Designing Multi-Layer WDM Networks withReliability Constraints

Steven Chamberland and Abderraouf BahriEcole Polytechnique de Montreal

Department of Computer and Software EngineeringMontreal (Quebec), Canada

e-mail: {steven.chamberland, abderraouf.bahri}@polymtl.ca

Abstract—In this paper, we address the global problemof designing reliable wavelength division multiplexing (WDM)networks including the traffic grooming. This global problemconsists in finding the number of optical fibers between eachpair of optical nodes, finding the configuration of each node withrespect to transponders, finding the virtual topology (i.e., the setof lightpaths), routing the lightpaths, grooming the traffic (i.e,grouping the connections and routing them over the lightpaths)and, finally, assigning wavelengths to the lightpaths. Instead ofpartitioning the problem into subproblems and solving themsuccessively, we propose a mathematical programming modelthat addresses it as a whole. This approach has the advantageof providing better results since, in general, optimal solutions toall subproblems do not provide an optimal solution to the globalproblem. Numerical results show the relevance of designing thephysical layer and finding the traffic grooming simultaneously.

Keywords-Wavelength division multiplexing (WDM) networks,network design, traffic grooming, virtual and physical topologies,mathematical programming.

I. INTRODUCTION

Wavelength division multiplexing (WDM) is now a matureand reliable technology. It is widely deployed over opticalnetworks to exploit the huge optical fiber bandwidth. WDMnetworks is a convenient infrastructure for synchronous opticalnetwork (SONET) and multiprotocol label switching (MPLS)based networks. It is able to establish optical lightpathsto carry the traffic between the network nodes. A detaileddescription of the optical networks can be found in [7], [11]and [13].

Nowadays, a wavelength may operate at up to 40 Gbps(OC-768) and dense WDM (DWDM) allows 64 wavelengthsper optical fiber. Therefore, the available bandwidth (overa terabit) is outsized compared to the requests. Typically, aconnection between two network edge-nodes is up to OC-12(622.080 Mbps) and rarely more than the gigabit per second.As a result, only a fraction of each wavelength is used. Thisunder exploitation leads to a loss of provider incomes andto a premature saturation of the network. Consequently, theproblem is less a bandwidth one than the management of thisbandwidth.

Traffic grooming can be an appropriate solution to thismanagement. It is a well known traffic engineering techniquewhich packs low-speed traffic streams into high-capacity op-tical channels. This aggregation is allowed by space-divisionmultiplexing (SDM), frequency-division multiplexing (FDM)

and time-division multiplexing (TDM). An aggregation involv-ing these levels or granularities is called full grooming. A nodeperforming an aggregation at all the levels is a transparent nodeand a node performing only some of them is called translucent.An opaque node is a node without any grooming facilities [14].Virtual concatenation [10] is a grooming technique at the TDMlevel, used within SONET, which allows carrying, for instance,up to 16 OC-3 over an OC-48. Therefore, traffic groominghelps to optimize the network resources by increasing theutilization of the lightpaths and thus minimizing the requirednumber of lightpaths.

In order to illustrate the traffic grooming mechanism, anexample is provided in Fig. 1. Fig. 1 (a) illustrates the networktopology at the optical fiber level and Fig. 1 (b) at the lightpathlevel and connection level where the connection C1 usesthe lightpath L1 on the wavelength W0 on the optical fiberbetween the nodes N1 and N2 and the connection C2 usesthe lightpath L1 on the wavelength W0 on the optical fiberbetween the nodes N2 and N3. In the case of a network withno grooming facilities, if a connection between the nodes N1and N3 is requested, this connection is rejected because thelightpath L1 is already in use. This is not the case if thenetwork performs traffic grooming as illustrated in Fig. 1 (c)where the connection C3 is groomed with the connection C1into the lightpath L1 and with the connection C2 into thelightpath L2. Moreover, consider that an additional connectionof two capacity units is requested between the nodes N1and N3. If the node N2 does not perform traffic groomingat the wavelength level, the connection C4 cannot be routedto the node N3 because there is not enough spare capacityin the lightpath L2 and the wavelength W0 is already in use.Otherwise, if the node N2 have full grooming facilities, an ad-ditional lightpath L3 may be established between the nodes N2and N3 on the wavelength W1. Thereby the connection C4can be groomed with connections C1, C2 and C3 into thelightpath L1, then it arrives to node N3 into the lightpath L3,as illustrated in Fig. 1 (d).

