Photon Netw Commun (2012) 23:205–216DOI 10.1007/s11107-011-0351-x

Multi-domain grooming algorithm based on hierarchicalintegrated multi-granularity auxiliary graph in optical meshnetworks

Jingjing Wu · Lei Guo · Weigang Hou

Received: 10 June 2010 / Accepted: 22 November 2011 / Published online: 7 December 2011© Springer Science+Business Media, LLC 2011

Abstract With the size of traffic demands ranges from sub-wavelength-level to wavelength-level, traffic demands needto be aggregated and carried over the network in a cost-effective manner to make sure that the resources are utilizedeffectively. Therefore, the technique called multi-granularitygrooming is proposed to save the cost by reducing the numberof switching ports in optical cross-connects. However, theexisting multi-granularity grooming algorithms are mostlylimited in single-domain optical networks. Since the currentoptical backbone keeps enlarging and is actually divided tomultiple independent domains for achieving the scalabilityand the confidentiality, it is necessary to study the multi-gran-ularity grooming in multi-domain optical networks. In thispaper, we propose a new heuristic algorithm called hierar-chical multi-domain multi-granularity grooming (HMMG)based on hierarchical integrated multi-granularity auxiliarygraph (H-IMAG) to reduce the total number of optical switch-ing ports. The H-IMAG is composed of the inter-domain vir-tual topology graph (VTG) and the intra-domain integratedlayered auxiliary graph (ILAG), where VTG includes a wave-length virtual topology graph (WVTG) and a wavebandvirtual topology graph (BVTG), and ILAG includes awavelength layered auxiliary graph (WLAG) and a wave-Band layered auxiliary graph (BLAG). Then, we can groomthe sub-wavelength-level demands into lightpaths basedon WVTG and WLAG and groom the wavelength-leveldemands into high-capacity wavebands based on BVTGand BLAG. Simulation results show that performances of

J. Wu · L. Guo (B) ·W. HouCollege of Information Science and Engineering,Northeastern University, Shenyang 110819, Chinae-mail: haveball@gmail.com

H-IMAG can be significantly improved compared with pre-vious algorithm.

Keywords Optical mesh networks ·Multi-granularity ·Multi-domain · Grooming ·Hierarchical integrated multi-granularity auxiliary graph

1 Introduction

Wavelength division multiplexing (WDM) is an effectivesolution to satisfy the high bandwidth requirements in opti-cal network. Recently, since the number of wavelength onfiber keeps increasing, the communication control and man-agement become more and more complicated. Therefore,the technique of waveband switching in conjunction withnew multi-granular optical cross-connects (MG-OXCs) hasgot significant attention for its effectiveness in reducing thenumber of switching ports, associated control complexity,and cost of optical cross-connects [1]. In order to supportwaveband switching meanwhile provide efficiency for con-ventional wavelength switching, the authors in [2–4] pro-posed several waveband grouping schemes including samesource-destination grouping, same source grouping, samedestination grouping, and sub-path grouping, where the sub-path grouping scheme has the best performance for reducingswitching ports.

At the same time, with the development of intelligent opti-cal network, today’s optical networks are primarily hybridand can be divided into several domains. These domainsusually have different structures and provide different ser-vice types; moreover, they are typically run by differentoperators [5]. The emergence of multi-domain networks isposing a serious challenge to existing network mechanisms.

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206 Photon Netw Commun (2012) 23:205–216

In single-domain optical networks, an entity maintains aboutall the states, e.g., physical links, available resources, nodediversity, etc. In multi-domain networks, in order to sat-isfy the scalability requirements, only the aggregated routinginformation can be exchanged among domain by an exte-rior gateway protocol (EGP) such as BGP [6]. The lack ofcomplete and global knowledge of the network informationmakes it much more complex to apply the multi-granularitygrooming of single-domain optical networks to multi-domainoptical network.

Recently, a number of works addressed the multi-gran-ularity issue. The expression [7] performed traffic engi-neering in multi-granularity optical networks using dynamictraffic grooming. In [8], proposed waveband groupingschemes which is suitable for homogeneous networks. In[9], RA-IAG is proposed and the simulation results showedthat the average number of consumed switching ports issmaller than other algorithms. However, the existing multi-granularity grooming schemes mentioned above consideredonly the wavelength-level demands and did not consider thesub-wavelength-level demands, i.e., low-rate traffic streams.As opposed to single-domain settings, full topology infor-mation in multi-domain network is lacking and path com-putation needs to be done using the aggregated topologyand resource state. For example, [10] presented a domainby domain scheme in which border nodes maintain com-plete route state across networks, and [11] developed threedifferent inter-domain wavelength routing algorithms. Also,previous papers proposed some hierarchical model for multi-cluster traffic grooming. The authors in [12] proposed hier-archical approaches on SONET ring networks. In [13,14],with the objective of minimizing the total number of elec-tronic ports, a framework for hierarchical traffic groomingin mesh network is developed. The logic topology within acluster is formed as a virtual star. As a multi-granular multi-domain grooming problem, the authors in [15,16] presenteda hierarchical algorithm for grooming lightpaths into wave-bands. From the above references, we can see that currentworks focus on determining the logical topology of light-path or waveband grooming within each cluster or domainonly, while the multi-granularity grooming in multi-domainnetworks is not considered.

