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Optik 122 (2011) 1354– 1361

Contents lists available at ScienceDirect

Optik

j o ur nal homepage: www.elsev ier .de / i j leo

ynamic waveband grooming based on hierarchical integrated groominguxiliary graph in multi-domain mesh optical networks

ingjing Wua, Lei Guoa,b, Xingwei Wanga,∗, Weigang Houa

College of Information Science and Engineering, Northeastern University, Shenyang 110819, ChinaState Key Laboratory of Advanced Optical Communication Systems and Networks, Peking University, Beijing 100871, China

r t i c l e i n f o

rticle history:eceived 23 March 2010ccepted 29 August 2010

eywords:ulti-domainptical networksaveband switching

ierarchical grooming

a b s t r a c t

With the number of wavelengths in fibers increasing, the number of optical switching ports in conven-tional Optical Cross-Connect (OXC) keeps enhancing, so that waveband grooming technique is proposedto save the switching ports in OXC. Most of previous works focused on waveband grooming in single-domain optical network. Since the current optical backbone is actually divided to multiple domainsaccording to the different network providers, it is necessary to study the waveband grooming in multi-domain optical networks. However, waveband grooming in multi-domain optical networks is morechallenging than that in single domain networks because of the routing scalability and security issues.Therefore, in this paper, we propose a new heuristic Hierarchical Multi-domain Waveband Grooming(HMWG) algorithm based on Hierarchical Integrated Grooming Auxiliary Graph (H-IGAG) to reducethe total number of optical switching ports. The H-IGAG is compared of the Intra-domain WavebandIntegrated Auxiliary Graph (Intra-WIAG) and the Inter-domain waveband Virtual Topology Graph (Inter-VTG). For the demand in single-domain, HMWG directly computes the route from the source node todestination node in the single-domain with waveband grooming on Intra-WIAG. For the demand span-

ning different domains, HMWG first computes the route from the source node to the selected bordernode in source domain and computes the route from the selected border node to the destination node indestination domain with waveband grooming on Intra-WIAG, respectively. Then, HMWG computes theroute from the selected border node in source domain to the selected border node in destination domainwith waveband grooming on Inter-VTG. Simulation results show that, compared with previous grooming

tain b

algorithm, HMWG can ob

. Introduction

As the number of wavelengths in each fiber continues toncrease, the number of switching ports and the cost of ordinaryptical Cross-Connect (OXC) are increased rapidly. In order to

educe the cost of OXC [1], it is necessary to perform the wave-and grooming to bind several wavelength-level lightpaths intone waveband which can be switched by one port. Some papers2,3] have proposed several waveband grooming schemes includ-ng same source-destination grouping, same source grouping, sameestination grooming, and same sub-path grooming, where theub-path grooming scheme has the best performance for reducing

witching ports.

Recently, the waveband grooming problem in multi-domainptical networks has received growing interest so far because it isore interesting and challenging than that in single-domain optical

∗ Corresponding author. Tel.: +86 024 83687575; fax: +86 024 83687575.E-mail addresses: haveball@gmail.com, hwghtc@gmail.com (X. Wang).

030-4026/$ – see front matter © 2010 Elsevier GmbH. All rights reserved.oi:10.1016/j.ijleo.2010.08.021

etter performance.© 2010 Elsevier GmbH. All rights reserved.

networks [4]. In single-domain optical networks, an entity main-tains about all the states, e.g., physical links, available resources,node diversity, etc. As the size of the network increases, the statedatabase gets larger and the whole network is generally split intomultiple domains according to the different network providers[5]. In a multi-domain network, considering the scalability of thenetwork and the confidentiality of each domain, a domain maynot wish to exchange detailed information about the state of itsresources and the topology of the network with other domains. Thelack of complete and global knowledge of the network informationmakes it unfeasibly to apply the waveband grooming algorithms ofsingle-domain optical networks to multi-domain optical network.

As opposed to single domain settings, full topology informationin multi-domain network is lacking and path computation needsto be done using the aggregated topology and resource state. Forexample, [6] presents a domain by domain scheme in which bor-der nodes maintain complete route state across networks, and [7]

develops three different inter-domain wavelength routing algo-rithms. Also, previous papers proposed some hierarchical modelfor multi-cluster traffic grooming. The authors in [8] proposed hier-archical approaches on SONET ring networks. In [9,10], with the

122 (2011) 1354– 1361 1355

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J. Wu et al. / Optik

bjective of minimizing the total number of electronic ports, aramework for hierarchical traffic grooming in mesh network iseveloped. The logic topology within a cluster is formed as a vir-ual star. As a multi-granular multi-domain grooming problem, theuthors in [11,12] presented a hierarchical algorithm for groom-ng lightpaths into wavebands. From the above references, we canee that current works focus on determining the logical topologyf lightpath or waveband grooming within each cluster or domainnly, while the waveband grooming in multi-domain networks isot considered.

