A Regeneration Placement, Routing and Spectrum Assignment Solution

for Translucent Elastic Optical Networks: A Joint Optimization

Approach

Claudio Gonz

alez

1 a

, Nicol

as Jara

2 b

and V

ıctor M. Albornoz

1 c

Department of Industries, Universidad Tecnica Federico Santa Maria, Campus Santiago Vitacura, Chile

Department of Electronics Engineering, Universidad Tecnica Federico Santa Maria, Valpara

ıso, Chile

Keywords:

Regeneration Placement, Routing, Spectrum Assignment, Elastic Optical Networks, Binary

Integer Programming.

Abstract:

In this paper, we propose a novel joint approach to solve the regeneration placement, routing, modulation

level, and spectrum assignment (RP-RMLSA) problem using a binary integer program (BIP) model. Using

a mock and real-world network topology, we conduct extensive numerical experiments testing the proposed

optimization model’s performance and analyzing the characteristics of the solutions found. Our results show

that considering only an optimal solution occurs when signals in need of regeneration are concentrated in one

regeneration node when considering the regeneration devices’ capital and operational expenditure.

1 INTRODUCTION

Worldwide internet trafﬁc continues to grow due

to the ever-increasing popularity of established and

emerging network services and applications. For

instance, the main content and service providers

(Google, Facebook, Amazon, and Microsoft) have

become the primary source of bandwidth demands

(TeleGeography, 2020). Nowadays, such bandwidth

demands can only be supported by the current in-

stalled optical network infrastructure. However, the

capacity of these networks is expected to be insufﬁ-

cient. This situation, called “Capacity Crunch” (CC),

manifests an impending inability of current optical ar-

chitectures to support future bandwidth demands (El-

lis et al., 2016; Waldman, 2018).

Two different courses of action can be foreseen to

solve this CC problem. The ﬁrst option consists of

installing more network resources. This investment

cannot be avoided but should be postponed as long as

possible due to the signiﬁcant expenses involved. The

second strategy is to manage the already installed net-

work infrastructure efﬁciently. This second alterna-

tive has been an important focus of research. Current

optical WDM (wavelength division multiplexing) net-

https://orcid.org/0000-0001-9661-8822

https://orcid.org/0000-0003-2495-8929

https://orcid.org/0000-0002-8500-1250

works are inefﬁcient due to the spectrum grid’s coarse

granularity, typically of 50 GHz by channel, accord-

ing to the International Telecommunications Union

(ITU) standard (ITU-T, 2012). This situation implies

that regardless of the user’s bandwidth needs, the en-

tire channel will be reserved.

A new proposal, called Elastic Optical Networks

(EON), has been researched to face previous prob-

lems (Velasco et al., 2017). EON aims to allocate

resources according to the user’s bandwidth require-

ments, dividing the frequency spectrum into narrow

bands called Frequency Slot Unit (FSU), typically of

12.5 GHz. This way, different FSUs can be group

ﬂexibly to satisfy users’ needs. As a consequence, ef-

ﬁcient management of the spectrum is achieved (Ve-

lasco et al., 2017).

One of the main tasks that elastic optical network

operators must resolve is to compute a path and a por-

tion of the frequency spectrum to each network con-

nection, known as the “routing and spectrum assign-

ment” (RSA) problem. This problem becomes more

intricated in continental, and more extensive networks

since a maximum range (in kilometers) can be found

for each connection request due to the accumulation

of physical–layer impairments (PLI). Therefore, we

must add the modulation format on the tasks, called

the “routing, modulation level, and spectrum assign-

ment” (RMLSA) problem. This problem is subject to

González, C., Jara, N. and Albornoz, V.

A Regeneration Placement, Routing and Spectrum Assignment Solution for Translucent Elastic Optical Networks: A Joint Optimization Approach.

DOI: 10.5220/0010393604670474

In Proceedings of the 10th International Conference on Operations Research and Enterprise Systems (ICORES 2021), pages 467-474

ISBN: 978-989-758-485-5

467

the following constraints. First, each channel (FSU)

can host by one user at the same time; second, the

same FSU allocated to the said user must be available

in all the links on the user path (continuity constraint);

and in case that the user requires more than one FSU,

the spectrum assigned must be consecutive (contigu-

ity constraint).

The accumulation of PLI limits the generation of

end-to-end all-optical connections (transparent con-

nections) in wide-area optical networks. In fact,

several users may not achieve transparent commu-

nication through long distances despite the modula-

tion format chosen. Therefore, the use of 3R (Re-

ampliﬁcation, Reshaping, and Retiming) regeneration

in wide-area optical networks cannot be avoided. A

node with regeneration allows increasing connections

optical range, improving the network spectrum usage

by choosing more efﬁcient modulation formats, and

allowing to break the continuity constraint due to the

OEO process. However, these devices add additional

delays for the demands due to the optical transpon-

der (OEO) needed to regenerate and signiﬁcant de-

ployment and operational costs. Therefore, the use of

these devices should be avoided as much as possible.

