research article longest path reroute to optimize the...

Research ArticleLongest Path Reroute to Optimize the Optical MulticastRouting in Sparse Splitting WDM Networks

Huanlin Liu Hongyue Dai Fei Zhai Yong Chen and Chengying Wei

School of Communication and Information Engineering Chongqing University of Posts and TelecommunicationsChongqing 400065 China

Correspondence should be addressed to Huanlin Liu liuhlcqupteducn

Received 9 September 2015 Accepted 19 November 2015

Academic Editor Vasily Spirin

Copyright copy 2015 Huanlin Liu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Limited by the sparse light-splitting capability in WDM networks some nodes need to reroute the optical packet to differentdestination nodes with the high cost of routing for reducing packet loss possibility In the paper the longest path rerouteoptimization algorithm is put forward to jointly optimize the multicast routing cost and wavelength channel assignment cost forsparse splitting WDM networks Based on heuristic algorithms the longest path reroute routing algorithm calls multiple longestpaths in existing multicast tree to reroute the path passing from the nodes which are violating the light-splitting constraint to thenodes which are not violating light-splitting constraint with fewwavelength channels and low rerouting cost And a wavelength costcontrol factor is designed to select the reroute path with the lowest cost by comparing the multicast rerouting path cost incrementwith the equivalent wavelength channel required cost increment By adjusting wavelength cost control factor we can usually getthe optimizedmulticast routing according to the actual network available wavelength conversion cost Simulation results show thatthe proposed algorithm can get the low-cost multicast tree and reduce the required number of wavelength channels

1 Introduction

Optical multicast has attracted much considerable interestdue to supporting efficiently the transport for multicastapplication and providing flexible access to the immensebandwidth of the optical fiber and WDM networks [1ndash6]The classical multicast requests are realized by the way ofrepeating unicast in optical layer because of the constraintby network node light-splitting and leading to the problemof low wavelength resource utilization Therefore how tosupport multicast application in optical WDM networks isbecoming a research topic in recent years Several researchersstudied the multicast problem in optical networks with allor sparse multicast capable (MC) nodes But the problemanalyzed in [7] is that the MC node is complicated andexpensive So Ali and Deogun proposed a low-cost novelarchitecture called Tap-and-Continue (TaC) to constructoptical multicast node architecture without MC nodes [7]The proposed TaC node can reduce the routing cost for theroute from source to destination which is constructed as atrial instead of fibers link in MC node

In optical WDM networks an efficient solution of themulticast routing problem is to construct a multicast treewhich covers the networkrsquos source and all the destinationnodes [8 9] Unlike the multicast routing problem in IPlayer the establishment of the optical multicast routing notonly needs to determine a route for the source to eachdestination node but also needs to assign an idle wavelengthchannel for this route under certain constraints such as nodelight-splitting and wavelength number limit The problemof optical multicast routing belongs to the classical NP-complete problem The approximate optimal solution basedon heuristic algorithms is an available method [10ndash12] Afterproposing a low-cost novel architecture called Tap-and-Continue (TaC) for realizing multicast Ali and Deogundefined and formulated the problem of routing a multicastsession in a network equipped only with TaC cross-connectsand a heuristic algorithm multiple-destination trail (MDT)is proposed to find the low-cost multicast routing for themulticast request [7] For solving the routing problem ofmultiple-destination minimum-cost trail in WDM networksequipped only with TaC cross-connects the authors in [7]

Hindawi Publishing CorporationInternational Journal of OpticsVolume 2015 Article ID 489356 6 pageshttpdxdoiorg1011552015489356

2 International Journal of Optics

analyzed the routing optimization by finding an optimal trailthat starts from a source node and visits all destinationsTo decrease the optimization methodrsquos complexity Ali andDeogun developed a heuristic MDT algorithm which finds afeasible trail in polynomial time [7]MDTalgorithm includedtwo steps [7] In Step 1 a Steiner tree for themulticast sessionwas found by using the MPH (minimum path heuristic) InStep 2 rerouting around this tree was performed Reroutingallows internal nodes that have two or more branches toaccommodate the multicast connection But for the samemulticast request the cost of establishing a trail is higherthan that of establishing a route with optical tree structureIn [10 11 13] four centralized algorithms are put forwardto construct light-forest with sparse MC nodes to satisfythe optical multicast request But these algorithms do notconsider the optimization of the routing cost A distributedoptical multicast routing algorithm was proposed in [14]Although the algorithm can solve the routing andwavelengthassignment problem simultaneously it also only optimizesthe multicast routing cost without considering the numberof wavelengths cost Therefore the existing optical multicastrouting optimizes the multicast routing cost or optimizesnumber of wavelengths required independently which leadsto the problem of high wavelength resource consumption orhigh multicast routing cost potentially