Therefore, to well address the waveband grooming in multi-omain optical networks, in this paper we propose a new heuristicierarchical Multi-domain Waveband Grooming (HMWG) algo-

ithm based on Hierarchical Integrated Grooming Auxiliary GraphH-IGAG) since the grooming, routing and waveband assignmentroblem has been proven to be the NP-hard [13]. The H-IGAG

s compared of the Intra-domain Waveband Integrated Auxiliaryraph (Intra-WIAG) and the Inter-domain waveband Virtual Topol-gy Graph (Inter-VTG). For each connection demand, if the sourceode and the destination node are in the same domain, HMWG willirectly compute an intra-domain route from the source node toestination node in the single-domain based on Intra-WIAG, which

s compared of one virtual topology layer and multiple wavebandlane layers. If the source node and the destination node are inifferent domains, the inter-domain network is then topologicallyggregated to become a full-mesh topology which contains onlyorder nodes and virtual links. HMWG first computes the routerom the source node to the selected border node in source domainnd computes the route from the selected border node to theestination node in destination domain with waveband groomingn Intra-WIAG. Then, corresponding to Intra-WIAG, on Inter-VTGMWG first computes a single-hop or multi-hop waveband groom-

ng route. If the route cannot be found on Inter-VTG, HMWG willompute several exact intra-domain routes with waveband groom-ng meanwhile updating the corresponding virtual links based onhe low intra-domain topology. Finally, the full inter-domain routean be obtained. Compared with previous per-domain groominglgorithm [14], H-IGAG obtains better performance.

To the best of our knowledge, the work in this paper is the firsttudy to achieve the scalability based on aggregative virtual topol-gy of multi-domains meanwhile to reduce the size and the cost ofXC by performing waveband grooming in multi-domain opticaletworks.

This paper is organized as follows: Section 2 proposes thenter-domain and intra-domain waveband routing and groom-ng schemes. Section 3 describes the heuristic algorithm. Section

presents the simulation and analysis. Section 5 concludes thisaper.

. Network model and problem statement

.1. Network model

A multi-domain network is composed of several single-domainetworks that are connected by inter-domain links going from bor-er nodes of one domain to border nodes of another (see Fig. 1). Wedopt the full-mesh topology aggregation scheme [15]; namely, theulti-domain network is transformed to an aggregated graph con-

aining only the border nodes and the fully meshed set of virtualinks connecting all pairs of border nodes. Each virtual link can beomputed beforehand, and it denotes the physical route betweenwo border nodes in one single domain.

A multi-domain network is denoted as G(InterL, D),here InterL is the set of inter-domain links each of which

onnects two border nodes in different domains, and = {Dr(BNr, CNr, IntraLr)

∣∣r = 1, 2, . . . } is the set of physical

Fig. 1. A multi-domain network: (a) inter-domain network; (b) topology aggrega-tion.

topologies of all domains in which Dr is the physical topology ofdomain r, BNr is the set of border nodes in domain r, CNr is the set ofcore nodes in domain r and IntraLr is the set of intra-domain fiberlinks in domain r. Moreover, the aggregative virtual topology isdenoted as Gv(InterL, Dv

r ), where Dvr = {BNr, VLr} in which VLr is the

set of virtual links in domain r. Each core node can only view thelocal network physical topology information in its own domain,and the border node can view both the local information and theglobe network virtual topology information. We assume each nodehas the waveband conversion capacity and each border node isequipped with a MG-OXC. The Dijkstra’s algorithm is applied tocompute the shortest routes. In this paper, we assume the set ofwavebands and the set of wavelengths in each intra-domain fiberlink are denoted as B and W, respectively. Before detailing the totalalgorithm, some further notations are introduced as follows.

CDns,d

: Connection demand n from source node s to the destinationnode d;Inter-VTG: Inter-domain waveband virtual topology graph on H-IGAG;WVTLr: Intra-domain waveband virtual topology layer in Intra-WIAG of domain r;WPLr

y: Intra-domain waveband plane layers corresponding to

waveband y (1 ≤ y ≤∣∣B

∣∣) in domain r;

xr: Physical node in physical network topology of domain r;Vr

x : Virtual border node on Inter-VTG corresponding to bordernode xr in domain r;Wr

y,x: Waveband node in WPLry corresponding to node xr in domain

r;WVr

x : Virtual node on Intra-WIAG virtual topology layer corre-sponding to node xr in domain r;WBInter(Vr

i, Vl

j): Waveband-tunnel link between node Vr

iand node

Vlj

on Inter-VTG as the residual bandwidth of that waveband-tunnel is greater than zero from domain r to domain l;WBIntra(WVr, WVr): Waveband-tunnel link between node WVr

i j i

and node WVrj(∀i, j ∈ [1,

∣∣B

∣∣], i /= j) as the residual bandwidth of

that waveband-tunnel is greater than zero in domain r;

