Optimization Approach for Multi-domainOptical Network Provisioning

K. Liang, M. Rahnamay-Naeini, H. M. K. Alazemi, N. Min-Allah, M. Peng, and N. Ghani

Abstract—Multi-domain optical network provisioning isa key focus area as users continue to demand scalable band-width services across wider network regions. To date, arange of distributed schemes have been proposed toachieve lightpath routing across domain boundaries. Ingeneral, these solutions rely upon hierarchical routingand provisioning strategies and are mostly heuristicsbased. As such, it is difficult to gauge their true load-carrying capacity and effectiveness. Hence in order toaddress this concern, this effort proposes a formaloptimization-basedmodel formulti-domain lightpath setuppursuant to several key objectives, i.e., including through-put maximization, resource minimization, and load balanc-ing. This model is then solved for some sample networktopologies, and the results are compared versus existingheuristic strategies.

Index Terms—Multi-domain lightpath provisioning;Multi-domain optical networks; Optimization.

I. INTRODUCTION

O ptical wavelength division multiplexing (WDM) tech-nologies have evolved to provide very high levels of

bandwidth scalability over base fiber-optic substrates.Hence many backbone operators have extensively deployedWDM networking transport and switching systems to offernew bandwidth services for their clients. Now asWDMnet-works become increasingly prevalent, there is a pressingneed to interconnect and provision services acrossmultipleoptical networking domains, i.e., as delineated by geo-graphic regions, technology types, administrative owner-ship, etc. [1,2]. In particular, many applications in thescientific computing realm are readily dependent uponsuch offerings to support massive data transfers across ex-tended global regions; see [3].

Overall the topic of multi-domain WDM network provi-sioning has received notable attention in recent years; see

surveys in [1,2]. Here most of the proposed routing andwavelength (RWA) solutions have outlined distributed pro-visioning strategies, as it is quite difficult (if not impos-sible) for a single entity to maintain “global network”topology and resource information across all domains,i.e., due to obvious scalability and inter-region privacyconcerns. Furthermore, many of these strategies leveragefrom related inter-domain/inter-area routing concepts inubiquitous packet-switching networks. For example, earlyschemes have proposed path-vector strategies to allow bor-der gateway optical cross-connect (OXC) nodes to maintain“next-hop” information to other domains [4]. Meanwhileothers have proposed detailed hierarchical routing strate-gies in which border OXC nodes use topology aggregationto propagate abstract wavelength/converter state, i.e.,link-state routing [5–7]. This information is then used tocompute “end-to-end” skeleton routes across domainsfor further expansion via distributed signaling protocols.Finally, recent efforts have also studied decentralized(per-domain) lightpath computation using recursive back-ward computation/signaling techniques; see [8,9].

In general, the above solutions are mostly heuristics-based and use graph-theoretic path computation at theintra- and inter-domain levels. Moreover, these schemesoperate with delayed (path-vector, link-state) information,resulting in reduced provisioning effectiveness, e.g., interms of blocking performance and resource efficiency[10,11]. As such, it is difficult to ascertain the trueachievable performance of hierarchical provisioning strate-gies. Now many optical networking studies have usedoptimization-based algorithms to bound RWA performanceunder idealized conditions with full a priori knowledge ofrequests and network topologies; see [12–14]. However,these schemes are only applicable to single-domain settingsowing to their assumptions on the global network state. Assuch, further use of optimization-based methods for multi-domain lightpath provisioning has not been considered.Along these lines, this paper proposes a novel optimizationmodel for hierarchical multi-domain RWA pursuant to sev-eral objectives, e.g., throughput maximization, resourceminimization, and load balancing. The key aim here is todevelop a reference framework against which to gaugethe performance of distributed multi-domain heuristics.

Overall, this paper is organized as follows. First,Section II presents a survey of some recent work inmulti-domain optical network provisioning. Subsequently,Section III presents a detailed optimization model formulti-domain lightpath RWA, and its solution approachhttp://dx.doi.org/10.1364/JOCN.5.001413

Manuscript received September 11, 2013; accepted September 20, 2013;published November 27, 2013 (Doc. ID 197314).

K. Liang and M. Rahnamay-Naeini are with the University of NewMexico, 1 University Boulevard NE, Albuquerque, NewMexico 87131, USA.

H. M. K. Alazemi is with Kuwait University, Kuwait City, Kuwait.N. Min-Allah is with the COMSATS Institute of Information Technology,

Islamabad, Pakistan, and the Computer Science and Artificial IntelligenceLaboratory (CSAIL) at the Massachusetts Institute of Technology, Boston,Massachusetts, USA.

M. Peng is with Wuhan University, Wuchang, Wuhan, Hubei, China.N. Ghani (e-mail: nghani@usf.edu) is with the University of South

Florida, 4202 E. Fowler Avenue, Tampa, Florida 33620, USA.

Liang et al. VOL. 5, NO. 12/DECEMBER 2013/J. OPT. COMMUN. NETW. 1413

1943-0620/13/121413-12$15.00/0 © 2013 Optical Society of America

is then detailed in Section IV, i.e., including inter- andintra-domain optimizations. An existing multi-domainheuristic scheme is then briefly reviewed in Section Vfor comparison purposes, and its performance is analyzedversus the proposed optimization scheme in Section VI forseveral network topologies. Conclusions and future workdirections are then presented in Section VII.

II. BACKGROUND

Multi-domain lightpath provisioning is a challengingproblem as scalability and privacy concerns limit the typeof information that can be exchanged between domains. Asa result, network practitioners and researchers have devel-oped a range of distributed strategies to implement an end-to-end lightpath setup; see surveys in [1,2]. These solutionsrun hierarchical routing protocols to establish partial statevisibility across domains. This information is then used toperform distributed end-to-end route computation, e.g., bycomputing routes in a skeleton or incremental manner and“expanding” them via inter-domain signaling. Alterna-tively, others have also looked at more decentralized solu-tions that do not require hierarhical routing provisions. Forthe most part, all of these various optical multi-domainRWA solutions have their origins in related frameworksfor packet/frame-switching data networks, i.e., includinglink-state and path-vector routing. A review of some ofthese schemes is now presented; see also summary inTable I.