In this paper we consider the reduction of multicastrouting cost and number of wavelengths as an integratedoptimization goal for WDM networks with TaC nodes Thelongest path reroute joint optimization of wavelength andcost (LPR-JOWC) based on heuristic algorithm is proposedto jointly optimize multicast routing and wavelength assign-ment cost LPR-JOWC algorithm reroutes the nodes on mul-ticast route tree which violate the light-splitting constraintthrough longest path reroute strategy to get low numberof wavelengths for keeping more destinations share thewavelength channelwith low routing cost and lowwavelengthchannel consumption

The rest of the paper is organized as follows In Section 2we discuss the optical multicast routing problem And weput forward a longest path reroute to jointly optimize thererouting cost and required wavelength assignment cost inSection 3 In Section 4 the longest path reroute reroutingperformance is simulated and analyzed in Section 5

2 Optical Multicast RoutingProblem Description

The wavelength-routed optical switching node architecturewith TaC equipment configured with 119873 inputoutput fibers119882 wavelengths channel per fiber is shown in Figure 1 Thesource node can replicate an optical packet to multiplepackets while the relay node with TaC should satisfy thelight-splitting constraint

The multicast routing needs to satisfy the followingconstraints

(1) Wavelength Continuity Constraint A light-path mustuse the same wavelength on all the links from source

TCM

1

2

1

2

NN

1205821 middot middot middot 120582w






Dem

uxD

emux

Dem

ux

WRS

WRS

WRS

1205821

1205822

120582w

1205821 1205822 120582w 1205821 1205822 120582w

SW

SW

SW

SW

SW

SW

SW

SW

SW

Mux

Mux

Mux

Tx RxLocal station

1205821 middot middot middot 120582w wavelengthsWRS wavelength routed switchTx transmitterMux multiplexer

SW switchTCM TaC modulesRx receiverDemux demultiplexer

TCM

TCM

Figure 1 Optical switching node architecture with TaC

1

1

3

2

2

2

13

2

2

3

1

2

6 7

1

534

s

Source node

Destination nodes

Cost links

2

Figure 2 An example of a weighted undirected graph for multicastrouting

to destination node if the nodes in optical networksdo not have wavelength converters

(2) Wavelength Distinct Constraint All light-paths shar-ing the same link must use distinct wavelengths

(3) Light-Splitting Constraint Because TaC nodes in opti-cal network cannot serve as a branching node of themulticast tree so the degree of all the routing treenodes except the source should be less than 2

Figure 2 shows a weighted undirected graph and amulticast request 119903(119904 119863) = 119903(119904 (4 5 7)) The shortest path

International Journal of Optics 3

heuristic algorithm is used to find the lower cost tree from 119904

to 119863 and the resulting lower cost tree is marked with boldline Obviously the lower cost tree violates the light-splittingconstraint so the path 119875(119904 4) or 119875(119904 5) should be assigned toanother wavelength

An optical network can be modeled as a weightedundirected graph 119866(119881 119864 119908 119888) where 119881 is the set of nodes119864 is the set of links and 119908 is the number of wavelengthsper fiber link Each edge 119890 = (119906 V) isin 119864 is weightedby a real value named link cost 119888(119890) Assume that 119877(119904 119863)

represents the multicast requests the source node is 119904 and119863 sube (119889

1 1198892 119889

119898) sube 119881 minus 119904 represent the destination

nodes The node set 119904 cup 119863 is named the multicast group Anoptical multicast tree 119879(119881

119879 119864119879) is a subgraph of 119866 spanning

the source node 119904 and the set of destination nodes 119863 sube 119881 minus

119904 119881119879isin 119881 119864

119879isin 119864

According to the above definition let 119879119896(119904 119863119896) be the

multicast tree for the request 119877(119904 119863) on the 119896th wavelengthoptical network here 119863

119896isin 119863 The cost of optical tree 119879

119896is

defined as the sum of the cost of all fiber link edges on tree119879119896 which is shown in

119888 (119879119896(119904 119863119896)) = sum

119890isin119879119896(119904119863119896)

119888 (119890) (1)

Similarly the total cost of multicast tree 119879119896with same

source node on different wavelength networks is defined in

119888 (119879) =

119908

sum

119896=1

119888 (119879119896(119904 119863119896)) (2)

The number of wavelengths required is defined as (3) Ifthe wavelength 119896 is used by the multicast tree 119879 then 119910

119896= 1

otherwise 119910119896= 0

119882(119879) =

119908

sum

119896=1

119910119896 (3)

The optical multicast routing algorithm with joint opti-mization of wavelength and route cost needs to find an opticalmulticast tree with low route cost between a source andthe destinations while assigning fewer wavelengths for theroute treewhile nonviolating light-splitting constraint So theoptimization objective function of the problem is defined asfollows

(1) optimization objective function

min[

119908

sum

119896=1

119888 (119879119896(119904 119863119896)) + 120575 times 119882 (119879)] (4)

(2) restricted by

sum

120582isin119908

119875120582

(119904119889119894)le 1 119889

119894isin 119863 (5)

sum

119889119894isin119863

119875120582

(119904119889119894)(119906 V) le 1 120582 isin 119908 (6)