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WBE(Wry,i

, Wry,j

): Waveband edge between node Wry,i

and nodeWr

y,jon each WPLr

y in domain r;Inter − NTr

x : Number of available transceivers in node xr in domainr for inter-domain grooming;Intra − NTr

x : Number of available transceivers in node xr in domainr for intra-domain grooming;WVL(WVr

x , Wry,x): Transceiver virtual link between node WVr

x and

node Wry,x(∀y ∈ [1,

∣∣B

∣∣]) as the number of available transceivers on

node xr is greater than zero in domain r;R WBInter(Vr

i, Vl

j): Number of residual available wavelengths on

WBInter(Vri, Vl

j);

R WBIntra(WVri, WVr

j): Number of residual available wavelengths

on WBIntra(WVri, WVr

j).

.2. Hierarchical grooming

In order to solve the multi-domain waveband grooming prob-em, the hierarchical algorithm is operated in two phases: theigher skeleton grooming from the source domain to the desti-ation domain based on Inter-VTG and the intra-domain groomingased on Intra-WIGA. The grooming method of inter-domain traffic

s a “two-step” computation approach which attempts over existinglobe virtual topology graph and pending failure, further attemptsn underlying virtual link connecting two border nodes.

For each connection demand, the source node first checks itswn routing table to find that whether the destination node is inhe same domain. If the source node and the destination node aren the same domain, the intra-domain grooming can be performedased on the intra-WIGA. If they are in the different domains, theource node will select the nearest border node in the local domain.hen if the destination border has been selected determinately,he destination border node will perform intra-domain groomingo the destination node. Finally, the source border node will runnter-grooming on Inter-VTG to the destination border node on theetwork globe virtual topology. If the grooming on Inter-VTG is

ailure, re-attempts to groom the traffic on underlying virtual link.or each virtual link inside the intermediate domain, intra-domainrooming is performed from the ingress intermediate border nodeo the egress intermediate border node.

The Inter-VTG is a single-layered graph and composed ofaveband-tunnel links and virtual border nodes. A demand can be

roomed into an existing waveband-tunnel link which has enoughvailable residual bandwidth to establish the connection. Sincehe demand is allowed to reach the destination node by multi-op waveband-tunnel links, if there is not an appropriate existingingle-hop route, it can be groomed into another waveband-tunnelink. If number of available transceivers in virtual border node Vr

xs equal to zero, the new waveband-tunnel cannot be establishedrom or terminate at Vr

x .As to the Intra-WIGA, waveband-tunnel links start and ter-

inate on the WVTLr layer. In the start node of the traffic, theavelengths can be multiplexed to waveband and be switched

o the end node. Then the waveband can be de-multiplexed toavelengths. After the demand leaving, update the property of

he waveband-tunnel links. For the waveband-tunnel links carryinghe demand CDn

s,d, the capacities of the corresponding waveband-

unnel links are decreased by the amount of the carried traffic.or each newly setup waveband-tunnel links, it will consume aransceiver at the two end nodes, respectively.

The waveband plane layers are composed of free wavebands

dges and waveband nodes. The number of layers corresponds tohe number of wavebands and each WPLr

y corresponds to a wave-

and y (1 ≤ y ≤∣∣B

∣∣). If a connection demand cannot be satisfied

n WVTLr, it may find a new route on some WPLry. First, we com-

2011) 1354– 1361

pute the shortest path from the node Wry,i

to the node Wry,j

. If wecan find the path successfully, we assign the corresponding wave-band to this path. Meanwhile, remove the corresponding wavebandedges since these waveband edges cannot be used to satisfy anotherdemand later on and add a new waveband-tunnel link on the WVTLr

layer.If all of the above procedure cannot groom a connection demand

successfully, the routing computation of the demand can be per-formed to achieve a hybrid route based on the Intra-WIGA that isformed by connecting virtual transceiver links with infinite band-width assumption between WVTLr and WPLr

y. For a connectiondemand, some sub-paths may select the waveband-tunnel linkswith the residual available bandwidth on WVTLr, while other sub-paths may select new waveband edges on WPLr

y. If there is no freetransceiver at node WVr

x , all virtual transceiver links connectingWVr

x will be removed.To illustrate how the hierarchical graph constructs and the algo-