A. Hierarhical Routing/Provisioning Schemes

In link-state routing, network nodes generate updatemessages to notify each other about changes in thestatus/resources of their attached links. This disseminationallows all nodes to build and maintain their own link-statetopology and resource databases and thereby make inde-pendent provisioning decisions. Now when applying thisconcept at the hierarchical inter-domain level, the associ-ated border gateway nodes usually run another (higher)level of link-state routing between themselves to dissemi-nate the inter-domain link state. This distribution allowsgateways to maintain inter-domain databases with “global”connectivity information between domains, i.e., skeleton

views. Topology abstraction is also widely used here to gen-erate condensed “abstract” representations of the domain-internal state. This approach transforms physical domaintopologies into smaller resource graphs with fewer abstractnodes/links and was originally proposed for packet-switching networks to help summarize bandwidth and de-lay information, e.g., simple node, star, tree, and full-meshabstractions; see [2] and [10,11]. For example, simple nodeabstraction reduces a domain to a single (weighted) vertexand represents the highest level of summarization. Mean-while the other schemes reduce a domain to itsrespective border nodes interconnected via appropriatestar, tree, or full-mesh topologies, i.e., with O�N�, O�N�,and O�N2� abstract links, respectively. Leveraging this,researchers have also proposed hierarchical routingschemes for multi-domain optical networks.

In one of the first studies on hierarchical routing forall-optical WDM networks [5], the authors develop noveltopology aggregation algorithms to condense wavelengthand delay information on path routes between bordernodes. A relative update triggering policy is also used todisseminate state information across domain boundariesalong with loose route (LR) computation and signaling ex-pansion schemes. Further provisions are also added in theLR computation to handle inaccurate (summarized) stateinformation, i.e., via bypass links. Simulations show goodreduction in inter-domain routing overheads, but blockingperformance still lags behind an idealized “flat” routing sol-ution, i.e., a single idealized provisioning entity with fullyaccurate global domain state. Meanwhile, [6] also studiesall-optical multi-domain RWA using simple node and full-mesh topology abstraction. The latter approach uses ab-stract links to summarize domain-traversing wavelengthinformation. Graph-theoretic k-shortest path (k-SP) algo-rithms are then used to compute/select skeleton pathLRs to achieve load balancing. Signaling expansion is alsodone using the ubiquitous resource reservation (RSVP) pro-tocol. The overall findings show notably lower blockingwith full-mesh abstraction as well as lower signalingoverheads. However, inter-domain routing overheads areseveral factors higher and increase with the number of bor-der nodes.

In general, most real-world multi-domain networks useopto-electronic wavelength conversion/regeneration at do-main boundaries to ensure bit-level user service level agree-ments (SLAs), especially in inter-carrier settings [2].Moreover, extended multi-domain distances will also man-date increased signal regeneration. Hence studies havealso looked at opto-electronic conversion at border gate-ways. For example, [15] studies lightpath routing with fullconversion at border OXC nodes and outlines three heuris-tic schemes (assuming simple node abstraction). The firstbaseline solution computes end-to-end routes over a “flat”global topology and serves as an idealized reference. Mean-while, the second approach computes skeleton paths withthe shortest (inter-domain) hop counts in the skeletongraph. Finally, the third solution performs “domain-to-domain” segment expansion along a fixed sequence of do-mains, akin to the “per-domain” PCE computation [16].Several gateway selection strategies are also proposed to

TABLE ISUMMARY OF MULTI-DOMAIN OPTICAL NETWORK PROVISIONING

RESEARCH

Reference Summary

[5,6] Hierarchical link-state routing with full-meshtopology abstraction

[7,17,18] Hierarchical link-state routing with full-meshtopology abstraction (opto-electronic conversion)

[15] Hierarchical link-state routing with simple nodeabstraction (opto-electronic conversion)

[19–22] Hierarchical distance/path-vector routing[8,9] Per-domain provisioning using backward

recursive path computation (BRPC)

1414 J. OPT. COMMUN. NETW./VOL. 5, NO. 12/DECEMBER 2013 Liang et al.

handle multiple border nodes, including random, closest-distance, and least-loaded selection. Results show thatthe hierarchical skeleton path scheme gives the lowestblocking and is closely matched by domain segmentexpansion.

However, the opto-electronic multi-domain RWAschemes in [15] only compute fixed routes and do not incor-porate any “active” link-load information. To address thislimitation, [7] presents amore dynamic solution that uses amodified full-mesh abstraction scheme based upon themost congested subpaths between border nodes. Skeletonpath computation is also done using “load-based” weightsto minimize wavelength/converter usages on critical linksand nodes. Overall, the findings here show the lowestblocking and setup signaling overheads with full-mesh ab-straction, i.e., as compared to simple node abstraction with-out any domain-level converter state information. Theresults also indicate that sparse opto-electronic conversionat domain boundaries (coupled with full-mesh topology ab-straction) gives sizeable blocking reduction versus fullopto-electronic conversion and simple node abstraction.Nevertheless, full-mesh abstraction schemes pose notablescalability challenges as they have high routing overheadsand require shorter inter-domain routing update intervals[2,17]. Hence some specialized update policies have alsobeen proposed to limit routing overheads, e.g., partial ad-vertising [17] and gradient-based triggering [18].

