Optical Fiber Technology 18 (2012) 146–156

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Optical Fiber Technology

www.elsevier .com/locate /yof te

Survivable integrated grooming in multi-granularity optical networks

Jingjing Wu a, Lei Guo a,b,⇑, Xuetao Wei c, Yejun Liu a

a College of Information Science and Engineering, Northeastern University, Shenyang 110819, Chinab State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, Chinac Department of Computer Science and Engineering, University of California, Riverside, USA

a r t i c l e i n f o a b s t r a c t

Article history:Received 14 January 2012Revised 22 February 2012Available online 20 March 2012

Keywords:Optical networksSurvivabilityMulti-domainWaveband groomingAuxiliary graph

1068-5200/$ - see front matter � 2012 Elsevier Inc. Adoi:10.1016/j.yofte.2012.02.005

⇑ Corresponding author at: College of InformatioNortheastern University, P.O. Box 365, Shenyang 183684219.

E-mail address: haveball@yahoo.com (L. Guo).

Survivability is an important issue to ensure the service continuity in optical network. At the same time,with the granularity of traffic demands ranging from sub-wavelength-level to wavelength-level, trafficdemands need to be aggregated and carried over the network in order to utilize resources effectively.Therefore, multi-granularity grooming is proposed to save the cost and reduce the number of switchingports in Optical-Cross Connects (OXCs). However, current works mostly addressed the survivable wave-length or waveband grooming. Therefore, in this paper, we propose three heuristic algorithms calledMulti-granularity Dedicated Protection Grooming (MDPG), Multi-granularity Shared Protection Groom-ing (MSPG) and Multi-granularity Mixed Protection Grooming (MMPG), respectively. All of them are per-formed based on the Survivable Multi-granularity Integrated Auxiliary Graph (SMIAG) that includes oneWavelength Integrated Auxiliary Graph (WIAG) for wavelength protection and one waveBand IntegratedAuxiliary Graph (BIAG) for waveband protection. Numerical results show that MMPG has the lowest aver-age port-cost, the best resource utilization ratio and the lowest blocking probability among these threealgorithms. Compared with MDPG, MSPG has lower average port-cost, better resource utilization ratioand lower blocking probability.

� 2012 Elsevier Inc. All rights reserved.

1. Introduction

In Wavelength-Division-Multiplexing (WDM) optical networks,traffic grooming addresses the gap between the high bandwidthcapacity of wavelength channels and the low bandwidth require-ment of connections. On the other hand, fiber failures may affecta large volume of traffic since each wavelength channel in fiber linkcarries a lot of data. Therefore, survivability is critical for opticalnetworks [1–3]. Survivable traffic grooming that addresses bothgrooming provisioning and survivability [4] seeks to provide sur-vivable capability for connections and minimize the consumptionof spare capacity in the network.

At the same time, since the number of wavelengths in fibers isincreasing, the communication control and management becomemore and more complicated. Therefore, the technique of wavebandswitching in conjunction with new multi-granular optical cross-connects (MG-OXCs) has got significant attention for its effective-ness in reducing the number of switching ports, associated controlcomplexity and cost of optical cross-connects [5]. In order tosupport waveband switching meanwhile improve efficiency forconventional wavelength switching, the authors in Refs. [6–9]

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proposed several waveband grouping schemes including samesource–destination grouping, same source grouping, same destina-tion grouping and sub-path grouping, where the sub-path group-ing scheme has the best performance of reducing switchingports. But recently, the traffic demands with sub-wavelength gran-ularity, wavelength granularity and even waveband granularitysynchronously exist in the optical network. Although transmit-ting all the demands by waveband switching can save theaverage number of switching ports, the drawback is that for sub-wavelength demands the higher waveband granularity mayconsume more All-Optical (OOO) ports in MG-OXC with thefunctionality of band-to-wavelength (BTW) de-multiplexing andwavelength-to-band (WTB) multiplexing. Accordingly, the conceptof using sub-wavelength and waveband switches in a hierarchicalmanner has received growing attention [10].

By combining the survivable traffic grooming with the multi-granularity switching technique, which has two possible switchinggranularities for protection in the optical layer, it remains arelatively unexplored issue and gains much attention recently[11–14]. One of the possible switching granularities is wavebandprotection, which can minimize the overhead of protectionprocessing. The other one is wavelength protection, which canminimize the OOO ports cost. For practicality, it is necessary toimplement the survivability of optical path layer in order toaccommodate different granularities of demands.

J. Wu et al. / Optical Fiber Technology 18 (2012) 146–156 147

Recently, a lot of work has addressed the multi-granularity pro-tection issue. For example, in Ref. [15], heuristic algorithms fordedicated and shared protection were proposed under the condi-tion that the network had wavelength or waveband converters.In Ref. [16], the authors proposed a multi-granularity protectionalgorithm based on the threshold Q, where the traffic is propor-tional to several physical link-disjoint working Label SwitchingPaths (LSPs) and each LSP has a Q working capacity. In Ref. [17],the authors proposed a multi-granularity protection algorithmbased on priority.

On the other hand, a lot of works have addressed the survivabletraffic grooming issue. For example, the authors in Ref. [18] showedhow grooming decisions can be directly integrated into an overallp-cycle network design for more efficiency. The authors [19,20]considered the dynamic traffic grooming with a single workingpath. In Ref. [19], the authors proposed three approaches for groom-ing a connection with shared protection. The research in Ref. [20]was an extension of that in Ref. [19] which applied multipath rout-ing. It is obvious that traffic grooming and survivability have beenstudied extensively. Although these papers above investigated theprotection in waveband switching optical networks with consider-ing the shared backup wavelengths and proposed the Integer LinearProgramming (ILP), it did not propose efficient heuristic algorithms.The authors in Ref. [21] proposed heuristic algorithm, but it is onlysuitable for the same source–destination waveband grouping thatmay consume more switching ports in MG-OXCs.

