1752 journal of lightwave technology, vol. 35, no. 10, … · 1752 journal of lightwave technology,...

1752 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 35, NO. 10, MAY 15, 2017

Migration From Fixed to Flexible Grid OpticalNetworks With Sub-Band Virtual ConcatenationYa Zhang, Yao Zhang, Sanjay K. Bose, Senior Member, IEEE, and Gangxiang Shen, Senior Member, IEEE

Abstract—A novel strategy is presented to operate a mixedfixed/flexible grid optical network which may be used to gradu-ally migrate from a fixed to a flexible mode of operation. Routingand spectrum allocation (RSA) in an optical network where fixedand flexible grids co-exist using a multi-path sub-band virtual con-catenation (VCAT) or split spectrum (SS) technique is considered.Mixed integer linear programming models and an efficient heuris-tic algorithm based on spectrum window planes are proposed forthe RSA optimization. The results obtained for the static trafficdemand indicate that it is operationally more convenient to use themulti-path VCAT only by itself in a mixed grid optical network toguarantee performance comparable to that of the joint multi-pathand single-path VCAT case. Network performance is also evaluatedin terms of bandwidth blocking probability (BBP) under a dynamictraffic demand. Simulation results show that the multi-path VCATscheme can efficiently utilize the overall spectrum resources withlow blocking. The results of studies with both static and dynamictraffic demands also confirm that migration from a pure fixed gridoptical network to a pure flexible grid will be desirable for betternetwork capacity utilization.

Index Terms—Bandwidth blocking probability (BBP), networkmigration, routing and spectrum allocation (RSA), sub-band vir-tual concatenation (VCAT), spectrum window plane (SWP).

I. INTRODUCTION

THE expanding usage of data centers and cloud storage sys-tems, coupled with the increasing diversity and volumes of

high data rate applications will inevitably lead to a rapid growthof Internet traffic. Tackling this growth in traffic demands willdrive the need for high-capacity backbone networks which usecost-effective and efficient optical fiber transmission systems.Traditional dense wavelength division multiplexing (DWDM)networks operate with a coarse fixed grid, i.e., 50-GHz grid.This results in considerable capacity wastage when the trafficdemand is actually less than the capacity of one unit of thisgrid. To meet the diverse demand requirements of the Internet,future optical transmission and networking technologies need

Manuscript received January 3, 2017; revised February 17, 2017; acceptedMarch 18, 2017. Date of publication March 21, 2017; date of current versionApril 20, 2017. Part of the work was presented in ICTON 2016 [28]. This workwas supported by the National Natural Science Foundation of China underGrants 61671313 and 61322109. (Corresponding Author: Gangxiang Shen).

Y. Zhang, Y. Zhang, and G. Shen are with the School of Electronic andInformation Engineering, Soochow University, Suzhou 215006, China (e-mail:[email protected]; [email protected]; [email protected]).

S. K. Bose is with the Department of Electronics and Electrical Engineer-ing, Indian Institute of Technology Guwahati, Guwahati 781039, India (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JLT.2017.2685622

to be efficient, flexible, and scalable [1], [2]. This would be hardto achieve with fixed grids of large size. The flexible grid tech-nique makes the wavelength switched optical network (WSON)elastic by dividing the optical spectrum into smaller 12.5-GHzfrequency slots (FSs) [3]. Such elastic optical networks (EONs)[4] are promising for future high-speed optical communications.

It is anticipated that, eventually, DWDM optical networkswould migrate to the more efficient and flexible EONs becauseof their greater flexibility in bandwidth allocation and moreefficient spectral utilization. However, the actual migrationprocess is expected to be gradual and may be spread over afairly long time period. As a result, intermediate scenarioswill emerge where both fixed and flexible grid optical nodesmay co-exist and will be expected to operate together [5]–[13].In this paper, we have considered a mixed fixed/flexible gridoptical network, called mixed grid optical network in short,where both fixed and flexible grid optical nodes may co-existand the two types of optical nodes are expected to operatetogether to provision capacity for different traffic demandscenarios. As a key contribution of this paper, we focus on thepotential benefits of applying the sub-band VCAT technique[14] (also called split spectrum [15]) in mixed grid opticalnetworks for lightpath establishment between different typesof nodes. This would both improve the spectral efficiency andreduce the network bandwidth blocking probability.

We specifically consider the routing and spectrum assignment(RSA) problem for the VCAT scheme in the mixed grid opticalnetwork. In order to fully explore the potential of the flexi-ble grid technique for improving network spectral efficiency,we develop an MILP model for this and also propose efficientheuristic algorithms which would be easier to implement in apractical system where only the multi-path VCAT techniqueis supported. To verify the efficiency of the multi-path VCATtechnique, we have also developed an MILP model that sup-ports both the multi-path and single-path VCAT techniques andcompared its performance with the former. An efficient heuris-tic algorithm is also presented which uses the proposed VCATscheme in the mixed grid optical network for reducing networkservice connection blocking under a dynamic traffic demand.Simulation results show that the proposed multi-path sub-bandVCAT technique is an effective approach to use in an opticalnetwork where both fixed and flexible grids co-exist.

The rest of the paper is organized as follows. In Section II,we introduce the basic concept of the mixed grid optical net-work and the sub-band VCAT technique. For the RSA prob-lem of the VCAT scheme in the mixed grid optical network,

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ZHANG et al.: MIGRATION FROM FIXED TO FLEXIBLE GRID OPTICAL NETWORKS WITH SUB-BAND VIRTUAL CONCATENATION 1753

we develop MILP models and efficient heuristic algorithms inSections III and IV, where both the MILP models and heuris-tic algorithms can incorporate different modulation formats, asneeded. Section V presents case studies with corresponding testconditions, and the results of different approaches are presentedand discussed. Section VI concludes the paper.

A. Literature Review

Considerable attention is currently being paid to evaluate thepotential benefits of migration from traditional fixed grid to flex-ible grid optical networks. Tahon et al. [5] investigated variousmigration options from fixed grid to flexible grid optical net-works, and discussed their impacts on flexibility and cost. Ruizet al. [6] reviewed the main drivers for the migration towardflexible grid optical networks, and introduced a planning tool tooptimize the migration process. Yu et al. [7]–[10] addressed thestatic RSA problem in mixed fixed and flexible grid optical net-works so as to minimize the total spectrum used in the fiber link.They also proposed several migration strategies to decide whichnodes should be upgraded first to a flexible grid node with thegoal of reducing the bandwidth blocking ratio of the network.Zami et al. [11] proposed the design of elastic WDM networksthat align channels on irregular grids of optical frequenciesin transmission links so as to mitigate the routing constraintsand avoid additional spectral fragmentation. Rofoee et al. [12]proposed a novel hybrid multi-rate, multi-technology networkarchitecture which can support the co-existence of fixed-gridand flex-grid networking by providing flexible sub-wavelength,wavelength, waveband, and super-channel services. Eria et al.[13] evaluated the impact on network capacity of deploying aflexible-grid solution over a network which is partially loadedwith fixed-grid channels, and proposed several possible migra-tion strategies from fixed grid to flexible grid networks.