RMLSA standard approaches establish transpar-

ent communication between source-destination node

pairs (Velasco et al., 2017; Calder

on et al., 2020).

However, due to the need of regenerating on wide–

area networks, some approaches consider the use

of regeneration devices, resulting on translucent (re-

generators found on some nodes) or opaque net-

works (all network nodes have regeneration capa-

bilities) (Chaves et al., 2012; Chaves et al., 2015;

Brasileiro et al., 2019).

The use of regenerator devices must be as efﬁ-

cient as possible, locating them strategically in or-

der to avoid additional costs related to these devices.

This problem is known as “regeneration placement”

(RP) problem. In literature, we can ﬁnd several op-

timization approaches (Wang et al., 2015; Yıldız and

Karas¸an, 2017). However, optimization approaches

lack a joint solution for the RP and RMLSA prob-

lems or cannot be implemented in real-sized network

topologies. To take advantage of the opportunities of-

fered by the EON requires the jointly solution of RP

and RMLSA problems.

In this work, we propose an integrated optimiza-

tion model for solving the regeneration placement,

routing, modulation format, and spectrum assignment

(RP–RMLSA) problems for translucent elastic optical

networks. We rely on a physical impairment model to

compute the maximum reach of a given modulation

format and bit-rate of a connection request. This strat-

egy focuses on minimizing the use of regenerators due

to the capital and operational expenditure needed, as

well as analyzing the characteristics of good solutions

found through optimality.

The remainder of this article is organized as fol-

lows: Section 2 reviews the main strategies found in

the literature considering regeneration devices. Sec-

tion 3 presents the network assumptions and the opti-

mization model proposal. Section 4 shows some nu-

merical experiments for two network topologies. Fi-

nally, section 5 illustrates conclusions and ﬁnal re-

marks of the work.

2 STATE OF THE ART

In this section, we conduct a review of the leading

strategies and contributions considering regeneration

found in the literature.

The joint solution for the regenerator place-

ment, routing, modulation level, and spectrum assign-

ment problems (RP–RMLSA) is known to be NP–

hard (Brasileiro et al., 2019; Calder

on et al., 2020).

Even some of these problems by themselves are also

known to be NP–hard (Velasco et al., 2017).

Therefore, several ways to solve the regeneration

problem can be found in the literature but with some

sort of simpliﬁcation. In (Klinkowski, 2012), the au-

thors propose a heuristic algorithm to solve the regen-

eration placement and spectrum assignment problem

jointly, but considering a static demand structure and

a pre–computed ﬁxed path for each network demand.

Relaxing the ﬁx route constraint, in (Kahya, 2013) the

authors present a sequential solution approach, solv-

ing the regeneration placement, routing, spectrum as-

signment problem in EON, but for only one modula-

tion format.

In (Wang et al., 2015) the authors present a

Mixed–Integer Linear Programming (MILP) formu-

lation to solve the regeneration placement problem in

an elastic optical network. Since their proposal can

not solve real-size problems, they proposed a sequen-

tial heuristic approach randomly partitioning the set

of demands.

In (Yıldız and Karas¸an, 2017) the authors present

a branch–and–price algorithm to jointly solve the RP–

RMLSA problem for real–size network topologies.

They introduce a path segment formulation of the

route to simplify the problem, imposing the maximum

optical reach for the network demands. In our study,

we use the same strategy but differing on the spectrum

assignment treatment. Yildiz et al. compute only the

usage of FSUs on each link by not calculating the por-

tion of the spectrum used by all the network users; this

way simplifying the model. However, network opera-

ICORES 2021 - 10th International Conference on Operations Research and Enterprise Systems

468

tors demand the position of the FSUs assigned to each

network user in order to conﬁgure the network and as-

sess the quality of the solution.

On the other hand, the regeneration problem in

EON has been solved considering two different prob-

lems in a hierarchical modeling approach: the Re-

generator Placement (RP) and Regenerator Assign-

ment (RA) problems (Fontinele et al., 2016). The

RP problem deﬁnes which nodes will allow regener-

ation capacity, and the RA problem deﬁnes, in each

node, which connections are regenerated. Hence, the

RP problem must be solved during the network plan-

ning phase while the RA problem during the network

operation phase. The algorithms used to solve the

RP problem are: Maximum Simultaneously Used Re-

generator Placement (MSU), Most Used Regenera-

tor Placement (MU), Distance Adaptive Regenerator

Localization Algorithm (DA), and Node Degree First

(NDF) (Chaves et al., 2012). The algorithms used to

solve the RA problem are: First Longest Reach Re-

generator Assignment (FLR), First Narrowest Spec-

trum Regenerator Assignment (FNS) (Chaves et al.,

2015) and Circuit Invigorating Regenerator Assign-

ment (CIRA) (Brasileiro et al., 2019).