Since the inter-domain routing in multi-domain opticalnetworks based on aggregative virtual topology is an inter-esting and challenging work to achieve the scalability andalso the multi-granularity grooming can reduce the size andthe cost of MG-OXC, in this paper, we consider the problemof multi-granularity grooming in multi-domain optical net-works and propose a new algorithm called hierarchical multi-domain multi-granularity grooming (HMMG) to achieve thescalability of routing computation in multi-domains mean-while to reduce the size and the cost of MG-OXC. Sincethe grooming, routing and waveband/wavelength assign-

ment problem has been proven to be the NP-complete[17], we adopt the heuristic algorithm based on hierarchi-cal integrated multi-granularity auxiliary graph (H-IMAG).For each demand, first we distinguish the demand classifica-tion, i.e., wavelength-level or sub-wavelength-level, and thenaccording to the size of the traffic demand, we determine theroute for each wavelength-level demand and to aggregatethem into a waveband. If the demand is in sub-wavelength-level size, we just determine the wavelength route. The reasonis that the higher waveband granularity grooming may con-sume more All Optical (OOO) ports in MG-OXC with thefunctionality of band-to-wavelength (BTW) de-multiplexingand wavelength-to-band (WTB) multiplexing.

To the best of our knowledge, the work in this paper is thefirst study to achieve the scalability based on aggregative vir-tual topology of multi-domains meanwhile to reduce the sizeand the cost of MG-OXC by performing multi-granularitygrooming in multi-domain optical networks.

This paper is organized as follows: Sect. 2 proposes theinter-domain and intra-domain multi-granularity routing andgrooming schemes. Section 3 describes the heuristic algo-rithm. Section 4 presents the simulation and analysis. Sec-tion 5 concludes this paper.

2 Multi-granularity grooming scheme

2.1 Network model

The physical network graph is denoted as G(I nter L , D),where I nter L is the set of inter-domain links each of whichconnects two border nodes in different domains, and D ={Dr (B Nr , C Nr , I ntraLr ) |r = 1, 2, . . . } is the set of phys-ical topologies of all domains in which Dr is the physicaltopology of domain r, B Nr is the set of border nodes indomain r, C Nr is the set of ordinary nodes in domain r andI ntraLr is the set of intra-domain fiber links in domain r .Moreover, the aggregative virtual topology is denoted asGv(I nter L , Dv

r ), where Dvr = {B Nr , V Lr } in which V Lr

is the set of virtual links in domain r .In this paper, we adopt the full-mesh abstract scheme [19],

in which each domain is transformed to a sub-graph contain-ing the border nodes interconnected via a fully meshed set ofvirtual links. Each virtual link can be computed beforehand,and it denotes the physical route between two border nodes inone single domain. We assume that the capacity of the inter-domain link is higher than the intra-domain link, shown inFig. 1. After abstracting, the whole network is divided intotwo-hierarchy topologies, high-level topology and low-leveltopology. Each ordinary node can only view the local net-work physical topology information in its own domain, andthe border node can view both the local information and theglobe network virtual topology information.

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Photon Netw Commun (2012) 23:205–216 207

1

5

2

4 3

6

7 8

11 10

9

18 19

17

20

2122

12 13

16

15 14

Domain 0

Domain 1

Domain 2

Domain 3

Ordinary node

Border node

inter-domain link

intra-domain physical link

7 8

virtual link

high-level topology

low-level topology

(a)

(b)

69

1011 1213

16

14

15

1 2

34

5

17

18 19

20

2122

2

3

69

10 12

14

15

20

21

17

Fig. 1 Multi-domain mesh network: a physical network; b high-leveland low-level topology obtained from topology aggregation

We assume each node is equipped with a MG-OXC. TheMG-OXC with two-layer structure can achieve the wave-length-level switching by wavelength cross-connect (WXC)and waveband-level switching by waveband cross-connect(BXC). The grooming fabric determines which group ofwavelengths belongs to a given waveband and which group ofwavebands/wavelengths belongs to a given fiber. TheDijkstra’s algorithm is applied to compute the shortest routesand waveband or wavelength assignment scheme is first-fit.In this paper, we assume the set of wavebands and the set ofwavelengths in each intra-domain fiber link are denoted as Band W , respectively. The waveband granularity is G, whichdenotes the number of contiguous wavelengths in one wave-band. For instance, each fiber has total W available wave-length. If the number of wavebands is |B|, the number of addi-tional wavelengths which are not included in any waveband is(|W |−|B|×|G|)where |W | ≥ |B| · |G|. Before detailing thetotal algorithm, some further notations are introduced first.

W Dns,d Wavelength-level demand n from

source node s to destination node d;

SDns,d Sub-wavelength-level demand n from

source node s to destination node d;VTG Inter-domain virtual topology graph on

H-IMAG;BVTG Waveband virtual topology graph layer in

VTG;WVTG Wavelength virtual topology graph layer in

VTG;BV T Lr Intra-domain waveband virtual topology layer

in BLAG contained in ILAG of domain r ;W V T Lr Intra-domain wavelength virtual topology layer

in WLAG contained in ILAG of domain r ;B P Lr

y Intra-domain waveband plane layerscorresponding to waveband y(1 ≤ y ≤ |B|)in domain r ;

W P Lry Intra-domain wavelength plane layers

corresponding to wavelength y(1 ≤ y ≤ |W |)in domain r ;

xr Physical node in physical network topologyof domain r ;

BV rx Virtual border node on BVTG corresponding

to border node xr in domain r ;W V r

x Virtual border node on WVTG correspondingto border node xr in domain r ;

