Strategies and Benefits of DeployingUltralow-Loss Fiber Links inan Elastic Optical Network

Yongcheng Li, Yonghu Yan, Wei Chen, Sanjay K. Bose, and Gangxiang Shen

Abstract—Superchannels using efficient formats formodulation [e.g., 16-quadrature amplitude modulation(QAM), 64-QAM] and transmitting high data rates (e.g.,400 Gb/s, 1 Tb/s, or even 10 Tb/s) are expected to dominatein future optical networks. Ultralow-loss (ULL) fibers prom-ise greater efficiencies for carrying such superchannels, andthe current trend is to deploy ULL fibers for new networklinks.However, thiswouldgenerallybedone ina stagedman-ner because of budgetary constraints, strategically selectingthe links for new ULL fiber deployments so as to maximizenetwork performance improvement at each stage. We ad-dress thisprobleminthecontextofanelasticopticalnetworkand propose approaches for doing this for both static anddynamic traffic demands. For static traffic demands, we for-mulate the problem using mixed-integer linear-programingmodels and also propose efficient heuristic algorithms. Fordynamic traffic demands, we propose a deployment strategybased on lightpath blocking because of inadequate opticalsignal-to-noise ratios. Simulation studies show the efficiencyof the proposed strategies and an interesting performancesaturation behavior in test scenarios.

Index Terms—Elastic optical networks; Spectrum win-dow plane; Ultralow-loss fiber.

I. INTRODUCTION

N etwork operators installing optical cables typicallypresume a cable service life of 25 years [1].

Because a large number of fiber cables were deployed inthe 1990s, operators would be considering installing newfiber cables now and in the near future. We also expectsuperchannels to dominate in the future optical transportnetwork. Although a large number of dark standard single-mode fibers (SSMFs) may still be lying unused under-ground, the maximum transparent reach of a superchannelusing these fibers would be significantly limited. Usingthem would require the usage of a large number of signalregenerators, significantly increasing the cost of thenetwork. A better strategy would be to transmit these

superchannels for longer distances using optical fibers withbetter transmission performance. Ultralow-loss (ULL)fibers have been considered a good candidate for this.

From the technology and market point of view, deployingULL fibers in a backbone optical network is becomingincreasingly common. The technology of fabricating ULLfibers has become fairly mature. There are several key fiberfabricators that have been able to produce ULL fibers on alarge scale, e.g., Corning SMF-28 ULL fibers [2], YOFCFullBand ULL fibers [3], and Hengtong NGFCom ULL fi-bers [4]. The market for ULL fiber cables is also increasing.For example, in China, large carriers have started to deployULL fibers for their backbone links. China Telecom [5] firstdeployed a 105 km ULL fiber link between Xuzhou andSuining in Jiangsu Province in 2015. China Unicom [6] car-ried out two trials indifferent areas, includinga430kmULLfiber link deployed in easternChina and a 150 kmULL fiberlink deployed in western China in 2016. Likewise, ChinaMobile [7] also deployed the world’s longest 1500 km ULLfiber link from Beijing to Nanjing in 2017. This trend isexpected to continue andwould eventually drive optical net-works to use ULL fibers in all of their links.

However, considering the large scale of a typical carrier’snetwork, we expect a carrier to deploy ULL fiber links in astaged manner, where, in each stage, only a partial set ofnetwork links are deployed with ULL fibers. It is alsoexpected that during the deployment, the carrier will alsoexploit the new ULL fiber links deployed for better signaltransmission and higher network spectrum utilization.In each stage, selecting the network links for ULL fiberdeployment would be important. A good strategy shouldselect links so that maximum performance improvementis obtained when these are deployed with ULL fibers.

In addition, in the course of ULL fiber-link deployment,network links with SSMFs and ULL fibers would coexistin an optical network. In this study, on a link that isdeployed with both new ULL fibers and old SSMFs inparallel, we assume that the newly deployed ULL fibersare always first used to establish new optical channelsfor better transmission performance, leaving the oldSSMFs on the same link untouched.1 However, for the links

https://doi.org/10.1364/JOCN.11.000238

Manuscript received January 2, 2019; revised February 18, 2019;accepted March 11, 2019; published April 9, 2019 (Doc. ID 354810).

Y. Li and G. Shen (e-mail: shengx@suda.edu.cn) are with the School ofElectronic and Information Engineering, Soochow University, Suzhou,Jiangsu Province 215006, China.

Y. Yan and W. Chen are with Jiangsu Hengtong Fiber Science andTechnology Corporation, Suzhou, China.

S. K. Bose is with the Department of Electronics and ElectricalEngineering, Indian Institute of Technology Guwahati, Guwahati, India.

1It is interesting to also consider using dark SSMFs on the links that aredeployed with ULL fibers. This is, however, not considered in this studyand would be a topic for a future study.

238 J. OPT. COMMUN. NETW./VOL. 11, NO. 5/MAY 2019 Li et al.

1943-0620/19/050238-12 Journal © 2019 Optical Society of America

that have not deployed ULL fibers, we continue usingthe old SSMFs to establish optical channels. A lightpathestablished in this type of network can often traversedifferent segments of ULL fibers and SSMFs. Therefore,to efficiently utilize network spectrum resources, it isimportant to consider the routing, modulation format,and spectrum assignment (RMSA) problem for this mixedscenario.

This paper aims to tackle the two key research problemsmentioned, and its main contributions are as follows. Welook into the problem of ULL fiber-link deployment inthe context of an elastic optical network (EON) [8,9], forwhich both static and dynamic traffic demands are consid-ered. For the static traffic demand, we formulate theproblem using mixed-integer linear-programming (MILP)models, aiming to minimize the maximum number offrequency slots (FSs) used. We also decompose the probleminto two subproblems, i.e., the subproblem of deployingULL fiber links (DUFL) and the RMSA subproblem for anEON with different types of fiber links (RMSA-DTFL). Forthe DUFL subproblem, we consider four different strate-gies to select network links for ULL fiber deployment,including random, physical length (PL), shortest routetraversed (SRT), and least-cost (LC)-based strategies. Wethen extend the conventional spectrum window plane(SWP)-based heuristic algorithm to tackle the RMSA-DTFL subproblem. For the dynamic traffic demand, inaddition to the strategies proposed for the static trafficdemand, we also propose an optical signal-to-noise ratio(OSNR) blocking (OB)-based strategy, which selects net-work links for ULL fiber deployment based on the links’transmission performance. We aim to minimize the band-width-blocking probability (BBP) of an entire networkafter the network links are deployed with ULL fibers.The results show the effectiveness of the proposed ap-proaches. In addition, it is interesting to see that, for thesimulation study cases considered, there is a saturationphenomenon between the network performance and thefiber attenuation coefficient. That is, deploying ULL fiberswith a 0.168 dB/km attenuation coefficient is sufficientto achieve a good network performance, and reducingthe coefficient further would not significantly improveperformance.

