Hybrid Graph-Based Traffic Grooming for MulticastConnections in Mesh Optical Networks

Tania Panayiotou and Georgios EllinasKIOS Research Center for Intelligent Systems and Networksand the Department of Electrical and Computer Engineering,

University of Cyprus, Nicosia 1678, Cyprus.Email:{panayiotou.tania, gellinas}@ucy.ac.cy

Neophytos AntoniadesDepartment of Engineering Science and Physics,College of Staten Island, CUNY, New York, NY.Email: {neo.antoniades}@csi.cuny.edu

Abstract—This paper investigates the problem of multicasttraffic grooming in transparent optical networks utilizing agrooming approach that is based on routing/grooming of mul-ticast calls on hybrid graphs (HGs). HGs are constructed dy-namically upon the arrival of each multicast call, in such away that they are consisting of both the available physical linksand the logical links with available free capacity. Two schemesfor building the HGs are proposed, namely the minimum freecapacity light-tree first (MCF) and the maximum free capacitylight-tree first (MXCF), and also a novel hybrid Steiner tree(HST) heuristic for routing/grooming on HGs is presented. Theproposed routing/grooming approach exhibits improved perfor-mance in terms of blocking probability compared to existingmulticast grooming approaches that route/groom multicast callsby considering physical and logical links separately.

I. INTRODUCTION

Nowadays, a typical connection request requires bandwidththat is only a fraction of the wavelength bandwidth. Therefore,in order to efficiently utilize the capacity of each wavelengthchannel, several independent lower-speed traffic streams (sub-wavelengths) must be multiplexed onto a single lightpath.The process of allocating sub-wavelength traffic demands tolightpaths such that the wavelength resources are shared isknown as traffic grooming [1]. Traffic grooming in meshWDM networks has received considerable attention from theresearch community [2]-[7]. However, in these studies, onlyunicast traffic was considered while only a small number ofstudies have been performed on grooming multicast traffic [8]-[10]. As next generation networks are expected to supportboth unicast and multicast applications such as multipartyconferencing, software and video distribution, and distributedcomputing, it is important to design and dimension networksin order to be able to support unicast and multicast traffic,while grooming sub-wavelength traffic demands.

To support multicasting in transparent optical networks, alight-tree is created from the source to the destination nodesof the multicast call. In these networks, optical splitters can beused in network nodes to split the incoming signal to multipleoutputs, thus enabling the establishment of connections withmultiple destinations. An effective solution to the multicastrouting problem would be to calculate the Steiner MinimumTree (SMT) between the source and destination nodes. How-ever, as the SMT problem was proven to be NP-complete,

numerous heuristics were developed to compute a multicasttree [11]-[13].

This paper, addresses the problem of dynamically provi-sioning low-speed multicast connection requests in wavelengthdivision multiplexed (WDM) optical networks with arbitrarymesh topologies. Specifically, it focuses on building a dynamichybrid topology consisting of both the available physical andlogical links and then routing the arriving multicast call onthe hybrid graph. For the construction of the hybrid graphtwo schemes are proposed for solving the problem that ariseswhen more than one logical links are created between twonodes (this problem is related to the bin-packing optimizationproblem). Specifically, both schemes are based on the free ca-pacity of each link and according to the scheme the maximumfree capacity or the minimum free capacity link is chosen. Bydoing so, the multicast traffic routing and grooming problemsare solved jointly as the available resources can be exploredover a single (hybrid) graph topology. The proposed approachthat routes/grooms the traffic on hybrid graphs is compared toexisting approaches that explore available physical and logicalresources separately and sequentially. Attempts for solving thetraffic grooming problem jointly have been made in [6],[7].In these works however, only unicast connection requestswere assumed. Furthermore, in [7] full wavelength conversionat every node is present and the problem of multiple linksbetween two nodes is not considered.