Bry,x Waveband node in B P Lr

y correspondingto node xr in domain r ;

W ry,x Wavelength node in W P Lr

y corresponding tonode xr in domain r ;

N Brx Virtual node on BV T Lr corresponding to

node xr in domain r ;N W r

x Virtual node on W V T Lr corresponding to nodexr in domain r ;

BTinter Waveband-tunnel link between nodes(BV r

i , BV lj ) BV r

i and BV lj on BVTG if the residual

bandwidth of that waveband-tunnel isgreater than zero from domainr to domain l;

BTintra Waveband-tunnel link between nodes(N Br

i , N Brj ) N Br

i and N Brj (∀i, j ∈ [1, |B|], i �= j)

as the residual bandwidth of thatwaveband-tunnel is greater than zeroin domain r ;

B E(Bry,i , Br

y, j ) Waveband edge between nodes Bry,i

and Bry, j on each B P Lr

y in domain r ;W Tinter Wavelength-tunnel link between nodes(W V r

i , W V lj ) W V r

i and W V lj on WVTG

if the residual bandwidth of thatwavelength-tunnel is greater thanzero from domain r to domain l;

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208 Photon Netw Commun (2012) 23:205–216

W Tintra Wavelength-tunnel link between nodes(N W r

i , N W rj ) N W r

i and N W rj (∀i, j ∈ [1, |W |], i �= j)

on W V T Lr as the residual bandwidth ofthat wavelength-tunnel is greaterthan zero in domain r ;

W E Wavelength edge between nodes(W r

y,i , W ry, j ) W r

y,i and W ry, j on

each W P Lry in domain r ;

N T rI nter ,x Number of available transceivers in

node xr in domain r forinter-domain grooming;

N DrI nter ,x Number of available multiplexer/

de-multiplexer in node xr in domain r forinter-domain grooming;

N T rI ntra,x Number of available transceivers

in node xr in domain r forintra-domain grooming;

N DrI ntra,x Number of available multiplexer/

de-multiplexer in node {intra,xr } indomain r for intra-domain grooming;

BV L Multiplexer/de-multiplexer virtual(N Br

x , Bry,x ) link between node N Br

x and nodeBr

y,x (∀y ∈ [1, |B|])as the number of availablemultiplexer/de-multiplexer on nodexr is greater than zero in domain r .Transceiver virtual link between nodesN W r

x and W ry,x (∀y ∈ [1, |W |]) as

the number of available transceivers onnode xr is greater than zero in domain r .

R_BT Residual bandwidth on(BV r

i , BV lj ) BTinter (BV r

i , BV lj );

R_BT Residual bandwidth on(N Br

i , N Brj ) BTintra(N Br

i , N Brj );

R_W T Residual bandwidth on(W V r

i , W V lj ) W Tinter (W V r

i , W V lj );

R_W T Residual bandwidth on(N W r

i , N W rj ) W Tintra(N W r

i , N W rj );

2.2 Hierarchical grooming on H-IMAG

The hierarchical integrated multi-granularity auxiliary graph(H-IMAG) contains the inter-domain virtual topology graph(VTG) corresponding to the high-level topology and theintra-domain integrated layered auxiliary graph (ILAG) cor-responding to the low-level topology.

The inter-domain grooming is based on VTG that is com-posed of two virtual topology layers, waveband virtual topol-ogy graph (BVTG) and wavelength virtual topology graph(WVTG), respectively, each of which is a single-layeredgraph and is composed of virtual links and virtual nodes.According to the size of the demand, one demand can be

groomed into an existing virtual link which has enough resid-ual bandwidth. If there is not an appropriate existing single-hop route, the demand is allowed to reach the destination nodeby multi-hop virtual links. The numbers beside the virtualnodes on BVTG denote the available multiplexers/de-multi-plexers and the numbers beside the virtual nodes on WVTGdenotes the available transceivers. If the number beside onevirtual node is equal to zero, the new virtual link cannot beestablished from or terminate at that node.

The intra-domain grooming is based on ILAG whichincludes two multi-layered graph waveband layered auxil-iary graph (BLAG) and wavelength layered auxiliary graph(WLAG). Waveband-tunnel links or wavelength-tunnel linksstart and terminate on the BV T Lr or W V T Lr . For the virtuallinks carrying a demand, the capacities of the correspondingvirtual links are decreased by the amount of the carried traffic.For each newly setup virtual links, it will consume a mul-tiplexers/de-multiplexer or a transceiver at two end nodes,respectively.

The BLAG also contains |B| independent sub-graphscalled waveband plane layers (B P Lr

y) and WLAG contains(|W | − |B| · |G|) independent sub-graphs called wavelengthplane layers (W P Lr

y). If we can find a route on some B P Lry

or W P Lry , we can assign the corresponding waveband or

wavelength to this route. Meanwhile, we should remove theused waveband from the B P Lr

yor wavelength edges from theW P Lr

y since these waveband or wavelength edges cannot beused to satisfy another demand later on. Finally, we can adda new waveband-tunnel link on the BV T Lr layer or a newwavelength-tunnel link on the W V T Lr layer.