In this paper, we consider the problem of multi-granularitygrooming in survivable optical networks and propose three heuris-tic algorithms called Multi-granularity Dedicated ProtectionGrooming (MDPG), Multi-granularity Shared Protection Grooming(MSPG) and Multi-granularity Mixed Protection Grooming(MMPG), respectively. These three algorithms are all based onthe Survivable Multi-granularity Integrated Auxiliary Graph(SMIAG) that includes one Wavelength Integrated Auxiliary Graph(WIAG) for wavelength protection and one waveBand IntegratedAuxiliary Graph (BIAG) for waveband protection. Since the groom-ing problem is known to be an NP-complete task [22], the idea oflayered graph has been shown to well solve the problem of groom-ing, routing and wavelength/waveband assignment.

In particular, for each demand, we first distinguish the demandclassification, i.e., wavelength-level or sub-wavelength-level, andthen according to the classification of the demand, we build aWIAG/BIAG based on the network physical topology. For instance,the WIAG is composed of one Wavelength Virtual Topology Layer(WVTL), multiple Wavelength Plane Layers (WPLs) correspondingto the number of wavelengths in the fiber, and some virtual linksconnecting the WVTL to each WPL. We first compute a single-hop or multi-hop route pair on WVTL. If the route pair is not foundon the WVTL, we compute the new route pair on the WPLs. Con-versely, if the new route pair is not found on the WPLs, we com-pute the hybrid multi-hop route pair on the WIAG. On the BIAG,the survivable grooming is in the same situation. Simulation re-sults show that MMPG has the lowest average port-cost, the bestresource utilization efficiency and the lowest blocking probabilityin these three algorithms. While comparing with MDPG, MSPGhas lower average port-cost, better resource utilization efficiencyand lower blocking probability.

To the best of our knowledge, the work in this paper is the firststudy to achieve the survivable grooming of optical network mean-while to reduce the size and the cost of MG-OXC by performingmulti-granularity grooming. This paper is organized as follows:Section 2 proposes the contribution of the Survivable Multi-granu-larity Integrated Auxiliary Graph (SMIAG) and the multi-granular-ity routing and grooming schemes. Section 3 describes the threeheuristic algorithms. Section 4 presents the simulation and analy-sis. Section 5 concludes this paper.

2. Problem statement

2.1. Network model

The physical network is denoted as G(N,L), where N representsthe set of nodes that are equipped with MG-OXCs, and L representsthe set of links, each of which is bidirectional and contains two uni-directional fibers with contrary direction. Moreover, we assumeeach demand requires the bandwidth of one wavelength channel,and the waveband or wavelength assignment is implemented bythe first-fit scheme. The shortest-path algorithm, i.e., Dijkstra’salgorithm, is applied to compute the routes.

To accommodate a fixed number of wavelength paths andwaveband paths simultaneously in a fiber, we assume that eachnode has the full wavelength conversion capacity and each nodeis equipped with a MG-OXC. The configuration of the MG-OXC withtwo-layer structure is shown in Fig. 1. From Fig. 1 we can see that itcan achieve the wavelength-level switching by Wavelength Cross-Connect (WXC) and waveband-level switching by WavebandCross-Connect (BXC). Obviously, the output/input of BXC containsboth the waveband and wavelength channels simultaneously aslong as the total number of wavebands/wavelengths does not ex-ceed the fiber capacity. The grooming fabric determines whichgroup of wavelengths belongs to a given waveband, and whichgroup of wavebands/wavelengths belongs to a given fiber. In thispaper, we assume the set of wavebands and the set of wavelengthsin each intra-domain fiber link are denoted as B and W, respec-tively. The waveband granularity is represented by G, which de-notes the number of contiguous wavelengths in one waveband.For instance, each fiber has total W available wavelengths. If thenumber of wavebands is |B|, the number of additional wavelengthswhich are not included in any waveband is (|W| � |B| � G) wherejWjP jBj � G.

2.2. Construction of the Survivable Multi-granularity IntegratedAuxiliary Graph (SMIAG)

The SMIAG includes one WIAG for wavelength protection andone waveBand Integrated Auxiliary Graph (BIAG) for wavebandprotection. The WIAG contains one WVTL and multiple WPLs towell support the grooming, routing and wavelength assignment.On the other hand, the BIAG contains one waveBand Virtual Topol-ogy Layer (BVTL) and multiple waveBand-Plane Layers (BPLs) tominimize the number of consumed ports under the wavelength re-source constraints. Before explaining the details, the followingnotations are presented firstly.

WDns;d

wavelength-level demand n from source

node s to destination node d

SDn

s;d

sub-wavelength-level demand n from sourcenode s to destination node d

BVTL

waveband virtual topology layer in BIAG WVTL wavelength virtual topology layer in WIAG BPLy waveband plane layers corresponding to

waveband y ð1 6 y 6 jBjÞ

WPLy wavelength plane layers corresponding to

wavelength y ðjBj � jGj < y 6 jWjÞ

x physical node in physical network topology BVx virtual node on BVTL corresponding to node x WVx virtual node on WVTL corresponding to node

x

By,x waveband node in BPLy corresponding to

node x

(continued on next page)

148 J. Wu et al. / Optical Fiber Technology 18 (2012) 146–156

Wy,x

wavelength node in WPLy corresponding tonode x

BT(BVi, BVj)

waveband-tunnel link between node BVi andnode BVj("i, j e [1, |B|], i – j) on BVTL as theresidual bandwidth of that waveband-tunnelis greater than zero

BE(By,i, By,j)

waveband edge between node By,i and nodeBy,j on each BPLy

WT(WVi, WVj)

wavelength-tunnel link between node WVi

and node WVj ("i, j e (|B| � |G|, |W|], i – j) onWVTL as the residual bandwidth of thatwavelength-tunnel is greater than zero

WE(Wy,i, Wy,j)

wavelength edge between node Wy,i andnode Wy,j on each WPLy

NTx

number of available transceivers in node x forwavelength grooming

NDx

number of available multiplexer/de-multiplexer in node x for wavebandgrooming

BVL(BVx, By,x)

multiplexer/de-multiplexer virtual linkbetween node BVx and node By,x("y e [1, |B|])as the number of available multiplexer/de-multiplexer on node x is greater than zero

WVL(WVx, Wy,x)

transceiver virtual link between node WVx

and node Wy,x ("y e (|B| � |G|, |W|]) as thenumber of available transceivers on node x isgreater than zero

R BTðBVi;BVjÞ

number of residual available bandwidth onBT (BVi, BVj)