rithm works, we give an example based on the network in Fig. 1,where it is a four domain network with bidirectional fiber-linksand all nodes are assumed to have grooming functionality. Eachintra-domain fiber link has 2 available wavebands each of whichcontains 4 available wavelengths. Since there is more traffic onthe inter-domain fiber links, the capacity on inter-domain fiberlinks can be set to larger; that is, each inter-domain fiber link has2 available wavebands each of which contains 8 available wave-lengths. Suppose the capacity of each wavelength is OC-24 and eachwaveband is OC-96 in intra-domain fiber links while the capacity ofeach wavelength is OC-24 and each waveband is OC-192 in inter-domain fiber links. Each core node has 2 tunable transceivers forintra-domain grooming. On the other hand, each border node hasexcess 4 tunable transceivers for inter-domain grooming becausethey will carry more traffic, that is, each border node has total 6tunable transceivers, 2 for intra-domain grooming and 4 for inter-domain grooming. We assume that there are 8 demands, CD1

2,20,

CD219,17, CD3

1,20, CD41,15, CD5

6,15, CD61,9, CD7

17,13, and CD813,17 which

arrive at the network orderly.The first connection demand is from source node 2 in domain

0 to destination node 20 in domain 2. First, source node 2will compute the shortest path to the nearest border node 1,shown in Fig. 3(b). It is easy to see that there exists a pathalong WV0

2 − W01,2 − W0

1,1 − WV01 that consumes the waveband

edge WBE(W01,2, W0

1,1). Second, destination border node will com-pute the shortest path 19–20, shown in Fig. 6(b), which routes alongWV3

19 − W31,19 − W3

1,20 − WV320 and consumes the waveband edge

WBE(W31,19, W3

1,20). Third, source border node 1 will find a hopby hop route by waveband-tunnel links on Inter-VTG as shownin Fig. 2(a). Since there are no demands initially, there are nowaveband-tunnel links between nodes on Inter-VTG. The sourceborder node 1 will find a route 1–6–9–19 on the inter-domaintopology layer on the network virtual link shown in Fig. 1(b).Fourth, the virtual link 6–9 will be mapped to the physical path6–7–8–9 that will route along WV1

6 − W11,6 − W1

1,7 − W11,8 − W1

1,9 −WV1

9 which consumes the waveband edges WBE(W11,6, W1

1,7),

WBE(W11,7, W1

1,8) and WBE(W11,8, W1

1,9) shown in Fig. 4(b). Finally,after completing the segment grooming and waveband assign-ment, inter-domain waveband-tunnel links can be built segment bysegment on Inter-VTG, which are WBInter(V0

1 , V16 ), WBInter(V1

6 , V19 )

and WBInter(V19 , V3

19) as shown in Fig. 2(b) from node V01 to

node V319. In each end domain, the new built waveband-tunnel

links can be seen in Fig. 3(c) which is WBIntra(WV02 , WV0

1 ) and3 3

in Fig. 6(c) which is WBIntra(WV19, WV20). Meanwhile, the cor-

responding waveband edges should be removed from the enddomains and the intermediate domain waveband plane layerssince these waveband edges cannot be used to satisfy another

J. Wu et al. / Optik 122 (2011) 1354– 1361 1357

Fig. 2. Inter-domain topology (a) inter-domain waveband virtual topology graph(b), (c), (d), (e), (f) waveband assignment.

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wiWi

Fig. 4. Waveband assignment in domain 1.

Fig. 5. Waveband assignment in domain 2.

Fig. 3. Waveband assignment in domain 0.

emand later on. Because each waveband-tunnel link will con-ume two transceivers at two end nodes, Intra − NT0

1 , Intra − NT02 ,

ntra − NT319 and Intra − NT3

20 for intra-domain grooming will all bepdated to 1, Inter − NT0

1 and Inter − NT319 will both be updated

o 3, and Inter − NT16 , Inter − NT1

9 for inter-domain grooming willoth be updated to 2. The numbers beside the waveband-tunnel

inks denote the residual available wavelengths. Since each intra-omain waveband contains 4 wavelengths and the first demandill consume 1 wavelength on each waveband-tunnel links, so

WBIntra(WV02 , WV0

1 ) and R WBIntra(WV319, WV3

20) are both equal to. Since the inter-domain waveband-tunnel link WBInter(V1

6 , V19 ) is

uilt from the intra-domain fibers, R WBInter(V16 , V1

9 ) is equal to. The number of transceivers for intra-domain grooming is alsoemaining 2. The situation in intermediate domain is shown inig. 4(b) and (c). Corresponding to the intra-domain fibers, eachnter-domain waveband-tunnel link contains 8 wavelengths andhe demand will also consume 1 wavelength, so R WBInter(V0