By adding the multiplexer/de-multiplexer virtual linksbetween the corresponding nodes on BV T Lr and B P Lr

y ,we can obtain the whole BLAG. If the number of availablemultiplexer/de-multiplexer N Dr

I ntra,x = 0, all multiplexer/de-multiplexer virtual links connecting with node N Br

x willbe removed. Based on BLAG, the routing computation canbe performed to achieve hybrid multi-hop waveband route,that is, for each route from source node to destination node,some sub-paths may select the waveband-tunnel links withthe residual available bandwidths on BV T Lr , while othersub-paths may select new waveband edges on B P Lr

y . Thesituation of the demands of sub-wavelength-level is as sameas the wavebands but the transceiver virtual links connectingthe corresponding nodes on W V T Lr and W P Lr

y .For each intra-domain demand, if the source node and

the destination node are in the same domain, the HMMGfirst grooms the demand to a single-hop or multi-hop routeon BV T Lr or W V T Lr . If the route cannot be found onBV T Lr or W V T Lr , HMMG then finds a route on someB P Lr

y or W P Lry . If all the above procedure are failed,

HMMG computes a hybrid multi-hop route by jointingBV T Lr and B P Lr

y . If the source node and the destina-tion node are in different domains, HMMG will groom the

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Photon Netw Commun (2012) 23:205–216 209

demand to a single-hop or multi-hop route on VTG. If theroute cannot be found on VTG, HMMG will compute sev-eral exact intra-domain routes based on the abstract virtuallinks.

To illustrate how the hierarchical graph is constructedand the algorithm works, we give an example, for a fourdomain network with bidirectional fiber links and all nodesare assumed to have grooming functionality. The phys-ical network topology is shown in Fig. 1, where eachfiber link has totally six wavelengths, and we assumethat two available wavebands and each of which con-tains two available wavelengths (i.e., G = 2). In addi-tion, the residual number of wavelengths for groomingsub-wavelength-level is two. Suppose the capacity of eachwavelength-tunnel link is OC-24 and each waveband-tunnel link is OC-48. Each ordinary node has two tun-able transceivers and two multiplexers/de-multiplexers forintra-domain grooming. On the other hand, each bordernode has excess two tunable transceivers and two mul-tiplexers/de-multiplexers for inter-domain grooming. Weassume that there are eight demands, W D1

5,9, W D29,20,

W D32,20, W D4

3,5, W D55,20, SD6

2,9, SD76,12, and SD8

6,12 whicharrive at the network orderly. For each demand, we first dis-tinguish the demand classification, i.e., wavelength-level orsub-wavelength-level.

The first connection demand is from source node 5 indomain 0 to destination node 9 in domain 1. First, sourcenode 5 will compute the shortest path to the nearest bor-der node 2, shown in Fig. 3a in Domain 0. It is easy to seethat there exists a path along N B0

5 − B01,5 − B0

1,2 − N B02

that consumes the waveband edge B E(B01,5, B0

1,2). Sec-ond, destination border node will compute the shortest pathfrom the destination border node to the destination node ifnecessary, but we omit this for simplicity. Third, sourceborder node 2 will find a hop by hop route by waveband-tunnel links on BVTG as shown in Fig. 2a. Since there areno demands initially, there are no waveband-tunnel linksbetween nodes on BVTG. The source border node 2 willfind a route 2-6-9 on high-level topology shown in Fig. 1b.Fourth, the virtual link 6-9 will be mapped to the physicalpath 6-7-8-9 that will route along N B1

6 − B11,6 − B1

1,7 −B1

1,8 − B11,9 − N B1

9 which consumes the waveband edges

B E(B11,6, B1

1,7), B E(B11,7, B1

1,8) and B E(B11,8, B1

1,9) shownin Fig. 3a in Domain 1. Finally, after completing the segmentgrooming and waveband assignment, inter-domain wave-band-tunnel links can be built segment by segment on BVTG,which are BTinter (BV 0

2 , BV 16 ) and BTinter (BV 1

6 , BV 19 )

as shown in Fig. 2b from node BV 02 to node BV 1

9 .Update the numbers on the figures. In the source domain,the new built waveband-tunnel link isBTintra(N B0

5 , N B02 ).

Meanwhile, the corresponding waveband edges should beremoved from the source domain and the intermediate

domain waveband plane layers, shown in Fig. 3b in Domain0 and Domain 1. Because each waveband-tunnel linkwill consume two multiplexers/de-multiplexers at two endnodes, N D0

I ntra,5 and N D0I ntra,2 for intra-domain groom-

ing will be updated to 1, N D0I nter,2 and N D1

I nter,9 willboth be updated to 1. The numbers beside the wave-band-tunnel links denote the residual available bandwidthR_BT (BV 0

2 , BV 16 ), R_BT (BV 1

6 , BV 19 ) and R_BT (N B0

5 ,

N B02 ) are all equal to OC-24. Since the inter-domain wave-

band-tunnel link BTinter (BV 16 , BV 1

9 ) is built from the intra-domain fibers, the number of transceivers for intra-domaingrooming is also remaining 2.

Following the same procedure as above, on the step ofinter-domain grooming, the source border node 9 finds theroute 9-12-15-20 on the high-level topology in Fig. 1b, wherethe virtual link 12-15 will be mapped to the physical path12-16-15 that will route along N B2

12 − B21,12 − B2

1,16 −B2

1,15−N B215 consuming waveband edges B E(B2

1,12, B21,16)

and B E(B21,16, B2

1,15) in Fig. 3a in Domain 2. Update the cor-responding BVTG. The new built inter-domain waveband-tunnel links from node BV 1

9 to node BV 320 on BVTG can be

also seen in Fig. 3b which are BTinter (BV 19 , BV 2

12), BTinter

(BV 212, BV 2

15) and BTinter (BV 215, BV 3

20). Update R_BT(BV 1

9 , BV 212), R_BT (BV 2

12, BV 215) and R_BT (BV 2

15, BV 320)

to OC-24, respectively. Remove the corresponding wavebandedges in domain 2. Then, N D1

I nter,9 and N D3I nter,20 will be

updated to 0 and 1.For the third demand which is between nodes 2 and 20,

on Fig. 3b we can find an available route BV 02 − BV 1

6 −BV 1

9 − BV 212− BV 2

15− BV 321 on BVTG, and then we update

the number besides the links. Finally, BVTG is shown inFig. 3c. By multi-domain grooming, we can satisfy the thirddemand without consuming new multiplexer/de-multiplexer.