The remainder of this paper is structured as follows.Section II reviews related works on ULL fibers, theestimation of quality of transmission of a lightpath, androuting and spectrum resource allocation in an EON.Section III introduces the problem of DUFL in an EON.Section IV presents MILP models for the deployment prob-lem, which include a node-arc and a path-arc model.Section V introduces the proposed heuristic algorithmfor the deployment of ULL fiber links, which is dividedinto the steps of selecting network links for ULL fiber de-ployment and RMSA for an optical network with differenttypes of fiber links. We conduct simulation studies inSection VI under both the static and dynamic trafficdemands. Performance results are presented to show theeffectiveness of the proposed schemes. Section VII con-cludes the paper.

II. RELATED WORK

Advanced fiber technology has been extensively devel-oped to reduce the attenuation of fibers and to enhancethe transmission performance of fiber-optic transmissionsystems. Ten gave a review on major attenuation compo-nents in a silica-based fiber and discussed common tech-niques to lower them [10]. By embedding a pure silicacore, Yamamoto et al. successfully lowered a fiber’s attenu-ation coefficient to 0.154 dB/km at 1550 nm [11]. Similarly,Hirano fabricated a pure-silica-core fiber with an ultralowloss of 0.15 dB/km [12]. Recently, Makovejs et al. reducedthe attenuation coefficient to a record-low value of0.146 dB/km at 1560 nm and 0.1467 dB/km at 1550 nm fora silica-core fiber [13]. This progress has significantly con-tributed to the maturity of the ULL fiber technology. Wenow have several commercially available ULL fibers,such as Corning’s SMF-28ULL fibers [2], YOFC’s FullBandULL fibers [3], and Hengtong’s NGFCom ULL fibers [4].

To optimize the performance of an optical network withdifferent types of fibers, it is important to develop an effec-tive model for evaluating the transmission quality of alightpath. The signal quality of a lightpath is generally af-fected by various impairments, e.g., optical amplifier noise,dispersion, cross talk, and nonlinear effects. Several param-eters, such asQ factor, OSNR, and bit error rate (BER), havebeen employed to evaluate the quality of an optical signal,and extensive studies have been conducted on estimatingthe signal quality of a lightpath. Saradhi and Subramaniammade a comprehensive survey for a physical layer impair-ment-aware network design based on various signal qualityestimationmodels [14]. Based onQ factor, Tomkos et al. pro-vided an accurate signal quality estimation for lightpaths ina transparent optical network [15]. Pandya et al. developedseveral impairment-aware routing and wavelength assign-ment algorithms [16]. Based on the OSNR parameter, Shenet al. developed an OSNR-aware routing and regeneratorplacement algorithm to reduce the number of regeneratorsrequired with the condition that all of the traffic demandsbe fully accommodated [17]. Similarly, based on the BERparameter, Cukurtepe et al. investigated the impairment-aware lightpath-provisioning problem for a mixed line rateoptical network and proposed two heuristic algorithms tomaximize the number of lightpaths established [18].

RMSA is also important for anEON. Several studies havebeen carried out to efficiently assign spectrum resources inanEON. For static traffic demand, Christodoulopoulos et al.developed two efficient RMSA algorithms, i.e., a jointRMSA algorithm and a decomposed RMSA algorithm [19].For dynamic traffic demand, Aibin and Walkowiak pro-posed a new adaptive and regenerator-aware algorithmfor the RMSA problem [20]. In addition, assuming thatthe service holding time is preknown, Wang and Jue devel-oped an RMSA algorithm to reduce resource fragmenta-tions by properly scheduling requests [21]. For multicastservices with shared protection, Cai et al. formulated theRMSA problem into a MILP model and then developed aheuristic algorithm for the problem [22]. Abkenar andRahbar surveyed various RMSA algorithms and compared

Li et al. VOL. 11, NO. 5/MAY 2019/J. OPT. COMMUN. NETW. 239

the performance of these algorithms from the aspects ofspectrum efficiency and computational complexity [23].

Though there have been studies onULL fiber technology,the signal quality estimation of optical channels, and theRMSA problem of an EON, these studies were carriedout independently, with little effort toward jointly address-ing the ULL fiber-deployment problem for an EON and therelated RMSA problem when an EON is deployed with dif-ferent types of fiber links. As a preliminary study, we hadrecently considered this in [24] to propose three strategiesfor selecting links with ULL fiber deployment and furtherexplored the related RMSA issue. We also studied the ULLfiber-link-deployment problem in [25] under static trafficdemand with 1� 1 path protection. Building on these pre-liminary studies, this paper makes a comprehensive studyon the problem of ULL fiber-link deployment and its re-lated RMSA problem. As key differences, in [24], we onlyconsidered dynamic traffic demands, whereas in this study,we focus on both static and dynamic traffic demands.Moreover, more strategies for selecting the network linksdeployed with ULL fibers are considered. In [25], only apath-arc MILP model was developed for the RMSA prob-lem with 1� 1 protection, and in this study, we considerboth node-arc and path-arc MILP models, which is morecomprehensive.

III. DUFL IN AN EON

In this section, we first give an example for the ULLfiber-link deployment, which is followed by the formaldefinition of the research problem being considered.