II. NODE ARCHITECTURE

In this work we assume the translucent node architectureshown in Fig. 1 that implements both electronic duplicationand optical light splitting. This architecture is an extensionof the node architecture proposed in [14], in which a trafficgrooming fabric (GF) is added to support multicast traf-fic grooming. The architecture of Fig. 1 can provide all-optical bypass for light-trees passing through the node withoutany electronic processing. Alternatively, a light-tree can bedropped if the node is the final destination of all the trafficcarried by the light-tree or otherwise the light-tree is droppedto the GF where other traffic can be multiplexed (groomed)onto this light-tree to increase the bandwidth utilization ofwavelength channels. After the grooming operation, the traffic

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Fig. 1. Grooming and Multicast-capable Node Architecture

is switched to a corresponding optical splitter to split theincoming signal to the output links.

III. EXISTING MULTICAST TRAFFIC GROOMINGHEURISTICS

The authors in [9] investigated the dynamic multicast trafficgrooming problem for which two heuristic approaches, namelythe Logical First Hybrid Routing (LFHR) and the PhysicalFirst Sequential Routing (PFSR) heuristics were proposedamongst others. For both heuristics, the physical and logicallayers of the network are treated separately and sequentially.Specifically, upon the arrival of a multicast call, the PFSRheuristic first seeks a new light-tree from the source to thedestination nodes and only if this fails, the existing (singleor multihop) logical routes are then inspected. For example,in Fig. 2 where the logical and physical layers are shownseparately, two requests are already established into the net-work when a new multicast connection from source node Ato destination nodes F,C is accepted. It is assumed that thisnetwork operates utilizing one wavelength only. Based on thedescription above, PFSR first routes the request on the physicallayer from node A to node F . Then, since destination nodeC cannot be reached from the physical layer (no availablewavelength), free capacity on logical link (F,C) is used toconnect node C to the source node of the request.

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Fig. 2. Physical and Logical Layer Graphs

Unlike PFSR, LFHR first seeks existing light-tree(s) toprovision the request or part of the source/destination nodesin the request, and if this fails or only part of the requestis served, a new light-tree is created. In this case, for the

TABLE IBASIC STEPS OF MOL HEURISTIC

Step 1 Initialize w = 1.Step 2 Create list L consisting of all the currently established light-

trees with free capacity equal to or greater than r.Step 3 For each light-tree i in list L count the number ki of

source/destination nodes that are similar to nodes in set R,and associate each light-tree to its ki number.

Step 4 Identify light-tree R′ = [s′, D′], with its ki number beingthe maximum amongst the other light-trees in list L.

Step 5 If ki > 0 then go to Step 6 else go to Step 9.Step 6 Multiplex R with R′ and according to the overlapping case

that occurs update multicast set R as follows:• if s = s′ and (D ∩D′) = D, then R = ∅.• if s �= s′ and (D ∩D′) = D then R = [s, s′].• if s = s′ and (D ∩ D′) ⊂ D = Ds then R =

[s,D −Ds].• if s �= s′ and (D ∩ D′) ⊂ D = Ds then R =

[s, s′, D −Ds].

Step 7 Increase w by one and if w > h then go to Step 9, else goto Step 8.

Step 8 If R �= ∅ then go to Step 2, else go to Step 9.Step 9 Return R.

example of Fig. 2, the new multicast call with source A anddestination nodes F and C is first provisioned on the logicallayer by reusing logical link (F,C) and then the physical layeris examined, for a lightpath that will connect the source nodeof the request to the link (F,C). Based on Fig. 2 there existsan available lightpath (A−D−H −G−F ) from node A tonode F .

As pointed out, both heuristics are decomposed into thephysical provisioning phase and the logical provisioning phaseand depending on the heuristic followed, the two phasesare performed sequentially. The LFHR and PFSR heuristicswere implemented in this work for comparison purposes asdescribed below.

A. Logical Provisioning

For the logical provisioning phase, the maximum over-lapping light-tree (MOL) heuristic is developed aiming atminimizing the session blocking probability by grooming eachmulticast call onto the maximum overlapping light-tree. Eachtime a multicast call arrives into the network, MOL computesa list L consisting of the already established light-trees withfree capacity that is equal to or greater than the rate of the newcall. Then each light-tree in L is compared to the new multicastcall, and the light-tree that can serve the maximum number ofsource/destination nodes is chosen for grooming the new call.The basic steps of the MOL heuristic for a multicast requestR with rate r and multicast set R = [s,D], where s standsfor the source node and D is the destination set, are given inTable I. Note that in Table I parameter h is also included asa constraint to the maximum number of logical hops MOL isallowed to perform.