The fourth demand is an intra-domain demand and willbe assigned the route N B0

3 − B02,3 − B0

2,4 − B02,5 − N B0

5

that consumes the waveband edges B E(B02,3, B0

2,4) and

B E(B02,3, B0

2,4) on B P L02, shown in Fig. 3a in Domain 0.

Then, we remove the consumed waveband edges from B P L02

and add BTintra(N B03 , N B0

5 ) on BV T L0 with the numberOC-24 beside it, shown in Fig. 3b in Domain 0. N D0

I ntra,3

and N D0I ntra,5 will be, respectively, updated to 1 and 0.

For the fifth demand, because there is no available wave-band-tunnel link on BVTG, we should build a new routefor it. First, we can find a hybrid route N B0

5 − N B02 −

B02,2 − B0

2,3 − N B03 that includes an existing waveband-

tunnel link BTintra(N B05 , N B0

2 ) and a new waveband edgeB E(B0

2,2, B02,3). Remove the waveband edge from B P L0

2,

and R_BT (N B05 , N B0

2 ), N D0I ntra,2 and N D0

I ntra,3 will be,respectively, updated to 0, 0 and 0, shown in Fig. 3b inDomain 0. Second, on the step of inter-domain grooming,the source border node 3 finds the route 3-17-20 on the

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210 Photon Netw Commun (2012) 23:205–216

Domain 0

Domain 1

Domain 2

Domain 3

(a)

BV101

BV91BV6

1

BV20

BV30

BV122

BV152

BV142

BV173

BV203

BV213

2

2

2

2

2

2

22

22

2

OC-24

OC -24OC-24

OC -24

OC-24

Domain 0

Domain 1

Domain 2

Domain 3

(b)

BV101

BV91BV6

1

BV20

BV30

BV122

BV152

BV142

BV173

BV203

BV213

1

2

2

2

0

2

22

21

2

OC-0

OC -0

OC-0

OC -0

OC-0

Domain 0

Domain 1

Domain 2

Domain 3

(c)

BV101

BV91

BV61

BV20

BV30

BV122

BV152

BV142

BV173

BV203

BV213

1

2

2

2

0

2

22

2

1

2

Domain 0

Domain 1

Domain 2

Domain 3

(d)

BV101

BV91

BV61

BV20

BV30

BV122

BV152

BV142

BV173

BV203

BV213

1

1

2

2

0

2

22

20

2

OC-24OC-24

Fig. 2 Waveband virtual topology graph of VTG a Initial inter-domain waveband virtual topology graph b–d waveband assignment

high-level topology in Fig. 1b, where the virtual link 17-20will be mapped to the physical path 17-18-19-20 that willroute along N B3

17 − B32,17 − B3

2,18 − B32,19 − B3

2,20 − N B320

shown in Fig. 3b in Domain 3. Remove the correspond-ing waveband edges and update the number of availablemultiplexer/de-multiplexer, as shown in Fig. 3c in Domain3. Update the corresponding BVTG. The new built inter-domain waveband-tunnel links from node BV 0

3 to node BV 320

on BVTG can be seen in Fig. 2d.For the next three sub-wavelength-level demands, the

grooming procedure is on WVTG and WLAG, respectively.For simplicity, we omit the procedure.

3 Algorithmic description

3.1 All optical and electro-optical port calculation

If the demand is on the wavelength-level and we can find asingle-hop or multi-hop waveband-tunnel link on BV T Lr ,the port-cost is written as:

Cost = COEO ×i<H∑

i=1

β · ϕi + 2× COOO,

β ={

1, H ≥ 20, H < 2

and ϕi ={

1, Bi �= Bi+1

0, Bi = Bi+1(1)

where H is the number of hops of waveband-tunnel linkson BV T Lr , COEO and COOO are the cost of OEO ports andOOO ports, respectively. β is a Boolean variable and it takesthe value of 1 if we can find a multi-hop waveband-tunnellink, otherwise, it takes the value of 0. Bi denotes the i thwaveband on a waveband-tunnel link.