As a limitation, most of the existing studies in this directionfocused on the spectrum operation and lightpath establishmentbetween the same type of nodes (i.e., both the source and desti-nation nodes are either DWDM ROADMs or EON ROADMs)during the process of migration; they also did not consider theoption to split the traffic demand between a pair of nodes whichtransmit simultaneously on different optical paths. In this study,we employ the sub-band VCAT technique [14] to enable light-path connections to be established between different types ofnodes (i.e., one node is a DWDM ROADM and the other nodeis an EON ROADM) and allow the traffic demand to be split andtransmitted via multiple optical sub-channels for better flexibil-ity and greater spectral efficiency. The sub-band VCAT tech-nique was also referred to as split spectrum (SS) in [15]. Thistechnique is inherited from the VCAT technique in the tradi-tional optical transport network (OTN), where an OTN trafficflow between the same node pair can be split at the source nodeand each split sub-flow can travel via different routes and even-tually combine at the destination node. The sub-band VCATor SS technique extends the VCAT technique used in OTN forthe sub-band spectra in the optical domain. While some studies(e.g., [15]) have called it SS, in order to be consistent with theVCAT technique in OTN, we prefer to refer to it as sub-band

VCAT. There is however no difference between the sub-bandVCAT and SS techniques.

The sub-band VCAT technique is currently also a popularresearch topic. Cai et al. [16] applied the VCAT techniqueto the frequency domain by transmitting the sub-bands of asuper-channel via different routes and showed that the VCATtechnique can significantly reduce network lightpath blocking.Shen et al. [17] developed two analytical models for the perfor-mance evaluation of the VCAT technique in the elastic opticalnetwork, one with spectrum conversion and the other withoutsuch conversion. They showed that the VCAT scheme can sig-nificantly improve lightpath blocking performance over a non-VCAT scheme. Yuan et al. [18] focused on the study of thestatic RSA problem for performance evaluation of the multi-path VCAT technique and found that the benefit of the multi-path sub-band VCAT technique is highly dependent on networktopologies. Their results show that with increasing nodal de-gree of the network, the multi-path sub-band VCAT techniquecan help improve spectrum efficiency compared to a non-VCATscheme. Padhi et al. [19] studied the performance of uneven andeven traffic splitting mechanisms for multi-path routing in trafficgroomed optical WDM mesh networks and showed that unevensplitting can help reduce blocking probability. Yang et al. [20]proposed a novel multi-flow virtual concatenation implemen-tation model in flexible spectrum networks to utilize spectralfragments effectively in advance without influencing existingservices. Dahlfort et al. [15] introduced the split spectrum ap-proach to EONs and showed that split spectrum allows at least50% more non-blocking traffic and 50% higher network spec-tral efficiency at non-blocking loads for the scenarios that wereinvestigated. Infinera [21] also implemented “split spectrum”super-channels by combining multiple carriers offering around8 Tb/s in the C-band with 5–10 times the spectral efficiencyoffered by 10-Gb/s directed modulation systems using a tradi-tional 50-GHz grid. All these studies on the sub-band VCATtechnique were performed for an optical network with the sametype of nodes, either EON nodes or DWDM nodes. To the bestof our knowledge, there are no studies to apply the VCAT tech-nique in a mixed grid optical network.

II. MIXED GRID OPTICAL NETWORKS AND MULTI-PATH

SUB-BAND VIRTUAL CONCATENATION

As indicated earlier, during the process of migration from anetwork with only fixed grid nodes to one where all the nodesare flexible ones, there would be intermediate stages whereboth fixed and flexible grid nodes would co-exist in the net-work. Fig. 1 shows an example of such a mixed grid opticalnetwork, in which two types of ROADM nodes, i.e., DWDMand EON ROADMs, co-exist. In Fig. 1, Nodes 0, 1, and 5 areDWDM ROADMs, while Nodes 2, 3, and 4 are EON ROADMs,respectively.

In this type of network, several communication possibilitiesmay arise between the different types of nodes, as given below.

1) Both the source and destination nodes are DWDMROADMs, and the route may traverse an intermediatenode that is a DWDM ROADM or an EON ROADM [see


Fig. 1. Network example where DWDM and EON ROADMs co-exist.

Fig. 2. Spectrum usage in different cases.

Fig. 2(a)]. The transponders at both source and destinationnodes are regular 50-GHz DWDM transponders. In thisscenario, the RSA problem is the same as the routing andwavelength assignment (RWA) problem in DWDM net-works, i.e., each optical channel must be established on asingle 50-GHz grid. A bandwidth requirement higher thana single DWDM channel should be supported by multipleDWDM optical channels.

2) One node is an EON ROADM and the other is a DWDMROADM, and the route may traverse an intermediate nodethat is a DWDM ROADM or an EON ROADM [seeFig. 2(b)]. A transponder that supports a super-channelbased on the sub-band VCAT technique is needed at onenode, while multiple 50-GHz DWDM transponders or asame type of super-channel transponder is required at theother node (if the super-channel occupies the spectra ofmultiple 50-GHz channels). For the latter case, an opti-cal coupler is required to combine the spectra droppedfrom multiple DWDM ROADM add/drop ports onto thesuper-channel transponder, and vice versa. To establish asuper-channel (i.e., larger than a 50-GHz grid), the sub-band VCAT technique would combine multiple sub-bandscarried on different 50-GHz DWDM grids to form thesuper-channel. A guard band (e.g., one FS) is requiredbetween the sub-bands of the super-channel if their corre-sponding DWDM grids are neighboring. In this scenario,the RSA problem is the same as that in (1) due to theconstraint from the DWDM ROADM node.

3) Both the source and destination nodes are EON ROADMs,but the route passes an intermediate node that is a DWDMROADM [see Fig. 2(c)]. This scenario is similar toFig. 2(b) except that the destination node is a different typeof ROADM, i.e., an EON ROADM. Thus, the transpon-der at the destination node can be directly connected toan add/drop port, not requiring any optical splitter as inFig. 2(b).

4) All the nodes are EON ROADMs [see Fig. 2(d)]. Opti-cal channels are adjustable according to the bandwidthrequirement with the spectrum granularity of 12.5 GHz,and a super-channel can be set up without guard band asshown in Fig. 2(d). The transponders at both the source anddestination nodes are super-channel transponders. Clearly,this scenario is the most spectrally efficient one as it hasone fewer FS than that in (3).

For all the examples in Fig. 2, the sub-band VCAT techniqueis applied on a single path for the case of neighboring DWDMchannels. In addition to this, the single-path VCAT techniquecan actually be generally applied to the sub-bands that are spec-trally far away from each other, more than neighboring DWDMchannels. To distinguish these two cases, we call the formerneighboring single-path VCAT and the latter general single-path VCAT. In the following sections, without explicitly indicat-ing, all the single-path VCAT cases refer to the general single-path VCAT, where the DWDM channels making up a super-channel must be spectrally separate from each other by at least a50-GHz grid, while neighboring single-path VCAT is consid-ered as the situation where there is no VCAT implemented(though actually physically required). More specifically, inFig. 2(b) and (c), though physically the single-path VCAT isimplemented, for performance modelling we consider them asnon-VCAT.

The sub-band VCAT technique can also be employed in amulti-path manner as shown in Fig. 1. Assume that there are Ndisjoint routes between a pair of nodes and the traffic demandbetween the two nodes is S FSs. We split these FSs into several(no more than N) sub-bands, then transmit each sub-band overone of the routes, and recombine them at the receiver. In theexample of Fig. 1, a 10-FS super-channel between nodes 2 and 4is provisioned by two different paths (i.e., 2–3–4, 2–5–4) usingthe VCAT technique, where the two routes carry 5 FSs each.

It should be noted that though the sub-band VCAT techniquecan resolve the difficulty of the co-existence of the conventionalDWDM network and the new-generation flex-grid optical net-work, the guard-band required between neighboring split sub-channels may waste fiber spectra and also increase the numberof transponders and signal regenerators used. Thus, it is vitalto efficiently plan a mixed grid optical network by proposingeffective approaches, which is just the focus of this study.