To the best of our knowledge, our study is the

ﬁrst to consider every aspect of EON for the regen-

eration placement problem. To solve the regeneration

placement, routing, modulation format, and spectrum

assignation problem, we use the same path–segment

formulation found in (Yıldız and Karas¸an, 2017) but

including the spectrum utilization decision and con-

straints.

3 NETWORK ASSUMPTIONS

AND MODEL

This section comprises the main contribution of the

article. First, we describe the physical–layer impair-

ment model used to determine the number of FSU’s

assigned to each demand. Then, we present the opti-

mization model used to jointly solve the regeneration

placement problem (RP) and the RMLSA problem.

3.1 Physical-layer Impairments Model

The quality of transmission (QoT) of optical signals

is degraded by different phenomena occurring during

the modulation, propagation, and detection processes.

In particular, to solve the RMLSA problem, we con-

sider the impact that the ampliﬁed spontaneous emis-

sion (ASE) noise and non–linear interference noise

has on the QoT. The accumulation of noise during

propagation determines the maximum optical reach

that a signal can have for a given modulation level

and bit error rate (BER) combination. With a high

number of bits per symbol, complex modulation for-

mats increase the transmission sensitivity to degra-

dation. Thus, the transmission reach is shorter for

higher modulation levels compared to simpler for-

mats (Yaghubi-Namaad et al., 2018). To consider this

route length - modulation level trade–off, the most

common approach is to associate any modulation for-

mat available at the transponder to its maximum trans-

mission reach for a given BER value (Talebi et al.,

2014). This approach is also used in this work.

The modulation formats used in this work are bi-

nary phase-shift keying (BPSK), quadrature phase-

shift keying (QPSK), and Λ–quadrature amplitude

modulation (Λ-QAM), where Λ takes values 8 and 16.

Table 1 shows the transmission reach, using single-

polarization, as a function of the modulation format

and bit–rates available at the transponders. The ﬁrst

two columns in Table 1 show the maximum achiev-

able reach (MAR) that an optical signal can travel

without exceeding a BER of 10

−6

. – assuming single-

polarization – as a function of the modulation format

available at the transponders. The optical reach values

were obtained using the GN model (Poggiolini et al.,

2014) to estimate the received signal–to–noise ratio

(SNR) degraded by ASE noise and non–linear inter-

ference noise. For more details about the optical reach

calculation, the reader is referred to (Calder

on et al.,

2020), Section III.

Table 1: Maximum achievable reach (MAR) per modula-

tion format and FSU requirements per bit–rate and modula-

tion format pair, for a BER value equal to 10

−6

Modulation MAR [km]

Bit-rates

10 40 100

BPSK 5525 1 4 8

QPSK 2720 1 2 4

8-QAM 1360 1 2 3

16-QAM 560 1 1 2

3.2 Optimization Model

This subsection presents a binary integer program

(BIP) to solve the regenerator placement, routing,

modulation format, and spectrum assignment prob-

lem (RP–RMLSA), as well as its notation.

Let G(N, A) be a directed graph representing an

elastic optical network with node set N, and optical

arc set A. The arc length are denoted by l

i, j

for each

arc (i, j) ∈ A. We denote the set M as the available

modulation formats, where l

represents the maxi-

mum achievable reach of modulation m ∈ M. We de-

ﬁne D as the set of transmission demands. For each

A Regeneration Placement, Routing and Spectrum Assignment Solution for Translucent Elastic Optical Networks: A Joint Optimization

Approach

469

demand d ∈ D we denote o

as the source node, t

the destination node, and b

as the requested bit–rate

in Gbps.

For the route assignment part of the problem

we use the path segments formulation (Yıldız and

Karas¸an, 2017). A path segment p is a directed sim-

ple path with an associated modulation level m(p). A

directed path is simple if it does not repeat any node.

We denote the source and destination nodes of a path

segment p as o

and t

, respectively. Let in

i, j, p

a parameter equal to 1 if the arc (i, j) ∈ A is part of

the path segment p. This way, we can calculate the

length of the path–segment l

∑

(i, j)∈A

i, j

· in

i, j, p

the sum of the arcs contained within p. Considering

that each path–segment p is associated with a mod-

ulation format m(p), a path–segment is feasible if it

respects the MAR limitation of its own modulation

format(Table 1). Namely, a path–segment p is feasi-

ble if l

≤ l

m(p)

. We deﬁne P as the set of all feasi-

ble path–segments. Then, a route is an ordered union

of feasible path–segments p

∈ P, i ∈ 1, ··· , k where

= o

i+1

for all i = 1, · · · , k − 1. For that route to

be assigned to demand d it must satisfy that o

= o

and t

= t

. With this path–segment formulation, the

MAR restriction is implicitly taken into consideration

by using only the feasible path–segments.

We denote S as the set of FSU available for all

optical ﬁbers. The amount of FSU required for a de-

mand d depends on the modulation level used and the

amount of bit–rate requested. So, we denote the set of

connections C(m, b

) = {1, 2, · · · ,c} as all the differ-

ent positions inside the spectrum where it can be as-

signed the signal depending on the bit–rate and mod-

ulation format. It does not depends on the ﬁber used.