If there are no available waveband-tunnel links and wecan find a new route on some B P Lr

y , the port-cost is:

Cost = 2× (H + 1)× COOO (2)

If all the above procedures fail, HMMG computes a hybridmulti-hop route, and then the ports cost is written as:

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Photon Netw Commun (2012) 23:205–216 211

Domain 0 Domain 1 Domain 2(a)

(b)

NB40

NB10

NB20

NB50

NB30

2

2

2

2 2

B1,40

B1,10

B1,20

B1,50

B1,30

B2,40

B2,10

B2,20

B2,50

B2,30

BPL01

BPL02

BVTL0

B1,61

B1,71

B1,91

B1,81

B1,101

BVTL

BPL11

B1,111

NB61

NB71

NB91

NB81

1NB111

1

B2,61

B2,71

B2,91

B2,81

B2,101B2,11

1

2

2

2 2

2

2

NB10

BPL12

B1,152

B1,122

B1,132

B1,162

B1,142

BPL21

NB152

NB122

NB132

NB162

NB142

B2,152

B2,122

B2,132

B2,162

B2,142

BVTL2

2

2

2

2

2

BPL22

NB40

NB10

NB20

NB50

NB30

2

0

1

2 1

B1,40

B1,10

B1,20

B1,50

B1,30

B2,40

B2,10

B2,20

B2,50

B2,30

BPL01

BVTL0

B1,61

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B1,91

B1,81

B1,101

BVTL

BPL11

B1,111

NB61

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NB81

1NB111

1

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B2,71

B2,91

B2,81

B2,101B2,11

1

2

2

2 2

2

2

NB10

B1,152

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B1,132

B1,162

B1,142

BPL21

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NB142

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B2,132

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BVTL2

2

2

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2

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2

0

0

2 0

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BPL11

B1,111

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1NB111

1

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1

2

2

22

2

2

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B1,142

BPL21

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B2,122 B2,13

2

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B2,142

BVTL2

2

2

2

2

2

OC-0

OC-24

(c)

OC-24

B1,203

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B1,173

B1,183

B1,223

BVTL

BPL31

B1,213

NB203

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NB183

3NB213

3

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B2,193

B2,173

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B2,223B2,21

3

2

2

2 2

2

2

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3NB213

3

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B2,193

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3

2

2

2 2

2

2

NB22

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B1,203

B1,193

B1,173

B1,183

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BVTL

BPL31

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NB203

NB193

NB173

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3NB213

3

B2,203

B2,193

B2,173

B2,183

B2,223B2,21

3

2

2

22

2

2

NB22

BPL32

BPL02

BPL02

BPL12

BPL12

BPL2

2

BPL22

Fig. 3 Waveband assignment in each domain

Cost = COEO ×i<N∑

i=1

β·ϕi + 2× COOO

×N∑

k=1

αk · Hk + 2× COOO,

αk ={

1, new built waveband-tunnel link0, an existing waveband-tunnel link

(3)

where N is the number of existing waveband-tunnel links onhybrid route. Hk is the number of hops on the kth waveband-tunnel link.

If the demand is sub-wavelength-level and we can groomthe demand to a single-hop or multi-hop wavelength-tunnellink, the port-cost is:

Cost = COEO ×i<H∑

i=1

β · ϕi , ϕi ={

1, λi �= λi+1

0, λi = λi+1(4)

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212 Photon Netw Commun (2012) 23:205–216

where λi denotes the i th wavelength on a wavelength-tunnellink.

If the route cannot be found on W V T Lr and we can finda new route on some W P Lr

y , the port-cost is:

Cost = 2× H × COOO (5)

If all the above procedures are failed, we compute a hybridmulti-hop route by jointing W V T Lr and W P Lr

y , and thenthe port-cost is:

Cost = COEO ×i<N∑

i=1

β·ϕi + 2× COOO ×N∑

k=1

αk · Hk (6)

3.2 Heuristic algorithm

The algorithm module works as follows:Input: Physical network topology G(I nter L , D) and aggre-gative virtual topology Gv(I nter L , Dv

r ); Physical topol-ogies of all domains D = {Dr (B Nr , C Nr , I ntraLr )

|r = 1, 2, . . . };Output: Number of traffic demands identified by δ whichare successfully groomed between a source-destination pair(s, d).Begin:

1. Initialize the VTG for inter-domain grooming andI L AGr for intra-domain grooming of domain r .

2. Waiting for the demand arrival. If the demand is for estab-lishing a new connection, go to step 3; if the demand isfor releasing a connection, go to step 15.

3. If source node s and destination node d are in the samedomain, let source be s and destination be d, and goto step 4; otherwise, go to step 8.

4. According to the size of traffic demand, compute theshortest path from node source to node destination onthe corresponding BV T Lr or W V T Lr , which is wave-length-level demand on BV T Lr and sub-wavelength-level demand on W V T Lr . If the path has been found,go to step 5; otherwise, go to step 6.

5. Accept the demand and let δ← δ+1. Update the residualbandwidth on each intra-domain waveband-tunnel linkor wavelength-tunnel link. If the residual bandwidth on awaveband-tunnel link or wavelength-tunnel link is equalto zero, remove this intra-domain waveband-tunnel linkfrom BV T Lr or wavelength-tunnel link from W V T Lr ,and go back to step 2.

6. Compute the shortest path on I L AGr . If the path hasbeen found, go to step 7; otherwise, block this demandand go back to step 2.

7. Accept the demand and let δ ← δ + 1. Add new intra-domain waveband-tunnel links on BV T Lr or wave-length-tunnel link on W V T Lr , update the number of

free multiplexer/de-multiplexer or transceivers at eachnode, and go back to step 2.

8. Compute the shortest path from s to the nearest bordernodes′. Consider source s and destination s′, if thepath has been found, go to step 4. If the path has not beenfound, block this demand and go back to step 2.

9. Compute the shortest path from d to the nearest bordernoded ′. Consider source d ′ and destination d, if thepath has been found, go to step 4. If the path has not beenfound, block this demand and go back to step 2.

10. Compute the shortest path on VTG between two bordernodes s′ and d ′. If the path has been found, go to step 11;otherwise, go to step 12.