A. Example of ULL Fiber-Link Deployment

We use the example in Fig. 1 to explain the problem ofULL fiber-link deployment in an EON, where differentstrategies for selecting links to be deployed with ULL fibersare considered. Figure 1(a) shows a network before theULL fiber-link deployment, in which all of the fiber linksare SSMFs. We assume that there are four traffic demandsin the network, i.e., (A-B, 160 Gb/s), (A-C, 180 Gb/s), (B-C,100 Gb/s), and (C-D, 170 Gb/s). The routes for establishinglightpaths between the corresponding node pairs are A-B,A-C, B-C, and C-B-D, respectively. Based on the capacitysupported by each FS and the OSNR threshold requiredby each modulation format in Table I, Fig. 1(a) showsthe RMSA of the lightpaths established. Specifically,because the OSNR of lightpath (A-B) is 19 dB, which meetsthe OSNR requirements of both quaternary phase-shiftkeying (QPSK) and binary phase-shift keying (BPSK),we assign QPSK to the lightpath for better spectrum effi-ciency, which would require 4 FSs to fully accommodate thetraffic demand between the node pair. Similarly, for light-paths (A-C), (B-C), and (C-D), we also assign the most effi-cient modulation formats, and the corresponding numbersof FSs are as shown in Fig. 1(a).

Figures 1(b) and 1(c) compare how different strategies forselecting links to be deployed with ULL fibers impact the

spectrum efficiency of an EON. Figure 1(b) shows a scenariowhere linksA-B andA-C are deployedwithULL fibers. Thisimproves the OSNRs of optical channels (A-B) and (A-C)and consequently allows them to use more efficient modu-lation formats, i.e., 8-quadrature amplitude modulation(QAM) and 16-QAM, respectively. Although these two opti-cal channels require fewer FSs on links A-B and A-C, themaximum number of FSs used in the whole network is still11 because there is no reduction of FSs on link B-C. In con-trast, if we deploy ULL fibers on links B-C and B-D asshown in Fig. 1(c), the number of FSs used in the whole net-work can be reduced to six because the numbers of FSsrequired by optical channels (C-D) and (B-C) are reducedto four and two, respectively. This corresponds to more than45% reduction of FSs required in the whole network com-pared to the first ULL fiber-deployment scenario. Thisexample therefore shows the importance of properly select-ing network links to be deployed with ULL fibers.

B. ULL Fiber-Link-Deployment Problem

Based on the previous example, we next present the for-mal ULL fiber-link-deployment problem in the context of

(a)

(b) (c)

B

A

C

D

7

11

4

4

OSNR =19QPSK

OSNR =18

QPSK

OSNR =15BPSK

OSNR=16

BPSK

SSMFs

B

A

C

D

7

2

11

3

ULL fibers

OSNR =2316-QAM

OSNR=16

BPSK

OSNR =15BPSK

OSNR =21

8-QAM

B

A

C

D

4

4

6

4

ULL fibers

OSNR =1916-QAM

OSNR =18

QPSKOSNR

=19

QPSK

OSNR =18QPSK

Fig. 1. Deploying ULL fibers for different sets of network links.(a) Original network before ULL fiber deployment. (b) DeployingULL fibers for links A-B and A-C. (c) DeployingULL fibers for linksB-C and B-D.

TABLE IFS CAPACITIES AND OSNR THRESHOLDS OF THE FOUR

MODULATION FORMATS [24]

ModulationFormat

FS Capacity(Gb/s)

OSNR Threshold(dB)

BPSK 25 14.03QPSK 50 17.018-QAM 75 20.3716-QAM 100 22.4

240 J. OPT. COMMUN. NETW./VOL. 11, NO. 5/MAY 2019 Li et al.

an EON. Consider an EON represented as Gp � �N,L�,where N is a set of network nodes and L is a set of networklinks. We have a traffic demand matrix denoted as �λsd�, inwhich each element λsd is the amount of traffic demand inunits of gigabits per second between node pair �s,d�. Thesetraffic demands will be carried by lightpaths establishedbetween different node pairs. The lightpaths use differentnumbers of FSs based on the modulation formats assigned.We aim to minimize the maximum number of FSs used inthe whole network when a certain percentage of the networklinks (measured in terms of length) deploy ULL fibers.

The problem is subject to the following constraints. All ofthe traffic demands must be served and the constraints ofspectrum contiguity and spectrum continuity [26] must besatisfied when establishing a lightpath in an EON. EachFS in a fiber link can only be used by a single lightpath.The most efficient modulation format is assigned whenthe OSNR of a lightpath is greater than the OSNR thresh-old required by the modulation format. To estimate theOSNR of each lightpath, we employ the estimation modeland the assumption for the erbium-doped fiber amplifier(EDFA) placement as in [17].

IV. PATH-ARC AND NODE-ARC MILP MODELS

For the previous ULL fiber-link-deployment problem,we develop both path-arc and node-arc MILP models, inwhich the DUFL and RMSA-DTFL subproblems are solvedjointly. Moreover, as another key novel aspect, the modelsincorporate the lightpath OSNR calculation in the optimi-zation process.

A. Path-Arc MILP Model

For the path-arc model, we assume that a set of candidateroutes is precalculated for each node pair by the link-disjointk-shortest path (KSP) algorithm. The candidate routes areused to establish lightpaths between the node pair. The sets,parameters, and variables of the model are as follows.

Sets:N The set of network nodes.L The set of network links. Link ij ∈ L means

that its two end nodes are i and j.R The set of node pairs. Node pair sd ∈ Rmeans

that its source and destination nodes are sand d, respectively.

Psd The set of candidate paths between node pairsd, sd ∈ R.

M The set of modulation formats (16-QAM, 8-QAM, QPSK, and BPSK) for use.

Parameters:σa,sd2b,sd1 A binary parameter that equals 1 when

lightpath a between node pair sd2 and light-path b between node pair sd1 share a commonlink; 0, otherwise. Here we assume that only asingle lightpath is established to carry all ofthe traffic demand between each node pair.

f sdm The number of FSs required for establishingthe lightpath between node pair sd whenmodulation format m is used. This is calcu-lated as the traffic demand between the nodepair divided by the spectral efficiency of themodulation format.

OSNRmrec The reciprocal of the OSNR threshold required

for establishing a lightpath with modulationformat m. Note that this OSNR is a linearvalue.

OSNRSij,rec The reciprocal of the OSNR value contributed

by link ij if it is an SSMF. This is also a linearvalue.