III. MILP MODEL FOR MIXED GRID OPTICAL NETWORKS

A. Problem Statement

The problem of applying the sub-band VCAT scheme to en-able the mixed grid optical network can be formally stated asfollows.


TABLE IOPTICAL TRANSPARENT REACHES [22] AND FS CAPACITIES

OF DIFFERENT MODULATION FORMATS

Given:1) A general network topology represented by a graph

G(V, E), where V is the set of nodes and E is the setof (bi-directional) fiber links connecting nodes in V ;

2) A set D of static traffic demands given a priori. Eachdemand d ∈ D is represented by a triple (Sd, Dd,Rd ),where Sd and Dd are the source and destination nodes ofd respectively, and Rd is the requested bandwidth;

3) A set of eligible modulation formats M = {8-QAM,QPSK, BPSK}.

Find:Multiple sub-band lightpaths to be established between

each node pair, subject to the following assumptions and/orconstraints:

1) Fiber capacity constraint: For the DWDM optical net-work, there are 80 wavelengths in each fiber link withspectrum granularity of 50 GHz, and for the EON, thereare 320 FSs in each fiber link with spectrum granularityof 12.5 GHz.

2) Wavelength continuity (DWDM): The same wavelengthmust be used on all hops on an end-to-end lightpath.

3) Spectrum contiguity (EON): The set of FSs allocated to alightpath must be neighboring.

4) Spectrum continuity (EON): The same set of contiguousFSs must be allocated on each link along a lightpath.

5) Modulation formats: If F is the number of FSs to be as-signed, B is the bandwidth provided by each FS, and SEis the spectrum efficiency of a selected modulation for-mat (in units of bit/s/Hz), to support a data rate R, thenthe condition of 2 · F ·B · SE ≥ R should be satisfied.Here we assume that polarization multiplexing (PM) isused, and thus the spectrum efficiency SE is effectivelydoubled. The SEs of BPSK, QPSK, and 8-QAM are typ-ically 1, 2, and 3 bit/s/Hz, respectively. Given that eachFS has a bandwidth of 12.5 GHz, Table I shows the op-tical transparent reach and the FS capacity (in multiplesof 12.5 GHz) under different modulation formats. Notethat this study has assumed that the transparent reach ofthe BPSK modulation format is long enough to cover thewhole network being considered. However, there could besituations where a network is larger and requires signal re-generation for a lightpath to be established between a pairof nodes that are far away. Thus, an extended study canconsider lightpath signal regeneration, which is howeverbeyond the scope of this study.

B. MILP Model for Multi-PATH VCAT Scheme

In this part, we consider the case of multi-path VCAT asshown in Fig. 3(a), where a VCAT super-channel is made up

Fig. 3. Examples of multi-path and single-path sub-band VCAT techniques.(a) Multi-path VCAT scenario. (b) Joint multi-path and single-path VCATscenario.

of sub-bands on different routes and on each of the route thespectrum of the corresponding sub-band is contiguous.1 Thismeans that there is no single-path VCAT on each sub-bandlightpath. As shown in Fig. 3(a), there are three sub-bands spliton three different routes, and each route carries only a singlespectrally contiguous sub-band. For this, we develop an MILPmodel as follows.

Sets:L: Set of network links.R: Set of node pairs in the network.P r: Set of candidate routes between node pair r (r ∈ R).P W

r : Set of candidate routes between node pair r (r ∈ R)that contains DWDM ROADMs.

P Er : Set of candidate routes between node pair r (r ∈ R)

that only contains EON ROADMs.Λr

p: Set of links traversed by route p (p ∈ P r) between nodepair r (r ∈ R).

Parameters:

Tr : The required bandwidth (in units of Gb/s) between nodepair r (r ∈ R).

δrp : The spectrum efficiency of path p (p ∈ P r) between

node pair r (r ∈ R) when the most efficient modulationformat is used on the route. δr

p = 1, 2, 3 for BPSK,QPSK, and 8-QAM, respectively.

1Note that here, for the case where multiple neighboring DWDM channelsmake up a super-channel, we consider the spectra of these DWDM channelscontiguous in spite of a 12.5-GHz FS guard band between any two neighboringDWDM channels. Only if these DWDM channels are separate and are far enoughaway with at least one 50-GHz grid in-between would we consider them to benon-contiguous.


£rp : A binary parameter that equals 1 if route p (p ∈ P r) be-

tween node pair r (r ∈ R) traverses DWDM ROADMs;0, otherwise.

θr,pi : A binary parameter that equals 1 if route p (p ∈ P r)

between node pair r (r ∈ R) traverses link i (i ∈ L); 0,otherwise.

M : A large value.ε: The bandwidth (in units of Gb/s) provided by each FS.ρ: The number of FSs that can be provisioned by a DWDM

channel including the guard band. Here each 50-GHzDWDM channel can provide four 12.5-GHz FSs, i.e.,ρ = 4.

G: The number of FSs assigned for the guard band betweenneighboring optical channels. In this study, we set it tobe one 12.5-GHz FS.

σ: The number of effective FSs for user data transmissionin a DWDM channel excluding the guard band. In thisstudy, we have σ = ρ−G.

α: A weight factor.

Variables:

frp : An integer variable denoting the starting FS index of

route p (p ∈ P r) between node pair r (r ∈ R). Thisvariable can be generally used for both routes contain-ing DWDM ROADMs and only EON ROADMs. How-ever, if it is used for a DWDM channel, this indexwill be ρ times of the corresponding DWDM channelindex.

ϕr,pt,q : A binary variable that equals 1 if the starting FS index

of route p (p ∈ P r) between node pair r (r ∈ R) islarger than that of route q (q ∈ P t) between node pair t(t ∈ R); 0, otherwise.

drp : The bandwidth (in units of Gb/s) assigned on route p

(p ∈ P r) between node pair r (r ∈ R).xr

p : An integer variable denoting the number of FSs assignedon route p (p ∈ P E

r ) between node pair r (r ∈ R). Thisis a variable only used for the route that contains onlyEON ROADMs.

yrp : An integer variable denoting the starting wavelength

index of route p (p ∈ P Wr ) between node pair r (r ∈ R).

This is a variable only used for the route that traversesDWDM ROADMs.

krp : A binary variable that equals 1 if the number of FSs

assigned to route p (p ∈ P r) between node pair r (r ∈R) is larger than 0; 0, otherwise.

ξrp : An integer variable denoting the number of DWDM

channels assigned on route p (p ∈ P Wr ) that contains

DWDM ROADMs between node pair r (r ∈ R).c: The maximum index of FSs used in the whole network.Si : An integer variable denoting the total number of FSs

used in link i (i ∈ L).Ts : An integer variable denoting the total number of FSs

used in the network.