Now earlier, some researchers also proposed hierarchicaldistance/path-vector routing for multi-domain lightpathprovisioning. In particular, these schemes leverage the bor-der gateway protocol (BGP) for inter-autonomous systemprovisioning between Internet domains and add new ex-tensions for lightpath routing/wavelength assignment.For example, the “optical” BGP (O-BGP) scheme [4] aug-ments BGP reachability update messages (containing pathroutes to other domains) to include the wavelengthavailability state. Meanwhile [19] presents anotherWDM path-vector routing scheme that advertises multipleroutes to a destination domain, each based upon differentconstraints. A two-phase backward reservation protocol isalso defined to achieve fast setup, leveraging from stand-ardized RSVP signaling. However, none of the above stud-ies conduct any performance evaluation of their proposeddesigns, e.g., in terms of blocking, resource utilization,etc. However, subsequent work in [20] and [21] doespresent a more detailed performance analysis of path-vector routing in multi-domain WDM networks. In particu-lar, here the authors use adaptive filtering techniques tofirst estimate the number of available wavelengths on eachdestination domain path. Distributed signaling methodsare then proposed to expand intra-domain routes alongthese end-to-end paths, and simulations show good block-ing reduction versus (fixed) shortest-path selection.Finally, another study in [22] also proposes a distance-vec-tor solution that maintains several alternate “next-hop”routes to destination domains and uses a distributedscheme to concatenate domain sequences and buildend-to-end lightpath routes. Analog signal impairmentconcerns are also addressed in the expansion phase to limitbit error rate (BER) degradation for end-to-end routes.

B. Decentralized Provisioning Schemes

Alternatively, some designers have studied more decen-tralized multi-domain RWA schemes based upon the pathcomputation element (PCE) framework [16]. This standarddefines dedicated PCE entities for each domain and allowsthem to interact in a distributed manner to compute andexpand inter-domain routes, e.g., via PCE communicationprotocol (PCEP) signaling [23]. Now one of the mostnotable schemes here is the backward recursive pathcomputation (BRPC) algorithm [24,25], which computesa reverse-spanning tree from the destination to the sourcedomain. Although originally defined for bandwidth-routingnetworks, further adaptations of this solution have alsobeen developed for optical WDM networks; see [8,9]. How-ever, BRPC-based schemes generally assume fixed(precomputed) “end-to-end” domain sequences and hencedo not operate with much inter-domain visibility. Instead,the main focus is on resolving intra-domain routes and per-forming gateway node selection along these skeletonroutes. As such these strategies will give suboptimal per-formance under dynamic conditions with varying load con-ditions on inter-domain links.

C. Open Issues

In summary, most of the above-detailed multi-domainlightpath provisioning studies have only looked at distrib-uted heuristics-based strategies. Therefore it is quite diffi-cult to gauge the true effectiveness of these schemes interms of carried loads or resource efficiencies. Indeed, thereis a clear need to develop more formalized models to bound/quantify the achievable performance of hierarchical multi-domain lightpath RWA strategies, e.g., under idealizedconditions with a priori demands. Along these lines, thispaper presents a detailed optimization-based model formulti-domain lightpath provisioning. This solution is thensolved for some sample topologies, and its performance iscompared against some advanced multi-domain heuristicstrategies. To the best of our knowledge, this is the firstsuch study on optimization in (optical) hierarchicalmulti-domain networks.

III. OPTIMIZATION MODEL

A novel integer linear programming (ILP) optimizationmodel is now presented for multi-domain lightpath provi-sioning. This formulation assumes full a priori knowledgeof multi-domain user requests and mimics the overall hier-archical routing and provisioning process via a two-stepoptimization process; see Fig. 1. Namely, skeleton pathsequences are first derived for all requests over a globalabstract topology subject to specific traffic engineering ob-jectives and constraints. This abstract topology uses full-mesh abstraction to condense domains as a mesh of linksbetween their respective border nodes. Next, the individualdomain-traversing lightpath segments (subpaths) are ex-tracted from the skeleton paths and then optimized over

Liang et al. VOL. 5, NO. 12/DECEMBER 2013/J. OPT. COMMUN. NETW. 1415

their respective local domain topologies. Now in order tomodel realistic settings here, it is assumed that alldomains are transparent (i.e., all-optical) but support fullopto-electronic wavelength conversion at their bordergateway OXC nodes. Indeed, similar considerations havealso been made in other studies [7,15] owing to the in-creased distances (signal degradation) across multipledomains and the need for bit-level SLAmonitoring at boun-dary nodes. The requisite notation is now introducedfollowed by the detailed optimization objectives andconstraints.

A. Notation Overview

Consider a multi-domain WDM network with D do-mains, with the ith domain having ni nodes and bi bordernodes, 1 ≤ i ≤ D. Here each ith domain is represented by asubgraph, Gi�Vi;Li�, where Vi � fvi1; vi2;…; ving are thephysical domain OXC nodes and Li � fliikmg are the physicalintra-domain links; i.e., liikm is the link between OXC nodesvik and vim �1 ≤ i ≤ D; 1 ≤ k;m ≤ ni�. All intra-domain linksare assumed to be bidirectional withmaximumwavelengthcapacity C1. In addition, the border OXC nodes in domain iare also denoted by the set Bi ⊆ Vi, i.e., where jBij � bi.

Now assuming hierarchical multi-domain routing withfull-mesh abstraction, an associated “higher-level” abstracttopology is defined comprising all border OXC nodesand their interconnecting physical (inter-domain) and ab-stract (intra-domain) links. This topology is represented bythe graph H�U;E�, where U � P

ifBig is the global set ofborder nodes and E is the global set of links, i.e.,E � Ephy ∪

PiE

imesh, where Ephy is the set of physical

inter-domain links and Eimesh is the set of abstract intra-

domain links for domain i �1 ≤ i ≤ D�. Specifically,Ephy � feijkmg, where eijkm is the physical link interconnectingOXC node vik in domain i with OXC node vjm in domain j(1 ≤ i; j ≤ D, 1 ≤ k ≤ bi;1 ≤ m ≤ bj). Without loss of general-ity, it is also assumed that all inter-domain links in Ephyhave maximum wavelength capacity C2. Meanwhile, theabstract link set for domain i is given by Ei

mesh � feiijkg,

where eiijk is the abstract link between border nodes vijand vik and jEi

meshj � bi�bi − 1� (1 ≤ i ≤ D, 1 ≤ j; k ≤ bi).