OSNRUij,rec The reciprocal of the OSNR value contributed

by link ij if it is a ULL fiber. This is also a lin-ear value.

λb,sdij A binary parameter that equals 1 when path bof node pair sd traverses link ij; 0, otherwise.

ψ ijn A binary parameter that equals 1 if n is a

starting node of link ij; 0, otherwise.ξijn A binary parameter that equals 1 if n is an

ending node of link ij; 0, otherwise.ηij The length of link ij (in units of kilometers).Q The percentage (in terms of length) of the

links that are deployed with ULL fibers in thewhole network. This is defined as the ratio ofthe total length of links deployed with ULLfibers to the total length of all of the linksin the network. This can be subject to thebudget that a carrier has to invest in its net-work infrastructure in a certain period.

∇ A large value.

Variables:Ssdb An integer variable denoting the starting

index of FSs assigned to lightpath b betweennode pair sd.

φa,sd2b,sd1 A binary variable that equals 1 when the

starting index of FSs assigned to lightpath bbetween node pair sd1 is larger than light-path a between node pair sd2, i.e., Ssd1 >Ssd2; 0, otherwise.

ρsdb A binary variable that equals 1 if candidatepath b of node pair sd is selected for establish-ing a lightpath; 0, otherwise.

OSNRsdrec The reciprocal of the OSNR value of the

lightpath between node pair sd. This is also alinear value.

δsdm A binary variable that equals 1 when modu-lation format m is used for lightpath estab-lishment between node pair sd; 0, otherwise.

τij A binary variable that equals 1 if networklink ij is deployed with a ULL fiber; 0, other-wise.

Fsd The number of FSs required for the lightpathestablished between node pair sd.

C The maximum index of FSs used in the wholenetwork.

The objective and the constraints of the model are asfollows:

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Objective: Minimize C

Constraints:

C ≥ Ssdb � Fsd ∀ sd ∈ R, b ∈ Psd, (1)

X

b∈Psd

ρsdb � 1 ∀ sd ∈ R, (2)

Ssdb ≤ ∇ · ρsdb ∀ sd ∈ R, b ∈ Psd, (3)

Ssd2a − Ssd1

b ≤ ∇ · �1 − φa,sd2b,sd1 � 3 − ρsd2a − ρsd1b − σa,sd2b,sd1� − 1

∀ sd1, sd2 ∈ R, a ∈ Psd2, b ∈ Psd1: sd1 ≠ sd2,

(4)

Ssd1b �Fsd1 −Ssd2

a ≤∇ · �φa,sd2b,sd1 �3− ρsd2a − ρsd1b − σa,sd2b,sd1�,∀ sd1,

sd2∈R, a∈ Psd2, b∈ Psd1:sd1≠ sd2 (5)

OSNRb,sdrec �

X

ij∈Lλb,sdij · �τij ·OSNRU

ij,rec � �1 − τij� ·OSNRSij,rec�

∀ sd ∈ R, b ∈ Psd, (6)

OSNRb,sdrec −OSNRm

rec ≤ ∇ · �2 − ρsdb − δsdm �∀ sd ∈ R, b ∈ Psd, m ∈ M, (7)

Fsd �X

m∈Mδsdm · f sdm ∀ sd ∈ R, (8)

X

m∈Mδsdm � 1 ∀ sd ∈ R, (9)

X

ij∈Lτij · ηij ≤ Q ·

X

ij∈Lηij: (10)

Explanations of the equations: The objective of themodel is to minimize the maximum number of FSs usedin the whole network when a certain percentage (in termsof length) of network links is deployed with ULL fibers,which helps reduce the network congestion level.

Constraint (1) ensures that the maximum index of FSsused in the whole network is greater than the ending FSindex of the lightpath established between any nodepair. Constraint (2) ensures that there is only one pathselected for lightpath establishment between any nodepair. Constraint (3) means that if a path is not selected forestablishing a lightpath, then there is no starting FS indexgreater than zero for the path. Constraints (4) and (5) en-sure that there is no spectrum overlap between lightpathsthat share common links. Constraint (6) calculates thereciprocal of the ONSR value for each lightpath in the net-work after upgrading links with ULL fibers. Constraint (7)

ensures that each established lightpath needs to meet theOSNR threshold required by its adopted modulation format.Constraint (8) finds the number of FSs assigned to the light-path established between each node pair. Constraint (9) en-sures that there is only one modulation format selected forestablishing a lightpath. Constraint (10) ensures that thepercentage (in terms of length) of deployed ULL fibers inthe whole network is no greater than a specific percentageQ.

We count the dominant numbers of variables and con-straints to evaluate the computational complexity of thispath-arc MILP model. The model has a total of O�jNj4 ·jPj2� variables (because of variable φa,sd2

b,sd1) and a total ofO�jNj4 · jPj2� constraints [because of constraints (4) and(5)], where jNj is the total number of network nodes andjPj is the maximum number of candidate routes consideredbetween each node pair.

B. Node-Arc MILP Model

For the previous ULL fiber-link-deployment problem, wealso develop a node-arc MILP model, which is extendedfrom the model in [26]. For this, new sets and variablesin addition to those defined in the path-arc model are asfollows.

Sets:Li The set of network links, each of which starts

or ends at node i.

Variables:PLsd

ij A binary variable that equals 1 if the light-path between node pair sd traverses link ij; 0,otherwise. We assume that there is only onelightpath established to accommodate all ofthe traffic demand between each node pair.

Ysdij A binary variable that equals 1 if the light-

path between node pair sd traverses link ijwhen link ij is deployed with a ULL fiber;0, otherwise.

PNsdi A binary variable that equals 1 if the light-

path between node pair sd traverses node i; 0,otherwise.

Esd An integer variable denoting the ending indexof FS assigned to the lightpath between nodepair sd.

Ssd An integer variable denoting the startingindex of FS assigned to the lightpath betweennode pair sd.

θsd2sd1 A binary variable that equals 1 when thestarting index of FSs assigned to the lightpathbetween node pair sd1 is larger than that ofnode pair sd2, i.e., Ssd1 > Ssd2; 0, otherwise.

This node-arc model has the same objective as that of thepath-arc model. For the constraints, we use the followingnew ones to replace constraints (1)–(7).