In this paper, we address the global problem of designingWDM networks including the traffic grooming. This globalproblem consists in finding the number of optical fibersbetween each pair of optical nodes, finding the configurationof each node with respect to transponders, finding the virtualtopology, routing the lightpaths, grooming the traffic and,finally, assigning wavelengths to the lightpaths. This global

2010 Ninth International Conference on Networks

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DOI 10.1109/ICN.2010.8

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Optical fiber

Lightpath L1 onwavelength W0

Opticalfiber

(a)

(b)

(c)

(d)

N1 N2

N3

N1 N2

N3

Lightpath L2 onwavelength W0

N1 N2

N3

Lightpath L1 onwavelength W0

Lightpath L2 onwavelength W0

N1 N2

N3

Lightpath L1 onwavelength W0

Lightpath L2 onwavelength W0

Lightpath L3 onwavelength W1

Lightpath (capacity = 5)Connection C1Connection C2Connection C3Connection C4

Fig. 1. Illustration of the traffic grooming mechanism

approach has the advantage of providing better results since, ingeneral, optimal solutions to all subproblems do not provide anoptimal solution to the global problem. Considering that WDMcomponents are still expensive, network optimization is animportant issue for the telecommunications service providersto remain competitive. An additional key issue is networkreliability. Indeed, since WDM links can carry a large amountof information, failure can be much more damageable tonetwork operations than was the case for one-wavelengthnetworks. As a result, in this paper, network reliability isconsidered within the network design process.

The literature contains many articles relating to trafficgrooming for WDM networks, but the global problem ofdesigning WDM networks (including traffic grooming) hasnot been considered before (for instance, see [2], [4], [5] and

the references contained therein). Moreover, the focus of thispaper is to provide a general framework by considering the useof many optical fibers per link, many wavelengths per opticalfiber and many grooming granularities. The objective is to finda robust network that accommodates all connections requestswhile reducing the cost of the network.

This paper is organized as follows. Section II presentsthe mathematical model for the global problem of designingWDM networks and grooming the traffic. Numerical resultsare presented and discussed in Section III and concludingremarks follow in Section IV.

II. THE GLOBAL WDM NETWORK DESIGN PROBLEM

A. Problem Formulation

For the global WDM network design problem, the followinginformation is considered known: (I1) the location of theoptical nodes; (I2) the origin-destination connection demand(in term of OC-3, OC-12, etc.) between each pair of nodes;(I3) the maximum number of transponders that can be installedfor the transmission and for the reception at each node; (I4)the costs of the optical fibers and transponders including theinstallation cost (for instance, for the racks, patch panels, patchcords, electrical installations, labor, etc.).

We make the following assumptions concerning the orga-nization of the network: (A1) a link can be installed betweeneach pair of nodes; (A2) a link can be composed of one ormore optical fibers; (A3) an optical fiber can contain multiplewavelengths; (A4) an optical fiber can be used exclusivelyin one way; (A5) each node is a transparent node; (A6) anoptical cross-connect is installed in each node; (A7) there is nowavelength conversion in the network; (A8) a connection canuse more than one lightpath; (A9) a connection stay packedduring its transport.

The global WDM network design problem consists infinding

• the number of optical fibers between each pair of nodes;• the configuration of each node with respect to transpon-

ders;• the virtual topology, i.e., the set of the lightpaths;

as well as• grooming the traffic;• routing the lightpaths and, finally,• assigning wavelengths to the lightpaths.

The objective is to minimize the cost of the network subjectto all of the previous assumptions (A1-A9) and facts (I1-I4).