Objective:

Minimize c + α · Ts (1)

Subject to:∑

p∈P r

drp = Tr ∀r ∈ R (2)

ξrp · σ · ε · δr

p ≥ drp ∀r ∈ R,∀p ∈ P W

r (3)(ξrp − 1

) · σ · ε · δrp ≤ dr

p − 1 ∀r ∈ R,∀p ∈ P Wr (4)

frp = ρ · yr

p ∀r ∈ R,∀p ∈ P Wr (5)

xrp · ε · δr

p ≥ drp ∀r ∈ R,∀p ∈ P E

r (6)(xr

p − 1) · ε · δr

p ≤ drp − 1 ∀r ∈ R,∀p ∈ P E

r (7)

xrp ≤M · kr

p ∀r ∈ R,∀p ∈ P Er (8)

xrp ≥ kr

p ∀r ∈ R,∀p ∈ P Er (9)

ϕr,pt,q + ϕt,q

r,p = 1

∀r, t ∈ R,∀p ∈ P r,∀q ∈ P t, r �= t,Λrp ∩Λt

q �= ∅ (10)

frp +

(1−£r

p

) · (xrp + G · kr

p

)+ ρ ·£r

p · ξrp − ft

q ≤M · ϕr,pt,q

∀r, t ∈ R,∀p ∈ P r,∀q ∈ P t, r �= t,Λrp ∩Λt

p �= ∅ (11)

Si =∑

r∈R,p∈P r

(1−£r

p

) · (xrp + G · kr

p

) · θr,pi

+∑

r∈R,p∈P r

£rp · ρ · ξr

p · θr,pi ∀i ∈ L (12)

Ts =∑

i∈LSi (13)

c ≥ frp +

(1−£r

p

) · (xrp + G · kr

p

)+ ρ ·£r

p · ξrp

− 1 ∀r ∈ R,∀p ∈ P r (14)

c ≥ Si − 1 ∀i ∈ L (15)

In this model, we assume that the spectrum of a lightpathassigned on a route follows the constraint of spectrum conti-guity. That is, no VCAT technique is employed on a singleroute. Objective (1) is to minimize the maximum number ofFSs used and the total number of FSs used in the whole net-work. Here α is a weight factor, which is a small value suchthat the first objective has a higher priority. In this study, weset α = 0.001. Constraint (2) ensures that the total bandwidthassigned on different routes of the same node pair is equal tothe total bandwidth required between the node pair. Constraints(3) and (4) calculate the number of DWDM channels neededto be set up on the route which contains DWDM ROADMs.Constraint (5) indicates the relationship between the DWDMchannel index and the corresponding starting FS index of theDWDM channel. More specifically, the FS index will be ρ timesof the corresponding DWDM channel index. As shown in Fig. 4,assume that each fiber link contains 28 12.5-GHz FSs (indexedfrom 0 to 27); these FSs correspond to 7 DWDM channels (in-dexed from 0 to 6) with each DWDM grid containing 4 FSs.For example, referring to constraint (5), we can have the corre-sponding relationship for the 8th FS in Fig. 4(a) as yr

p = 2 andfr

p = ρ · yrp = 8.

Constraints (6) and (7) calculate the number of FSs requiredaccording to the bandwidth assigned on the route which only


Fig. 4. Relationship between the indexes of DWDM channels and correspond-ing FSs.

traverses EON ROADMs. Constraints (8) and (9) check whetherthe bandwidth assigned on the route which only traverses EONROADMs is larger than 0, or tells if the route is chosen tocarry any traffic demand. Constraints (10) and (11) ensure thatthe allocated spectra to any two lightpaths do not overlap onany common link. Here we consider two situations. If it isa path that only contains EON ROADMs, then £r

p = 0, sothe term (1−£r

p) · (xrp + G · kr

p ) takes effect, where G · krp

counts for the guard band, and the term ρ ·£rp · ξr

p for DWDMchannels disappears. Otherwise, if it is a path that containsDWDM ROADMs, then the spectrum assignment on the pathis based on the DWDM fixed grids, so £r

p = 1 and the term(1−£r

p) · (xrp + G · kr

p ) disappears, while ρ ·£rp · ξr

p takes ef-fect. Constraint (12) calculates the total number of FSs used ineach fiber link. Constraint (13) calculates the total number ofFSs used in the whole network. Constraints (14) and (15) arethe smallest upper bounds on the index of FSs used on a routeand a link, respectively.

C. MILP Model Jointly Considering Multi- and Single-PathVCAT Schemes

To be more flexible and efficient, we allow the VCAT tech-nique to be applied also for the single-path scenario as shownin Fig. 3(b). That is, even on a single route, a spectrum flowsplit from a multi-path sub-band VCAT super-channel can befurther split into multiple non-contiguous sub-bands and trans-mitted along the same route. As shown in Fig. 3(b), the sub-band spectrum on the second route is further split onto twonon-contiguous sub-bands which are transmitted along the sameroute. Thus, Fig. 3(b) essentially demonstrates the most generalVCAT scenario, where multiple sub-bands are transmitted ondifferent routes and non-contiguous sub-bands are transmittedon the same route. We develop an MILP model that jointly sup-ports both the multi-path and single-path VCAT technique inmixed grid optical networks so as to minimize the maximumnumber of FSs used in the fiber links. The set of the model arethe same as those of the model that only supports the multi-pathVCAT technique except that it excludes the set Λr

p. In additionto the parameters and variables defined earlier, we also havesome other parameters and variables which are defined next.

Parameters:

μr,pt,q : A binary parameter that equals 1 if route p (p ∈ P r)

between node pair r (r ∈ R) and route q (q ∈ P t)between node pair t (t ∈ R) share any common link;0, otherwise.

Fmax : The maximum number of flows that can be split on asingle route (for single-path VCAT).

Variables:

fkr,p : An integer variable denoting the starting FS index of

the kth (k ≤ Fmax ) flow on route p (p ∈ P r) betweennode pair r (r ∈ R).

ϕr,p,k2t,q ,k1

: A binary variable that equals 1 if the starting FS indexof the kth

2 (k2 ≤ Fmax ) flow on route p (p ∈ P r)between node pair r (r ∈ R) is larger than that of thekth

1 (k1 ≤ Fmax ) flow on route q (q ∈ P t) betweennode pair t (t ∈ R); 0, otherwise. Here subscript k1or superscript k2 is the flow index of a request split ona single path.

dkr,p : An integer variable denoting the bandwidth of the kth

(k ≤ Fmax ) flow that is assigned on route p (p ∈ P r)between node pair r (r ∈ R).

xkr,p : An integer variable denoting the number of FSs of

the kth (k ≤ Fmax ) flow that are assigned on routep (p ∈ P E

r ) between node pair r (r ∈ R). This is avariable only used for the route that contains onlyEON ROADMs.

ykr,p : An integer variable denoting the starting wave-

length index of the kth (k ≤ Fmax ) flow on routep (p ∈ P W

r ) between node pair r (r ∈ R). This is avariable only used for the route that traverses DWDMROADMs.

kkr,p : A binary variable that equals 1 if the number of FSs of

the kth (k ≤ Fmax ) flow that are assigned to the routep (p ∈ P r) between node pair r (r ∈ R) is larger than0; 0, otherwise.

ξkr,p : An integer variable denoting the number of DWDM

channels of the kth (k ≤ Fmax ) flow assigned on routep (p ∈ P W

r ) that contains DWDM ROADMs betweennode pair r (r ∈ R).