Constraints:

X

ij∈Ls

PLsdij � 1 ∀ sd ∈ R, (11)

242 J. OPT. COMMUN. NETW./VOL. 11, NO. 5/MAY 2019 Li et al.

X

ij∈Ld

PLsdij � 1 ∀ sd ∈ R, (12)

X

pq∈Li

PLsdpq � 2 · PNsd

i ∀ sd ∈ R, i ∈ N: i ≠ s,d, (13)

PNsdi · ψ ij

i � PNsdj · ξijj ≥ 2 · PLsd

ij

∀ sd ∈ R, ij ∈ L, i, j ∈ N,(14)

θsd1sd2 � θsd2sd1 � 1 ∀ sd1, sd2 ∈ R: sd1 ≠ sd2, (15)

Esd1 − Ssd2 ≤ ∇ · �θsd2sd1 � 2 − PLsd1ij − PLsd2

ij � − 1

∀ sd1, sd2 ∈ R, ij ∈ L: sd1 ≠ sd2,(16)

C ≥X

sd∈RFsd · PLsd

ij ij ∈ L, (17)

C ≤X

sd∈RFsd, (18)

C ≥ Ssd � Fsd ∀ sd ∈ R, (19)

Ysdij ≤ PLsd

ij ∀ sd ∈ R, ij ∈ L, (20)

Ysdij ≤ τij ∀ sd ∈ R, ij ∈ L, (21)

Ysdij ≥ PLsd

ij � τij − 1 ∀ sd ∈ R, ij ∈ L, (22)

OSNRsdrec �

X

ij∈L�Ysd

ij ·OSNRUij,rec � �PLsd

ij − Ysdij � ·OSNRS

ij,rec�

∀ sd ∈ R, (23)

OSNRsdrec −OSNRm

rec ≤ ∇ · �1 − δsdm � ∀ sd ∈ R, m ∈ M:

(24)

Explanations of the equations: Constraints (11)–(14)find a path for lightpath establishment between each nodepair. Specifically, constraint (11) ensures that the first linkof a lightpath between node pair sd starts from node s.Constraint (12) ensures that the last link of a lightpath be-tween node pair sd ends at node d. Constraint (13) ensuresthat there are two links associated with any intermediatenode traversed by a lightpath between node pair sd.Constraint (14) ensures that if the lightpath between nodepair sd traverses link ij, it must also traverse nodes i and j.Constraints (15) and (16) ensure that the spectra of light-paths that share common links should not overlap.Constraints (17) and (18) are actually not required but al-low the problem to be solved fast by reducing the searching

space of the MILP model. Constraint (19) ensures that themaximum index of FSs used in the whole network is nosmaller than the ending FS index of the lightpath betweenany node pair. Constraints (20)–(22) represent the relation-ship of Ysd

ij � PLsdij & τij, which ensures that if a link

traversed by a lightpath is deployed with a ULL fiber, thenYsd

ij � 1. Constraint (23) calculates the reciprocal of theONSR value for the lightpath established between a pairof nodes after the deployment of ULL fiber links.Constraint (24) ensures that an established lightpathmeets the OSNR threshold required by the modulation for-mat that it uses.

As before, we count the dominant numbers of variablesand constraints to evaluate the computational complexityof this node-arc model. There are a total of O�jNj2 · jLj� var-iables (because of variables PLsd

ij and Ysdij ) and a total of

O�jNj4 · jLj� constraints [because of constraint (16)], wherejNj is the total number of network nodes and jLj is the totalnumber of network links.

V. HEURISTIC ALGORITHMS

The MILP models can solve the problem considered inthis study for small networks. However, their computa-tional complexities would be high for large networks, whichwould make them infeasible to solve large models within areasonably short time. Therefore, we also develop an effi-cient heuristic algorithm for the previous optimizationproblem. For this, the problem considered in this studycan be decomposed into two subproblems, i.e., the DUFLand RMSA-DTFL subproblems. For the DUFL subproblem,we consider five different strategies to select the set of net-work links to be deployed with ULL fibers, including therandom strategy, the PL strategy, the SRT strategy, theLC strategy, and the OB-based strategy. For the RMSA-DTFL subproblem, we extend the SWP-based algorithmin [26] for the lightpath establishment in an EON withdifferent types of fibers. We first introduce the strategiesfor selecting the network links for ULL fiber deployment,followed by the extended SWP-based algorithm.

A. Strategies for Selecting Links to Be DeployedWith ULL Fibers

In the context of different traffic demand scenarios, thissection introduces five strategies for selecting links to bedeployed with ULL fibers.

1) Random Strategy: The random strategy simply se-lects randomly the network links to be deployed withULL fibers until a certain percentage (in terms of length)of links is selected.

2) PL Strategy: This strategy orders network links fromthe longest to the shortest (in terms of length) and thenselects links to be deployed with ULL fibers following thisorder.

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3) SRT Strategy: In this strategy, we first run the short-est path algorithm to find the shortest routes based on thephysical distance between each node pair. Then, we countthe total number of routes traversing each link. We sort thelinks based on the numbers of routes traversing it, from thelargest to the smallest, and then select the links to be de-ployed with ULL fibers from the ordered list until a re-quired percentage (in terms of length) of links is selected.

4) LC Strategy: In this strategy, we select network linksto be deployed with ULL fibers based on a criterion calledthe maximum number of FSs used in the whole network.Specifically, we keep on trying to deploy a ULL fiber forone network link each time. In each trial, we employ theSWP-based algorithm (introduced later) to find the numberof FSs used in the network for serving all of the demands.We then select the link where the deployment of ULL fiberswill reduce most the number of FSs used. (If there are twoor more such links, then we will select a link from theselinks based on the SRT strategy.) This link is then selectedfor the deployment of ULL fiber. We carry out the same tri-als for the remaining links until the required percentage (interms of length) of network links is deployed withULL fibers.The pseudocode of this strategy follows in Algorithm 1.