Equations (5) and (6) represent the wavelength indepen-dence constraint and the wavelength continuity constraint

respectively If light-path uses wavelength 120582 on the route treewhen packet traverses from source to all destination nodes119875120582

(119904119889119894)= 1 otherwise 119875120582

(119904119889119894)= 0 If light-path uses wavelength

120582 between the intermediate nodes 119906 and V here (119906 V) isin 119864 and119906 V isin 119881 then 119875

120582

(119904119889119894)(119906 V) = 1 otherwise 119875120582

(119904119889119894)(119906 V) = 0

(3) Wavelength assignment cost control factor 120575 120575 isdefined as the ratio of the wavelength assignment cost to thereroute path tree cost increment According to the controlfactor we can flexibly implement the minimized cost toresolve the light-splitting constraint by rerouting the treeor increase wavelength assignment To reduce the routingcost rerouting the path to destination with a new wavelengthmay increase the number of wavelengths Thus there is atradeoff between the choices of a routing path on used ornot new wavelength If the 120575 is large which indicates thatthe wavelength channel is expensive and scare source itmay prefer to find a longer rerouting path on the samewavelength network rather than a shorter routing path ona new wavelength network to get total low cost Otherwiseit may prefer to find the shorter rerouting path on a newwavelength network

3 Longest Path Rerouting Algorithm

According to the definition of optical multicast routingproblem the optimization goal of the problem is to reducethe multicast routing cost which is related to the routepath and number of wavelengths Since the problem belongsto NP-complete problem so in this paper we propose anoptimized solution based on heuristic algorithm to solve theoptical multicast routing problem with joint optimizationof wavelength and cost which is called longest path reroutejoint optimization of wavelength and cost (LPR-JOWC)algorithm LPR-JOWC algorithm includes two processesFirst we construct the lower cost multicast tree by usingshortest path algorithm Second we reroute the nodes on thetreewhich violate the light-splitting constraint by LPR-JOWCalgorithm

In the LPR-JOWC algorithm the longer path has thepriority to reroute the tree with low tree route cost byreducing the number of wavelengths The process of LPR-JOWC algorithm is as follows firstly the shortest pathalgorithm is used to find the lower cost multicast route tree119879 from source to all destinations Secondly some tree pathsare modified and rerouted to keep away from the nodes onthe tree which violate the light-splitting constraint wherewe first check the farthest path from source node to onedestination with maximal route cost to reroute the violationnode Lastly the available wavelengths are assigned to themodifiedmulticast treeTherefore the LPR-JOWC algorithmguarantees that the multicast tree requires fewer wavelengthsand lower route cost also

In order to describe the LPR-JOWC algorithm somedefinitions are introduced in advance as follows

(1) 119879(V119894) is the subtree whose root is node set V

119894 where V

119894

is the node set which is directly adjacent to the sourcenode 119904 with 119894 node degree


(2) Edge(119875(119904 119889)) is the set of all edges on the path119875(119904 119889)

(3) Far(V119894) is the farthest destination node with the

maximal route cost in subtree 119879(V119894)

(4) Live(Far(V119894)) is the edge set whose one endpoint

belonged to Far(V119894)

(5) UNREACH is the set of multicast destination nodeswhich have not been routed by multicast route tree

(6) 1198661015840 is the graph of 119866 that remained by removing edgesand nodes included in set of Edge(119875(119904 119889))

(7) 119875119895(119904 119889) is the fewer cost paths from source node 119904

to destination node 119889 in the 119895th wavelength layeredgraph 119866

119895

(8) 119888(119875119895(119904 119889)) is the cost of path 119875119895(119904 119889)

So the steps of LPR-JOWC algorithm are shown asfollows

Step 1 Input network topology graph 119866(119881 119864 119908 119888) Initializethe wavelength cost control factor 120575 value which representsthe ratio of wavelength cost and reroute path length costincrement 119896 is the wavelength index setting 119896 = 1 119866

119896

represents 119896th layered wavelength network in 119908 wavelengthsnetwork 119866

Step 2 Let 119866119896= 119866 Call the shortest path algorithm to find

the lower cost multicast tree 119879 for multicast request If thereare nodes on the tree119879 violating the light-splitting constraintthen go to Step 3 Otherwise output the lower cost multicasttree and go to the end

Step 3 Divide the tree 119879 into subtrees according to degreeof source node 119904 and store the subtree rooted by V

119894as 119879(V

119894)

For each subtree find the farthest (maximal cost) destinationFar(V119894) the path 119875

119896(119904 Far(V

119894)) the Edge(119875119896(119904 Far(V

119894))) and

the lower cost path of each Far(V119894) in subtree 119879(V

119894) Remove

the Edge(119875119896(119904 Far(V119894))) from graph 119866

119896and obtain subgraph

1198661015840

119896 Then construct node set UNREACH and edge set

Live(Far(V119894)) in graph 119866

119896 If UNREACH is not empty and

119896 le 119908 go to Step 4 else output the cost optimized multicasttree 119879