R WTðWVi;WVjÞ

number of residual available bandwidth onWT (WVi, WVj)

Fig. 1. The configuration of MG

2.3. Illustration of survivable multi-granularity grooming on theSMIAG

Waveband-tunnel links or wavelength-tunnel links start andterminate on the BVTL layer or the WVTL layer. After the demandleaves, we update the residual bandwidth of the waveband-tunnellinks or the wavelength-tunnel links. For each waveband-tunnellink that carries a demand, its residual bandwidth to the corre-sponding waveband-tunnel link should be decreased by theamount of the carried demand. For each newly setup waveband-tunnel link, it will consume a multiplexer/de-multiplexer in thetwo end nodes, respectively. For each wavelength-tunnel link thatcarries a demand, its residual bandwidth to the correspondingwavelength-tunnel link should be decreased by the amount ofthe carried demand. For each newly setup wavelength-tunnel link,it will consume a transceiver in the two end nodes, respectively.

The BPLs are composed of free waveband edges and wavebandnodes. The number of layers corresponds to the number of wave-bands and each BPLy corresponds to a waveband yð1 6 y 6 jBjÞ.The WIAG contains (|W| � |B| � G) layers and each layer WPLy cor-responds to a wavelength y ðjBj � jGj < y 6 jWjÞ. If a demand can-not be satisfied on BVTL or WVTL, it may find a new route onsome BPLy or WPLy. If we can find the path successfully, we assignthe corresponding waveband or wavelength to this path. Mean-while, we remove the corresponding waveband/wavelength edges(since these waveband/wavelength edges cannot be used to satisfyanother demand later) and add a new waveband-tunnel link orwavelength-tunnel link on the BVTL layer or the WVTL layer.

By adding the multiplexer/de-multiplexer virtual links betweenthe corresponding nodes on BVTL and BPLy, we can obtain thewhole BIAG. If NDx = 0, all multiplexer/de-multiplexer virtual linksconnecting to node BVx will be removed. Based on the BIAG, therouting computation can be performed to achieve hybrid multi-

-OXC in a network node.

J. Wu et al. / Optical Fiber Technology 18 (2012) 146–156 149

hop waveband route, that is, for each route from source node todestination node, some sub-paths may select the waveband-tunnellinks with the residual available bandwidths on BVTL, while othersub-paths may select new waveband edges on BPLy. The situationof the demands for sub-wavelength-level is the same as the wave-bands. But on the WIAG, the links connecting between the corre-sponding nodes on the WVTL and the WPLy are the transceivervirtual links.

To illustrate how the SMIAG is constructed and how the surviv-able multi-granularity grooming works, we show an example inFig. 2a. For simplicity, we assume that all the demands are wave-length-level demands and groom them based on the BIAG. The pro-cedure of survivable grooming the sub-wavelength-level is as sameas survivable grooming the wavelength-level demands, but it is onthe WIAG. In the physical network topology, each fiber link has twoavailable wavebands B1 and B2, each of which contains four avail-able wavelengths. In Fig. 2b, there are one BVTL and two BPLs in theinitial BIAG, and the number beside the virtual nodes denotes thenumber of available multiplexers/de-multiplexers. Since there areno initial demands, there are no links between nodes on BVTL.We assume that there are five demands: WD1

6;2;WD23;6;WD3

3;2;

WD46;2 and WD5

6;4, arriving at the network orderly. For each demand,

1 2

6 5 4

BVTL

BPL1

BPL2

3

(a)

BV1

BV5BV6

B1,1

B1,5B1,6

B2,1

B2,5B2,6

(

4

4 4

BVTL

BPL1

BPL2

BV1 BV2 BV3

BV4BV5BV6

B1,1 B1,2 B1,3

B1,4B1,5B1,6

B2,1 B2,2 B2,3

B2,4B2,5B2,6

(d)

4 2 2

0 4 4

(1, 1)(2, 2)

BV1

BV5BV6

B1,1

B1,5B1,6

B2,1

B2,5B2,6

(

4

0 4

(1, 1)

Fig. 2. Illustration of survivable multi-granularity groom

we first compute the working path from the source node to thedestination node with a single-hop waveband tunnel-link or mul-ti-hop waveband-tunnel links on BVTL. If the working path was notfound on BVTL, we perform the routing computation on some BPLs.If the working path was still not found, we perform the routingcomputation based on BIAG which is formed by some hybridroutes. As to the backup path, the route finding process followsthe same technique.

In Fig. 2b, the first demand WD16;2 can be assigned to the surviv-

able route-pair, which are working path BV6–B1,6–B1,1–B1,2–BV2 andbackup path BV6–B1,6–B1,5–B1,4–B1,2–BV2. The consumed wavebandedges are BE(B1,6, B1,1), BE(B1,1, B1,2), BE(B1,6, B1,5), BE(B1,5, B1,4) andBE(B1,4, B1,2) on BPL1. The second demand WD2

3;6 can be assignedto the survivable route-pair, which includes working path BV3–B2,3–B2,4–B2,5–B2,6–BV6 and backup path BV3–B2,3–B2,2–B2,1–B2,6–BV6. The consumed waveband edges are BE(B2,3, B2,4), BE(B2,4, B2,5),BE(B2,5, B2,6), BE(B2,3, B2,2), BE(B2,2, B2,1) and BE(B2,1, B2,6) on BPL2.Then the BIAG should be updated as shown in Fig. 2c by removingthe consumed waveband edges from BPL1 and BPL2, and by addingwaveband tunnel-links BT(BV6, BV2) and BT(BV3, BV6) on the BVTL.The numbers beside BT(BV6, BV2) and BT(BV3, BV6) denote the num-ber of residual available wavelengths. Since each waveband con-

BV2 BV3

BV4

B1,2 B1,3

B1,4

B2,2 B2,3

B2,4

b)

4 4

4

BV1 BV2 BV3

BV4BV5BV6

B1,1 B1,2 B1,3

B1,4B1,5B1,6

B2,1 B2,2 B2,3

B2,4B2,5B2,6

(c)

4 2 2

0 4 4

(3, 3)(3, 3)

BV2 BV3

BV4

B1,2 B1,3

B1,4

B2,2 B2,3

B2,4

e)

2 2

4(2, 2)

BV1 BV2 BV3

BV4BV5BV6

B1,1 B1,2 B1,3

B1,4B1,5B1,6

B2,1 B2,2 B2,3

B2,4B2,5B2,6

(f)

4 0 2

0 4 2

(0, 0)

(2, 2)

( 3, 3)

ing for wavelength-level demand based on SMIAG.