A sample abstract graph,H�U;E�, for a three-domain net-work topology is shown in Fig. 2. Here, topology abstractionreduces the physical topology for domain 2, G2�V2;L2�, to afull-mesh subgraph consisting of three border nodes (v21, v

22,

v23) and six abstract links (e2212, e2221, e

2213, e

2231, e

2223, e

2232).

B. Objectives and Constraints

As mentioned earlier, the proposed solution (Fig. 1)applies optimization at both the inter- and intra-domaintopology levels, i.e., over the graphs H�U;E� andGi�Vi;Li�, respectively. Now at the inter-domain level,the assumption of full opto-electronic conversion at borderOXC nodes obviates the need for wavelength selection onskeleton routes; i.e., only path selection is required. Mean-while, at the intra-domain level, the proposed formulationdecouples lightpath route computation from wavelengthselection. Namely, an ILP optimization is first used to com-pute the intra-domain route segments, and then an appro-priate wavelength selection policy is used to assign thewavelengths, i.e., akin to other (single-domain) RWA stud-ies in [12,13,26–28]. As a result, similar traffic engineeringobjectives can be pursued at each level, i.e., global inter-domain and local intra-domain, and hence only the inter-domain optimization model is presented here for brevity’ssake, i.e., for abstract graph H�U;E�.

Consider an a priori set of user lightpath demands, de-noted by the set ot 3-tuples f�sn; dn; rn�g, where n repre-sents the request index, sn is the source OXC node, dn isthe destination OXC node, and rn is the number of requiredwavelengths, i.e., sn ∈ Vi, dn ∈ Vj, and i ≠ j. Also, let f ndenote the number of wavelengths allocated to the nthrequest, xnijkm denote the number of wavelengths routed over

link eijkm for request n, and α denote the maximum link uti-lization (MLU) allowed, i.e., in order to prevent link satu-ration. Furthermore, without loss of generality, assumethat all links in H�U;E� have capacity cij � C2.

Using these variables, a multi-objective function, F, isdefined to pursue several objectives across the full batchof input user requests:

MaxF � w1

Xn∈N

f n −w2

Xn∈N

Xlijkm

∈E

xnijkm −w3α; (1)

where w1, w2, and w3 are fractional weighting factors thatsum to unity, i.e., w1 �w2 �w3 � 1, and

F1 �Xn∈N

f n; (2a)

F2 � −Xn∈N

X�i;j�∈E

xnij; (2b)

F3 � −α; (2c)

Sec

ond

re-o

ptim

izat

ion

pass

(op

tiona

l)

Inter-domain skeleton paths

Hierarchical inter-domain optimization

over H(U,E)

Inter-domain requests

Expanded end-to-end inter-domain routes

Local inter-domain optimizations over Gi (Vi, Ei)

Fig. 1. Two-step multi-domain optimization solution.

1416 J. OPT. COMMUN. NETW./VOL. 5, NO. 12/DECEMBER 2013 Liang et al.

subject to the following constraints:

X�j;m�∶lij

km∈E

xnijkm −X

�j;m�∶ljimk

∈E

xnjimk �

8>><>>:

f n; if vik � sn

−f n; if vik � dn

0; otherwise

; (3)

Xn∈N

xnijkm ≤ αC2; lijkm ∈ E; (4)

f n ≤ rn; n ∈ N; (5)

xnijkm ∈ f0; 1; 2;…g; n ∈ N; lijkm ∈ E; (6)

f n ∈ f0;1;2;…; rng; n ∈ N; lijkm ∈ E; (7)

0 ≤ α ≤ 1: (8)

Overall, F comprises three parts and is similar to the ob-jective function proposed in [27] for single-domain WDMnetworks (and is shown to give improved load balancingand decreased resource consumption). The key aim hereis to achieve a weighted balance between maximizing

aggregate throughput, minimizing resource consumption,and achieving load balancing. Namely, Eq. (2a) representsthe total throughput for the given requests and networktopology, Eq. (2b) represents the negative of total resourceconsumption, and Eq. (2c) is the negative of MLU. Mean-while Eqs. (3)–(8) specify the model constraints. Specifi-cally, Eq. (3) represents a flow constraint between theincoming and outgoing flows at each (border) node in theabstract graph. Meanwhile, Eq. (4) restricts the total rela-tive traffic carried on a link to below the MLU value, i.e.,less than αC2. Also, Eq. (5) ensures that the number of al-located wavelengths is less than the number of requestedwavelengths for each request. Finally, Eqs. (6) and (7) re-present integrality constraints, and Eq. (8) restricts theMLU for all links to be below α. Note that this optimizationmodel directly incorporates load balancing via the F3 termand also Eq. (8). In particular, the solution tries to route alllightpath requests in a batch (simultaneous) manner so asto try to balance traffic distribution across all links and notexceed the prespecified (static) MLU value. The ILP solu-tion approach is now presented.