As an example, for modulation format BPSK and a

bit–rate of 40 Gbps, the amount of FSU required is

4 and C(m = BPSK, b

= 40) represent the c different

ways to assigned those 4 consecutive FSU in the spec-

trum represented by S. Let p

c,s

be a parameter equal

to 1 if the connection c ∈ C uses the FSU s ∈ S within

the spectrum. Then, forall c ∈ C(m, b

) the contiguity

constraint is implicitly imposed by the proper deﬁni-

tion of p

c,s

such that ∀i, j ∈ S : p

c,i

= p

c, j

= 1, i < j ⇒

c,k

= 1, ∀k ∈ {i, ··· , j}. And

∑

s∈S

c,s

is equal to the

amount of FSU needed given in Table 1. We denote C

as the set of all possible positions for any amount of

FSU required. So, C(m, b

) is a subset of C.

For the regeneration aspect, we denote c

as the

capital cost of installing a regenerator in node i ∈ N,

and η as the cost of operating that regenerator for

each signal regenerated. Using the path–segment for-

mulation, where the route is the ordered union of

, i ∈ 1, ··· , k, we can identify t

as a regeneration

node for all i = 1, ··· , k − 1. In other words, to use

Table 2: Outline of notation.

N Set of nodes, index n.

A Set of arcs.

M Set of modulation formats, index m.

D Set of demands, index d.

P Set of feasible path–segments, index

S Set of FSU, index s.

C Set of all connections available.

C(m, b

) Subset of connections available for

modulation m and bitrate b

Source node of demand d.

Destination node of demand d.

Bitrate requested by demand d.

Source node of path–segment p.

Destination node of path–segment p.

m(p) Modulation format associated with

the path–segment p.

i, j, p

Equal to 1 if arc (i, j) ∈ A is part of

the path–segment p.

c,s

Equal to 1 if connection c uses slice

s ∈ S.

Cost for regenerator placement.

η Regenerator usage cost.

more than one path–segment the signal must be regen-

erated. Another aspect to consider is that there must

be only one connection used for each path–segment

used by demand d.

Since it is of interest to use the least amount of re-

generators, the main objective is to minimize the to-

tal capital and operational cost of regeneration. So

the RP–RMLSA problem can be formally stated as

follow: given a graph G(N, A), the total spectrum

S, the modulation formats M and the trafﬁc demand

D, we obtain as output the route composed by path–

segments and the connection for each demand and the

nodes where the demands regenerated, resulting from

the minimization of the total cost of regeneration. The

notation we use throughout this paper is outlined in

Table 2.

The decision variables of the model are:

d pc

a binary decision that takes a value

equal to 1 if demand d use path–

segment p with connection c and 0

otherwise.

a binary decision that takes a value

equal to 1 if node n is a regeneration

point and 0 otherwise.

We name x

d pc

as the ﬂow variable that represents

the routing and spectrum assignment decision. As

we mentioned, the route is a concatenation of path–

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470

segments, and in every path–segment where the de-

mand passes through, we need to assign only one

position inside the spectrum. So if

∑

p∈P

d pc

≥ 1 it

means that it regenerated because it use more than one

path–segment. We name r

, n ∈ N as the regeneration

variable and indicates if node n is a regeneration site

or not.

Then, the RP-RMLSA formulation is as follows:

min

∑

n∈N

∑

d∈D

p∈P

c∈C

6=t

ηx

d,p,c

(1)

subject to:

∑

p∈P

∑

c∈C(d)

d pc

−

∑

p∈P

∑

c∈C(d)

d pc







1 if i = o

−1 if i = t

0 e.o.c

∀i ∈ N, d ∈ D

(2)

∑

c∈C

d pc

≤ 1 ∀d ∈ D, p ∈ P (3)

∑

p∈P

d pc

≤ r

∀d ∈ D, c ∈ C, n ∈ N \ t

(4)

∑

p∈P

∑

d∈D

∑

c∈C(m(p),b

)

i, j, p

· p

c,s

· x

d pc

≤ 1

∀(i, j) ∈ A, s ∈ S

(5)

d pc

∈ {0, 1}, ∀d ∈ D, p ∈ P, c ∈ C (6)

∈ {0, 1}, ∀n ∈ N (7)

The objective function (1) minimize both the total

cost of installing a regeneration site on the nodes and

the cost of regenerating a signal. The ﬁrst term rep-

resents the ﬁxed cost of setting a regenerator site in

node n. The second term represents the cost of adding

a regenerator device to the regenerator site.

Constraints (2) are the ﬂow balance equations that

force each demand to be carried from its source to

its destination. Constraints (3) are the continuity con-

straint which ensures that only one connection is used

for every path–segment and demand. Constraints (4)

enforce regeneration requirements by ensuring regen-

eration at the end of each possible path–segment that

does not end in the destination node of the associated

demand. Constraints (5) guarantees that every FSU at

every arc is assigned at most to one demand. Finally,

constraints (6) and (7) deﬁne the binary nature of the

variables. This formulation is quite compact but con-

tains every aspect of the regeneration and the RMLSA

problems.