According to Table I, if the MOL heuristic is used inconjunction with the PFSR approach, a multicast request isblocked if there are no logical light-tree(s) that can accommo-date the set of nodes that the physical provisioning phase failed

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Fig. 3. Hybrid Graph created based on the Physical and Logical LayerGraphs

to accommodate; otherwise the multicast request is accepted.However, if MOL is used in conjunction with the LFHRapproach, a multicast request is accepted if it can be groomedonto one or more light-trees. Otherwise, if only a subset of themulticast call can be accommodated to the logical layer (MOLheuristic returns R �= ∅), the physical provisioning phase takesplace as described next.

B. Physical Provisioning

During the physical provisioning phase, the Multicast Rout-ing and Wavelength Assignment (MC-RWA) is solved fora multicast set R. The MC-RWA algorithm, first solves therouting sub-problem and then assigns wavelength for that routebased on the first-fit algorithm. The entire multicast set isaccepted if a route and a wavelength assignment is possible formulticast set R. Note that for the LFHR approach the SteinerTree (ST) heuristic [11] is used for the routing subproblem.However, for the PFSR approach the ST heuristic is slightlymodified in order to allow for feasible sub-light-trees to beestablished (a sub-light-tree contains the source node andpart of the destination set), in case the entire light-tree isnot feasible. Destination nodes not reached by the physicallayer have a chance of been reached by the logical layer byremoving from set R the destination nodes already reached bythe physical layer, before moving to the MOL heuristic.

IV. GROOMING ON HYBRID GRAPHS

A novel hybrid routing algorithm is proposed aiming atimproving the session blocking probability by performingrouting/grooming on pre-calculated HGs consisting of boththe available physical links and logical light-trees with freecapacity. A HG is created for each wavelength in the networkupon a connection arrival, based on the available physical linksand the logical light-trees with free capacity at the time. OnceHGs are created, an extension of the Steiner tree heuristic,namely the hybrid Steiner tree (HST) heuristic, is used tocalculate the hybrid light-tree that may be consisting of bothphysical and logical links.

Fig. 3 is used as an illustrative example of a HG createdby the combination of logical and physical layers shown inFig. 2. In this example it is shown that the two light-trees

already established in the network, do not overlap in the logicallayer, which makes the combination of the two layers trivial.In other systems however, more than one logical links maybe present, originating from the same source and reaching thesame destination node(s). For example, if lightpath A−D−Ewas also present in the physical topology of Fig. 2, withsource node A and destination node E, then two logical links(A,D) would be present in the logical topology of Fig. 2.The problem that arises here concerns the creation of theHG in which case only one logical link must be chosenfor the connection of any two nodes in the HG. This isdone in order to save resources and eventually reduce theblocking probability in the network. Thus two schemes aredeveloped, namely the minimum free capacity light-tree first(MCF) and the maximum free capacity light-tree first (MXCF)that prioritize logical links according to their free capacity.This is similar to the bin-packing optimization problem thatappears in the literature [15]. In the next subsection the MCFand MXCF schemes developed for the construction of the HGare described in detail.

A. Building the Hybrid Graph

As pointed out, the HG is created upon the arrival of arequest, based on both the available physical links and thelight-trees that have already been created at the time of thenew request. More precisely, given a network G, hybrid graphHG is created on wavelength λi by first adding to HG allnodes of graph G and then adding to HG all the arcs withfull wavelength capacity on wavelength λi. Then the light-trees already established in the network are examined and thelight-trees that have free capacity that is less than the rate ofthe arriving request are discarded. The rest of the light-treesare placed in a sorted list which is created according to oneof the MCF/MXCF schemes. Specifically, in the MCF schemethe light-tree with minimum free capacity is placed first on thelist while in the MXCF scheme the light-tree with maximumfree capacity is placed first.