IV. SOLUTION APPROACH

As mentioned in Section III, the ILP model is solved ina “top-down” manner by first optimizing skeleton

Physical Multi-Domain Topology

Abstract View

Domain 1 Domain 3

Domain 2

G1(V1,L1)

G2(V2,L2)

G3(V3,L3)

U={v11, v1

2, v22, v3

2,v13, v2

3}

v11

v21

v31v4

1

v51

v12 v2

2

v32

v42 v5

2 v62

v13

v23

v33 v4

3

v53

Physical View

1 border node4 interior nodes

3 border nodes3 interior nodes

2 border nodes3 interior nodes

Border node (wavelength conversion)Interior node

H (U, E) = H (U, Ephy Ui Eimesh)

v11

v12 v2

2

v32

v13 v2

3

{ }2232

2223

2231

2213

2221

2212 ,,,,, eeeeeeE2

mesh=

{ }3321

3312 ,eeE3

mesh=

E1mesh={}

Abstract Links

Ephy ={ }Physical LinksBorder Nodes

Abstract TopologyPhysical inter-domain linkAbstract intra-domain link

Fig. 2. Full-mesh topology abstraction and notation overview.

Liang et al. VOL. 5, NO. 12/DECEMBER 2013/J. OPT. COMMUN. NETW. 1417

inter-domain routes for all requests over H�U;E�. Theseroutes are then used to identify the traversed abstractlinks, from which the required “all-optical” intra-domainrequests are generated to drive the second optimizationstep, i.e., solving ILP formulations for the individual sub-graphs Gi�Vi;Li� (see Section IV.B). Subsequently, the en-tire end-to-end lightpaths are resolved by concatenatingall intra-domain segments (with the same flow index) withtheir respective inter-domain links inH�U;E�. Without lossof generality, it can be assumed that all multi-domainlightpath requests are for one wavelength, i.e., rn � 1.Overall, this two-step optimization approach is much morefeasible as it is difficult (impossible) to solve a single ILPformulation for a very large “flat” single-domain networkcomprising all domain nodes and links, i.e., the idealizedcase of global state. To the best of our knowledge, this isthe first such application of optimization for the hierarchi-cal inter-domain RWA problem. Consider the details here.

A. Hierarchical Inter-domain Optimization

Consider the case of skeleton route optimization over theglobal abstract topology, H�U;E�. Since this topology repre-sents a “domain-level” summary of the entire network, it isreasonable to assume that this problem can be be solved ona standard workstation computer. Hence assuming a validsolution here, the computed number of unit flows (wave-lengths) routed along on each physical inter-domain linkand abstract intra-domain link can be determined. Specifi-cally, let the outputted (computed) values for xnijkm bedenoted by Xnij

km � f0; 1g, i.e., due to single-wavelength re-quest assumption (rn � 1). Using these values, the numberof requests routed on any given (inter-domain physical orintra-domain abstract) link can be determined by simplysumming up the Xnij

km values over all requests,i.e., Xij

km � Pn∈NX

nijkm.

Now for the case of abstract links, i.e., i � j, the totalnumber of wavelengths routed over link eiikm is equivalentto the number of “local” intra-domain (subpath) requeststhat must be routed between ingress border node vik andegress border node vim in domain i. Hence these requestscan be grouped into the set f�vik; vim;1�g for domain i andthen used to drive the second stage of the optimization, de-tailed next in Section IV.B. Carefully note that the abovenumbering scheme assigns the same request indices to

the local domain requests as those for the correspondinginter-domain requests, essentially matching which “end-to-end” lightpath each subpath request belongs to. Indeed,this is possible due to the assumption of single-wavelengthrequests, i.e., as the optimization solution may otherwiseyield multiple routes for multi-wavelength requests.

An example of hierarchical skeleton path computationand subpath request generation is also shown for the sam-ple three-domain network in Fig. 3. In particular, there aretwomulti-domain lightpath requests that need to be routedhere, request 1 �v12; v33;1� and request 3 �v22; v33;1�. Now as-suming that the ILP solution returns valid skeleton pathsover H�U;E� for both requests, the associated skeletonpaths are shown in Fig. 3 via dashed colored lines, i.e.,e1221 − e2213 − e2331 − e3313 (for request 1) and e2223 − e2331 − e3312 (forrequest 2). From these sequences, the associated intra-domain subpath requests can also be generated for eachdomain, as shown in Table II.

B. Local Intra-domain Optimization

The second optimization phase takes the subpath re-quests generated from the skeleton paths and attempts toprovision (domain-traversing) lightpaths over the individualdomain topologies. In particular, intra-domain route selec-tion is done using the same optimization formulation inSection III.B, i.e., by applying it over the local domain top-ology, Gi�Vi;Li�. Now once the local subpath routes havebeen resolved, wavelength selection is done in order to en-sure wavelength continuity across all-optical domains. Inparticular, the most-used (MU) wavelength assignmentstrategy is used here as it shown to give good results in bothsingle- and multi-domain networks; see [6,12]. If, however,an available wavelength cannot be found for a particularsubpath, then the lightpath request for that particular indexis dropped (failed). Finally, once all intra-domain wave-lengths have been assigned, the complete “end-to-end”multi-domain lightpath route can be generated. This is donefor each request index by concatenating the physical linkson its inter-domain skeleton route with the expandedintra-domain subpath routes with the same request index.As wavelength selection on inter-domain links is not an is-sue, i.e., due to full opto-electronic conversion at gatewayOXC nodes, any available wavelength can be selected here.The overall pseudocode description of this two-stage ILPsolution is also given in Fig. 4.

C. Optional Reoptimization Pass

Carefully note that special cases may arise if requeststraversing two (or more) common domains fail the

Fig. 3. Inter-domain skeleton path routing for sample three-domain network.