11. Accept the demand and let δ← δ+ 1. Update the resid-ual bandwidth on each inter-domain waveband-tunnellink or wavelength-tunnel link. If the residual bandwidthon a waveband-tunnel link or wavelength-tunnel link isequal to zero, remove this inter-domain waveband-tunnellink from BVTG or wavelength-tunnel link from WVTG,and go back to step 2.

12. Compute a skeleton path on high-level topology betweentwo border nodes s′ and d ′. If the path has been found,go to step 13; otherwise, block this demand and go backto step 2.

13. Compute the exact intra-domain routes for each virtuallinks traversed by the skeleton inter-domain route basedon each domain original topology, and go to step 4.

14. Accept the demand and let δ ← δ + 1. Add newinter-domain waveband-tunnel links on BVTG or wave-length-tunnel link on WVTG, update the number of freemultiplexer/de-multiplexer or transceivers at each bordernode, and go back to step 2.

15. Remove the demand from the network, release the con-sumed resources, and go back to step 2.

End

4 Simulation and analysis

In simulation, we use the five domain interconnected networktopology shown in Fig. 4. In the network, all nodes are con-sidered to be capable of switching wavelength to wavebands.Further, each link in the network is assumed to be a bidirec-tional fiber. The number of wavelength-level demands andthe number of sub-wavelength-level demands are even dis-tributed in total 104 demands. The demands are modeled by aPoisson distribution and the demand holding time is assumedto be exponentially distributed. If the algorithm could notgroom a demand successfully, the demand is rejected imme-diately without waiting in a queue.

In simulation, we test the performances of blockingprobability and average port-cost for HMMG on various

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Photon Netw Commun (2012) 23:205–216 213

21

0

4

3

5

9

6

8

710

11

12

14 13

18

1715

16

21

22

20

19

Domain 0

Domain 1Domain 2

Domain 3

Domain 4

Fig. 4 Multi-domain optical networks topology

situations. Blocking probability is defined as the ratio of thenumber of blocked connection demands over the number ofarrival connection demands. Average port-cost is defined asthe number of average consumed ports by all accepted con-nection demands. We have different kinds of average port-cost for different function of ports, i.e., average port-costwith the function of waveband conversion, average port-cost with the function of wavelength conversion and averageport-cost with the function of band-to-wavelength (BTW)de-multiplexing and wavelength-to-band (WTB) multiplex-ing. Obviously, lower blocking probability means higher net-work throughput and smaller average port-cost means lessports consumption.

We first test the performances of blocking probability forHMMG with different parameters of the number of wave-bands and the number of wavelengths. First, if we assumethat the number wavelengths is enough, that is, all the sub-wavelength-level demands can be groomed into a lightpath,the blocking probabilities are all produced by wavelength-level demands. On the contrary, if we assume that the numberof waveband is enough, all the blocking probabilities are allproduced by sub-wavelength-level demands.

In Fig. 5, we assume the waveband granularity is 2. Wecan see that the blocking probability gradually reduced withthe number of wavebands increases in different network load.The reason for this is that bigger number of wavebands meansmore wavebands are available to carry on wavelength-leveldemands. The same situation can be also seen in Fig. 6 withthe parameter of the number of wavelength.

In Fig. 7, we assume the waveband granularity is 2, thenetwork load is 150 and the total number of wavelengthson each fiber is fixed on 16. We test the performances ofblocking probability for HMMG with different parameters of

54320.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Blo

ckin

g pr

obab

ility

Number of wavebands

network load = 150 network load = 180 network load = 210

Fig. 5 Blocking probability in different number of wavebands

4 5 6 7 8 9 100.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Blo

ckin

g pr

obab

ility

Number of wavelengths

network load = 150 network load = 180 network load = 210

Fig. 6 Blocking probability in different number of wavelengths

wavebands and wavelengths ratio. We can see that with thenumber of wavebands increases, blocking probability firstdecreases, then gradually increases. The reason for this is thatwhen the number wavelength is enough (e.g., 12), the block-ing probability is mainly produced by lacking of wavebandsto carry on wavelength-level demands. When the number ofwavebands is greater than some value (e.g., 3), the block-ing probability is mainly produced by sub-wavelength-leveldemands.

Because when the ratio of the number of wavebands overthe number of wavelengths is equal to 3/10, the performanceof blocking probability is the smallest, so that we will adoptthis ratio in the following simulation. In Fig. 8, we assumethe waveband granularity is 2. It is shown that with the num-ber of wavebands increases, average port-cost for BTW de-multiplexing and WTB multiplexing increases. The reasonfor this is that for merging more wavelength-level traffic,the higher waveband granularity may consume more All

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214 Photon Netw Commun (2012) 23:205–216

2 3 4 5 60.00

0.05

0.10

0.15

0.20

0.25

0.30B

lock

ing

prob

abili

ty

Number of wavebands in total 16 wavelengths

Fig. 7 Performance of blocking probability in different number ofwavebands in total 16 wavelengths

4321

18

19

20

21

22

23

Ave

rage

por

t-co

st

Number of wavebands

network load = 150 network load = 180 network load = 210

Fig. 8 Average port-cost in different available wavebands

Optical (OOO) ports in MG-OXC with the functionality ofBTW de-multiplexing and WTB multiplexing.

In Fig. 9, it is shown that blocking probability increaseswith the network load increasing in different wavebandgranularities. When we groom demands into existing wave-band-tunnel links, if the residual bandwidth is too small toaccommodate new demands, these demands will be blocked.Therefore, bigger waveband granularity means the existingwaveband-tunnel link can carry more demands.