The objective and constraints of the model are as follows.Objective:

Minimize c + α · Ts (16)

Subject to:

∑

p∈P r ,k≤Fm a x

dkr,p = Tr ∀r ∈ R (17)

ξkr,p · σ · ε · δr

p ≥ dkr,p

∀r ∈ R, ∀p ∈ P Wr , k ≤ Fmax (18)

(ξkr,p − 1

) · σ · ε · δrp ≤ dk

r,p − 1

∀r ∈ R,∀p ∈ P Wr , k ≤ Fmax (19)

fkr,p = ρ · yk

r,p ∀r ∈ R, p ∈ P Wr , k ≤ Fmax (20)

xkr,p · ε · δr

p ≥ dkr,p ∀r ∈ R, p ∈ P E

r , k ≤ Fmax (21)(xk

r,p − 1) · ε · δr

p ≤ dkr,p − 1

∀r ∈ R,∀p ∈ P Er , k ≤ Fmax (22)


xkr,p ≤M · kk

r,p ∀r ∈ R, p ∈ P Er , k ≤ Fmax (23)

xkr,p ≥ kk

r,p ∀r ∈ R, p ∈ P Er , k ≤ Fmax (24)

ϕr,p,k2t,q ,k1

+ ϕt,q ,k1r,p,k2

= 1

∀r, t ∈ R,∀p ∈ P r,∀q ∈ P t, k1 , k2 ≤ Fmax (25)

fk2r,p +

(1−£r

p

) · (xk2r,p + G · kk2

r,p

)+ ρ ·£r

p

· ξk2r,p − fk2

t,q ≤M ·(ϕr,p,k2

t,q ,k1+ 1− μr,p

t,q

)(26)

∀r, t ∈ R,∀p ∈ P r,∀q ∈ P t, k1 , k2 ≤ Fmax

Si ≥∑

r∈R,p∈P r

(1−£r

p

) · (xkr,p + G · kk

r,p

)

· θr,pi +

∑

r∈R,p∈P r

£rp · ρ · ξk

r,p · θr,pi − 1 (27)

∀i ∈ L, k ≤ Fmax

Ts ≥∑

i∈L

Si (28)

c ≥ fkr,p +

(1−£r

p

) · (xkr,p + G · kk

r,p

)+ £r

p · ρ·ξkr,p − 1 ∀r ∈ R,∀p ∈ P r, k ≤ Fmax (29)

c ≥ Si ∀i ∈ L, k ≤ Fmax (30)

Objective (16) is the same as that in the previous model. Con-straint (17) ensures that the total bandwidth of different flowsthat are assigned on different routes between the same node pairequals the total bandwidth required between the node pair. Con-straints (18) and (19) calculate the number of DWDM channelsneeded to be set up by the kth flow on the route which traversesDWDM ROADMs. Constraint (20) corresponds to constraint(5) to indicate the relationship between the DWDM grid in-dex and the starting FS index for the kth flow of a route thatcontains DWDM ROADMs. Constraints (21) and (22) calcu-late the number of FSs required according to the bandwidth ofthe kth flow assigned on the route which traverses only EONROADMs. Constraints (23) and (24) check whether the band-width of the kth flow assigned on the route which only tra-verses EON ROADMs is larger than 0. Constraints (25) and(26) ensure that the allocated spectra of any two flows donot overlap on any common link. Here we also consider twosituations. If it is a path that only contains EON ROADMs,then £r

p = 0, so the term (1−£rp) · (xk

r,p + G · kkr,p) takes ef-

fect, where G · kkr,p counts for the guard band, and the term

£rp · ρ · ξk

r,p for DWDM channels disappears. Otherwise, if itis a path that contains DWDM ROADMs, then the spectrumoperation on the path is based on the DWDM fixed grids, so£r

p = 1 and the term (1−£rp) · (xk

r,p + G · kkr,p) disappears

with the term £rp · ρ · ξk

r,p taking effect. Constraint (27) calcu-lates the number of FSs used in each fiber link. Constraint (28)calculates the total number of FSs used in the whole network.Constraints (29) and (30) are the smallest upper bounds on theindex of FSs used on a route and on a link, respectively.

Fig. 5. Spectrum windows (SWs) in a fiber link.

D. Complexity of the MILP Models

The computational complexity of an MILP model is decidedby the dominant numbers of variables and constraints. For themulti-path VCAT MILP model, the computational complexityis analyzed as follows. The dominant number of variables is de-cided by the variable ϕr,p

t,q , which is of the order O(|R|2 · |Pr |2),where |R| is the total number of node pairs in the network and|Pr | is the number of candidate routes between each node pair.Similarly, the dominant number of constraints of the model is ofthe order O(|R|2 · |Pr |2) due to constraints (10) and (11). Forthe MILP model with multi- and single-path VCAT, the com-putational complexity is as follows: both dominant numbers ofvariables and constraints are of the order O(|R|2 · |Pr |2 · F 2

max)where Fmax is the maximum number of flows that can be spliton a single route.

IV. HEURISTIC ALGORITHMS FOR SUB-OPTIMAL DESIGN

The MILP model will find the optimal solution to the RSAproblem where the VCAT scheme is used in mixed grid opticalnetworks. Since this problem is NP-complete, for large or evenreasonably sized networks, the MILP model cannot be solvedto obtain an optimal solution within reasonable time. Therefore,we develop efficient heuristic algorithms for the RSA problem.

A. Related Concepts

Assume that each source-destination pair requests a band-width R, based on which we can calculate the number of FSsrequired by using the equation F = R/(2 ·B · SE) . Withthe use of the VCAT technique, these F FSs are required to meetthe constraints of spectrum contiguity and continuity along eachsub-band lightpath in EONs. For this, we introduce the conceptof spectrum window (SW) as in [23], which is made up of a cer-tain number of continuous FSs. The size F of an SW may varyaccording to different user bandwidth requests and modulationformats. In the example of Fig. 5, if each fiber link is assumedto contain 29 FSs, then there can be a total of 25 SWs of size 5in the fiber link.

Based on this concept of SW, we then define the conceptof a spectrum window plane (SWP) [23] as shown in Fig. 6.An SWP is similar to the concept of waveplane [24] in thetraditional WDM network. In a WDM network, each waveplanecorresponds to a specific wavelength. Similarly, in an EON,each SWP corresponds to an SW. For each F-slot SWP, we usestartindex and endindex to denote the index of the starting andending FSs assigned on each SWP, respectively. For example, inFig. 6, plane 1 corresponds to SW1, where its startindex = 1and endindex = 5.

We also incorporate a multi-iteration process to evaluate theperformance for multiple shuffled demand sequences and then


Fig. 6. Spectrum window planes (SWPs) of a n6s8 network [23].

Fig. 7. General diagram of the RSA process for a splitting combination.

choose the demand sequence with the best performance so asto handle the performance variation due to different demandorders [23]. A “shuffled demand sequence” is referred to as alist of request services which is obtained by randomly shufflingan initial request list.

B. Heuristic Algorithm for Static Traffic Demand

We propose an SWP-based heuristic algorithm for the RSAproblem to evaluate the potential benefit of applying the VCATtechnique in mixed grid optical networks. The main steps of thealgorithm are as follows.

In Step 1, given a traffic demand, we generate all the com-binations of flow splitting. Each combination contains multipleroutes, each of which carries a split traffic flow. Here for flowsplitting, we use 25 Gb/s as the basic splitting granularity. Thisis because for BPSK a 12.5-GHz FS can carry 25-Gb/s capacitywith PDM and for the other more advanced modulation formats,the capacity carried by each 12.5-GHz FS is an integral multipleof 25 Gb/s.

Step 2 is key to the SWP-based algorithm. It considers differ-ent modulation formats when establishing a split traffic flow foreach combination. Fig. 7 shows a general diagram to illustratethe RSA process for a certain splitting combination Ci . Herethe term dr denotes the total bandwidth required by a serviceconnection, and {d1

r , d2r , · · · , dk

r } denotes the set of the band-widths of each split traffic flow, where dr =

∑1≤i≤k di

r alwaysholds. Different modulation formats MF := {8-QAM, QPSK,BPSK} are considered, ranging from the most efficient to theleast efficient for each lightpath establishment. The maximumtransparent reach limit and the data rate of an FS with eachmodulation format are given in Table I.