TABLE IIINTRA-DOMAIN REQUESTS

Domain 1 Domain 2 Domain 3

Request 1 — �v21; v23;1� �v31; v33; 1�Request 2 — �v22; v23;1� �v31; v33; 1�

1418 J. OPT. COMMUN. NETW./VOL. 5, NO. 12/DECEMBER 2013 Liang et al.

optimization setup at different domains. These scenarioscan result in multiple requests being denied even if thereare available resources to support at least some of them.Hence in order to improve setup success rates, a second op-tional “reoptimization” step is added, i.e., depicted via thedashed line in Fig. 1. Namely, the goal here is to prune (i.e.,deliberately fail) some of the “overlapping” requests in or-der to allow others to be successful. This is perhapsbest shown via an example in Fig. 5, where request 1 (fromv12 to v

33) overlaps with request 2 (from v21 to v

33) at domains 2

and 3. Now both requests experience blocking, with request1 failing at domain 3 and request 2 failing at domain 2;i.e., intra-domain optimization cannot find wavelength-continuous subpaths. However, a slight resource reassign-ment can allow at least one of these requests to besuccessful. Specifically, if the two failed domain subpathsin Fig. 5 are both assigned to request 1, then request 2can be routed across domain 2, i.e., without changingthe total number of wavelengths used in the originalassignment.

The reoptimization procedure is formally detailed nowand tries to reallocate resources between failed requeststraversing one or more common domains (but experiencing

blocking at different domains). Carefully note that sincethere can bemultiple overlaps between the skeleton routes,in turn there can be many potential combinations for prun-ing failed skeleton routes; i.e., this can be treated as an op-timization problem itself. However, to simplify mattershere a different strategy is used. Namely, the two-stage op-timization is rerun with the capacities of the abstract linksin H�U;E� set to the number of successful traversing intra-domain routes between the respective border nodes, i.e.,Xij

km as obtained from the first pass of the optimization(Section IV.A). This approach ensures that the number ofresources used at the inter-domain level is the same as thatcomputed in the initial optimization.

V. REFERRENCE HEURISTIC SCHEME

As per Section II, most existing multi-domain RWAschemes use graph-based heuristics. Along these lines,an advanced hierarchical routing solution from [7] ischosen here for comparison purposes. This scheme com-putes full-mesh topology abstractions to summarizeintra-domain wavelength resource state information be-tween border nodes, i.e., via “abstract” links. Namely, theexact set of available wavelengths on an abstract link iscomputed by searching the k-shortest paths between therespective border node pair and selecting the path withthe maximum number of free wavelengths. The abstractlink’s wavelength availability vector is then determinedby AND-ing the individual binary wavelength availabilityvectors of all physical intra-domain links on the selectedroute. Next, abstract link entities are advertised betweenborder nodes as part of a hierarchical routing process inconjunction with updates for physical inter-domain links.Namely, a relative change triggering strategy is used togenerate these updates, i.e., if the change in wavelengthresources exceeds a significance change factor (SCF) andthe time since the last update exceeds a hold-down (HT)timer; see [6,7] for details.

Overall, inter-domain routing dissemination allows do-main PCE systems to maintain global topology databaseswith active “aggregated” network state. This information isthen used to field incoming lightpath requests and computeassociated skeleton LR sequences over the abstract topol-ogy, i.e., by using either hop-count or load-basedmetrics [7].Finally, these resultant path sequences are fully expandedusing inter-PCE signaling via the PCE protocol [23], i.e.,with each intermediate domain PCE computing a localdomain-traversing segment between the specifiedingress/egress border nodes in the skeleton route; see [7]for complete details.

VI. PERFORMANCE EVALUATION

The multi-domain optimization solution is now testedand also compared against the distributed heuristicscheme in [7] (as overviewed in Section V). Here two differ-ent topologies are used, including a smaller-sized six-domain network as well as a larger 16-domain network(reflective of a national backbone). In particular, the former

Fig. 5. Overlapping inter-domain requests failing setup at differ-ent domains.

Fig. 4. Pseudocode for two-stage ILP solution (single-pass only).

Liang et al. VOL. 5, NO. 12/DECEMBER 2013/J. OPT. COMMUN. NETW. 1419

topology is shown in Fig. 6, and has an average domain sizeof seven nodes and nine bidirectional inter-domain links.Meanwhile, the 16-domain network is a modification ofthe NSFNET backbone topology that replaces all of thenodes with domains; see Fig. 7. Here the individual domainsizes are varied between 7 and 10 nodes and there are atotal of 25 bidirectional inter-domain links.

The ILP model in Section III is specified using the PuLPpackage, which is a Python-based linear programmingmodeler. This formulation is then solved hierarchically(as explained in Section IV) using the GNU Linear Pro-gramming Kit (GLPK) for a randomly generated set ofmulti-domain requests, i.e., uniform random source anddestination domains and uniform random nodes withinthese domains. Furthermore, the weights for the objectivefunction [Eq. (1)] are set to fw1; w2; w3g � f0.9;0.05;0.05g.In general, these values emphasize throughput maximiza-tion but also try to reduce resource consumption byassigning a nonzero weight to F2, i.e., to account for thegenerally higher cost of bandwidth usage on inter-domainlinks. In addition, load balancing is also taken into accountby assigning a nonzero weight to F3.

Meanwhile, the multi-domain hierarchical routingheuristic scheme (outlined in Section V) is analyzedusing custom-developed OPNET Modeler discrete-event

simulation models. Here, the inter-domain routing updatethresholds are set to SCF � 0.1 (10%) and the correspond-ing HT timers to 120 s, i.e., 20% of the average connectionholding time. Furthermore, in order to ensure a fair com-parison between the optimization and heuristics-basedstrategies, the same randomly generated set of lightpathrequests is tested for each particular input “load” point,i.e., measured by the number of requests. All incoming re-quests are also given infinite holding times in order to com-pare the findings with those from the hierarchical ILPsolution, i.e., no departures. However, since the order ofthese input requests can affect the resulting route selectionand success rates for the heuristic scheme, the input se-quences are randomly shuffled to generate 10 different var-iations, and the best results are taken for comparison withthe ILP model. The detailed findings are now presented.