150 J. Wu et al. / Optical Fiber Technology 18 (2012) 146–156

tains four wavelengths, and the first and the second demandsrespectively consumed one working wavelength and one backupwavelength1 on BT(BV6, BV2) and BT(BV3, BV6), the numbers are bothequal to (3,3). At the same time, ND6, ND2 and ND3 should be respec-tively updated to 0, 2 and 2, because each survivable route-pair willconsume four multiplexers/de-multiplexers at the two end nodes.Since ND6 = 0, the multiplexer/de-multiplexer virtual linksBVL(BV6, B1,6) and BVL(BV6, B2,6) should be removed from BIAG.

For the third demand WD33;2, we can find an available two-hop

route BV3–BV6–BV2 on BVTL, and the numbers beside BT(BV3, BV6)and BT(BV6, BV2) should be updated to (2, 2) and (2, 2), respectively.For the fourth demand WD4

6;2, we can find an available single-hoproute BV6–BV2 on BVTL, and then the number besides BT(BV6, BV2)should be updated to (1,1) as shown in Fig. 2d. Since these two sur-vivable route-pairs are established on the existing waveband tun-nel-links on BVTL, they do not consume new multiplexers/de-multiplexers.

For the last demand, in Fig. 2e, we can find a hybrid survivableroute-pair including an existing waveband tunnel-link BV6–BV2

and a newly built waveband tunnel-link between BV2 and BV4.The consumed waveband edges BE(B1,2, B1,3), BE(B1,3, B1,4) andBE(B2,2, B2,4) should be removed. The number besides BT(BV6, BV2)should be updated to (0, 0), and ND2 and ND4 should be updatedto 0 and 2. Therefore, the final BIAG is shown in Fig. 2f.

For the sub-wavelength-level demands, the survivable groom-ing procedure is on WIAG. For simplicity, we omit the proceduredescription.

3. Algorithm description

3.1. All-optical and electro-optical port calculation

If the demand is on the wavelength-level and we can find a sin-gle-hop or multi-hop waveband-tunnel link on BVTL, the port-costis written as:

Cost ¼ COEO �Pi<H

i¼1b �ui þ 2� COOO;

b ¼1;H P 20;H < 2

�and ui ¼

1; Bi – Biþ1

0; Bi ¼ Biþ1

�ð1Þ

where H is the number of hops of waveband-tunnel links on BVTL.COEO and COOO are the cost of OEO ports and OOO ports respectively.b is a Boolean variable, taking 1 if we can find a multi-hop wave-band-tunnel link and 0 otherwise. Bi denotes the ith waveband ona waveband-tunnel link.

If there are no available waveband-tunnel links and we can finda new route on some BPLy, the port-cost is:

Cost ¼ 2� ðH þ 1Þ � COOO ð2Þ

If all the above procedures fail, we compute a hybrid multi-hoproute, and then the ports cost is written as:

Cost ¼ COEO �Pi<N

i¼1b �ui þ 2� COOO �

PNk¼1

ak � Hk þ 2� COOO;

ak ¼1; new built waveband-tunnel link0; an existing waveband-tunnel link

�ð3Þ

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

1 The working wavelength is consumed only by the working path of wavelength-level demand to carry the traffic at the normal situation. The backup wavelength isconsumed only by the backup path of wavelength-level demand to carry the trafficafter the working path is interrupted.

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

Cost ¼ COEO �Pi<H

i¼1b �ui; ui ¼

1; ki – kiþ1

0; ki ¼ kiþ1

�ð4Þ

where ki denotes the ith wavelength on a wavelength-tunnel link.If the route cannot be found on WVTL and we can find a new

route on some WPLy, the port-cost is:

Cost ¼ 2� H � COOO ð5Þ

If all the above procedures fail, we compute a hybrid multi-hoproute by jointing WVTL and WPLy, and then the port-cost is:

Cost ¼ COEO �Pi<N

i¼1b �ui þ 2� COOO �

PNk¼1

ak � Hk ð6Þ

3.2. MDPG algorithm

In the MDPG, each demand will be assigned two paths, a work-ing path and a physical link-disjoint backup path. Both paths havethe same source node as well as destination node. The workingpath and the backup path dedicatedly consume resource.

An example is given in Fig. 3a, where we assume that there arethree sub-wavelength-level demands SD1

1;3, SD210;11, and SD3

7;5 whoseworking paths are 1-2-3, 10-11, and 7-6-5, respectively. We as-sume that each fiber link has total 12 available wavelengths, whichcontains four wavelengths (for low speed traffic grooming) andtwo wavebands each of which contains four wavelengths (i.e.,G = 4). In addition, the number of residual wavelengths for surviv-able grooming sub-wavelength-level demands is four. In theMDPG, the shortest backup paths are 1-8-3, 10-9-4-11, and 7-1-10-5, respectively. The number of reserved backup wavelengthsis eight. Now, if two new sub-wavelength-level demands SD4

10;5

and SD51;3 arrive, we cannot compute two paths for each demand.

We assume that the demands arrive at the network one-by-one,and each node is equipped with the wavelength and wave-band convertible MG-OXC to support the wavelength and wave-band switching. The procedure of the MDPG can be described asfollows:

Step 1: Initialize SMIAG based on the physical topology andresource information. Build the WIAG and the BIAG respec-tively. Initialize the parameters on each link to flagw = 1 andflagb = 1.Step 2: Waiting for the arrival of the demand. If the demand is toestablish a sub-wavelength-level connection, go to Step 3. If thedemand is to establish a wavelength-level connection, go toStep 6. If the demand is to release a connection, go to Step 9.Step 3: Compute the working path pw for the sub-wavelength-level demand as follows.

(1) On the WVTL, compute a single-hop or multi-hop surviv-able grooming route with the parameter (flagw = 1) usingDijkstra’s algorithm. If successful, let (flagw = 1, flagb = 0),and go to Step 4. Otherwise, execute 2).