With this model’s output, we can compute the

number of signals regenerated in the regeneration site

and see the spectrum utilization. The ﬁrst one states

as follows:

∑

d∈D

p∈P

c∈C

6=t

d,p,c

∀n ∈ N (8)

where nr

is the number of signals regenerated in

node n. The second one can be compute as follows:

i, j,s

∑

p∈P

∑

d∈D

∑

c∈C(m(p),b

)

i, j, p

· p

c,s

· x

d pc

∀(i, j) ∈ A, s ∈ S.

(9)

where u

i, j,s

is equal to 1 if FSU s is used by a demand

in arc (i, j). With these extra results we expand the

amount of info the RP-RMLSA gives without making

more complex the formulation.

4 NUMERICAL EXPERIMENTS

In this section, several numerical experiments are

conducted to test the proposed solution and derive

insights from the instances. We implemented the

optimization model using AMPL under MacOS and

GUROBI 9.0.2. All experiments were done on a 3.1

GHz Dual–Core Intel Core i5 with 8 GB of RAM.

Table 3: Network characteristics summary.

Parameter Value

Topology Basic Net, NSFNet

Links Capacity 40 slots

Bitrates 10, 40, 100 Gbps

Modulation

formats

BPSK, QPSK, 8-QAM, 16-QAM

FSUs and MAR Table 1

Table 3 summarizes the network characteristics in

which we execute our proposal. First, we studied a

mock network called Basic Net (Figure 1) in order

to preliminary test the model. Then, we use the well-

known real network topology NSFNet (Figure 2). Ex-

tra network information can be found in Table 4.

Table 4: Network topologies parameters.

Network Nodes Links Demands

Basic Net 7 11 42

NSFNet 14 21 182

A Regeneration Placement, Routing and Spectrum Assignment Solution for Translucent Elastic Optical Networks: A Joint Optimization

Approach

471

Figure 1: Basic Net network.

Figure 2: NSFNet network.

We compute the feasible set S composed of path–

segments based on each network arc length and the

available modulation formats available for each exer-

cise. The network capacity was set to 1/8 of the to-

tal C-band spectrum frequency (40 FSUs per network

link) (Calder

on et al., 2020).

We assume that every source–destination node

pair demand communication (|D| = |N| · (|N| − 1).

The bit–rate requests were deﬁned for each connec-

tion request using two criteria: the ﬁrst one assigns

randomly the bit–rate to each user uniformly dis-

tributed between the values 10, 40, and 100 Gbps; and

the second one assigns the worst–case scenario with

only the highest bit–rate available, this is 100 Gbps

for all connection requests. The second scenario is

considered the worst one since demands would need

the highest amount of FSU possible, increasing link

usage, and even increasing demand regeneration to

reach destination nodes.

For this study, we run ﬁve instances of the pro-

posed model considering different scenarios. Table 5

shows the solutions of the RP-RMLSA model for

these instances. The ﬁrst four columns represent the

different characteristics of the instances. The Basic

Net was only executed for the two criteria of bit–rate

assignment, both using BPSK to 8QAM as an option

for their connection modulation formats. On the other

hand, the NSFNet was solved for both bit–rate as-

signment criteria and two different ranges of modu-

lation formats (MF). These are BPSK to 8QAM and

QPSK to 16QAM. The differences in modulation for-

mats availability are based on increasing the chances

of regeneration on the execution since complex mod-

ulation formats have a higher spectrum efﬁciency but

with a lesser optical reach, incurring a higher use of

regeneration.

The PS column represents the number of path–

segments pre–computed. Lastly, the remaining

columns represent the solution obtained by executing

our model. For instance, the Basic Net with random

bit–rate (Instance 1), the solution takes 17.8 seconds

(RunTime column), it only used the node 3 (RN col-

umn) to regenerate two connection requests (NR), and

with a spectrum frequency usage of 31.4% (%FSU

column).

As shown in Table 5, almost on all the instances,

the RP-RMLSA model chooses one at most one re-

generation node as a regeneration site, then concen-

trating the regeneration of several connections in only

one network node despite the number of connections

being regenerated along their paths. This situation

makes sense because the objective function is to mini-

mize the costs related to regenerate optical signals. As

expected, the running time of the instances with Basic

Net was shorter than the ones with NSFNet because of

the number of nodes, links, and demands. In fact, the

computational complexity of the RP-RMLSA prob-

lem makes more difﬁcult to solve large instances of

the problem, as we can see at Instance 5.

In the Basic Net it regenerated on node 3 for both

instances. In this case, the regeneration site is on the

network core, also the node serving a larger number

of users. We can see that the result of both random

and worst–case instances is the same; the difference

is in the running time and the spectrum’s utilization.