Initial tests are done for the six-domain network for twodifferent intra-/inter-domain link sizes, i.e., C1, C2 � 8, 16wavelengths, respectively. Here both the (single-pass) opti-mization and (double-pass) reoptimization schemes aretested, and the overall setup success rates for varying inputrequest sizes (input loads) are plotted in Fig. 8. Overall,these results indicate relatively close performance betweenthe ILP and (hierarchical routing) heuristic schemes atvery low input load regimes for C1 � C2 � 16. However,as loads increase to moderate levels, the heuristic schemetends to saturate around a certain number of successfulconnections, whereas the ILP schemes continue to improve.For example, the ILP solutions give well more than twotimes the success rate of the heuristic strategy at high in-put loads. In addition, these results also show very little(no) improvement with the optional ILP reoptimizationstep for this smaller topology.

Next, the corresponding average hop counts are mea-sured and plotted in Fig. 9 for successful lightpath setups.For the most part, these values indicate declining trendswith increased load, and this is expected as higher conten-tion levels generally result in increased failure rates forlonger paths. The optional reoptimization pass also yieldslittle change in the average hop count. Now carefully notethat these results exhibit higher variability at lower loadsdue to the reduced request (sample) sizes. As a result, the

Fig. 6. Six-domain network topology.

Fig. 7. Modified 16-domain NSFNET topology.Fig. 8. Successful requests, six-domain (C1, C2 � 8 and C1,C2 � 16).

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batch sizes may not be uniformly distributed and have sig-nificantly more (less) long (short) path connections. How-ever, as the batch sizes increase, this variability reducesnotably. Furthermore, averaging the results over moreruns (than the 10 currently done) will also help reducethis variability. The overall run times for the differentoptimization steps are also shown in Fig. 10 for the smallerC1, C2 � 8 wavelength scenario and indicate super-linear growth. As expected, hierarchical optimization (overabstract skeleton graph) yields the lowest overheads as runtimes are dominated by the intra-domain optimizations.

Additional tests are also done for the six-domain sce-nario with differing intra- and inter-domain link sizes.Namely, the number of inter-domain link wavelengths isset to double the number of intra-domain wavelengths inorder to model more realistic network scenarios with in-creased inter-domain trunk sizes, i.e., C2 � 2C1. The asso-ciated lightpath setup success rates here are plotted inFig. 11 for varying request sizes and show similar behav-iors to the equivalent-link scenario for varying input loads.For example, for C1 � 8 and C2 � 16, the ILP-basedschemes closely track the hierarchical routing heuristicsto about 150 requests, i.e., low-medium load regime, but

then give much better performance at higher loads, i.e.,more than 200% gain in setup success rates. Furthermore,unlike earlier results for equivalent intra-/inter-domainlink sizes, the second reoptimization step does yield someslight improvement in setup success rates, i.e., about3%–5% less blocking at higher loads. Meanwhile, theaverage hop-count values are also shown in Fig. 12 andgenerally follow a declining trend. However, the ILP-basedschemes yield slightly higher lightpath resource consump-tion, i.e., as they are more successful at finding longerroutes at higher load/congestion.

The larger 16-domain modified NSFNET topology istested next for both the optimization and heuristics-basedapproaches. Here Fig. 13 plots the number of successfulsetup requests for this network with two different intra-and inter-domain link sizes, i.e., 8 and 16 wavelengths.Again, these results reconfirm earlier findings with thesix-domain network, with the optimization strategies giv-ing well more than twice the number of successful light-path setups at higher loads. In addition, the optional“reoptimization” pass tends to yield little reduction inblocking. The corresponding average hop counts are alsoplotted in Fig. 14 and show a more definitive downward

Fig. 9. Average hop count, six-domain (C1, C2 � 8 and C1,C2 � 16).

Fig. 10. Sample ILP run times for 16-domain network (C1,C2 � 8).

Fig. 11. Successful requests, six-domain (C2 � 2C1 � 16 andC2 � 2C1 � 32).

Fig. 12. Average hop count, six-domain (C2 � 2C1 � 16 andC2 � 2C1 � 32).

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trend with increasing input loads for both the ILP and heu-ristic schemes, i.e., about 30% lower at extremely highloads. In general, this behavior is expected as increasedloads will drive up link utilization and lower the probabil-ity of finding longer domain-traversing subpath routes

with free (and continuous) wavelength channels. Moreover,the ILP objective function in Eq. (1) also takes into accountresource usage, and hence this will also try to minimize thenumber of links used.

Now careful analysis of the optimization results forthe 16-domain topology indicates very few setup failuresin the second intra-domain ILP step. In other words, forequivalent sized intra-/inter-domain link scenarios, nearlyall blocking tends to occur due to inter-domain link conges-tion. As a result, further tests are with larger inter-domainlinks in order to reflect more realistic operator link sizingstrategies, i.e., C2 � 2C1. Along these lines, Fig. 15 plotsthe number of successful setups and Fig. 16 plots thecorresponding average hop-count values for this modifiedscenario. Again, these findings indicate much better block-ing performance with the ILP-based strategies, yieldingbetween 2 and 3 times more successful setups atmedium-to-high loads. As per similar runs with the six-domain network, slight blocking reduction is also observedwith the optional reoptimization pass, in the range ofabout 3%.

VII. CONCLUSION

This paper presented an optimization-based study oflightpath routing in multi-domain optical networks. In par-ticular, the hierarchical routing/provisioning frameworkwas modeled by developing objectives to capture through-put, resource utilization, and load balancing at both theinter-domain (skeleton graph) and intra-domain (localgraph) levels. A solution was then presented to solve thisformulation by using a two-step approach that applies op-timization at the global “abstract” inter-domain level aswell as the local intra-domain level. The proposed schemewas then tested using sample multi-domain network topol-ogies, and its results were compared against those with anadvanced distributed heuristic scheme (using link-staterouting and skeleton path computation/expansion). Over-all, detailed findings show much-improved performancewith the proposed optimization approach, yielding severalfactors improvement (reduction) in setup success (requestblocking) rates. As such, this work provides an invaluable

Fig. 14. Average hop count, 16-domain (C1, C2 � 8 and C1,C2 � 16).