(2) On WPLy("y e (|B| � |G|, |W|]), compute a new route withthe parameter (flagw = 1) using Dijkstra’s algorithm. Ifsuccessful, let (flagw = 1, flagb = 0), and go to Step 4.Otherwise, execute 3).

(3) On the WIAG, compute a hybrid survivable groomingroute with the parameter (flagw = 1) using Dijkstra’salgorithm. If successful, let (flagw = 1, flagb = 0), and goto Step 4. Otherwise, block this demand and go back toStep 2.

1 4

2 3

567

8

9

10 11

1 4

2 3

567

8

9

10 11

1 4

2 3

567

8

9

10 11

1 4

2 3

567

8

9

10 11

(a)

(b)

(c)

Working wavelength

Backup wavelength

Fig. 3. Illustration of backup resources assignment in: (a) MDPG, (b) MSPG, (c) MMPG.

J. Wu et al. / Optical Fiber Technology 18 (2012) 146–156 151

Step 4: Compute the backup path pb for the sub-wavelength-level demand as follows.

(1) On the WVTL, compute a link-disjoint single-hop ormulti-hop backup route with the parameter (flagb = 1)using Dijkstra’s algorithm. If successful, let (flagw = 0,flagb = 0), go to Step 5. Otherwise, execute 2).

(2) On WPLy("y e (|B| � |G|, |W|]), compute a new link-dis-joint route with the parameter (flagb = 1) using Dijkstra’salgorithm. If successful, let (flagw = 0, flagb = 0), go to Step5. Otherwise, execute 3).

(3) On the WIAG, compute a hybrid link-disjoint survivablegrooming route with the parameter (flagb = 1) usingDijkstra’s algorithm. If successful, let (flagw = 0, flagb = 0)and go to Step 5. Otherwise, block this demand and goback to Step 2.

Step 5: Allocate the resource for this demand, update the WIAG.Remove all consumed wavelength edges on wavelength-planelayers, add new wavelength-tunnel links on WVTL, update thenumber of free transceivers at each node and the number offree bandwidth on each wavelength-tunnel link, and go backto Step 2.

Step 6: Compute the working path pw for the wavelength-leveldemand as follows.

(1) On the BVTL, compute a single-hop or multi-hop surviv-able grooming route with the parameter (flagw = 1) usingDijkstra’s algorithm. If successful, let (flagw = 1, flagb = 0),and go to Step 7. Otherwise, execute 2).

(2) On BPLy("y e [1, |B|]), compute a new route with theparameter (flagw = 1) using Dijkstra’s algorithm. If suc-cessful, let (flagw = 1, flagb = 0), go to Step 7. Otherwise,execute 3).

(3) On the BIAG, compute a hybrid survivable groomingroute with the parameter (flagw = 1) using Dijkstra’salgorithm. If successful, let (flagw = 1, flagb = 0), and goto Step 7. Otherwise, block this demand and go back toStep 2.

Step 7: Compute the backup path pb for the wavelength-leveldemand as follows.

(1) On the BVTL, compute a link-disjoint single-hop or multi-hop backup route with the parameter (flagb = 1) usingDijkstra’s algorithm. If successful, let (flagw = 0, flagb = 0),and go to Step 8. Otherwise, execute 2).

152 J. Wu et al. / Optical Fiber Technology 18 (2012) 146–156

(2) On BPLy("y e [1, |B|]), compute a new link-disjoint routewith the parameter (flagb = 1) using Dijkstra’s algorithm.If successful, let (flagw = 0, flagb = 0), and go to Step 8.Otherwise, execute 3).

(3) On the BIAG, compute a hybrid link-disjoint survivablegrooming route with the parameter (flagb = 1) usingDijkstra’s algorithm. If successful, let (flagw = 0, flagb = 0)and go to Step 8. Otherwise, block this demand and goback to Step 2.

Step 8: Allocate the resources for this demand, update the BIAG.Remove all consumed waveband edges on waveband-plane lay-ers, add new waveband-tunnel links on BVTL, update the num-ber of free multiplexers/de-multiplexers at each node and thenumber of free wavelength on each waveband-tunnel link,and go back to Step 2.Step 9: Release and update the working and backup path con-sumed by this demand, and go back to Step 2.

3.3. MSPG algorithm

In the MSPG, the backup wavelengths on a backup path can beshared by other backup paths if their corresponding working pathare physical link-disjoint. Thus, the MSPG can save more wave-lengths than MDPG. For example, in Fig. 3b, the backup paths willbe encouraged to traverse the links for sharing the common back-up wavelengths. Thus, the backup paths are 1-9-4-3, 10-1-9-4-11,and 7-1-9-4-5, respectively, and then the number of reversedbackup wavelengths is only seven since the common backupwavelengths on links 1-9 and 9-4 can be shared. Compared withMDPG, MSPG can save more backup resources, and then the re-source utilization ratio will be improved. A better resource utili-zation ratio will lead to lower blocking probability since therewill be more free resources that can be used by new arriving con-nection requests. Now, the new arriving sub-wavelength-leveldemand SD4

10;5 can be accepted with the backup path 10-1-9-4-5. Because there is no free bandwidth along the path 1-9-4, thesub-wavelength-level demand SD5

1;3 also cannot be accepted inMSPG.

The procedure of the MSPG can be described as follows:

Step 1: Initialize SMIAG based on the physical topology andresources information. Build the WIAG and the BIAG respec-tively. Initialize the parameters on each link to flagw = 1 andflagb = 1.Step 2: Waiting for the arrival of the demand. If the demand is toestablish a sub-wavelength-level connection, go to Step 3. If thedemand is to establish a wavelength-level connection, go toStep 6. If the demand is to release a connection, go to Step 9.Step 3: Compute the working path pw for the sub-wavelength-level demand as follows.

(1) On the WVTL, compute a single-hop or multi-hop surviv-able grooming route with the parameter (flagw = 1) usingDijkstra’s algorithm. If successful, let (flagw = 1, flagb = 0),and go to Step 4. Otherwise, execute 2).

(2) On WPLy("y e (|B| � |G|, |W|]), compute a new route withthe parameter (flagw = 1) using Dijkstra’s algorithm. Ifsuccessful, let (flagw = 1, flagb = 0), and go to Step 4.Otherwise, execute 3).