In the SWP-based algorithm, we would consider two typesof lightpaths. The first is to accommodate a split flow us-ing a DWDM lightpath if there are any DWDM nodes inthe network. The second is to accommodate the split flow by

establishing an EON lightpath after removing all the links in-cident to DWDM nodes in the network. These two scenarioswill be tried to find two ending FS indexes of the SWPs that arechosen to establish lightpaths. We compare them to choose thesmaller one and the corresponding lightpath is used to accom-modate the split flow. We first introduce the detailed steps for thescenario of an EON lightpath, and then the scenario of a DWDMlightpath.

For an EON lightpath, given a split demand dir and the modu-

lation format employed, the number of FSs required, FSi , can becalculated as FSi = Fi + G, where Fi = di

r /(2 ·B · SE) ,G is the number of FSs required for the guard band, and B is12.5 GHz. We then create a SWP list as in Fig. 6, each of whichcontains FSi frequency slots, and furthermore, an eligible routeis searched based on the SWP list in the first-fit mode. If aneligible route is found, we will return the last FS index of thefirst eligible SWP and store it in ej

EON .The scenario of a DWDM lightpath can be considered as a

special case of the former where the bandwidth of each FS is50 GHz and the effective bandwidth of each FS excluding theguard band is calculated as B50 GHz = 50 GHz −12.5 GHz·G.Thus, to accommodate a split demand di

r , the required numberof FSs is calculated as FSi = di

r/(2·B50 GHz ·SE) . Based onthis new FSi , the remaining steps are the same as those for anEON lightpath. In this process, we will find the last FS indexof the first eligible SWP and store it in wj

DWDM . Because thebandwidth of each FS of a DWDM lightpath is 50 GHz, we canfurther convert wj

DWDM to the index with the 12.5-GHz gridby using ej

DWDM = ρ·wjDWDM − 1 where ρ is the number of

12.5-GHz FSs contained by each 50-GHz DWDM channel and−1 is because the starting FS index is 0.

We compare the two indexes ejEON and ej

DWDM to choosethe smaller one as the final index for the RSA of the split flowdi

r , i.e., ej = min{ejEON , ej

DWDM}. Once all the split flows in{d1

r , d2r ,· · ·, dk

r } are established in this way, we further find eir

by eir = max1≤j≤k {ej} for the combination Ci (1 ≤ i ≤ n),

which is the smallest FS index that can be achieved. We willfollow the same process for all the combinations Ci ∈ C (1 ≤i ≤ n) to obtain their corresponding ei

r .In Step 3, we choose the combination that has the smallest

ending FS index to accommodate the traffic demand between thenode pair, i.e., Copt

r = arg minCi{ei

r}. In Step 4, we continueapplying the same process as described before for the remainingrequests until they are all served.

For the purpose of performance comparison, we also developa KSP-based algorithm in addition to the SWP-based algorithm.The KSP-based algorithm has the same steps as those of theSWP-based algorithm, but it is much simpler since all the eli-gible routes for lightpath establishment between each node pairhave been pre-calculated and therefore we do not need to findeligible routes based on each SWP one by one. In this study, wehave considered the cases of k = 1, 2, 3 for the KSP-based al-gorithm, where k is the maximum number of link-disjoint routesconsidered between each pair of nodes.

It should be noted that apart from the proposed SWP ap-proach, an alternate approach called the candidate channel ap-proach has also been proposed in [25], [26]. Very similar to the


Algorithm 1: SWP-based heuristic algorithm for the RSAproblem.

Step 1: Get the first service connection request from thedemand list, split its traffic demand dr into k parts(k is no larger than the maximum number ofVCAT routes that are allowed) with each partdenoted by di

r (1 ≤ i ≤ k); different splittingscenarios make up a combination setC := {C1 , C2 , . . . , Cn}, and for each Ci ∈ C

(1 ≤ i ≤ n), the relationship dr =∑k

j=1 djr holds.

Step 2: For each Ci ∈ C (1 ≤ i ≤ n) and each djr

(1 ≤ j ≤ k), generate corresponding SWPs andfind a suitable route from the lowest to the highestindexed SWPs with the first-fit rule, ej ← endingFS index of the current SWP. ei

r = max1≤j≤k {ej}.Step 3: Considering all the Ci ∈ C (1 ≤ i ≤ n), choose

the one with the minimum value, i.e.,er = min1≤i≤n

{eir}, to serve the bandwidth demand and assign

the corresponding spectra to the routes.Step 4: Remove the served request from the demand list;

if the demand list is empty, terminate the RSAprocess; otherwise, go to Step 1.

above KSP-based algorithm, the candidate channel approach ex-haustively lists out all possible combinations of contiguous FSsalong a predetermined route or a predetermined set of routes.The SWP approach differs from the candidate channel approachas follows. The SWP approach does not pre-calculate any routesor channels, but creates all the SWPs first and then searches foran eligible route on these SWPs in an online fashion. Here allthe SWPs can be considered as a network’s virtual topologies.The relationship between the SWP approach and the candidatechannel approach is similar to that between adaptive routingversus alternate (or fixed) routing. The SWP approach is moreflexible in route selection for optical channels and therefore isexpected to perform more efficiently. Of course, this is at thecost of a higher computational complexity because for each ser-vice request, we need to first create all the corresponding SWPsand then carry out the route searching process based on theseSWPs.

C. Heuristic Algorithm for Dynamic Traffic Demand

We also consider the dynamic traffic demand scenario toevaluate the bandwidth blocking probability (BBP) performancefor the proposed mixed grid optical network. The SWP-basedheuristic algorithm for the static traffic demand is modified forthis scenario and the main steps of the algorithm are presentedas follows.

Given a traffic demand, Step 1 decides the most efficientmodulation format MFmost for an arrived service request basedon its shortest path. Some initializations are also made.

In Step 2, for a certain modulation format, the SWP-based al-gorithm in Algorithm 1 is repeatedly implemented to establishlightpaths based on the current remaining network resource.

Algorithm 2: SWP-based algorithm for a dynamic arrivedservice.

Step 1: Initialization. For a certain traffic demand r, Br

denotes the total bandwidth required, and wedecide the most efficient modulation formatMFmost that can be employed for the currentdemand based on the shortest path between thedemand node pair. Set i = 1, MFc = MFmost ,and ΔB0

r = Br .Step 2: With the modulation format MFc , we employ the

SWP-based algorithm to find an eligible route(i.e., route i) for lightpath establishment based onthe minimum-hop principle; calculate themaximum capacity Bi

r that can be provisioned bythe ith route, and update the remaining capacityas ΔBi

r = max{ΔBi−1r −Bi

r , 0}. If (Bir == 0

‖ ΔBir == 0 ‖ i == k) where k is the maximum

number of allowed split flows, move to Step 3;otherwise, i + +, and repeat Step 2.

Step 3: If ΔBir == 0, the current request is served; else

if i == k ‖ (MFc == BPSK && Bir == 0),

the request is blocked; otherwise, set MFc to bethe next modulation format in the set fromMFmost to BPSK and go to Step 2.

That is, once a route is found and a split flow is served, weapply the SWP-based algorithm again based on the same mod-ulation format to find the next route until no such a route canbe found. To find a route that consumes the least spectrum re-source, we take the minimum-hop strategy to find eligible routeson all the SWPs and then choose the one with minimum hopcount. Equation ΔBi

r = max{ΔBi−1r −Bi

r, 0} is to calculatethe remaining bandwidth after a new split flow is established.