In the regeneration model, the primary constraint is

the MAR, so increasing trafﬁc in this network did not

affect the regeneration decision.

On the NSFNet network, Instance 3 did not need

to regenerate. This situation is due to the short dis-

tances of the arcs, where the minimum, average and

maximum lengths are 212, 509, and 1140 km, respec-

tively. By removing BPSK and adding 16QAM as

a modulation format option, we are forcing the net-

work to regenerate. So as expected, Instance 4 regen-

erate six demands in node 0. This node is on the net-

work fringe, in contrast to the Basic Net solution. Ta-

ble 6 exempliﬁes the six connection demands regen-

erated on the ﬁfth instance separated by their path–

segments. Notice that the users with regeneration are

three nodes pairs communicating in a round–trip, For

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472

Table 5: Results of the RP-RMLSA model.

Instances Network Bitrate MF PS RunTime RN N

R %FSU

1 Basic Net Random BPSK to 8QAM 122 17.885 3 2 31.4

2 Basic Net Worst Case BPSK to 8QAM 122 50.845 3 2 50.3

3 NSFNet Random BPSK to 8QAM 682 4472.390 None 0 60.5

4 NSFNet Random QPSK to 16QAM 404 46375.800 0 6 55.0

5 NSFNet Worst Case QPSK to 16QAM 404 298426.400 0 6 68.3

FSU

(0, 1)

(0, 2)

(0, 7)

(1, 2)

(1, 3)

(2, 5)

(3, 4)

(3, 10 )

(4, 5)

(4, 6)

(5, 9)

(5, 13 )

(6, 7)

(7, 8)

(8, 9)

(8, 11 )

(8, 12 )

(10, 11 )

(10, 12 )

(11, 13 )

(12, 13 )

(1, 0)

(2, 0)

(7, 0)

(2, 1)

(3, 1)

(5, 2)

(4, 3)

(10, 3)

(5, 4)

(6, 4)

(9, 5)

(13, 5)

(7, 6)

(8, 7)

(9, 8)

(11, 8)

(12, 8)

(11, 10 )

(12, 10 )

(13, 11 )

(13, 12 )

1 1 0 1 0 1 1 1 1 0 1 0 0 1 1 1 0 1 0 0 0 1 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 0 0 0 0 0 0

2 1 0 1 0 1 1 0 1 0 1 0 0 1 1 1 1 1 0 0 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 0

3 0 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 0 0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 1 0 0

4 0 1 1 0 0 1 0 1 1 1 0 1 1 1 1 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 0 0

5 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 0 0 0 0 1 1 1 1 1 1 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0

6 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 1 1 1 1 0 1 0 0 1 0 1 0 0 1 0 0 0 0

7 1 1 1 0 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0

8 1 1 1 0 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 1 1 0 0 0 1 0 0 0 0 0

9 1 1 0 0 1 1 1 0 1 1 1 1 0 1 0 0 1 1 0 0 0 0 0 1 1 0 1 0 1 1 1 1 1 1 0 0 1 0 0 0 0 0

10 1 1 0 0 0 1 1 1 0 1 0 1 0 1 0 0 1 1 0 0 0 0 0 1 0 0 1 0 1 1 1 1 1 1 1 0 1 0 0 0 0 0

11 0 1 0 0 0 0 1 1 1 1 0 1 0 1 0 0 1 1 0 1 0 0 1 0 1 0 1 0 1 1 0 1 1 1 1 0 1 0 0 0 1 0

12 0 0 0 0 1 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 0 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 1 1 0 0 1 1

13 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 0 0 1 0 0 0 1 1 1 0 1 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 1

14 0 1 1 0 1 1 0 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 1 1 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 0 1

15 1 1 1 0 1 1 0 0 1 0 1 0 1 1 1 1 0 0 0 0 1 0 1 1 1 0 1 1 0 1 0 0 1 0 1 0 0 1 1 0 1 1

16 0 0 1 0 0 1 1 0 1 0 1 0 1 0 0 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 0 0 1 0 0 0 0 1 0 1 0

17 0 0 1 0 1 0 1 1 1 1 1 0 0 1 1 1 0 0 0 0 0 1 1 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 0 0 0 1

18 0 0 1 0 1 0 1 1 1 1 1 0 1 1 1 0 1 0 0 0 0 0 1 1 1 0 0 1 0 1 1 0 1 1 1 1 1 1 0 0 0 0

19 0 0 0 1 1 1 0 1 1 0 1 1 1 1 0 1 1 1 1 0 0 0 0 0 1 0 1 1 0 1 1 1 0 1 1 1 1 0 0 0 0 1

20 0 0 1 1 1 1 0 1 1 1 1 1 0 1 0 1 1 1 1 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 1 1 1 0 0 0 0 1

21 1 0 1 1 0 1 1 0 1 1 0 1 0 1 0 1 1 1 0 0 0 0 0 1 0 0 1 0 1 1 1 1 1 0 1 0 0 1 1 0 0 1