There is a strong interaction between these subproblems andseveral of them are NP-hard, for instance, the traffic groomingsubproblem [12] and the wavelength assignment subproblem(transformation from the graph coloring problem [6]).

An additional issue to consider is network reliability. Twomajor types of reliability measures are generally consideredin the reliability literature: connectivity and performabilitymeasures (for a survey of network reliability measures andalgorithms see [1]). Connectivity measures are concerned withfinding, evaluating or preserving some standard topology. Onthe other hand, performability notions, relate to the assessmentof performance measures that include more than pure topology

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concerns. Moreover, the group of measures, empirical studiesand technological features that guarantee that the network cansurvive failure situations have been lately found under thegeneral term “survivability”. Survivability techniques can beimplemented at different layers of the network. Accordingto the layer and the technology implemented, survivabilitymodels can be related to connectivity, performability or both.

In this paper, we use a connectivity measure to considernetwork reliability. In fact, we impose the network to be 2-edge-connected. A graph is 2-edge-connected if between eachpair of nodes there are two or more different paths without anycommon edge. This insures that if a link failure happens in thenetwork, at least one path between every pair of nodes is stillworking. For more information concerning k-edge-connectedsee [3] and [9].

B. Notation

The following notation is used throughout this paper. Thenotation is composed of sets, decision variables, constants andcost parameters.

1) Sets:

• N , the set of optical nodes;• T , the set of connection types (e.g., OC-3 and OC-12);• Ω, the set of wavelengths that can be used on each optical

fiber.

2) Decision Variables:

• wmn, the number of lightpaths between nodes m ∈ Nand n ∈ N ;

• xij , a 0–1 variable such that xij = 1 if and only if nodei ∈ N is connected to node j ∈ N ;

• xfij , a 0–1 variable such that xf

ij = 1 if and only if theoptical fiber f is used to connect node i ∈ N to nodej ∈ N ;

• xfωij , a 0–1 variable such that xfω

ij = 1 if and only ifwavelength ω ∈ Ω is used on optical fiber f from nodei ∈ N to node j ∈ N ;

• xfωijmn, a 0–1 variable such that xfω

ijmn = 1 if and only ifwavelength ω ∈ Ω is used on optical fiber f from nodei ∈ N to node j ∈ N for a lightpath from node m ∈ Nto n ∈ N ;

• yodktmn , a 0–1 variable such that yodkt

mn = 1 if and only ifthe connection k of type t ∈ T between the origin o ∈ Nand the destination d ∈ N uses a lightpath between thenodes m ∈ N and n ∈ N ;

• zodkt, a 0–1 variable such that zodkt = 1 if and only ifthe connection k of type t ∈ T , between the origin o ∈ Nand the destination d ∈ N is established.

3) Constants:

• αodt, the number of connections of type t ∈ T requestedbetween the nodes o ∈ N and d ∈ N ;

• βij , the maximum of optical fibers that can be usedbetween nodes i ∈ N and j ∈ N ;

• δt, the number of capacity units (i.e., the number of OC-1) needed for a connection of type t ∈ T ;

• ε, the number of units of the wavelength capacity (i.e.,the number of OC-1);

• TRi, the maximum number of transponders for the trans-mission that can be installed in node i ∈ N ;

• RRi, the maximum number of transponders for the re-ception that can be installed in the node i ∈ N .

4) Cost Parameters:• aij(n), the link cost for n optical fibers to connect node

i ∈ N to node j ∈ N including the installation cost;• bi, the transponder cost including the installation cost at

node i ∈ N .