1 , V16 )

nd R WBInter(V19 , V3

19) are both equal to 7.Following the same procedure as above, the second demand

2 2 2 2

ill be assigned to the route WV15 − W1,15 − W1,17 − WV17n destination domain which consumes the waveband edge

BE(W21,15, W2

1,17) in Fig. 5(b) On the step of inter-domain groom-ng, the source border node 19 finds the route 19–21–15 on the

Fig. 6. Waveband assignment in domain 3.

network virtual link in inter-domain topology layer in Fig. 1(b),where the virtual link 19–21 will be mapped to the physi-cal path 19–18–21 that will route along WV3

19 − W32,19 − W3

2,18 −W3

2,21 − WV321 consuming waveband edges WBE(W3

2,19, W32,18) and

WBE(W32,18, W3

2,21) in Fig. 6(b). Update the corresponding Inter-VTGand Intra-WIGA. The new built inter-domain waveband-tunnellinks from node V3

19 to node V215 on Inter-VTG can be seen

in Fig. 2(b) which are WBInter(V319, V3

21) and WBInter(V321, V2

15),and on WVTL2 layer in domain 2 can be seen in Fig. 5(c)which is WBIntra(WV2

15, WV217). Update R WBInter(V3

19, V321) to 3,

R WBInter(V321, V2

15) to 7 and R WBIntra(WV215, WV2

17) to 3, respec-tively. Remove the corresponding waveband edges in domain 2 anddomain 3. Then, Inter − NT3

19 and Inter − NT321 are both updated to

2, and Inter − NT215 for inter-domain grooming will be updated to 3.

For the third and the fourth demand, since the procedure ofthe grooming in source domain and destination domain are assame as the former demands, we just explain the second stepof the inter-domain grooming. For the third demand which isbetween border nodes 1 and 19, in Fig. 2(b) we can find an avail-able route V0

1 − V16 − V1

9 − V319 with three waveband-tunnel links

WBInter(V01 , V1

6 ), WBInter(V16 , V1

9 ) and WBInter(V19 , V3

19) on inter-VTG,

and then we update the number besides the links, R WBInter(V0

1 , V16 )

and R WBInter(V19 , V3

19) are both equal to 6 and R WBInter(V16 , V1

9 ) isequal to 2 shown in Fig. 2(c). For the fourth demand from nodes 2 to

1 122 (

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358 J. Wu et al. / Optik

7, we can find an available route V01 − V1

6 − V16 − V3

19 − V321 − V2

15ith five waveband-tunnel links WBInter(V0

1 , V16 ), WBInter(V1

6 , V19 ),

BInter(V19 , V3

19), WBInter(V319, V3

21) and WBInter(V321, V2

15) on inter-TG, and then R WBInter(V0

1 , V16 ) and R WBInter(V1

9 , V319) are both

pdated to 5, R WBInter(V16 , V1

9 ) is updated to 1, R WBInter(V319, V3

21)s updated to 2 and R WBInter(V3

21, V215) is updated to 6, as shown

n Fig. 2(d). Since the two demands are established on the exist-ng waveband-tunnel links on inter-VTG, they will not consumeew inter-domain transceivers. After grooming the fifth demand,here is no available wavelength on WBInter(V1

6 , V19 ), so that we need

o remove this waveband-tunnel link from the graph. Meanwhile,ince the waveband-tunnel link is removed from node V1

6 and node19 , the number of the transceivers on these two nodes should beenew to 3 again. Update R WBInter(V1

9 , V319) to 4, R WBInter(V3

19, V321)

o 1 and R WBInter(V321, V2

15) to 5 as shown in Fig. 2(e).To satisfy the sixth demand, the inter-domain grooming should

o on the network virtual link again. The source border node 1ill find a route 1–6–9 on the inter-domain topology layer on theetwork virtual link shown in Fig. 1(b). At this time, the virtual

ink 6–9 will be mapped to the physical path 6–11–10–9 whichill route along WV1

6 − W12,6 − W1

2,11 − W12,10 − W1

2,9 − WV19 shown

n Fig. 4(b) and then we will remove the consumed wavebanddges WBE(W1

2,6, W12,11), WBE(W1

2,11, W12,10) and WBE(W1

2,10, W12,9)

s shown in Fig. 4(c). Thus, we can set new inter-domain waveband-unnel link WBInter(V1

6 , V19 ) between V1

6 and V19 again and another

BInter(V01 , V1

6 ) in Fig. 2(f). Inter − NT01 , Inter − NT1

6 and Inter − NT19

or inter-domain grooming will be updated to 2, 1 and 2, respec-ively. The numbers R WBInter(V1

6 , V19 ) beside the waveband-tunnel

ink WBInter(V16 , V1

9 ) is updated to 3 and R WBInter(V01 , V1

6 ) is updatedo 7. The former built waveband-tunnel link between V0

1 and V16 is

till exist and may be used to groom other new demands if it isecessary.