(3) On the WIAG, compute a hybrid survivable groomingroute with the parameter (flagw = 1) using Dijkstra’salgorithm. If successful, let (flagw = 1, flagb = 0), and goto Step 4. Otherwise, block this demand and go back toStep 2.

Step 4: Compute the backup path pb for the sub-wavelength-level demand as follows.

(1) On the WVTL, compute a link-disjoint single-hop ormulti-hop backup route with the parameter (flagb = 1)using Dijkstra’s algorithm. If successful, let (flagw = 0,flagb = 1), and go to Step 5. Otherwise, execute 2).

(2) On WPLy("y e (|B| � |G|, |W|]), compute a new link-dis-joint route with the parameter (flagb = 1) using Dijkstra’salgorithm. If successful, let (flagw = 0, flagb = 1), and go toStep 5. Otherwise, execute 3).

(3) On the WIAG, compute a hybrid link-disjoint survivablegrooming route with the parameter (flagb = 1) usingDijkstra’s algorithm. If successful, let (flagw = 0, flagb = 1),and go to Step 5. Otherwise, block this demand and goback to Step 2.

Step 5: Allocate the resources for this demand, update theWIAG. Remove all consumed wavelength edges on wave-length-plane layers, add new wavelength-tunnel links on WVTL,update the number of free transceivers at each node and thenumber of free bandwidth on each wavelength-tunnel link,and go back to Step 2.Step 6: Compute the working path pw for the wavelength-leveldemand as follows.

(1) On the BVTL, compute a single-hop or multi-hop surviv-able grooming route with the parameter (flagw = 1) usingDijkstra’s algorithm. If successful, let (flagw = 1, flagb = 0),and go to Step 7. Otherwise, execute 2).

(2) On BPLy("y e [1, |B|]), compute a new route with theparameter (flagw = 1) using Dijkstra’s algorithm. If suc-cessful, let (flagw = 1, flagb = 0), go to Step 7. Otherwise,execute 3).

(3) On the BIAG, compute a hybrid survivable groomingroute with the parameter (flagw = 1) using Dijkstra’salgorithm. If successful, let (flagw = 1, flagb = 0), and goto Step 7. Otherwise, block this demand and go back toStep 2.

Step 7: Compute the backup path pb for the wavelength-leveldemand as follows.

(1) On the BVTL, compute a link-disjoint single-hop or multi-hop backup route with the parameter (flagb = 1) usingDijkstra’s algorithm. If successful, let (flagw = 0, flagb = 1),and go to Step 8. Otherwise, execute 2).

(2) On BPLy("y e [1, |B|]), compute a new link-disjoint routewith the parameter (flagb = 1) using Dijkstra’s algorithm.If successful, let (flagw = 0, flagb = 1), and go to Step 8.Otherwise, execute 3).

(3) On the BIAG, compute a hybrid link-disjoint survivablegrooming route with the parameter (flagb = 1) usingDijkstra’s algorithm. If successful, let (flagw = 0, flagb = 1)and go to Step 8. Otherwise, block this demand and goback to Step 2.

Step 8: Allocate the resources for this demand, update the BIAG.Remove all consumed waveband edges on waveband-plane lay-ers, add new waveband-tunnel links on BVTL, update the num-ber of free multiplexers/de-multiplexers at each node and thenumber of free wavelength on each waveband-tunnel link,and go back to Step 2.Step 9: Release and update the working and backup path con-sumed by this demand, and go back to Step 2.

3.4. MMPG algorithm

In the above two algorithms, the consumed wavelength is cate-gorized into working wavelength and backup wavelength, wherein

J. Wu et al. / Optical Fiber Technology 18 (2012) 146–156 153

the bandwidth in the working wavelength is only assigned to theworking path and the bandwidth in the backup wavelength is onlyassigned to the backup path. In the MMPG, however, the consumedwavelength can be regarded as mixed wavelength, since the band-width can be assigned to both working path and backup path.

In the MMPG, the performance of bandwidth utilization will bebetter than that in the MDPG and the MSPG. As shown in Fig. 3c,the new arriving sub-wavelength-level demand SD5

1;3 can be ac-cepted with the backup path 1-2-3. The backup path can traversethe working path of demand SD1

1;3. Since there will be more freebandwidth that can be utilized by the new arriving demand, theMMPG will have the lower blocking probability than that of theMDPG and the MSPG.

The procedure of the MMPG can be described as follows:

Step 1: Initialize SMIAG based on the physical topology andresource information. Build the WIAG and the BIAGrespectively.Step 2: Waiting for the arrival of the demand. If the demand is toestablish a sub-wavelength-level connection, go to Step 3. If thedemand is to establish a wavelength-level connection, go toStep 6. If the demand is to release a connection, go to Step 9.Step 3: Compute the working path pw for the sub-wavelength-level demand as follows.

(1) On the WVTL, compute a single-hop or multi-hop surviv-able grooming route using Dijkstra’s algorithm. If suc-cessful, go to Step 4. Otherwise, execute 2).

(2) On WPLy("y e (|B| � |G|, |W|]), compute a new routeusing Dijkstra’s algorithm. If successful, go to Step 4.Otherwise, execute 3).

(3) On the WIAG, compute a hybrid survivable groomingroute using Dijkstra’s algorithm. If successful, go to Step4. Otherwise, block this demand and go back to Step 2.

Step 4: Compute the backup path pb for the sub-wavelength-level demand as follows.

(1) On the WVTL, compute a link-disjoint single-hop ormulti-hop backup route using Dijkstra’s algorithm. Ifsuccessful, go to Step 5. Otherwise, execute 2).

(2) On WPLy("y e (|B| � |G|, |W|]), compute a new link-dis-joint route using Dijkstra’s algorithm. If successful, goto Step 5. Otherwise, execute 3).

(3) On the WIAG, compute a hybrid link-disjoint survivablegrooming route using Dijkstra’s algorithm. If successful,go to Step 5. Otherwise, block this demand and go backto Step 2.