Step 4 Choose the farthest destination node in set ofUNREACH and store it in variable V Construct a subgraph119878119866 for each Far(V

119894) in subtree 119879(V

119894) and let 119878119866 = 119866

1015840

119895 1198661015840

119895cup

Live(Far(V119894)) 119895 = 1 2 119896 + 1

Step 5 Find the lower reroute cost path for node V in 119878119866

set If the path 119875(119904 V) is found then we assign path 119875(119904 V) tothe corresponding wavelength 119895 and remove the destinationV and other destinations passed by path (119875(119904 V)) from setUNREACH Edge(119875(119904 V)) is excluded from graph 119866

1015840

119895 and

renew Live(Far(V119894)) Else let 119896 = 119896+1 If 119896 gt 119908 the algorithm

stops and returns FALSE If 119896 le 119908 go to Step 2

Furthermore some notations in the algorithm need to beintroduced and stated here

(1) If 119875119895(119904 V) passes destinations V

1 V2 V

119896

in UNREACH on 1198661015840

119895 then cost 119888(119875(119904 V)) =

119888(119875(119904 V)) minus 119888(119875(119904 V1)) minus sdot sdot sdot minus 119888(119875(119904 V

119896))

(2) If 119875119895(119904 V) uses the (119896 + 1)th wavelength graph where119895 is equal to 119896 + 1 the cost of path 119875

119895(119904 V) should be

increased by 120575

An example of LPR-JOWC algorithm execution is shownin Figure 3 A multicast request is 119903(119904 1 2 3 4 5 6) andvalue of parameter 120575 is set to 4 First as shown in Figure 3(a)we get the lower cost tree 119879 by performing Step 3 Thenwe find 119866

1015840

1= 1198661minus Edge(119904 2) minus Edge(119904 6) minus Edge(119904 4) and

UNREACH = 1 3 in Figure 3(b) Because destination 3 isthe farthest node in UNREACH by Steps 4 and 5 we tryto find the lower cost path from 119904 to 3 We find the path1198751(119904 3) = 119904 rarr 9 rarr 13 rarr 3 in119866

1015840

1 and 119888(119875

1(119904 3)) = 15 the

extended path 1198751(2 3) = 2 rarr 11 rarr 3 in 119866

1015840

1cup Live(Far(7))

119888(1198751(2 3)) = 9 path 119875

2(119904 3) = 119904 rarr 7 rarr 14 rarr 3

119888(1198752(119904 3)) = 7 + 120575 = 11 in 119866

2 The extended path 119875

1(2 3)

has lower cost so destination 3 is routed by the extended pathof destination 2 Similarly we find the path 119875

1(3 1) = 3 rarr

13 rarr 1 119888(1198751(3 1)) = 3 The number of wavelengths used is1The final result is shown in Figure 3(d) marked in black linewith one number of wavelengths

4 Simulation and Analysis

Performance of the proposed LPR-JOWC algorithm is sim-ulated and analyzed in this section The multiple-destinationtrial (MDT) heuristic algorithm proposed in [7] was used forcomparisons with our proposed LPR-JOWC algorithm Togenerate randomnetworks we use a random graph generatordeveloped by Salama et al [15] In thismodel edges are placedconnecting the pair of nodes 119906 V with probability

119875119890(119906 V) = 120573 exp minus119889 (119906 V)

119871120572 (7)

where 119889(119906 V) is the link distance from node 119906 to V and 119871 isthe maximum distance between two nodes We set 120572 = 015120573 = 22 The link cost function 119888(119890) is defined as the currenttotal bandwidth reserved on the link 119890 Source node anddestination nodes (multicast requests) are randomly selectedin the graph Simulation is being run for 200 times withdifferent topologies

The average tree costs of LPR-JOWC andMDT algorithmunder different number of destinations are shown in Figure 4In Figure 4 we can see that as the destination node numbersincrease the average tree cost also rises With the increaseof destination nodes more and more nodes on shortest treeviolate the light-splitting This leads to more paths needingto reroute with the longer path or assign new wavelengthchannel and therefore to more multicast tree route cost orwavelength cost Thus the average tree cost increases as thenumber of destination nodes increases But the average treecost generated by the LPR-JOWC algorithm is lower than the


s

6

1145

7 10

2

8

3

4

(a) The lower cost tree 119879

s

17

13

9

1516

311

1

1

3

11

10

23 1

(b) 11986610158401

s

15

13

9

2 311

1

3

11

10

23 1

16 17

6

32

1

(c) 11986610158401cup Live(Far(7))