Algorithm 1. LC StrategyInput: a network topology Gp � �N,L�, a demand matrix D,and a percentage Q (in terms of length) of network links tobe deployed with ULL fibers1: Let LSSMF � L, LULL � ∅; //LSSMF is the set of SSMF

links, and LULL is the set of ULL fiber links;2: For each l ∈ LSSMF {3: Deploy l with a ULL fiber;

Employ the SWP-based algorithm (introducedlater) to find the maximum number of FSs usedCl in the whole network;Revert l to be an SSMF;}

4: l� � argminlCl; //If there are two or more such links,then we will select a link from these links based onthe SRT strategy.

5: LSSMF � LSSMFnfl�g, LULL � LULL∪fl�g;6: Calculate the percentage P (in terms of length) of links

deployed with ULL fibers; if P < Q, return to Step 2;7: End.

5) OB-Based Strategy: This strategy is proposed for useonly for dynamic traffic demands. It selects network linksto be deployed with ULL fibers based on a lightpath block-ing counter set for each link. Specifically, for a network witha specific traffic loadmatrix, we run simulation for dynami-cal lightpath service establishment. Before the simulation,we set a blocking counter Kij as zero for each link ij ∈ L.During the simulation, when a lightpath request arrives,we employ the SWP-based algorithm to establish the light-path. If the lightpath request is blocked and it is because offailure in meeting the OSNR limit, we search the shortestroute between the node pair of the blocked request based onthe physical network topology and add one to the counter ofeach link traversed by the shortest route found. Note thatthere may be other reasons why the request is blocked,

e.g., the lack of spectrum resources. However, here we onlycount the cases when the OSNR requirement cannot bemet. After a large number (106 in our case) of lightpath re-quests are simulated, there are different counter values forthe links. We sort these links based on the counter valuesfrom the largest to the smallest. Then from this orderedlink list, we select the links for ULL fiber deployment.The rationale here is that a link with a large blockingcounter value is likely to be a bottleneck of signal transmis-sion because lightpaths trying to traverse it cannot meetthe OSNR requirement. Thus, it would be desirable to de-ploy ULL fibers with higher priority for the links withlarger blocking counter values.

B. SWP-Based Algorithm

We extend the SWP-based algorithm in [26] to efficientlyestablish lightpaths in an EON with different types offibers. The pseudocode of Algorithm 2 is as follows.

Algorithm 2. SWP-Based AlgorithmInput: a network topologyGp � �N,L�, a capacity demand dbetween a node pair, and an empty route R�

ω � NULL1: For eachm ∈ M; //M is the set of modulation formats for

use from the highest to lowest levels.2: Calculate the required number of FSs by f m �

Td∕SEm;Create a list of spectrum window planes, SWPs, basedon f m; //Td is the capacity required by d, and SEm is thespectrum efficiency of modulation format m.

3: LetHm � ∅; //Hm is a set used to store the routes foundon each spectrum window plane that are eligible to setup a lightpath for demand d.

4: For each ω ∈ SWPs {5: Using Dijkstra’s algorithm to find an eligible short-

est route Rω in spectrum window plane ω;If the OSNR of Rω meets the OSNR requirement ofm, let Hm � Hm∪fRωg;}

6: R�ω � minhopHm; //Choose a route from Hm that has the

smallest hop count. If there are two ormore routes withthe minimum hop, we select the one based on the first-fit strategy, i.e., the route with the smallest SWP index.If R�

ω ≠ NULL, establish a lightpath along route R�ω

and go to Step 8; otherwise, if m is not the last modu-lation format in M, consider the next modulation for-mat in M and return to Step 2;

7: If R�ω � NULL, block the request;

8: End.

For each modulation format (in Table I) from the highestto the lowest, we try to use it to establish a lightpath.Specifically, for a particular modulation format, we createa list of SWPs based on the number of FSs required accord-ing to the spectrum efficiency of the modulation format.Then based on this list of SWPs, we try to find eligibleroutes and check whether their OSNRs can meet theOSNR requirement of the modulation format employed.The route that fails to meet the OSNR requirement is

244 J. OPT. COMMUN. NETW./VOL. 11, NO. 5/MAY 2019 Li et al.

considered not eligible. If there are several eligible routesfor lightpath establishment based on the current modula-tion format, we select the one traversing the minimumnumber of hops to establish a lightpath for the demand(if there are two or more routes with the minimum hop,then we choose the one based on the first-fit strategy,i.e., the route with the smallest SWP index) and do not trythe subsequent modulation formats further because thecurrent one would bemore spectrally efficient than the sub-sequent ones; otherwise, we repeat the same process for thenext modulation format. The request is blocked only if wehave tried all of the modulation formats and no eligibleroutes are found.

Note that this SWP-based algorithm has been employedin the previous LC and OB-based strategies when selectingthe links to be deployed with ULL fibers. The current pseu-docode is presented for the scenario of dynamic traffic de-mand that is used in the OB-based strategy. For thescenario of static traffic demand in the LC strategy, a minormodification is required. This is that, when a request isblocked based on the current number of FSs in each fiberlink, we add one more FS to each network link and repeatthe same process to see if the service request is stillblocked. If so, we continue adding more until the servicerequest is not blocked. At that moment, the number ofFSs used is just the criterion of the maximum number ofFSs used in the whole network, which is needed by theLC strategy.

For the static traffic demand scenario, because the inputorder of lightpath requests has a significant impact on net-work performance, we add a shuffling mechanism toimprove the performance of the SWP-based algorithm.Specifically, we first perform a shuffling process for agiven traffic demand matrix to generate multiple shuffledsequences and then perform the SWP-based algorithm foreach of the sequences. We select the one with the best per-formance from the results obtained for all of the sequences.By using this shuffling process, we can largely avoid theinfluence from the lightpath request order.

Finally, it should be noted that the SWP-based algorithmis one of the most efficient heuristic algorithms for theRMSA problem available in the literature. Accompaniedby the shuffling process just mentioned, we can ensure avery good performance for the ULL fiber-deployment prob-lem. We have also tried other heuristic algorithms, e.g.,based on the KSP algorithm, and had the same observationon the performance of the DUFL strategies.