C. The Mathematical Model

The model for the global WDM network design problem,denoted GWNDP, can now be given.GWNDP:

min∑i∈N

∑j∈Ni�=j

aij

⎛⎝

βij∑f=1

xfij

⎞⎠ +

∑m∈N

∑n∈Nm �=n

(bm + bn) wmn (1)

subject toPhysical topological constraints

∑i∈H

∑j∈N\H

xij ≥ 2 ∀H⊂N, |H|≥1 (2)

∑m∈N

∑n∈Nm �=n

xfωijmn ≤ xfω

ij ∀i�=j, i,j∈N, f∈Fij , ω∈Ω (3)

where Fij = {1, . . . , βij}.

xfωij ≤ xf

ij ∀i�=j, i,j∈N, f∈Fij , ω∈Ω (4)

xfij ≤ xij ∀i�=j, i,j∈N, f∈Fij

(5)∑

m∈N

∑n∈Nm �=n

∑ω∈Ω

xfωijmn ≤ |Ω| ∀i�=j, i,j∈N, f∈Fij

(6)

Additional topological constraints (7)

Virtual topology constraints∑

n∈N\{m}wmn ≤ TRm ∀m∈N (8)

∑m∈N\{n}

wmn ≤ RRn ∀n∈N (9)

Virtual topology over physical topology constraints∑

�∈N\{m}

∑f∈Fm�

∑ω∈Ω

xfωm�mn = wmn ∀m �=n, m,n∈N (10)

∑�∈N\{n}

∑f∈F�n

∑ω∈Ω

xfω�nmn = wmn ∀m �=n, m,n∈N (11)

∑i∈Ni�=j

∑f∈Fij

xfωijmn =

∑�∈Nj �=�

∑f∈Fj�

xfωj�mn

∀j∈N, m �=n, m,n∈N\{j}, ω∈Ω (12)∑

�∈N\{m}

∑f∈F�m

∑ω∈Ω

xfω�mmn = 0 ∀m �=n, m,n∈N (13)

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∑�∈N\{n}

∑f∈Fn�

∑ω∈Ω

xfωn�mn = 0 ∀m �=n, m,n∈N (14)

Traffic constraints∑

m∈N\{d}yodkt

md = zodkt ∀o�=d, o,d∈N, t∈T, k∈Kodt (15)

where k ∈ Kodt = {1, . . . , αodt}.∑

n∈N\{o}yodkt

on = zodkt ∀o�=d, o,d∈N, t∈T, k∈Kodt (16)

∑m∈N\{�}

yodktm� =

∑n∈N\{�}

yodkt�n

∀�∈N,o �=d, o,d∈N\{�}, t∈T, k∈Kodt (17)∑

m∈N

yodktmo = 0 ∀o�=d, o,d∈N, t∈T, k∈Kodt (18)

∑n∈N

yodktdn = 0 ∀o�=d, o,d∈N, t∈T, k∈Kodt (19)

αodt∑k=1

zodkt = αodt ∀o�=d, o,d∈N, t∈T (20)

∑o∈N

∑d∈No�=d

αodt∑k=1

∑t∈T

δtyodktmn ≤ εwmn ∀m �=n, m,n∈N (21)

wmn ∈ IN, xij ∈ B, xfij ∈ B, xfω

ij ∈ B, xfωijmn ∈ B,

yodktmn ∈ B, zodkt ∈ B. (22)

The objective function (1) of GWNDP represents the costof the links and transponders installed in the network.

Constraints (2) are connectivity constraints and require atleast two links between the nodes in H and the nodes in N\H .These constraints force the network topology to be 2-edge-connected. Constraints (3) require that a wavelength is usedonly if a lightpath spans this wavelength and constraints (4)impose to install optical fiber f ∈ Fij between nodes i ∈ Nand j ∈ N only if a wavelength is used into this opticalfiber. Constraints (5) impose to install a link between nodesi ∈ N and j ∈ N only if an optical fiber is installedbetween these nodes and constraints (6) ensure the numberof wavelengths used into an optical fiber be less or equal tothe maximum number of wavelength that an optical fiber cancarry. Constraints (7) include additional topological constraintsdefined by the network planner (for instance, to increase thenetwork connectivity).

Constraints (8) require that the number of lightpaths startingfrom a node doesn’t exceed the maximum number of trans-mitters that can be installed into this node and constraints (9)impose that the number of lightpaths terminating at a nodedoesn’t exceed the maximum number of receivers that can beinstalled into this node.