Fig. 15. Successful requests (C2 � 2C1 � 16 and C2 � 2C1 � 32).

Fig. 16. Average hop count (C2 � 2C1 � 16 and C2 � 2C1 � 32).Fig. 13. Successful requests, 16-domain (C1, C2 � 8 and C1,C2 � 16).

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reference against which to gauge the performance of dis-tributed multi-domain optical lightpath provisioningschemes. Future efforts will look at developing improvedheuristic strategies to reduce the performance gap withthe optimization-based benchmarks developed herein. Inaddition, other efforts will also look at expanding theoptimization model to incorporate lightpath protectionunder single and multiple failures. In particular, thelatter pertain to scenarios with highly correlated andcascading outages, as triggered by large-scale catastrophicevents.

ACKNOWLEDGMENTS

This work has been funded by the Defense Threat Reduc-tion Agency (DTRA) under the Basic Research Program(Award No. HDTRA1-09-1-0026). The authors are verygrateful to this agency for its generous support.

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Kaile Liang received her B.Sc and Mastersdegrees in telecommunication engineeringfrom the Beijing University of Posts andTelecommunications (BUPT). She thenjoined the Electrical and Computer Engi-neering (ECE) Department at the Univer-sity of New Mexico under the supervisionof Prof. Ghani and completed her Ph.D. de-gree in July 2012. She is currently workingas a Software Engineer (Quality) at eBay,and her research interests include network

optimization, performance analysis, simulation, and software de-fined networking/network virtualization.

Mahshid Rahnamay-Naeini received herB.Sc in computer engineering from SharifUniversity of Technology in 2007 and herM.Sc in computer engineering with concen-tration on computer networks from Amirka-bir University of Technology (TehranPolytechnic) in 2009. She is currently anelectrical engineering (communication sys-tems) Ph.D. candidate in the Electricaland Computer Engineering Department atthe University of New Mexico. Her research

interests include reliability and performance analysis of commu-nication networks, smart power grids, smart-grid networking, datacenters and cloud computing, resource management, and stochas-tic modeling.

Hamed M. K. Alazemi received the B.Sc.and M.S. degrees in electrical engineeringfrom Washington University, St. Louis,MO, USA, in 1992 and 1994, respectively,and the Ph.D. degree from the Universityof Washington, Seattle, WA, USA, in 2000.He is currently an Associate Professor withthe Department of Computer Engineering,Kuwait University, Kuwait City, Kuwait,where his interests include analysis/designof computer communication networks. His

most recent research emphasis areas include wireless networks,combinatorics, graph theory, control and communication design,optimization in WDM networks, stochastic performance evalu-ation, and queuing analysis.

Nasro Min-Allah very successfully wearsmany hats. Currently he is affiliated withthe SuperTech group at the Computer Sci-ence and Artificial Intelligence Laboratory(CSAIL) at the Massachusetts Institute ofTechnology (MIT), Boston, MA, where heis a Visiting Scientist. In addition, he is alsoan Associate Professor and Head of theDepartment of Computer Science atCOMSATS Institute of InformationTechnology, Pakistan, and Director of its

Green Computing and Communication Laboratory. He receivedhis undergraduate and Masters degrees in electronics andinformation technology in 1998 and 2001, respectively, fromQuaid-i-AzamUniversity andHamdardUniversity, Pakistan. Sub-sequently, he obtained his Ph.D. in real-time and embedded sys-tems from the Graduate University of the Chinese Academy ofSciences (GUCAS), China, in 2008. His research interests includepipeline parallelism, green computing, chromatic scheduling, andreal-time systems.

Ming Peng is a Professor in the ComputerScience Department at Wuhan University,Wuhan, China. She received her B.Sc in ap-plied physics and M.S. in computer applica-tions from Wuhan University. She alsoreceived her Ph.D. in computer softwareand theory from Wuhan University. From2009 to 2011 she was a visiting facultymember in the Electrical and Computer En-gineering Department at the University ofNew Mexico. Currently, Dr. Peng is serving

as the Vice President of the Chinese National Multimedia Soft-ware Technology Research Center. To date, she has organizedand participated in many key projects funded by the Chinese Na-tional Natural Science Fund. In addition, she has also participatedin two optical-networking projects funded by the US National Sci-ence Foundation and US Department of Energy. She was also thetechnical committee chair of the 2011 IEEE INFOCOM Workshopon High Speed Networks, and her current research interests in-clude network services, performance evaluation, informationprocessing, and distributed computing.

Nasir Ghani is a Professor in the ElectricalEngineering Department at the Universityof South Florida. Earlier he was a facultymember and Associate Department Chairin the ECE Department at the Universityof New Mexico. He has also spent over 8years in industry working at several largehi-tech corporations (including Nokia,IBM, and Motorola) and several startups.Currently he is involved in a range ofresearch activities in the areas of cyberin-

frastructure design, disaster recovery, cloud computing, andcyber-physical systems (integrated power grids). His researchhas been supported by the National Science Foundation, DefenseThreat Reduction Agency, Department of Energy, QatarFoundation, Department of Education, NSWC, and Sprint-NextelCorporation. He also received the NSF CAREER Award in 2005for his work in multi-domain networking. Dr. Ghani has chairedthe IEEE ComSoc Technical Committee on High Speed Networksfrom 2008 through 2010 and has been a symposium co-chair forIEEE GLOBECOM, IEEE ICC, and IEEE ICCCN. He has alsorun a workshop series for IEEE INFOCOM and has served on nu-merous NSF, DoE, and international panels. He is an AssociateEditor for IEEE Systems and has also served on the editorialboard of IEEE Communications Letters. He received the Ph.D. de-gree in computer engineering from the University of Waterloo,Canada.

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