VI. TEST CONDITIONS AND RESULT ANALYSES

To evaluate the performance of the proposed strategiesfor ULL fiber-link deployment, we performed simulationstudies based on two test networks, i.e., a six-node, nine-link (n6s9) network and the 24-node, 43-link (USNET) net-work, as shown in Fig. 2. The length (in units of kilometers)of each link is shown next to the link. Corning SMF-28 ULLfiber [2] was assumed to be used for deployment in the twotest networks. The attenuation coefficient of the ULL fiberand SSMFare assumed to be 0.168 dB/km and 0.25 dB/km,

respectively. On each fiber link, optical amplifiers (i.e.,EDFAs) are assumed to be placed at equal distances, nogreater than 80 km. This amplification span distance is as-sumed to stay unchanged for a network link deployed witha ULL fiber. There are 320 FSs in each fiber link, and thebandwidth granularity of each FS is 12.5 GHz. Four modu-lation formats (including BPSK, QPSK, 8-QAM, and 16-QAM) were employed for lightpath establishment. TheFS capacity and the OSNR required by each modulationformat are shown in Table I. The OSNR estimation modelin [17] was employed to estimate the OSNR of eachlightpath.

We considered two types of traffic demands, includingstatic traffic demand and dynamic traffic demand. Forthe former, the traffic demand between each node pair is as-sumed to be randomly generated with a uniform distribu-tion in the range of �100, X � Gb∕s, where X is the maximumtraffic demand between the node pair. For the latter, weassume that each node pair has a traffic load in units ofErlang where lightpath request arrivals follow a Poissonprocess and their service holding times follow an exponen-tial distribution. We solved both the path-arc and node-arcMILP models with the commercial software AMPL/Gurobi(version 5.6.2) [27] and implemented the proposed heuristicalgorithms in Java. The results are presented next for thestatic and dynamic traffic demand scenarios, respectively.

A. Performance Comparison Under Static TrafficDemand

This section compares the performance of the differentschemes under the static traffic demand, where the trafficdemand between each node pair is assumed to be known inadvance.

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1) Number of Links Deployed With ULL Fibers: Given aspecific percentage of fiber-link length to be deployed withULL fibers, we first compare the number of links thatare deployed with ULL fibers by the different schemes.Tables II and III compare the results for the n6s9 andUSNET networks, respectively. Here the maximum trafficdemand X is assumed to be 400 Gb/s for both the n6s9 net-work and the USNET network.

For the n6s9 network, we show the results of both theMILP models and the heuristic algorithms. However, forthe USNET network, because of its large network size, onlythe results of the heuristic algorithms are provided due tothe intractability of the MILP models. We can see that thePL strategy has the smallest number of links deployed withULL fibers for the different percentages of ULL fiber-linklength. This is reasonable because the PL-based strategyalways deploys ULL fibers on the longest links at the firstpriority, which therefore minimizes the number of links de-ployed with ULL fibers. We also observe that the LC-basedstrategy has almost the same number of links deployedwith ULL fibers as that of the node-arc MILP model foreach percentage of ULL fiber-link length. This thereforeshows the optimality of the LC-based strategy in selectinglinks for ULL fiber deployment. Similar results were alsoobtained for the USNET network as shown in Table III,where the random strategy has the largest number of linksdeployed with ULL fibers, the PL strategy has the smallestnumber of such links, and the LC and SRT strategies are inthe middle for each percentage of ULL fiber-link length.

2) Maximum Number of FSs Used: We also compare themaximum number of FSs used for the different schemes.Figure 3(a) shows the results of the n6s9 network whenthe maximum traffic demand X is 400 Gb/s. Legends“Path-arc_MILP” and “Node-arc_MILP” correspond to theresults of the path-arc and node-arc MILP models, respec-tively. Legends “Random_SWP,” “PL_SWP,” “SRT_SWP,”and “LC_SWP” correspond to the results of the random,PL, SRT, and LC strategies, respectively. We can see thatwith an increasing percentage of ULL fiber-link length, the

maximum number of FSs used decreases. This is becauseusing ULL fibers can improve the OSNR of each traversinglightpath, which therefore allows for the use of more effi-cient modulation formats, and fewer FSs are required to beassigned. In addition, comparing the four strategies, we seethat the LC strategy requires the smallest number of FSs.This is because the LC strategy always selects a link thatcan give a maximum reduction of FSs used as the firstpriority for the ULL fiber deployment, which is exactlyin line with the optimization objective. In contrast, theother three strategies do not select links for the ULL fiberdeployment from the perspective of minimizing the num-ber of FSs used.

In addition, we also find that the heuristic algorithmbased on the LC strategy can perform close to the MILPmodels, which shows the efficiency of the proposed strategyin selecting the best links for the ULL fiber deployment. Inaddition, when all of the links are deployed with ULL fi-bers, all of the heuristic cases, including Random_SWP,PL_SWP, SRT_SWP, and LC_SWP, can perform close tothe MILP models. This therefore shows the efficiency ofthe SWP-based algorithm given that all of the schemesare based on the same network, in which all of the linksare ULL fibers.

Finally, comparing the results of the two MILP models,we see that the node-arc model performs better than thepath-arc model for someULL fiber-link length percentages.This is because the path-arc model limits the set of routesfor lightpath establishment between each node pair,whereas the node-arc model does not set such a constraintbut allows consideration of all possible eligible routes

TABLE IINUMBER OF LINKS DEPLOYED WITH ULL FIBERS (N6S9)

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TABLE IIINUMBER OF LINKS DEPLOYED WITH ULL FIBERS (USNET)

Q Random PL SRT LC

20% 9 5 9 840% 16 12 15 1560% 24 21 22 2480% 33 30 31 33100% 43 43 43 43

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between each node pair. Therefore, the node-arc model canachieve a better performance. This is, however, at the costof a higher computational complexity because the node-arcmodel considers all of the eligible routes.

We conducted similar studies for the USNET network,where the maximum traffic demand between each nodepair is also assumed to be X � 400 Gb∕s. The results forthis test network are shown in Fig. 3(b). Due to the compu-tational intractability of the MILP models in finding solu-tions for the USNET network, we do not provide the resultsof the two MILP models but only show the results of theheuristic schemes. In Fig. 3(b), we can see that the LC-based scheme performs the best among all of the schemes;the reason for this is the same as was mentioned for then6s9 network. In addition, unlike the results of the n6s9network, where the SRT-based scheme cannot performas well as the LC-based scheme, the performance of theSRT-based scheme is close to that of the LC-based schemein the USNET network. This is attributed to the topology ofthe USNET network, in which there are many bordernodes on both sides of the topology. This makes the linksin the middle highly critical for lightpath establishmentbetween the border nodes, and therefore deploying ULLfibers on these links can bring maximum benefits inimproving network spectrum efficiency.