The last two demands are just intra-domain demands which canxplain the grooming on Intra-WIGA further. The seventh demandill be assigned to the route WV2

17 − W22,17 − W2

2,12 − W22,13 −

V213 and will consume the waveband edges WBE(W2

2,17, W22,12)

nd WBE(W22,12, W2

2,13). Then, Intra − NT217 and Intra − NT2

13 wille respectively updated to 0 and 1 shown in Fig. 5(c). Since

ntra − NT217 = 0, the transceiver virtual links WVL(WV2

17, W21,17)

nd WVL(WV217, W2

2,17) will be removed from Intra-WIGA.For the eighth demand from nodes 13 to 17, as shown in Fig. 5(c),

e can find a hybrid route WV213 − W2

1,13 − W21,14 − W2

1,15 − WV215 −

V217 which includes the new waveband edges WBE(W2

1,13, W21,14)

nd WBE(W21,14, W2

1,15) on WPL21 and an exiting waveband-tunnel

ink WBIntra(WV215, WV2

17). Then, we will remove WBE(W21,13, W2

1,14)

nd WBE(W21,14, W2

1,15) from WPL21, set a new waveband-tunnel link

BIntra(WV213, WV2

15) and update Intra − NT213 and Intra − NT2

15 to 0nd 0, respectively. Finally, Intra-WIGA in domain 3 is shown inig. 5(d).

. Heuristic algorithm

The algorithm module works as follows:Input: Physical network topology G(InterL, D) and aggregative

irtual topology Gv(InterL, Dvr ); Physical topologies of all domains

= {Dr(BNr, CNr, IntraLr)∣∣r = 1, 2, . . . };

Output: Number of traffic demands identified by ı which areuccessfully groomed between a source destination pair (s, d).

Begin:

(1) Initialize the Inter-VTG for the inter-domain grooming and allthe Intra-WIGA for each single-domain grooming.

2011) 1354– 1361

(2) Wait for the demand arrival. If the demand is for establishinga new connection, go to step 3; if the demand is for releasinga connection, go to step 15.

(3) If source node s and destination node d are in the same domain,let source = s and destination = d, and go to step 4; otherwise,go to step 8.

(4) Compute the shortest path from node source to node desti-nation on WVTL. If the path has been found, go to step 5;otherwise, go to step 6.

(5) Accept the demand and let ı ← ı + 1. Update the number offree wavelength on each intra-domain waveband-tunnel link.If the number of free wavelength on a waveband-tunnel linkis equal to zero, remove this intra-domain waveband-tunnellink from WVTLr. Add the corresponding waveband edges onwaveband plane layers, and go back to step 2.

(6) Compute the shortest path on Intra-WIGA. If the path has beenfound, go to step 7; otherwise, block this demand and go backto step 2.

(7) Accept the demand and let ı ← ı + 1. Add new intra-domainwaveband-tunnel links on WVTLr, update the number of freetransceivers at each node, and go back to step 2.

(8) Compute the shortest path from s to the nearest border nodes′. Let source = s and destination = s′, and go to step 4. If the pathhas not been found, block this demand and go back to step 2.

(9) Compute the shortest path from d to the nearest border noded′. Let source = d′ and destination = d, and go to step 4. If the pathhas not been found, block this demand and go back to step 2.

(10) Compute the shortest path on Inter-VTG between two bor-der nodes s′ and d′. If the path has been found, go to step 11;otherwise, go to step 12.

(11) Accept the demand and let ı ← ı + 1. Update the number offree wavelength on each inter-domain waveband-tunnel link.If the number of free wavelength on a waveband-tunnel linkis equal to zero, remove this inter-domain waveband-tunnellink from Inter-VTG, and go back to step 2.

(12) Compute a skeleton path on global virtual topology betweentwo border nodes s′ and d′. If the path has been found, goto step 13; otherwise, block this demand and go back tostep 2.

(13) Map each virtual link of each intermediate domain, mapseriatim intermediate domain ingress border node to nodesource and egress border node to node destination, and go tostep 4.

(14) Accept the demand and let ı ← ı + 1. Add new inter-domainwaveband-tunnel links on Inter-VTG, update the number offree transceivers at each border node, and go back to step 2.

(15) Remove the demand from the network, release the consumedresources, and go back to step 2.