22 1 0 0 1 1 1 1 1 0 1 0 1 1 1 0 0 1 1 0 0 1 1 0 0 0 1 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 1

23 0 0 0 0 1 0 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 0 0 0 1 1 1 0 1 0 1 1 0 1 1 0 1 1 0 0 0

24 0 0 1 1 1 0 0 1 1 1 0 1 0 1 0 0 0 1 1 1 0 1 0 0 0 1 1 0 1 1 1 1 1 0 1 0 0 1 0 0 0 0

25 0 1 1 1 1 0 0 1 1 1 0 1 0 1 0 0 0 1 1 1 0 1 0 1 0 1 0 0 1 1 1 1 1 0 1 0 0 1 0 0 0 0

26 0 0 1 0 0 0 0 1 1 0 0 0 0 1 1 1 0 0 1 1 0 0 0 0 1 0 1 1 0 1 1 1 1 1 1 0 0 1 0 0 0 0

27 0 1 1 0 1 1 1 1 1 1 0 1 0 1 1 1 0 0 1 0 1 0 0 1 1 0 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0

28 1 1 0 0 1 1 0 1 1 0 0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 0 1 0 1 0 1 1 1 0 0 0 1 1 0 0

29 1 0 0 0 1 0 1 1 1 0 0 0 1 1 0 1 1 1 1 0 1 0 0 0 1 1 1 1 1 1 1 0 1 0 0 0 0 1 1 1 0 1

30 1 0 0 0 1 0 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 0 0 1 1 1 1 0 1 1 1 1 0 0 0 0 0 1 1 0 1

31 1 0 1 1 1 1 1 1 1 0 1 1 0 0 1 0 0 1 0 1 1 0 0 1 0 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0 1

32 0 0 1 1 0 1 1 0 1 0 1 1 0 1 0 0 0 0 0 0 1 1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 1

33 0 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 1 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1

34 0 0 0 1 0 1 0 0 1 1 0 1 1 1 1 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 1 0 1 0 1 1 0 0 0 0 0 0

35 0 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 0 0 0 1 1 1 0 1 0 0 0 1 0 1 1 1 1 0 1 1 0 0 0 0 1 0

36 0 0 1 0 0 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 1 0 1 0 0 0 1 0 1 1 0 0 1 0 0 1

37 1 0 1 0 1 1 0 1 0 0 1 1 0 1 1 0 1 1 0 0 0 0 1 1 0 0 1 1 1 0 1 0 1 1 1 1 1 0 1 1 0 1

38 1 0 1 1 1 1 0 1 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 0

39 1 0 1 1 1 1 0 1 1 0 0 1 0 1 0 0 1 0 0 1 0 0 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1

40 1 1 1 1 1 1 0 1 1 0 0 1 0 1 0 0 1 0 0 1 0 1 0 1 0 1 0 1 0 1 1 0 0 1 0 0 0 1 0 1 1 1

Figure 3: Spectrum utilization for instance 4.

instance, demands transmitting from node 1 to 12 and

vice–versa (see demand 25 and 158 in Table 6). The

same occurred in the Basic Net, with only one origin–

destination pair.

Additionally, we can see that some demands

changed the modulation format used on the differ-

ent segments. This situation can be explained since

users search for a room on each link’s used capacity,

therefore choosing a modulation format with higher

spectrum efﬁciency if needed. However, It does not

always select the most efﬁcient modulation because it

only minimizes the cost of using regeneration, not the

spectrum usage.

Another interesting analysis is related to the uti-

lization of the spectrum. By including regenera-

tor nodes, we decrease the percentage of spectrum

used. This reduction is coherent with previous ref-

erences (Klinkowski, 2012). However, since we do

Table 6: Demands with regeneration for instance 4.

Demand Path-Segment Modulation FSU used

25 (1,0) QPSK 32,33

25 (0,7,8,12) QPSK 20,21

37 (2,0) QPSK 28

37 (0,7,8,11) QPSK 26

47 (3,1,0) 8QAM 16,17

47 (0,7,8) QPSK 1,2

108 (8,7,0) QPSK 31,32

108 (0,1,3) 8QAM 1,2

146 (11,8,7,0) QPSK 20

146 (0,2) QPSK 33

158 (12,8,7,0) QPSK 21

158 (0,1) 16QAM 14

not minimize the spectrum usage on the model, the

utilization is not optimal. As we can see in Figure 3,

the spectrum assignment does not seem to follow any

observable rule. So the amount of fragmentation in

A Regeneration Placement, Routing and Spectrum Assignment Solution for Translucent Elastic Optical Networks: A Joint Optimization

Approach

473

the spectrum is very high. This performance opens

the possibility of applying a de-fragmentation method

like the ones found in (Velasco et al., 2017) or mod-

ifying the RP-RMLSA formulation to minimize the

network fragmentation.