s

10

4

5

12

61716

2

14

7

15

8

3

1

13

9

2

2

5

3

4

38

11 5

6

3

6

1

2

3

7

2

4

4

3

42

5

6

11 13

9

1

10

4

(d) LPR-JOWC optimized cost tree 119879

Figure 3 An example of LPR-JOWC algorithm execution

10 20 30 40 5050

100

150

200

250

300

350

400

450

The a

vera

ge tr

ee co

st

Number of destinations

MDTLPR 120575 = 50

LPR 120575 = 100

LPR 120575 = 150

Figure 4 Average tree cost versus number of destinations

MDT algorithm The reason is that the cost of establishing atrail is higher than that of establishing an optimized reroutetree for the same multicast request Furthermore as thewavelength control factor 120575 increases the multicast tree costincreases also But the multicast tree cost increasing speedis low when the wavelength cost control factor 120575 is low Thereason is that the proportion of new assignment wavelengthcost is little in the total re-route multicast tree cost

Figure 5 shows the number of required wavelength chan-nels versus the number of destination nodes for the proposedLPR-JOWC algorithm when the number of network nodesis 50 In Figure 5 we can observe that the consumptionwavelength number increases as the multicast requirementdestination nodes increases The reason is that the moremulticast destination nodes need more wavelength channelconsumption to avoid the node light-splittingThus themul-ticast tree total cost increases Moreover as the wavelengthcontrol factor 120575 increases the consumptionwavelength num-ber decreases The reason is that more multicast tree nodeschoose the longest path reroute to avoid the light-splittingand to decrease the increment of number of wavelengths So


10 20 30 40 50

2

4

6

8

10

12

14

16N

umbe

r of w

avele

ngth

s


LPR-JOWC 120575 = 50

LPR-JOWC 120575 = 100

LPR-JOWC 120575 = 150

Figure 5 Required number of wavelength channels versus numberof destinations

the wavelength cost control factor 120575 balances the number ofwavelengths

5 Conclusions

In this paper we propose an optimized LPR-JOWC to solvethe optical multicast routing problemwith joint optimizationof wavelength and cost based on heuristic algorithm Inthe LPR-JOWC algorithm the longest path has the priorityto reroute node violating the light-splitting to reduce thererouting total cost by decreasing the number of wavelengthsThe simulation and analysis indicate that the proposed LPR-JOWC algorithm can get the low-cost multicast tree andalso can reduce the number of wavelengths The LPR-JOWCalgorithm performs better in terms of average tree cost incomparison with the existing MDT algorithm

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was funded by the National Nature Sci-ence Foundation of China (NSFC 61275077) by the Scien-tific Research Fund of Chongqing Municipal Commission(KJ1400421) and by the Basic and Frontier Research Programof Chongqing (CSTC 2015jcyjA40024)

References

[1] D D Le F Zhou and M Molnar ldquoMinimizing blocking prob-ability for the multicast routing and wavelength assignment

problem inWDMnetworks exact solutions and heuristic algo-rithmsrdquo Journal of Optical Communications and Networkingvol 7 no 1 pp 36ndash48 2015

[2] H-L Liu X Xue Y Chen Q Fang and S Huang ldquoAn efficientdynamic multicast traffic-grooming algorithm for WDM net-worksrdquo Photonic Network Communications vol 26 no 2 pp95ndash102 2013

[3] J Lee B C Yeo J-S Kim M S Jang and J K Choi ldquoEnergyefficient scalable video coding based cooperative multicastscheme with selective layer forwardingrdquo IEEE CommunicationsLetters vol 17 no 6 pp 1116ndash1119 2013

[4] H Liu X Hu Y Chen T Hu and S Huang ldquoSchedulingbased onminimal conversion degreewith respect towavelengthconversion and coding in optical multicast noderdquo IEEE Com-munications Letters vol 18 no 11 pp 1935ndash1938 2014

[5] S Huang Y Wang and H Liu ldquoMulti-source multi-corerouting algorithm based on network coding in optical multicastnetworkrdquo Journal of Chongqing University of Posts and Telecom-munications vol 26 no 2 pp 143ndash149 2014

[6] X Wang M Hou X Yi and M Huang ldquoA QoS multicastrouting algorithm based on tabu-hierarchy genetic algorithm inIPDWDMoptical Internetrdquo inNetwork Architectures Manage-ment and Applications III vol 6022 of Proceedings of SPIE pp802ndash808 Shanghai China December 2005

[7] MAli and J S Deogun ldquoCost-effective implementation ofmul-ticasting in wavelength-routed networksrdquo Journal of LightwaveTechnology vol 18 no 12 pp 1628ndash1638 2000

[8] L H Sahasrabuddhe and B Mukherjee ldquoLight-trees opticalmulticasting for improved performance in wavelength-routednetworksrdquo IEEE Communications Magazine vol 37 no 2 pp67ndash73 1999

[9] X Zhang J Y Wei and C Qiao ldquoConstrained multicastrouting in WDM networks with sparse light splittingrdquo Journalof Lightwave Technology vol 18 no 12 pp 1917ndash1927 2000