Step 5: Allocate the resources for this demand, update the WIAG.Remove all consumed wavelength edges on wavelength-planelayers, add new wavelength-tunnel links on WVTL, update thenumber of free transceivers at each node and the number of freebandwidth on each wavelength-tunnel link, and go back to Step 2.Step 6: Compute the working path pw for the wavelength-leveldemand as follows.

(1) On the BVTL, compute a single-hop or multi-hop surviv-able grooming route using Dijkstra’s algorithm. If suc-cessful, go to Step 7. Otherwise, execute 2).

(2) On BPLy("y e [1, |B|]), compute a new route using Dijk-stra’s algorithm. If successful, go to Step 7. Otherwise,execute 3).

(3) On the BIAG, compute a hybrid survivable groomingroute using Dijkstra’s algorithm. If successful, go to Step7. Otherwise, block this demand and go back to Step 2.

2

Step 7: Compute the backup path u for the wavelength-leveldemand as follows.

The working bandwidth is consumed only by the working path of sub-wavelength-level demand to carry the traffic at the normal situation. The backupbandwidth is consumed only by the backup path of sub-wavelength-level demand tocarry the traffic after the working path is interrupted.

(1) On the BVTL, compute a link-disjoint single-hop or multi-hop backup route using Dijkstra’s algorithm. If success-ful, go to Step 8. Otherwise, execute 2).

(2) On BPLy("y e [1, |B|]), compute a new link-disjoint routeusing Dijkstra’s algorithm. If successful, go to Step 8.Otherwise, execute 3).

(3) On the BIAG, compute a hybrid link-disjoint survivablegrooming route using Dijkstra’s algorithm. If successful,go to Step 8. Otherwise, block this demand and go backto Step 2.

Step 8: Allocate the resources for this demand, update the BIAG.Remove all consumed waveband edges on waveband-plane lay-ers, add new waveband-tunnel links on BVTL, update the num-ber of free multiplexers/de-multiplexers at each node and thenumber of free wavelength on each waveband-tunnel link,and go back to Step 2.Step 9: Release and update the working and backup path con-sumed by this demand, and go back to Step 2.

3.5. Time complexity of the three algorithms

Although the three algorithms consume resource in differentways, the time complexity is mainly dependent on the times ofrunning the Dijkstra’s algorithm whose time complexity is O(X2)where X denotes the node number in the network topology. Sothe three algorithms have the same time complexity. For a sub-wavelength-level demand, the algorithms will run two times ofDijkstra’s algorithm to compute the working path and the backuppath on WVTL where the node number is |N|. In addition, in theworst case, the algorithms will run two times of Dijkstra’s algo-rithm to compute the working path and the backup path on WIAGwhere the node number is [(|W| � |B| � G + 1) � N] since there areone WVTL and (|W| � |B| � G) WPLs. Therefore, the time complex-ity of the three algorithms for a sub-wavelength-level demand isapproximately O[2|N|2 + 2(|W| � |B| � G + 1)2 � |N|2].

For a wavelength-level demand, the algorithms will run twotimes of Dijkstra’s algorithm to compute the working path andthe backup path on BVTL where the node number is |N|. In addi-tion, in the worst case, the algorithms will run two times of Dijk-stra’s algorithm to compute the working path and the backuppath on BIAG where the node number is [(|B| + 1) � N] since thereare one BVTL and |B| BPLs. Therefore, the time complexity of thethree algorithms for a wavelength-level demand is approximatelyO[2|N|2 + 2(|B| + 1)2 � |N|2].

4. Simulation and analysis

In simulation, we use the network topology with 15 nodes and27 links shown in Fig. 4. In the network, all nodes are considered tobe capable of switching wavelength to wavebands. In addition,each link in the network is assumed to be a bidirectional fiber.The number of wavelength-level demands and the number ofsub-wavelength-level demands are uniformly distributed amongtotal 104 demands. The arrival of demands is modeled as a Poissonprocess with average arrival rate b, and the connections’ holdingtimes are negatively exponentially distributed 1/l, i.e., the net-work load is b/l Erlang. If the algorithm could not groom a demandsuccessfully, the demand is rejected immediately without waitingin a queue.

In simulation, we compare these three algorithms in terms ofthe performances of bandwidth utilization ratio, wavelength utili-zation ratio, blocking probability, and average port-cost. The band-width utilization ratio is defined as the ratio of the total consumedbackup bandwidth over the total consumed working bandwidth2

4 6 8 10 12 14 16

0.20

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0.55

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0.65

Bloc

king

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Fig. 6. Comparison of blocking probability among the three algorithms withdifferent number of wavelengths.

2 3 4 5 6 7 8

0.22

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Fig. 7. Blocking probability of MDPG with different number of wavebands in total

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Fig. 4. The test network topology.

154 J. Wu et al. / Optical Fiber Technology 18 (2012) 146–156

for the sub-wavelength-level demands. The wavelength utilizationratio is defined as the ratio of number of current consumed backupwavelengths over the number of current consumed working wave-lengths for the wavelength-level demands. Blocking probability isdefined as the ratio of the number of blocked demands over thenumber of arrival demands. Average port-cost is defined as the num-ber of average consumed ports by all accepted demands. We havedifferent kinds of average port-cost for different function of ports,i.e., the average port-cost with the function of switching, and theaverage port-cost with the function of BTW de-multiplexing andWTB multiplexing. Here, we consider only the average port-costwith the function of BTW de-multiplexing and WTB multiplexing.Obviously, lower blocking probability means higher throughputand lower average port-cost means less ports consumption.

We first test the performances of blocking probability for thethree algorithms with different parameters of the number of wave-bands and the number of wavelengths. First, if we assume that thenumber of wavelengths is enough, that is, all the sub-wavelength-level demands can be groomed into a wavelength-tunnel link, theblocking probabilities are all produced by wavelength-level de-mands. On the contrary, if we assume that the number of wave-bands is enough, then the blocking probabilities are all producedby sub-wavelength-level demands.

In Fig. 5, we assume the waveband granularity is 2 and the net-work load is 270 Erlang. We can see that the blocking probabilitygradually reduced with the number of wavebands increases ofthe three algorithms. The reason for this is that bigger number of

2 4 6 8 10

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Fig. 5. Comparison of blocking probability among the three algorithms withdifferent number of wavebands.

wavebands means more wavebands are available to carry on wave-length-level demands. The same situation can be also seen in Fig. 6with the parameter of the number of wavelengths.