5 CONCLUSIONS

In this work, we propose a BLP formulation to jointly

solve the regeneration placement, routing, modulation

format, and spectrum assignment problems (known as

RP–RMLSA). The RP–RMLSA model formulated is

both complete and straightforward, considering every

characteristic of the elastic optical network architec-

tures, and regeneration devices. We show through dif-

ferent instances that the optimal number of regenera-

tion sites is one or none, located on different network

nodes depending on the topology. Finally, when re-

generation occurs on a given source–destination node,

it will also regenerate the same node pair but transmit-

ting on the opposite side, solving the problems sym-

metrically.

Future work intends to include a cost of frag-

mentation to the RP–RMLSA formulation, seeking

to minimize both the regeneration cost and the spec-

trum usage on the network links. Also, we intend to

test the model with larger networks trying to reduce

the execution time with OR techniques aiming to face

the computational complexity of the problem. Finally,

formulate an RP algorithm to reach a similar solution

found in the RP–RMLSA model but with consider-

ably lower running time, assessing the trade–off be-

tween complexity and optimality, and compare it with

the hierarchical modeling approach.

ACKNOWLEDGEMENTS

This work received ﬁnancial support from PI

LII

2020 74, and DGIIP masters scholarship program

from USM, as well as ANID FONDECYT Iniciaci

11201024.

REFERENCES

Brasileiro,

I., Valdemir, J., and Soares, A. (2019). Regen-

erator assignment with circuit invigorating. Optical

Switching and Networking, 34:58–66.

Calder

on, F. I., Lozada, A., B

orquez-Paredes, D., Olivares,

R., Davalos, E. J., Saavedra, G., Jara, N., and Leiva,

A. (2020). Ber-adaptive rmlsa algorithm for wide-area

ﬂexible optical networks. IEEE Access, 8:128018–

128031.

Chaves, D. A., Carvalho, R. V., Pereira, H. A., Bastos-Filho,

C. J., and Martins-Filho, J. F. (2012). Novel strate-

gies for sparse regenerator placement in translucent

optical networks. Photonic Network Communications,

24(3):237–251.

Chaves, D. A., da Silva, E. F., Bastos-Filho, C. J., Pereira,

H. A., and Almeida, R. C. (2015). Heuristic algo-

rithms for regenerator assignment in dynamic translu-

cent elastic optical networks. In 2015 17th Interna-

tional Conference on Transparent Optical Networks

(ICTON), pages 1–4. IEEE.

Ellis, A. D., Mac Suibhne, N., Saad, D., and Payne, D. N.

(2016). Communication networks beyond the capac-

ity crunch. Philosophical Transactions of the Royal

Society A: Mathematical, Physical and Engineering

Sciences, 374(2062).

Fontinele, A., Santos, I., Dur

aes, G., and Soares, A. (2016).

Achievement of fair and efﬁcient regenerator alloca-

tions in translucent optical networks using the novel

regenerator assignment algorithm. Optical Switching

and Networking, 19:22–39.

ITU-T (2012). Spectral grids for wdm applications: Dwdm

frequency grid. ITU-T G.694.1, Telecommunication

Standardization Sector of ITU, Ginebra, Switzerland.

Kahya, A. (2013). Routing, spectrum allocation and re-

generator placement in ﬂexible-grid optical networks.

PhD thesis, bilkent university.

Klinkowski, M. (2012). On the effect of regenerator place-

ment on spectrum usage in translucent elastic optical

networks. In 2012 14th International Conference on

Transparent Optical Networks (ICTON), pages 1–6.

IEEE.

Poggiolini, P., Bosco, G., Carena, A., Curri, V., Jiang, Y.,

and Forghieri, F. (2014). The gn-model of ﬁber non-

linear propagation and its applications. Journal of

Lightwave Technology, 32:694–721.

Talebi, S., Alam, F., Katib, I., Khamis, M., Salama, R., and

Rouskas, G. N. (2014). Spectrum management tech-

niques for elastic optical networks: A survey. Optical

Switching and Networking, 13:34–48.

TeleGeography (2020). The state of the network 2020 edi-

tion.

Velasco, L., Vela, A. P., Morales, F., and Ruiz, M. (2017).

Designing, operating, and reoptimizing elastic op-

tical networks. Journal of Lightwave Technology,

35(3):513–526.

Waldman, H. (2018). The Impending Optical Network Ca-

pacity Crunch. Sbfoton Conference, pages 1–3.

Wang, X., Brandt-Pearce, M., and Subramaniam, S. (2015).

Impact of wavelength and modulation conversion

on translucent elastic optical networks using milp.

Journal of Optical Communications and Networking,

7(7):644–655.

Yaghubi-Namaad, M., Rahbar, A. G., and Alizadeh, B.

(2018). Adaptive modulation and ﬂexible resource al-

location in space-division-multiplexed elastic optical

networks. Journal of Optical Communications and

Networking, 10(3):240–251.

Yıldız, B. and Karas¸an, O. E. (2017). Regenerator loca-

tion problem in ﬂexible optical networks. Operations

Research, 65(3):595–620.

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