[10] F Zhou M Molnar and B Cousin ldquoDistance priority basedmulticast routing in WDM networks considering sparse lightsplittingrdquo in Proceedings of the 11th IEEE Singapore InternationalConference on Communication Systems (ICCS rsquo08) pp 709ndash714IEEE Guangzhou China November 2008

[11] H Liu Y Xie Li Zhen and B Zhang ldquoStudy on minimizingnetwork coding links based on immune algorithm for opticalmulticast networkrdquo Journal of Chongqing University of Posts andTelecommunications vol 23 no 4 pp 384ndash388 2011

[12] W-Y Tseng and S-Y Kuo ldquoAll-optical multicasting onwavelength-routedWDM networks with partial replicationrdquo inProceedings of the IEEE International Conference on InformationNetworking (ICOIN rsquo01) pp 813ndash818 Beppu City Japan 2001

[13] C-Y Hsieh andW Liao ldquoAll-optical multicast routing in sparsesplitting WDM networksrdquo IEEE Journal on Selected Areas inCommunications vol 25 no 6 pp 51ndash62 2007

[14] T Rahman G Ellinas and M Ali ldquoLightpath- and light-tree-based groupcast routing and wavelength assignment inmesh optical networksrdquo Journal of Optical Communications andNetworking vol 1 no 2 Article ID 5173418 pp A44ndashA55 2009

[15] H F Salama D S Reeves and Y Viniotis ldquoEvaluation ofmulticast routing algorithms for real-time communicationon high-speed networksrdquo IEEE Journal on Selected Areas inCommunications vol 15 no 3 pp 322ndash345 1997

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analyzed the routing optimization by finding an optimal trailthat starts from a source node and visits all destinationsTo decrease the optimization methodrsquos complexity Ali andDeogun developed a heuristic MDT algorithm which finds afeasible trail in polynomial time [7]MDTalgorithm includedtwo steps [7] In Step 1 a Steiner tree for themulticast sessionwas found by using the MPH (minimum path heuristic) InStep 2 rerouting around this tree was performed Reroutingallows internal nodes that have two or more branches toaccommodate the multicast connection But for the samemulticast request the cost of establishing a trail is higherthan that of establishing a route with optical tree structureIn [10 11 13] four centralized algorithms are put forwardto construct light-forest with sparse MC nodes to satisfythe optical multicast request But these algorithms do notconsider the optimization of the routing cost A distributedoptical multicast routing algorithm was proposed in [14]Although the algorithm can solve the routing andwavelengthassignment problem simultaneously it also only optimizesthe multicast routing cost without considering the numberof wavelengths cost Therefore the existing optical multicastrouting optimizes the multicast routing cost or optimizesnumber of wavelengths required independently which leadsto the problem of high wavelength resource consumption orhigh multicast routing cost potentially

In this paper we consider the reduction of multicastrouting cost and number of wavelengths as an integratedoptimization goal for WDM networks with TaC nodes Thelongest path reroute joint optimization of wavelength andcost (LPR-JOWC) based on heuristic algorithm is proposedto jointly optimize multicast routing and wavelength assign-ment cost LPR-JOWC algorithm reroutes the nodes on mul-ticast route tree which violate the light-splitting constraintthrough longest path reroute strategy to get low numberof wavelengths for keeping more destinations share thewavelength channelwith low routing cost and lowwavelengthchannel consumption

The rest of the paper is organized as follows In Section 2we discuss the optical multicast routing problem And weput forward a longest path reroute to jointly optimize thererouting cost and required wavelength assignment cost inSection 3 In Section 4 the longest path reroute reroutingperformance is simulated and analyzed in Section 5

2 Optical Multicast RoutingProblem Description

The wavelength-routed optical switching node architecturewith TaC equipment configured with 119873 inputoutput fibers119882 wavelengths channel per fiber is shown in Figure 1 Thesource node can replicate an optical packet to multiplepackets while the relay node with TaC should satisfy thelight-splitting constraint

The multicast routing needs to satisfy the followingconstraints

(1) Wavelength Continuity Constraint A light-path mustuse the same wavelength on all the links from source

TCM

1

2

1

2

NN







Dem

uxD

emux

Dem

ux

WRS

WRS

WRS

1205821

1205822

120582w

1205821 1205822 120582w 1205821 1205822 120582w

SW

SW

SW

SW

SW

SW

SW

SW

SW

Mux

Mux

Mux

Tx RxLocal station

1205821 middot middot middot 120582w wavelengthsWRS wavelength routed switchTx transmitterMux multiplexer

SW switchTCM TaC modulesRx receiverDemux demultiplexer

TCM

TCM

Figure 1 Optical switching node architecture with TaC

1

1

3

2

2

2

13

2

2

3

1

2

6 7

1

534

s

Source node

Destination nodes

Cost links

2

Figure 2 An example of a weighted undirected graph for multicastrouting

to destination node if the nodes in optical networksdo not have wavelength converters