EndWe consider the time complexity of routing computation for

each connection request in the worst case. In inter-domain phase,the time complexity is approximately O(2 · (M + Y · log Y)) accordingto [16] where M is the total number of border nodes and Y is thetotal number of links in all domains since we will run two timesof Dijkstra’s algorithm to compute a shortest path on VTG and askeleton path on virtual link. In topology of each single-domain, thetime complexity is approximately O((N + L · log L) + (

∣∣B

∣∣ · N +

∣∣B

∣∣ ·

L · log(∣∣B

∣∣ · L))) where N is the total number of physical nodes and

L is the total number of physical links in each single-domain sincewe will run one time of Dijkstra’s algorithm to compute a route

on WVTL with N nodes and L links or run one time of Dijkstra’salgorithm to compute a route on WPLr

y with∣∣B

∣∣ · N nodes and

∣∣B

∣∣ · L

links if the route computation on WVTL layer is failed. Therefore, foreach connection request across

∣∣D

∣∣ domains, the time complexity

J. Wu et al. / Optik 122 (2011) 1354– 1361 1359

o

L

4

tattaidewtdtacqbpnTaim

tT

F

Fig. 9. Performance of port cost in different waveband merging ability.

Fig. 7. Multi-domain optical networks topology.

f our algorithm is approximately O(2 · (M + Y · log Y) +∣∣D

∣∣ · ((N +

· log L) + (∣∣B

∣∣ · N +

∣∣B

∣∣ · L · log(

∣∣B

∣∣ · L)))).

. Simulation and analysis

In simulation, we use the three domain interconnected networkopology shown in Fig. 7. The network is composed of 39 nodesnd 64 links. In the simulated network, all nodes are consideredo be nodes capable of switching wavelength to wavebands. Fur-her, all links in the simulator are assumed to be bidirectional. Wessume that the number of wavelengths on each intra-domain fibers assumed to be 64 while the number of wavelengths on each inter-omain fiber is assumed to be 256. The number of wavebands onach fiber can be selected from 2, 4, 8, and 16. The required band-idth of each connection request is one wavelength channel, and

he number of transceivers on each node is enough. Connectionemands are modeled by a Poisson distribution and the connec-ion holding time is assumed to be exponentially distributed. If thelgorithm could not groom a connection demand successfully, theonnection demand is rejected immediately without waiting in aueue. In simulation, we test the performances of blocking proba-ility and total port-cost for HMWG on various situations. Blockingrobability is defined as the ratio of the number of blocked con-ection demands over the number of arrival connection demands.otal port-cost is defined as the number of consumed ports by allccepted connection demands. Obviously, lower blocking probabil-ty means higher network throughput and smaller total port-cost

eans less ports consumption.

We compare the performance of our hierarchical algorithm with

he per-domain distributed grooming presented in [14] and [17].he per-domain distributed grooming operates with minimal inter-

ig. 8. Performance of blocking probability in different waveband merging ability.

Fig. 10. Performance of blocking probability in different waveband granularities.

domain visibility. Namely, end-to-end routes are expanded in adomain by domain manner with each domain specifying its next-hop along with the complete internal route via an egress node. Byconsulting routing tables, the next-hop solution may be makingfrom some fixed choices.

We first test the performances of blocking probability forHMWG algorithm with different parameters of waveband merg-ing ability that is the ability of merging wavelengths to wavebandsin MG-OXC; that is, bigger WMA means more wavebands are avail-able to carry on the grouped wavelengths. For example, WMB = 0.5means half of wavebands in a fiber are available to carry on thegrouped wavelengths, and WMB = 1 means all wavebands in a fiberare available to carry on the grouped wavelengths.

In Fig. 8, we assume the waveband granularity is 8; that is, thereare 8 wavebands. We can see that, blocking probability reduceswith waveband merging ability increases in different network load.When WMA = 1, blocking ratio is equal to zero. The reason for thisis that, bigger waveband merging ability means more wavebandsare available to carry on the grouped wavelengths.

In Fig. 9, we can see that, with the waveband granularity increas-ing, the total port-cost decreases. The reason for this is that,when the waveband granularity is larger, the utilization ratio ofexisting waveband-tunnel link is larger, so the number of newbuilt waveband-tunnel link is decreasing and the total port costdecreases.

In Fig. 10, it is shown that blocking probability increases withthe network load increases in different waveband granularities.In Fig. 11, we can see that blocking probability decreases withthe waveband granularly increases in different network loads. Thereasons for this is that, when the waveband granularly increases,more wavelength-level traffic can be grouped into wavebands to

be switched.

In Fig. 12, we assume the network load is 300. It is shown that,total port-cost of HMWG is smaller than that of per-domain groom-ing. The reason for this is that, on the inter-domain level grooming

1360 J. Wu et al. / Optik 122 (2011) 1354– 1361

Fig. 11. Performance of blocking probability in different network load.