In Fig. 10, we can see that with the waveband granularityincreasing, the average port-cost for waveband conversiondecreases. The reason for this is that when the wavebandgranularity is larger, the utilization ratio of existing wave-band-tunnel link is larger, so the number of new built wave-band-tunnel link is decreasing and the average port-cost forswitching waveband decreases.

We compare the performance of our hierarchical algo-rithm HMMG with the Per-domain Distributed Grooming

160 180 200 220 2400.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Blo

ckin

g pr

obab

ility

Network load in Erlang

G = 8 G = 4 G = 2

Fig. 9 Blocking probability for HMMG for different waveband gran-ularities

2 4 6 8 10 12 14 16

3.5

4.0

4.5

5.0

5.5

6.0

6.5

Ave

rage

por

t-co

st

Waveband granularity

Network load = 150 Network load = 180 Network load = 210

Fig. 10 Average port-cost for switching waveband for different wave-band granularities

(PDG) presented in [18]. The PDG operates with mini-mal inter-domain visibility. Namely, end-to-end routes areexpanded in a domain by domain manner with each domainspecifying its next-hop along with the complete internal routevia an egress node. By consulting routing tables, the next-hopsolution may be making from some fixed choices.

In Fig. 11, we assume the network load is 150. In Fig. 12,we assume the waveband granularity is 2. It is shown thatthe sum of average port-cost for waveband conversion andfor wavelength conversion of HMMG is smaller than that ofPDG. The reason for this is that, on the inter-domain levelgrooming HMMG first find a path on BVTG or WVTG, soHMMG may have higher probability to find a multi-hop pathon BVTG or WVTG without consuming new switching portswhile PDG needs to established new waveband-tunnel linksor wavelength-tunnel links with consuming new switchingports.

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Photon Netw Commun (2012) 23:205–216 215

0

5

10

15

20

25

30

35

40

45

50

HMMG PDG

16842

Ave

rage

por

t-co

st

Waveband granularity

Fig. 11 Comparison of average port-cost between HMMG and PDGfor different waveband granularities

150 180 210 2400

5

10

15

20

25

30

35

40

45

50

Ave

rage

por

t-co

st

Networl load in Erlang

HMMG PDG

Fig. 12 Comparison of average port-cost between HMMG and PDGfor different network loads

In Fig. 13, we assume the network load is 150. In Fig. 14,we assume the waveband granularity is 2. The results in twofigures show that blocking probability of HMMG is smallerthan that of PDG. The reason for this is that at the intra-domain level, the path computation of PDG is similar to theHMMG algorithm. However, at the inter-domain level, thePDG specifies the next domain by making fixed choices, i.e.,by consulting routing table. If the traffic in the next domain islarge, then the new coming connection will cause the chosendomain more congestion.

5 Conclusion

In this work, we proposed a new algorithm named hierar-chical multi-domain multi-granularity grooming (HMMG)

2 4 6 8 10 12 14 160.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

HMMG PDG

Blo

ckin

g pr

obab

ility

Waveband granularity

Fig. 13 Comparison of blocking probability between HMMG andPDG in different waveband granularities

160 180 200 220 2400.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

HMMG PDG

Blo

ckin

g pr

obab

ility

Network load in Erlang

Fig. 14 Comparison of blocking probability between HMMG andPDG in different network load

based on hierarchical integrated multi-granularity auxiliarygraph (H-IMAG) in multi-domain optical networks to per-form multi-granularity grooming. In order to achieve thescalability, H-IMAG performed the inter-domain groomingbased on the virtual topology graph (VTG) and the intra-domain grooming based on the intra-domain integrated lay-ered auxiliary graph (ILAG). Simulation results showed that,compared with other algorithm, HMMG obtained better per-formances on blocking probability and average port-cost.

Acknowledgments The preliminary work of this paper was presentedat the International Conference on Signal Processing Systems (ICSPS)2010. This work was supported in part by the National Natural ScienceFoundation of China (60802023, 61071124, 61172051), in part by theFok Ying Tung Education Foundation (121065), in part by the Pro-gram for New Century Excellent Talents in University (08-0095), andin part the Fundamental Research Funds for the Central Universities(N090504001, N090604007).

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Author Biographies

Jingjing Wu received the M.S. degreesin communication and information systemsfrom Northeastern University, China, in2006. She is currently pursuing the Ph.D.degree in the same university. Her researchinterests include multi-granularity and multi-domain optical networks, routing and surviv-ability.

Lei Guo received the Ph.D. degree in com-munication and information systems fromSchool of Communication and Informa-tion Engineering, University of ElectronicScience and Technology of China, Chen-gdu, China, in 2006. He is currently a fullprofessor in College of Information Sci-ence and Engineering, Northeastern Univer-sity, Shenyang, China. His research interests

include survivability, optical networks, and wireless mesh networks. Hehas published over 100 technical papers in the above areas. Dr. Guo isa member of IEEE and OSA. He was the recipient of the Best PaperAward from the International Conference on Communications, Circuitsand Systems (ICCCAS’04). He is currently servicing as the EditorialBoard Member of The Open Optics Journal.

Weigang Hou received the M.S. degreesin communication and information systemsfrom Northeastern University, China, in2009. He is currently pursuing the Ph.D.degree in the same university. His researchinterests include multi-granularity and greenoptical networks.

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