Fig. 4 and Table II are used as an illustrative example of theMCF scheme. Fig. 4 shows the state of the network G uponthe arrival of a multicast call requesting 2 units of capacity andTable II shows information regarding the wavelength, the freecapacity, and the logical links for each multicast call alreadyestablished in the network. Logical links of a light-tree aredefined here as all the links created by connecting the sourcenode of the tree to each destination node. Note that a logicallink between two destination nodes is not possible accordingto the above definition, since that would imply that groomingis possible at destination nodes that are intermediated nodesto the tree. Grooming at these nodes however, is not possiblesince although the signal is dropped at these nodes, it is notretransmitted. A portion of the the signal is dropped to thedestination node, and the rest passes through the node to reachits next destination. Returning back to the example of Table II,as the arriving request requires 2 units of capacity, none of thealready established light-trees is discarded and based on theMCF scheme, the light-trees of Table II are placed in the table

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Fig. 5. Hybrid Graph HG.

in an increasing order according to their free capacity.The HG for wavelength λi is created by first copying G to

HG and then removing from HG all the physical links thatare occupied by λi (Fig. 4). Then the logical links for eachlight-tree shown in Table II are added sequentially in the HG.During this procedure, if two nodes are found to be alreadyconnected in HG, either via a logical or via a physical link,then every logical link included in the conflicting light-tree isneglected. For example, Table II shows that λi and λw havea common link. However, since logical link (a, f) of λi isadded first on HG, then none of the logical links of λw areincluded in HG. The resulting HG is shown in Fig. 5.

While in Fig. 5 link weights are not shown, logical links areassigned weights that represent their free capacity while phys-ical links are assigned weights that represent their physicaldistance in order to avoid the creation of long paths that aremore susceptible to physical layer impairments. Furthermore, aphysical first priority (PP) scheme is followed by multiplyingthe weights of the logical links by a number that is muchgreater compared to the maximum link distance. In general,several different schemes can be created by modifying the link

Lambda Multicast Call Free Capacity Logical Linksλi {a, b, f, h} 3 (a, b), (a, f), (a, h)λk {b, h, s, k} 4 (b, h), (b, s), (b, k)λw {a, f, e} 6 (a, f), (a, e)

TABLE IIINFORMATION FOR ALREADY ESTABLISHED LIGHT-TREES.

weights, such as a logical first priority (LP) scheme or settingthe link weights in such a way that physical and logical linkshave equal importance. However, in this work only the formerapproach is investigated while a more in depth investigationof the problem is planned as future work.

B. Hybrid Steiner Tree Heuristic

The Hybrid Steiner Tree (HST) heuristic is developed forrouting on the HGs, as known multicast routing algorithmscannot be applied directly on a HG. The reason for thisis that logical links belonging to the same logical light-treeare grouped together and cannot be separated. Due to trans-parency and the lack of wavelength conversion in the networksexamined, light-trees originating from the same transmitterhave to reach every destination node of the light-tree firstestablished for that specific transmitter. Thus, the Steiner Tree(ST) heuristic [11] is modified, resulting in the Hybrid SteinerTree (HST) heuristic, to account for the inseparability oflogical links belonging to the same light-tree. Specifically,the HST heuristic differs from the ST heuristic in that itfinds the hybrid multicast tree HT by adding in the currentlyconstructed tree HT the path that leads to the destinationnode that is more closer to HT , but each time a new pathis added it has to identify if any of the newly added linkscorresponds to a logical link. For the newly added links thatdo correspond to a logical link it identifies their logical light-trees and adds the corresponding logical links to the HT . Ineach iteration the multicast set is updated by removing fromthe set all destination nodes added to the HT . The heuristicterminates when every destination node of the multicast callis added to the HT .

C. Multicast Connection Provisioning on Hybrid Graphs

For each multicast call, the Hybrid Multicast Routing andWavelength Assignment (HMC-RWA) algorithm builds k hy-brid graphs HGs, one for each of the k wavelengths inthe network. Each HG is created according to one of theMCF/MXCF schemes previously described. The wavelengthassignment subproblem is solved based on the first-fit algo-rithm while for the hybrid multicast routing subproblem theHST heuristic is used. Multicast requests are accepted into thenetwork if a hybrid tree exists in one of the k HGs.