Fig. 12. Comparison of total port cost between per-domain grooming and HWMGin different waveband granularities.

Fig. 13. Comparison of total port cost between per-domain grooming and HWMGin different network load.

Fig. 14. Comparison of blocking probability between per-domain grooming andHWMG in different waveband granularities.

Fig. 15. Comparison of blocking probability between per-domain grooming andHWMG in different waveband granularities (a) waveband granularity = 2.

Fig. 16. Comparison of blocking probability between per-domain grooming andHWMG in different waveband granularities (b) waveband granularity = 4.

Fig. 17. Multi-domain optical networks topology produced randomly.

Fig. 18. Comparison of blocking probability between per-domain grooming andHWMG in different waveband granularities (a) waveband granularity = 2.

J. Wu et al. / Optik 122 (2

FH

Hpinn

socnanTg

wrstgdbfiw

wgd

tdfiaapHIvp

5

Io

[

[

[

[

[

[

ig. 19. Comparison of blocking probability between per-domain grooming andWMG in different waveband granularities (b) waveband granularity = 4.

WMG first find a path on Inter-VTG, so HWMG may have higherrobability to find a multi-hop path on Inter-VTG without consum-

ng new switching ports while per-domain grooming algorithmeeds to established new waveband-tunnel links with consumingew switching ports.

In Fig. 13, we assume the waveband granularity is 2. We canee that total port-cost of per-domain grooming is larger than thatf HWMG. The reason for this is that, for each demand, HWMGan search a multi-hop path on Inter-VTG without consumingew switching ports while per-domain grooming need to search

path based on the routing table on network virtual link and buildew waveband-tunnel links with consuming new switching ports.herefore, HWMG can save more switching ports than per-domainrooming.

In Fig. 14, we assume the network load is 1000. In Figs. 15 and 16,e assumed the waveband granularity are 2 and 4, respectively. The

esults in three figures show that blocking probability of HWMG ismaller than that of per-domain grooming. The reason for this ishat at the intra-domain level, the path computation of per-domainrooming is similar to the HWMG algorithm. However, at the inter-omain level, the per-domain grooming specifies the next domainy making fixed choices, i.e., by consulting routing table. If the traf-c in the next domain is large, then the new coming connectionill cause the chosen domain more congestion.

By simulating the performances of blocking probability further,e follow to test the performance for HWMG and per-domain

rooming in a 5-domian topology with 8 pairs of bidirectional inter-omain links which produced randomly shown in Fig. 17.

In Figs. 18 and 19, when the waveband granularity is equalo 2, we can see that the largest blocking probabilities of per-omain grooming are about 50% and 40% in three-domain andve-domain networks, respectively, and the largest blocking prob-bilities of HWMG are about 35% and 15% in US and three-domainnd five-domain networks, respectively. Therefore, the blockingrobabilities of per-domain grooming are more 15–25% than theWMG. The reason for this is that HWMG will first find path on

nter-VTG while per-domain grooming only find path on networkirtual link so that per-domain grooming will have more blockingrobability than the HWMG.

. Conclusion

In this work, we proposed a new algorithm named Hierarchicalntegrated Grooming Auxiliary Graph (H-IGAG) in multi-domainptical networks to perform waveband grooming. In order to

[

[

011) 1354– 1361 1361

achieve the scalability, H-IGAG performed the inter-domaingrooming based on the Virtual Topology Graph (VTG) and the intra-domain grooming based on the Intra-domain Waveband IntegratedAuxiliary Graph (Intra-WIAG). In order to save the switching portsfor reducing the cost of OXC, we applied waveband grooming whichbinds several lightpaths of wavelength level into one wavebandthat can be switched by one port. Simulation results showed that,compared with other algorithm, H-IGAG obtained better perfor-mances on blocking probability and total port-cost.

Acknowledgment

The authors would like to thank reviewers and editors for valu-able comments. The preliminary work of this paper was presentedat the International Conference on Networking and InformationTechnology (ICNIT 2010). This work was supported in part bythe National Natural Science Foundation of China (60802023,61070162, 71071028, 70931001, 61071124), the Fok Ying TungEducation Foundation (121065), the Specialized Research Fundfor the Doctoral Program of Higher Education (20070145096,20070145017), the Program for New Century Excellent Talentsin University (08-0095), the Fundamental Research Funds for theCentral Universities (N090504001, N090504003, N090504006),the Hong Kong Polytechnic University Postdoctoral FellowshipsScheme (G-YX2E), and the Foundation of State Key Laboratory ofAdvanced Optical Communication Systems and Networks of China(2010BJ04).

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