B. Performance Comparison Under DynamicTraffic Demand

We also compare the performance of the differentschemes under the dynamic traffic demand. Here fourstrategies, including the random, PL, SRT, and OB strate-gies, are considered. Note that the LC strategy is only suit-able for the static traffic demand as it uses the maximumnumber of FSs used as the major criterion to decide whichnetwork link should be deployed with ULL fibers first. Wecan find the maximum number of FSs used only for a statictraffic demand. The OB-based strategy is the counterpartof the LC strategy for the dynamic traffic demand scenario.BBP, which is defined as the ratio of total blocked band-width to total requested bandwidth, is used here as thekey criterion for performance evaluation. A total of 106

lightpath requests were simulated for calculating the BBP.

Figure 4 shows the results of the USNET network whenthe traffic load between each node pair is uniform at 2.5Erlang and the bandwidth of each request is randomly gen-erated within the range of [100, 400] Gb/s. We can see thatwith an increasing percentage of ULL fiber-link length, theBBP of the network decreases. Deploying all of the linkswith ULL fibers (i.e., 100%) can reduce the BBP from0.155 to 0.042, i.e., a decrease of 73%. This is reasonablebecause more ULL fibers deployed in a network can leadto better lightpath OSNR, and therefore fewer FSs are as-signed. In addition, we see that the OB-based strategy canachieve the best performance among all of the strategiesbecause it considers both the number of shortest routes tra-versing each link and the OSNR bottlenecking effect ofeach link on blocked lightpaths. Specifically, when the per-centage of ULL fiber-link length is 80%, the OB-based

strategy can reduce the BBP by almost 33% and 15% com-pared to the PL- and SRT-based strategies, respectively.

We also compare, in Fig. 5, the BBPs of the four strate-gies with an increasing traffic load when the ULL fiber-linklength is 80% in the whole network for the USNET net-work. The results confirm the previous observation thatthe OB-based strategy performs best, the PL-based andrandom strategies perform worst, and the SRT strategyfalls in the middle.

C. Impact of Fiber Attenuation Coefficient

In all of the previous study cases, we assumed that theattenuation coefficient of a ULL fiber is 0.168 dB/km.However, changes in this value would affect the perfor-mance of the different schemes. Therefore, we also evaluatehow the change of fiber attenuation coefficient can impactthe performance of these schemes. Here we assume that allof the network links are using the same type of fiber, andwe only change the fiber attenuation coefficient. Theseresults are shown in Fig. 6. Here, for the static traffic de-mand, the maximum traffic demand between each nodepair is also assumed to be X � 400 Gb∕s and, for thedynamic traffic demand scenario, the traffic load is 2.5Erlang per node pair. We see that both the maximumnumber of FSs used (see the left y axis) and BBP (see theright y axis) increase with an increasing fiber attenuation

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coefficient in the networks. This is reasonable because alower attenuation coefficient corresponds to a lower gainon each optical amplifier, which leads to lower amplifica-tion noise and therefore better OSNR of each lightpath.Better OSNR leads to fewer FSs to be assigned to eachlightpath. This further leads to a smaller number of FSsused in the whole network and a lower BBP.

In addition, for the simulation cases considered, it is in-teresting to observe a saturation phenomenon; i.e., whenthe attenuation coefficient is lower than 0.168 dB/km, de-creasing it further will not significantly reduce either themaximum number of FSs used or the BBP of the network.Therefore, a ULL fiber with a low enough attenuation co-efficient, e.g., 0.168 dB/km in this example, would be suffi-ciently efficient to ensure good spectrum utilization andmore costly ULL fibers with even lower loss are not neces-sary. The saturation phenomenon is attributed to the factthat when the attenuation coefficient is low enough, a largenumber of optical channels will use the highest modulationformat, i.e., 16-QAM. (For example, 67% optical channelsusing 16-QAM in the n6s9 network when the attenuationcoefficient is 0.168 dB/km.) As a result, less performanceimprovement can be gained even if the attenuation coeffi-cient is reduced further. It is expected that this saturationphenomenon would occur at even lower attenuation coeffi-cients if more advanced modulation formats, e.g., 32-QAMand 64-QAM, were to be used.

VII. CONCLUSIONS

We studied the issue of new ULL fiber-link deploymentin an EON. Under the static traffic demand, we formulatedthe deployment problem into the path-arc and node-arcMILP models. In addition, for better computational trac-tability under large networks, we developed efficient heu-ristic algorithms to solve the DUFL and RMSA-DTFLsubproblems. For the DUFL subproblem, we consideredthe random, PL, SRT, and LC upgradation strategies, andfor the RMSA-DTFL subproblem, we extended the SWP-based algorithm to assign spectrum resources for light-paths in an EON with different types of fibers. Moreover,for the dynamic traffic demand, we specifically proposed anOB-based upgradation strategy for a low BBP. Simulationresults showed that, for the static traffic demand, the LCstrategy performs best among all of the strategies and isefficient enough to perform close to the MILP models in

terms of the number of links to be deployed with ULL fibersand the maximum number of FSs used in the whole net-work. In addition, for the dynamic traffic demand, the pro-posed OB-based strategy can achieve the best performanceamong all of the strategies in terms of BBP. For the simu-lation cases considered, the results showed a saturationphenomenon between the attenuation coefficient and theperformance of the network.

ACKNOWLEDGMENT

Part of this paper was presented at the Optical FiberCommunication Conference and Exposition 2017 [24]and the International Conference on Transparent OpticalNetworks 2018 [25]. This work was jointly supported by theNational Natural Science Foundation of China (NSFC)(61671313, 61801320), the State Key Laboratory ofAdvanced Optical Communication Systems and Networks,Shanghai JiaoTong University, China (2018GZKF03009),the Open Fund of IPOC (BUPT) (IPOC2018B006), and theNatural Science Foundation of Jiangsu Provincial HighEducational Institutions (18KJB510041).

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