V. PERFORMANCE EVALUATION

In order to evaluate the proposed techniques, a simulationmodel was developed. For the simulations, a network consist-ing of 50 nodes and 196 directed links was used, with anaverage node degree of 3.92 and an average distance betweenthe links of 60Km. We used a dynamic traffic model wheremulticast sessions arrive at each node according to Poissonprocess and the holding time is exponentially distributed witha unit mean. Thirty-two wavelengths per link were utilizedwith each wavelength utilizing 10 units of capacity and therate of each call was randomly generated between the setof integer numbers 1 to 10. Traffic requests were randomlygenerated, with the number of destinations for each request

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ranging between the numbers 1 and 39, thus allowing multicastas well as unicast requests to enter the network. Results wereevaluated for both the proposed HST heuristic in conjunctionto the MCF/MXCF schemes used for the creation of HGs, aswell as for the PFSR/LFHR heuristic algorithms [9] developedfor comparison purposes.

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Fig. 6. Blocking Probability versus Load in Erlangs. Results of the STheuristic are also shown for comparison purposes.

Fig. 6 shows the blocking probability versus the load inErlangs for a number of grooming approaches while the resultsof the ST heuristic are also illustrated in order for the groomingapproaches to be compared to the case where no groomingtechniques are present. According to the results, PFSR/LFHRoutperforms the ST heuristic for lighter loads (i.e., up to 100Erlangs), while the blocking probability for the PFSR/LFHRcases increases with the increment of parameter h, that denotesthe maximum number of logical hops in the MOL heuristic.Furthermore, for different network scenarios such as the casewhere every request requires the same units of capacity (i.e.,25% of the wavelength capacity), that are not shown here dueto space limitation, PFHR/LFHR also outperforms ST.

The proposed hybrid scheme utilizing the HST heuristic,in conjunction with the MCF/MXCF schemes, outperformsboth the PFSR/LFSR and ST heuristics, especially for heavilyloaded networks. Furthermore, the MXCF approach is alsoshown to outperform the MCF scheme, an indicator thatshows that it is better to utilize first the light-trees havingthe maximum free capacity. Increased blocking probability forthe PFSR/LFHR heuristics compared to the proposed HSTapproach is caused due to the fact that available physical andlogical resources are treated separately and sequentially andalthough physical or logical resources may exist to serve thenew call, these resources are either not able to be utilizedby PFSR/LFHR or cannot be combined in the most efficientway. In the proposed hybrid schemes, however, the HSTheuristic can have a global information of the availabilityand connectivity of physical and logical links, thus making itpossible for the resources to be utilized in a more efficientlyway, providing better blocking probability results.

VI. CONCLUSIONS

In this work the multicast traffic grooming problem wasinvestigated for transparent optical networks with arbitrarymesh topologies. A hybrid grooming approach was proposedduring which hybrid graphs were created consisting of both the

available physical and logical links for routing/grooming themulticast calls. Two schemes (MCF/MXCF) were developedfor the creation of the HGs, and the conventional ST heuristicwas extended to the HST heuristic in order to account for theinseparability of the logical links belonging to the same light-tree. HST in conjunction with the MCF/MXCF techniqueswas compared with the conventional ST heuristic as well aswith existing heuristics that route/groom multicast calls byconsidering resources on logical and physical layers separatelyand sequentially. Results showed that the HST heuristic outper-forms existing approaches since it works on HGs that havea global information of the available resources and of theirconnectivity. It was also shown that it is better to utilize firstthe light-trees having the maximum free capacity compared tothe light-trees having the minimum free capacity.

ACKNOWLEDGMENT

This work was supported by the Cyprus Research Pro-motion Foundation’s Framework Programme for Research,Technological Development and Innovation (DESMI 2009-2010), co-funded by the Republic of Cyprus and the EuropeanRegional Development Fund, and specifically under GrantTPE/EPIKOI/0311(BIE)/11.

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