In Step 3, we check if all the bandwidth of the demand isaccommodated. If so, the demand is served. Otherwise, whenthe maximum number of allowed split flows is reached, or allthe modulation formats are tried and no eligible route can befurther found, the service request is blocked.

Fig. 8 illustrates the above algorithm steps. Starting fromthe first split flow, for the ith route, if (MFc == BPSK &&Bi

r == 0), the service is blocked; else if ΔBir == 0, the ser-

vice is provisioned. If the service request is either not blocked orsatisfied, we will try a next route until the maximum number k ofallowed routes is reached. The pseudocode of Algorithm 2 hasdescribed the steps for new service establishment. For service re-lease, it is easy to simply release all the network resources used.

D. Computational Complexity of the Heuristic Algorithms

The computational complexities of the heuristic algorithmsare analyzed as follows. For the SWP-based heuristic algorithm,we remove all unavailable SW links on each SWP, which cor-respond to a computational complexity of (|F | · |L|), where |L|is the number of links in a network. Considering the possibilityof scanning all the SWPs, the computational complexity ofthe shortest path searching algorithm is O(|F | · |N |2). As aresult, the overall computational complexity of the SWP-based


Fig. 8. Illustration of the SWP-based algorithm for dynamic serviceprovisioning.

algorithm is of the order O(|F | · (|L|+ |N |2)). Moreover,since we are considering multiple types of modulation formatsand two types of lightpaths, i.e., DWDM and EON lightpaths,the overall computational complexity of establishing a lightpathis of the order O(|M | · (|F | · (|L|+ |N |2) · 2)), where |M |is the total number of modulation formats considered. Thus,for each static traffic demand, the overall computationalcomplexity with the SWP-based algorithm is of the orderO(|C| · k · |M | · (|F | · (|L|+ |N |2) · 2)), where k is themaximum number of VCAT flows of each service demand,|C| is the total number of splitting combinations, and foreach dynamic traffic demand, the overall computationalcomplexity with the SWP-based algorithm is of the orderO(k · |M | · (|F | · (|L|+ |N |2) · 2)).

V. CASE STUDIES AND PERFORMANCE RESULTS

For the scenario of static traffic demand, we first compare theperformance of the proposed heuristic algorithms with that ofthe MILP model which was specifically developed to evaluatethe performance of the algorithms for the multi-path VCAT sce-nario. We also show the results obtained by the MILP modelwhich supports both multi-path and single-path VCAT tech-nique. Finally, the performance while serving dynamic trafficdemands is also examined in terms of the BBP.

A. Test Conditions

We considered two test networks, a 10-node, 22-link Small-Net network and a 14-node, 21-link NSFNET network as shownin Fig. 9. The link distance (in km) is shown next to each link.Note that, since these are case studies, the link distances are notactual ones but have been appropriately scaled with a certain ra-tio. Three modulation formats (i.e., 8-QAM, QPSK, and BPSK)are assumed to be used for establishing lightpaths. For the sce-nario of static traffic demand, we assume that the traffic demandbetween each node pair is fixed and uniformly distributed over[100, 500] Gb/s. For the dynamic scenario, we assume that thebandwidth request between each node pair arrives accordingto a Poisson arrival process and their holding times follow a

Fig. 9. Test networks (unit of link length: km). (a) 10-node, 22-link SmallNetnetwork. (b) 14-node, 21-link NSFNET network.

negative exponential distribution. The bandwidth of each re-quest is uniformly distributed over [10, 400] Gb/s. The guardband between two neighboring channels is set to be 12.5 GHz.

To emulate the migration process of an optical network from apure DWDM network to an EON, we gradually replace DWDMnodes with EON nodes. The replacement strategy is based onthe nodal degree. That is, we replace an EON ROADM for aDWDM node with the highest nodal degree first.

For the MILP models, the candidate routes used for the MILPmodel were obtained based on the link-disjoint k-shortest path(KSP) algorithm. We employed the commercial AMPL/Gurobi[27] software package (version 5.6.2) to solve the MILP modelson a 64-bit machine with 2.4-GHz CPU and 24-GB memory, andwithout explicitly indicating, the MIPGAP of the MILP modelwas set to be 0.01%. It may be noted that, for large networks, itwas not computationally feasible to solve the MILP models foran optimal solution in a reasonable time. We therefore restrictedourselves to only the SmallNet network for the MILP-basedoptimal solution.

For the heuristic algorithm, we shuffled an initial demand list1000 times to form the shuffled demand sequences, for each ofwhich we ran the heuristic algorithm and selected the demandsequence with the best design performance as the final solution.For the dynamic traffic demand scenario, a total of 106 arrivalrequests were simulated for calculating the BBP, which is de-fined as the ratio of the total amount blocked bandwidth to thetotal amount of arrived bandwidth request. When provisioninga lightpath service, if a lightpath cannot be successfully estab-lished, the service request is blocked. When a lightpath serviceis released, we free all the FSs used by the lightpath.

B. Maximum Number of FSs Used (MILP and Heuristic)

In this section, we evaluate the maximum number of FSsused for accommodating all the static bandwidth requests under


Fig. 10. Maximum number of FSs with an increasing number of EON nodes.(a) SmallNet (MILP). (b) SmallNet. (c) NSFNET.

the multi-path VCAT scheme in mixed grid optical networks.Fig. 10 shows the maximum number of FSs required as a func-tion of the number of EON nodes in the network. It is importantto note that increasing the number of EON nodes is indica-tive of a migration process from a pure DWDM network to amixed grid network, and eventually to a pure EON. The legends“MILP”, “KSP”, and “SWP” correspond to the results of theMILP model, the KSP-based algorithm, and the SWP-based al-gorithm, respectively, and “MILP_x,” “KSP_x,” and “SWP_x”means splitting the bandwidth onto x routes via the correspond-ing VCAT technique. The legend “non-VCAT” means that thebandwidth requirement between a node pair should be fully

allocated to a single path, and “non-VCAT_x” means that oneroute is chosen from x routes to carry the entire non-VCATbandwidth requirement. The legend “VCAT_x” means that weimplement the VCAT technique on x routes. For all the cases,the bandwidth allocated onto a route should be reserved as acontiguous spectrum as in Fig. 3(a) where no sub-band VCATis implemented on a single route.

The results of Fig. 10 indicate that increasing the numberof EON nodes leads to a decrease in the maximum number ofFSs used in the fiber links. The performance improvement isup to 28% and 25% for the SmallNet and NSFNET networks,respectively. This is reasonable since the DWDM nodes oper-ate with a 50-GHz spectrum granularity, while the EON nodesoperate with a smaller 12.5-GHz spectrum granularity and aremore flexible and efficient in spectrum allocation. However, it isalso observed that the performance improvement is marginal atthe beginning with few EON nodes but that there is a significantimprovement when there are a larger number of EON nodes inthe network (we see a big drop in each curve when the numberof EONs changes from 8 to 10 or 12 to 14 for both networks).This therefore implies the importance of the EON nodes for theperformance enhancement of a mixed grid optical network andthe necessity for a DWDM optical network to migrate to a pureEON.

Comparing the VCAT and non-VCAT cases in Fig. 10(a) (theresults were obtained based on the MILP model), we see that theVCAT case can achieve better performance than the non-VCATone. This is because the multi-path VCAT technique helps theperformance by balancing the network bandwidth onto differentroutes, which reduces the maximum number of FSs used in thefiber links.