16 wavelengths.

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Fig. 8. Comparison of blocking probability among the three algorithms withdifferent network loads.

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elen

gth

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atio

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Fig. 10. Comparison of wavelength utilization ratio among the three algorithmswith different network loads.

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Fig. 11. Comparison of average port-cost among the three algorithms with differentnumber of wavebands.

J. Wu et al. / Optical Fiber Technology 18 (2012) 146–156 155

In Fig. 7, we assume the waveband granularity is 2, the networkload is 90 and the total number of wavelengths on each fiber isfixed on 16. Because the trends of the three algorithms are thesame, so we only test the performances of blocking probabilityfor MPDG with different parameters of wavebands and wave-lengths ratio. We can see that with the number of wavebands in-creases, blocking probability firstly decreases and then graduallyincreases. The reason for this is that when the number of wave-lengths become large (e.g., 12), the blocking probability is mainlyproduced by lacking of wavebands to carry on wavelength-leveldemands. When the number of wavebands is greater than somevalue (e.g., 4), the blocking probability is mainly produced bysub-wavelength-level demands.

In Fig. 8, we assume that each fiber link has total 16 availablewavelengths which contains eight wavelengths (for low speed traf-fic grooming) and four wavebands each of which contains twowavelengths (i.e., G = 2). In addition, the number of residual wave-lengths for survivable grooming sub-wavelength-level demand is8. It is shown that with the higher network load, the blocking prob-abilities of MUPG, MSPG, and MMPG all increase. The reason isthat, when the network load is higher, there will be less free re-sources for subsequent demands, and thus more demands will beblocked. We also observe that the blocking probability of MMPGis the lowest among the three algorithms. The reason is that, inMMPG, there will be more free bandwidth/wavelength that canbe utilized by the new incoming demands. Thus, MMPG can utilizebandwidth/wavelength more efficiently, which contributes to re-duce the blocking probability. In addition, MMPG considers themixed shared resources, where the working and backup pathscan more efficiently use the free bandwidth/wavelength withinthe same lightpath, thereby allowing the blocking probability tobe further reduced. Comparing with MDPG, the blocking probabil-ity of MSPG is lower, which means that the shared protection canestablish more demands than the dedicated protection. The reasonis that there are more free resources to be used by new demands inMSPG. Therefore, the blocking probability of shared protection islower than that of dedicated protection.

Now we test the performance of bandwidth utilization ratio andwavelength utilization ratio for the three algorithms with differentnetwork loads. In Figs. 9 and 10, we assume that each fiber link hastotal 16 available wavelengths which contains eight wavelengths(for low speed traffic grooming) and four wavebands each of whichcontains two wavelengths (i.e., G = 2). In addition, the number ofresidual wavelengths for survivable grooming sub-wavelength-le-vel demand is 8. In terms of bandwidth utilization ratio and wave-

30 60 90 120 150 1801.0

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1.4

1.6

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Band

wid

th u

tiliz

atio

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Network load in Erlang

MDPG MSPG MMPG

Fig. 9. Comparison of bandwidth utilization ratio among the three algorithms withdifferent network loads.

length utilization ratio, we can clearly see that MMPG has the bestperformance among the three algorithms, while the performanceof MSPG is better than that of MDPG. The reason is that, in MMPG,as long as there is free bandwidth/wavelength in the path, it can beassigned to a demand. In MSPG, any two backup paths can sharethe common backup bandwidth/wavelength in the same path iftheir corresponding primary paths are link-disjoint. In MDPG,any two backup paths cannot share the backup bandwidth/wave-length. Therefore, compared with MSPG and MDPG, MMPG con-sumes less backup bandwidth/wavelength, which makes MMPGhave the best performance of bandwidth utilization ratio andwavelength utilization ratio.

In Fig. 11, we assume that each fiber link has total 16 avail-able wavelengths and the number of wavebands varies from 2 to8 and each waveband contains two available wavelengths (i.e.,G = 2). In addition, the number of residual wavelengths for sur-vivable grooming sub-wavelength-level demand varies from 12to 0. It is shown that with the larger number of wavebands,average port-cost for BTW de-multiplexing and WTB multiplex-ing increases. The reason is that for merging more wavelength-level traffic, the higher waveband granularity may consumemore OOO ports in MG-OXC with the functionality of BTW de-multiplexing and WTB multiplexing. At the same time, we can

156 J. Wu et al. / Optical Fiber Technology 18 (2012) 146–156

see that the average port-cost of MMPG is the lowest among thethree algorithms. The reason is that MMPG considers the mixedshared resources, where the working and backup paths can moreeffectively use the common ports in the same lightpath, therebyallowing the average port-cost to be reduced. Comparing withMDPG, MSPG consumes fewer ports and saves more port-cost.The reason is that, any two backup paths in MSPG can sharethe common ports on the same route if their corresponding pri-mary paths are link-disjoint, while any two backup paths inMDPG cannot share the ports.

5. Conclusion

This paper analyzed the survivable multi-granularity groomingin optical networks and proposed three algorithms MDPG, MSPG,and MMPG. To support the survivable multi-granularity grooming,this paper presented the Survivable Multi-granularity IntegratedAuxiliary Graph (SMIAG) that includes one Wavelength IntegratedAuxiliary Graph (WIAG) for wavelength protection and one wave-Band Integrated Auxiliary Graph (BIAG) for waveband protection.Simulation results showed that MMPG has the lowest averageport-cost, the best resource utilization efficiency and the lowestblocking probability in these three algorithms. While comparingwith MDPG, MSPG has lower average port-cost, better resource uti-lization efficiency and lower blocking probability.

Acknowledgments

This work was supported in part by the National Natural Sci-ence Foundation of China (61172051, 60802023, 61071124), theFok Ying Tung Education Foundation (121065), the Program forNew Century Excellent Talents in University (08-0095), the Funda-mental Research Funds for the Central Universities (N110204001,N110604008), the Specialized Research Fund for the Doctoral Pro-gram of Higher Education (20110042110023, 20110042120035),and the Open Fund of State Key Laboratory of Information Photon-ics and Optical Communications (Beijing University of Posts andTelecommunications).

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