots. Whereas in “EON

there are no available FSs, the VN request isSS”, nodes are selected at random.

blocked. Whereas the second method denoted as

From this figure, we ﬁnd that the overall“EON SS” performs spectrum splitting if there areblocking rate for all schemes becomes large as the

not enough available FSs at each link of a

network load increases. Moreover, Fig. 6 shows

lightpath.

that the blocking rate of the proposed method is

Figure 6. Blocking rate vs. network load.

Figure 8. Number of VN requests per hops.

the lowest and that of “EON SS” is the highest.
This is because our proposed method considers
both the availability of CPU resource slots at link
mapping and FSs availability in link mapping
when constructing a VN. From the above results,
we conclude that the proposed method can reducethe blocking rate significantly compared to theother two conventional methods.
5.2 Impact of the number of spectrum splits
Next, we investigate the impact of the network
Figure 7. Spectrum splits vs. network load.

load on the average number of spectrum splits.
Figure 7 shows the average number of spectrum

5.1 Effect of the network load on the blocking rate

splits against the network load for the conventional

In this subsection, we analyze the effect of the“EON SS” and the proposed method. From Fig. 7,

network load on the blocking rate. Figure 6 shows

we can see that the number of spectrum splits

the overall blocking rate against the network loadincreases as the network load increases for both

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methods. Here, VN requests tend to get blocked
more frequently when the network load increases
because the network get congested and there are

In this paper, we proposed a spectrum continuity

fewer available network resources for the arriving

aware algorithm for VN construction, where theVN request.

objective is to decrease the blocking rate of VN

In addition, the number of spectrum splits is therequests. In this method, a VN is constructed if

smallest for the proposed method and the largest

node mapping and link mapping succeed underfor “EON SS”. This is because “EON SS” does not

the spectrum contiguity and continuity constraints.

consider the amount of available computing

If node mapping succeeds and link mapping fails,

resources at nodes at the node mapping stage

spectrum splitting is executed, and a VN iswhen constructing a VN. In contrast, the proposedconstructed if there are available FSs at alternative

method constructs VNs by mapping nodes thatpaths. Otherwise, the VN request is blocked. We

have the highest available CPU resource slots.

evaluated the performance of the proposed method

Moreover, we notice that there is a peak inby simulation for the NSFNET topology. From thespectrum splits for both methods when the

numerical results, we found that the proposed

network load is about 60 requests per millisecond.

method is effective in reducing the blocking rate.

Therefore, the number of spectrum splits is theThus, by using our proposed method, a larger

smallest for the proposed method because thenumber of VNs can be constructed over EONs.

network resources are allocated more effectively.
5.3 Percentage of number of VN requests per hops
Finally, we investigate how node mapping andthe use of spectrum splitting in link mapping
affect the percentage of the number of VN requests
per hops. Figure 8 shows the percentage of thetotal number of VN requests per hop for each of
the conventional “EON”, “EON SS” and the
proposed method. Note that we show in this figure
the results of one hop, two hops and three hops.
This is because in NSFNET the maximum numberof hops between any pair of nodes is three. Figure
8 illustrates the case where the network load is 60
requests per millisecond. From this ﬁgure, we ﬁndthat the percentage of the number of VN requests
for one hop, two hops and three hops is almost thesame for both the conventional “EON” and “EONSS” methods. However, for the proposed method,
the percentage of the number of VN requests fortwo hops is the largest, followed by one hop andthree hops. This is because, for the proposed
method, nodes with largest available CPU resource
slots are selected and mapped.

14■ 6. Conclusion

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2018. DOI 10.5281 / zenodo.1211087◆Author’s Information:

Badr Mochizuki
Assistant Professor
The Kyoto College of Graduate studies in Informatics
PhD candidate at the University of Fukui,Doctorate at Kyoto University,
M.S. at Nara Institute of Science and Technology，Member of the Institute of Electronics, Information andCommunication Engineers.

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