(2) Wavelength Distinct Constraint All light-paths shar-ing the same link must use distinct wavelengths

(3) Light-Splitting Constraint Because TaC nodes in opti-cal network cannot serve as a branching node of themulticast tree so the degree of all the routing treenodes except the source should be less than 2

Figure 2 shows a weighted undirected graph and amulticast request 119903(119904 119863) = 119903(119904 (4 5 7)) The shortest path






1 1198892 119889





119904 119881119879isin 119881 119864

119879isin 119864




119896is


119888 (119879119896(119904 119863119896)) = sum

119890isin119879119896(119904119863119896)

119888 (119890) (1)



119888 (119879) =

119908

sum

119896=1

119888 (119879119896(119904 119863119896)) (2)


119896= 1

otherwise 119910119896= 0

119882(119879) =

119908

sum

119896=1

119910119896 (3)



min[

119908

sum

119896=1

119888 (119879119896(119904 119863119896)) + 120575 times 119882 (119879)] (4)

(2) restricted by

sum

120582isin119908

119875120582

(119904119889119894)le 1 119889

119894isin 119863 (5)

sum

119889119894isin119863

119875120582

(119904119889119894)(119906 V) le 1 120582 isin 119908 (6)



(119904119889119894)= 1 otherwise 119875120582



120582

(119904119889119894)(119906 V) = 1 otherwise 119875120582

(119904119889119894)(119906 V) = 0







119894 where V

119894












119895




119896





119894as 119879(V

119894)


119896(119904 Far(V

119894)) the Edge(119875119896(119904 Far(V

119894))) and


119894) Remove



1198661015840






119894) in subtree 119879(V

119894) and let 119878119866 = 119866

1015840

119895 1198661015840

119895cup

Live(Far(V119894)) 119895 = 1 2 119896 + 1



1015840

119895 and





1 V2 V

119896


119895 then cost 119888(119875(119904 V)) =


119896))


119895(119904 V) should be

increased by 120575


1015840



1015840

1 and 119888(119875

1(119904 3)) = 15 the


1015840

1cup Live(Far(7))

119888(1198751(2 3)) = 9 path 119875

2(119904 3) = 119904 rarr 7 rarr 14 rarr 3

119888(1198752(119904 3)) = 7 + 120575 = 11 in 119866


1(2 3)


1(3 1) = 3 rarr




119875119890(119906 V) = 120573 exp minus119889 (119906 V)

119871120572 (7)




s

6

1145

7 10

2

8

3

4


s

17

13

9

1516

311

1

1

3

11

10

23 1

(b) 11986610158401

s

15

13

9

2 311

1

3

11

10

23 1

16 17

6

32

1

(c) 11986610158401cup Live(Far(7))

s

10

4

5

12

61716

2

14

7

15

8

3

1

13

9

2

2

5

3

4

38

11 5

6

3

6

1

2

3

7

2

4

4

3

42

5

6

11 13

9

1

10

4



10 20 30 40 5050

100

150

200

250

300

350

400

450

The a

vera

ge tr

ee co

st


MDTLPR 120575 = 50

LPR 120575 = 100

LPR 120575 = 150





10 20 30 40 50

2

4

6

8

10

12

14

16N

umbe

r of w

avele

ngth

s


LPR-JOWC 120575 = 50

LPR-JOWC 120575 = 100

LPR-JOWC 120575 = 150



5 Conclusions




Acknowledgments


References






















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics








1 1198892 119889





119904 119881119879isin 119881 119864

119879isin 119864




119896is


119888 (119879119896(119904 119863119896)) = sum

119890isin119879119896(119904119863119896)

119888 (119890) (1)



119888 (119879) =

119908

sum

119896=1

119888 (119879119896(119904 119863119896)) (2)


119896= 1

otherwise 119910119896= 0

119882(119879) =

119908

sum

119896=1

119910119896 (3)



min[

119908

sum

119896=1

119888 (119879119896(119904 119863119896)) + 120575 times 119882 (119879)] (4)

(2) restricted by

sum

120582isin119908

119875120582

(119904119889119894)le 1 119889

119894isin 119863 (5)

sum

119889119894isin119863

119875120582

(119904119889119894)(119906 V) le 1 120582 isin 119908 (6)



(119904119889119894)= 1 otherwise 119875120582



120582

(119904119889119894)(119906 V) = 1 otherwise 119875120582

(119904119889119894)(119906 V) = 0







119894 where V

119894












119895




119896





119894as 119879(V

119894)


119896(119904 Far(V

119894)) the Edge(119875119896(119904 Far(V

119894))) and


119894) Remove



1198661015840






119894) in subtree 119879(V

119894) and let 119878119866 = 119866

1015840

119895 1198661015840

119895cup

Live(Far(V119894)) 119895 = 1 2 119896 + 1



1015840

119895 and





1 V2 V

119896


119895 then cost 119888(119875(119904 V)) =


119896))