Constraints (10) necessitate that the number of lightpathsstarting from a node is equal to the number of lightpathshaving this node as a source and constraints (11) require the

TABLE ICOORDINATES OF THE OPTICAL NODES

Node x (km) y (km)1 0 6002 740 8403 2080 6204 3500 05 3800 180

TABLE IICOST OF THE NETWORK COMPONENTS

Component CostOptical link 2 000$/kmMultirate transponder 20 000$

number of lightpaths terminating at a node is equal to the num-ber of lightpaths having this node as a destination. Constraints(12) dictate that a lightpath passing through an intermediatenode doesn’t change its wavelength, constraints (13) imposethat a lightpath cannot enter to the source node of this lightpathand constraints (14) require that a lightpath cannot leave thedestination node of this lightpath.

Constraints (15) to (21) are traffic constraints, and finally,constraints (22) are integrality constraints where B = {0, 1}.

III. NUMERICAL RESULTS

In this section, we present the numerical results for severalinstances of the problem. The CPLEX Mixed Integer Opti-mizer 9.0 (see [8] for more information about CPLEX) isused to solve the model. Note that the algorithm used by theCPLEX is the branch-and-bound algorithm. For the computingplatform, we used a Sun Java workstation under Linux with aAMD Opteron 150 CPU and 2 GB of RAM.

Table I presents the (x, y) coordinates of the optical nodesand Table II presents the cost of the network components. Notethat for each lightpath, two transponders are needed. Finally,in Table III, the technological parameters are presented.

For the tests, full grooming is considered. The wavelengthcapacity considered for the tests in this subsection is OC-12.Four uniform connection demand scenarios are considered (seeTable IV).

Table V presents the results without traffic grooming andTable VI, with traffic grooming.

As can be gathered from the tables, the traffic groomingreduced significantly the network cost for scenarios 1 to 3.This can be explained by the fact that traffic groomingincreases the lightpath utilization when the capacities of thesource-destination connections are less than the capacity ofthe lightpaths (it is not the case for scenario 4).

Note that for the tests, the maximum CPU execution timeto solve the model is 373 seconds (scenario 3 with trafficgrooming). We have tried to solve instances with six nodes butCPLEX didn’t find the optimal solution within 30 hours. As aresult, heuristic algorithms should be explored to find “good”solutions rapidly for large-size instances of the problem.

IV. CONCLUSIONS

In this paper, we have studied the global problem of design-ing reliable WDM networks including the traffic grooming.

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TABLE IIITECHNOLOGICAL PARAMETERS

Parameter Value|Fij | 2|Ω| 2TRi 8RRi 8

TABLE IVDEMAND SCENARIOS

Scenario Demand1 1 OC-32 2 OC-33 1 OC-3 and 1 OC-124 2 OC-12

We have proposed an innovative mathematical programmingmodel for this problem. The objective is to find the minimumcost WDM network. The results obtain with the CPLEX MixedInteger Optimizer have shown the relevance of using thetraffic grooming as a part of the global WDM network designproblem.

Several research avenues that are open at this point. Wecurrently explore heuristic algorithms to find good solutionswithin a reasonable amount of computational time. Moreover,to evaluate the performance of the heuristics, a lower boundingprocedure can be developed. Another research avenue is toexplore the global expansion problem of WDM networks.

V. ACKNOWLEDGEMENTS

The completion of this research was made possible thanks toBell Canada’s support through its Bell University LaboratoriesR&D program.

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TABLE VRESULTS WITHOUT TRAFFIC GROOMING

Scenario Equivalent Number of Number of Cost Lightpathnumber of OC-3 links lightpaths (k$) utilization

1 20 7 20 22 342 25%2 40 10 40 44 150 25%3 100 10 40 44 150 62.5%4 160 10 40 44 150 100%

TABLE VIRESULTS WITH TRAFFIC GROOMING

Scenario Equivalent Number of Number of Cost Lightpathnumber of OC-3 links lightpaths (k$) utilization

1 20 5 8 15 938 100%2 40 5 14 16 780 94.7%3 100 8 28 30 256 100%4 160 10 40 44 150 100%

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