We also compare the performance of the different approaches[i.e., MILP model, KSP-based algorithm, and SWP-based algo-rithm in Fig. 10(b)]. It is interesting to see that the proposedSWP-based heuristic algorithm can perform better than boththe MILP model and the KSP-based algorithm. This is becausethe SWP-based algorithm adaptively searches for eligible routesfor each VCAT flow, and is therefore more flexible in routingand spectrum allocation than the other two approaches sincethey use k fixed routes instead.

The results of Fig. 10 also indicate that increasing the max-imum number of routes that can be set up between each nodepair decreases the maximum number of FSs used in the fiberlinks. This is because having a larger number of candidate routesprovides more options to serve the VCAT connections, therebyachieving better performance. In addition, it is important to notea saturation trend, i.e., while the performance improvement islarge going from k = 1 to k = 2, the improvement going fromk = 2 to k = 3 become smaller [see Fig. 10(c)]. This trendcontinues for larger values of k.

C. MILP Model With and Without Single-Path VCATTechnique

In this section, we consider the case of supporting both multi-path and single-path VCAT techniques [as shown in Fig. 3(b)].Fig. 11 shows the results of the MILP model under different


Fig. 11. Number of FSs used with an increasing number of EON nodes(SmallNet). “VCAT_x_y” means between each node pair, the traffic flow can becarried on at most x routes and on each route there are at most y split sub-flows.(a) Maximum number of FSs used in fiber links. (b) Total number of FSs usedin the whole network.

scenarios. The legend “VCAT_x_y” corresponds to the casewhere between each node pair, the traffic flow can be carried onat most x routes and on each route there are at most y sub-flowsthat can be split. Fig. 11(a) shows the maximum number of FSsused as a function of the number of EON nodes, and Fig. 11(b)shows the total number of FSs used in the whole network (i.e.,Ts in the objective function of the MILP model) as a functionof the number of EON nodes. However, due to the high com-putational complexity of the MILP model which supports bothmulti-path and single-path VCAT technique, only the SmallNetnetwork was solved with the MILP model, whose MIPGAPs arelisted in Table II. Note that we also did not use the heuristic algo-rithm due to the extreme complexity for considering multi-flowcombination on each path.

From the results of Fig. 11, we can see that, for the SmallNetnetwork, the MILP model proposed earlier that only supportsthe multi-path VCAT technique can achieve almost the samemaximum number of FSs used as the MILP model that sup-ports both the multi-path and single-path VCAT techniques [seeFig. 11(a)]. This means that the multi-path VCAT technique isby itself sufficient to balance the network bandwidth require-ment. This further implies that using VCAT on each path doesnot significantly improve the overall performance in terms ofthe maximum number of FSs used in each fiber link. However,the extra effort in using single-path VCAT does help to some-what reduce the total number of FSs used in the whole network

TABLE IIMIPGAPS OF THE MILP SOLUTIONS (x: NUMBER OF PATHS; y:

NUMBER OF FLOWS ON EACH PATH)

[see Fig. 11(b)] even though the improvement is not substantial.This is reasonable since the single-path VCAT does provide onemore optimization dimension for the spectrum resource allo-cation, thereby reducing the FSs used in the whole network.However, since this minor improvement is at the cost of signifi-cant extra complexity of the VCAT technique, we would suggestthat it is sufficient to apply the multi-path VCAT alone to ensurea good performance for a mixed grid optical network.

D. Bandwidth Blocking Probability (Heuristic)

We also consider the dynamic RSA problem to evaluate thebandwidth blocking probability for a mixed grid optical net-work. Fig. 12 shows the results of BBP performance under dif-ferent traffic loads and different numbers of EON nodes. Specif-ically, Fig. 12(a) and (b) show the results of BBP of SmallNetwith an increasing number of EON nodes (as indicated by thelegend “# EON nodes = x”) when there are at most two or threeroutes that can be used for the VCAT technique between eachpair of nodes. We can see that increasing the number of EONnodes leads to a decrease in BBP. This is reasonable since EONnodes operate with a finer spectrum granularity and are thereforemore flexible and efficient in routing and spectrum allocation.However, we can see in Fig. 12(a) and (b), that at the beginningof the migration process, there is only a slight improvementin reducing BBP, while with a greater number of EON nodes,the BBP can be greatly reduced. This is reasonable because ofthe switching granularity of the fixed grid WSSs in DWDMROADMs, which makes it inefficient in spectrum allocationon the routes that traverse a DWDM ROADM [e.g., the routeas shown in Fig. 2(c)]. However, when more EON nodes areadded, the limitation arising from the DWDM ROADMs grad-ually reduces. This observation is in line with the result for thestatic traffic demand shown in Fig. 10, where the performanceimprovement is minor when the number of EON nodes is small,while the improvement becomes significant when the numberof EON nodes is large. This therefore verifies once again fromanother angle the importance of the EON nodes for improvednetwork performance and the necessity for a DWDM opticalnetwork to eventually migrate to a pure EON.


Fig. 12. Bandwidth blocking performance with increase of traffic load (Small-Net). (a) BBP change with an increasing number of EON nodes (x = 2).(b) BBP change with an increasing number of EON nodes (x = 3). (c) Non-VCAT versus VCAT in the pure DWDM network. (d) Non-VCAT versus VCATin the pure EON network.

Fig. 12(c) and (d) compare the BBP results of the non-VCATand VCAT scenarios in the pure DWDM and EON networks, re-spectively. Legend “non-VCAT” means that no VCAT techniqueis applied. Legend “SWP_x” means that a maximum number ofx routes can be set up between each node pair via the VCATtechnique. From the results, we can see that the VCAT techniquecan help to reduce BBP compared to the non-VCAT scenarioand moreover, the larger number of routes used by the VCATtechnique also helps to reduce BBP. Moreover, with an increas-ing number of routes for the VCAT technique (i.e., k = 2 vs.k = 3), the blocking performance is improved as well. This isreasonable because more route options can provide more flex-ibility for routing and spectrum allocation, and will thereforeyield better performance.

VI. CONCLUSION

We proposed the application of the VCAT technique in amixed grid optical network in order to allow communicationbetween DWDM and EON ROADM nodes. The effectivenessof this technique was confirmed by solving the correspondingRSA problem. For the scenarios of multi-path VCAT and jointmulti-path and single-path VCAT, we developed two differentMILP models. Moreover, for the scenario where only multi-pathVCAT is used, we developed an SWP-based algorithm. Casestudies showed that the proposed multi-path VCAT technique isan effective approach to efficiently support an optical networkwhere both fixed and flexible grids co-exist. We also find that alimited number of VCAT routes are sufficient to achieve a goodnetwork performance in terms of the number of FSs used for thestatic traffic demand and the BBP performance for the dynamictraffic demand. In addition, comparing the results of multi-pathVCAT and joint multi-path and single-path VCAT, we concludethat multi-path VCAT is efficient enough to achieve a goodperformance. Therefore, we suggest that the single-path VCATtechnique need not be implemented as it requires significantlyhigher computational complexity in exchange for only a minorgain in performance. Comparing the results of the MILP modeland the proposed heuristic algorithm, we see that the SWP-basedalgorithm is efficient enough to outperform the MILP modelunder the static traffic demand due to the more flexible routeselection by the SWP-based algorithm. Finally, the results forboth static and dynamic traffic demands confirm the necessityof eventually migrating from a pure fixed grid optical networkto a pure flexible grid one for better network spectrum resourceutilization. In summary, this research provides insights on how tomigrate an optical network from the traditional DWDM networkto an advanced EON network, as well as efficient approachesthat may be followed for such a migration.

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Authors’ biographies not available at the time of publication.

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