119895(119904 V) should be

increased by 120575


1015840



1015840

1 and 119888(119875

1(119904 3)) = 15 the


1015840

1cup Live(Far(7))

119888(1198751(2 3)) = 9 path 119875

2(119904 3) = 119904 rarr 7 rarr 14 rarr 3

119888(1198752(119904 3)) = 7 + 120575 = 11 in 119866


1(2 3)


1(3 1) = 3 rarr




119875119890(119906 V) = 120573 exp minus119889 (119906 V)

119871120572 (7)




s

6

1145

7 10

2

8

3

4


s

17

13

9

1516

311

1

1

3

11

10

23 1

(b) 11986610158401

s

15

13

9

2 311

1

3

11

10

23 1

16 17

6

32

1

(c) 11986610158401cup Live(Far(7))

s

10

4

5

12

61716

2

14

7

15

8

3

1

13

9

2

2

5

3

4

38

11 5

6

3

6

1

2

3

7

2

4

4

3

42

5

6

11 13

9

1

10

4



10 20 30 40 5050

100

150

200

250

300

350

400

450

The a

vera

ge tr

ee co

st


MDTLPR 120575 = 50

LPR 120575 = 100

LPR 120575 = 150





10 20 30 40 50

2

4

6

8

10

12

14

16N

umbe

r of w

avele

ngth

s


LPR-JOWC 120575 = 50

LPR-JOWC 120575 = 100

LPR-JOWC 120575 = 150



5 Conclusions




Acknowledgments


References






















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics













119895




119896





119894as 119879(V

119894)


119896(119904 Far(V

119894)) the Edge(119875119896(119904 Far(V

119894))) and


119894) Remove



1198661015840






119894) in subtree 119879(V

119894) and let 119878119866 = 119866

1015840

119895 1198661015840

119895cup

Live(Far(V119894)) 119895 = 1 2 119896 + 1



1015840

119895 and





1 V2 V

119896


119895 then cost 119888(119875(119904 V)) =


119896))


119895(119904 V) should be

increased by 120575


1015840



1015840

1 and 119888(119875

1(119904 3)) = 15 the


1015840

1cup Live(Far(7))

119888(1198751(2 3)) = 9 path 119875

2(119904 3) = 119904 rarr 7 rarr 14 rarr 3

119888(1198752(119904 3)) = 7 + 120575 = 11 in 119866


1(2 3)


1(3 1) = 3 rarr




119875119890(119906 V) = 120573 exp minus119889 (119906 V)

119871120572 (7)




s

6

1145

7 10

2

8

3

4


s

17

13

9

1516

311

1

1

3

11

10

23 1

(b) 11986610158401

s

15

13

9

2 311

1

3

11

10

23 1

16 17

6

32

1

(c) 11986610158401cup Live(Far(7))

s

10

4

5

12

61716

2

14

7

15

8

3

1

13

9

2

2

5

3

4

38

11 5

6

3

6

1

2

3

7

2

4

4

3

42

5

6

11 13

9

1

10

4



10 20 30 40 5050

100

150

200

250

300

350

400

450

The a

vera

ge tr

ee co

st


MDTLPR 120575 = 50

LPR 120575 = 100

LPR 120575 = 150





10 20 30 40 50

2

4

6

8

10

12

14

16N

umbe

r of w

avele

ngth

s


LPR-JOWC 120575 = 50

LPR-JOWC 120575 = 100

LPR-JOWC 120575 = 150



5 Conclusions




Acknowledgments


References






















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




s

6

1145

7 10

2

8

3

4


s

17

13

9

1516

311

1

1

3

11

10

23 1

(b) 11986610158401

s

15

13

9

2 311

1

3

11

10

23 1

16 17

6

32

1

(c) 11986610158401cup Live(Far(7))

s

10

4

5

12

61716

2

14

7

15

8

3

1

13

9

2

2

5

3

4

38

11 5

6

3

6

1

2

3

7

2

4

4

3

42

5

6

11 13

9

1

10

4



10 20 30 40 5050

100

150

200

250

300

350

400

450

The a

vera

ge tr

ee co

st


MDTLPR 120575 = 50

LPR 120575 = 100

LPR 120575 = 150





10 20 30 40 50

2

4

6

8

10

12

14

16N

umbe

r of w

avele

ngth

s


LPR-JOWC 120575 = 50

LPR-JOWC 120575 = 100

LPR-JOWC 120575 = 150



5 Conclusions




Acknowledgments


References






















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics




10 20 30 40 50

2

4

6

8

10

12

14

16N

umbe

r of w

avele

ngth

s


LPR-JOWC 120575 = 50

LPR-JOWC 120575 = 100

LPR-JOWC 120575 = 150



5 Conclusions




Acknowledgments


References






















FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics








FluidsJournal of


Journal of










Superconductivity




GravityJournal of








Journal of






Volume 2014


PhotonicsJournal of


Journal of

Biophysics



research article longest path reroute to optimize the...

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