Liu Zhe,Guo Wei,Deng Changlin,Hu Weisheng

State Key Lab of Advanced Optical Communication Systems and Networks,Shanghai Jiao Tong University,Shanghai 200240,China

Wavelength dimensioning for wavelength-routed WDM satellite network

Liu Zhe,Guo Wei*,Deng Changlin,Hu Weisheng

State Key Lab of Advanced Optical Communication Systems and Networks,Shanghai Jiao Tong University,Shanghai 200240,China

Internet and broadband applications driven by data traffic demand have become key drivers for satellite constellations.The key technology to satisfy the high capacity requirements between satellites is optical satellite networks by means of wavelength division multiplexing intersatellite links(ISLs)with wavelength routing(WDM-OSN).Due to the limited optical amplifier bandwidth onboard the satellite,it is important to minimize the wavelength requirements to provision requests.However,ISLs should be dynamically established and deleted for each satellite according to its visible satellites.Furthermore,different link assignments will result in different topologies,hence yielding different routings and wavelength assignments.Thus,a perfect match model-based link assignment scheme(LAS-PMM)is proposed to design an appropriate topology such that shorter path could be routed and less wavelengths could be assigned for each ISL along the path.Finally,simulation results show that in comparison to the regular Manhattan street network(MSN)topology,wavelength requirements and average end-to-end delay based on the topology generated by LAS-PMM could be reduced by 24.8%and 12.4%,respectively.

1.Introduction

Internet and broadband applications driven by data traffic demand have become key drivers for satellite constellations.1In order to provide broadband communications to consumers,several satellite low-earth-orbit(LEO)constellations,which exhibit significantly low earth-to-space delay2,3,were constructedsuch as Orbcomm-2,4Globalstar-2,5Iridium-Next.6In these satellite constellations,Iridium-Next adopts inter-satellite links(ISLs)technology,while the others do not.The key technology to satisfy the high capacity requirements between satellites is optical satellite networks(OSN)by means of wavelength division multiplexing ISLs with wavelength routing(WDM-OSN),where WDM technology could satisfy the high bandwidth requirements by establishing multiple wavelength channels in each ISL and wavelength routing could guarantee simple routing of the optical channels in the optical domain.7,8In order to accommodate a request,a path is routed based on certain topology and the same wavelength should be assigned for each ISL along the path,namely the wavelength-continuity constraint.However,optical amplifier bandwidth onboard the satellite is limited and the wavelength spacing should maintain a safety margin for the Doppler effects.As a result,the amount of available wavelengths is finite.Thus,it is important to minimize the wavelength requirements to provision requests.

Different from terrestrial WDM optical network,each satellite could establish WDM ISL with its visible satellites until all the laser communication terminals(LCTs)onboard are assigned in WDM-OSN.Moreover,the satellite's relative position to the earth and the set of its visible satellites change continuously as it moves along its orbit.Therefore,ISLs for each satellite should be dynamically established and deleted according to its visible satellite set.Different link assignment schemes will result in different network topologies,hence yield different routings and wavelength assignments.Thus,a link assignment scheme(LAS)should design an appropriate topology such that shorter path could be routed and less wavelength could be assigned for each link along the path.

However,wavelength dimensioning of the previous works does not consider the impact of topology on routing and wavelength assignment,7,9–11and LAS of the previous works does not consider minimizing the wavelength requirements to provision requests.8,12,13For example,wavelength dimensioning is optimized on some simple regular network topologies with all LCTs active,such as ring network topology9and Manhattan street network (MSN)topology.7,10,11These regular topologies have large average inter-node distance in hops,resulting in large wavelength requirements.Some other studies focus on the target of link assignment to generate an arbitrary connected network topology,8maximize the remnant capacity of ISLs13or maximize the connectivity of network topology.14The other studies could only design topology for satellite networks with two planes.12,15,16

This paper mainly focuses on the relationship among link assignment,routing and wavelength assignment.In order to minimize the wavelength requirements to provision requests in WDM-OSN,we propose a novel link assignment scheme based on perfect match model(LAS-PMM)to design an appropriate network topology such that a shorter path could be routed and less wavelengths need to be assigned for the ISL along the path.Based on network topology generated by LAS-PMM,the partition coloring model is used to find the lowest label of wavelength channel for the assigned routing paths to provision request set.Finally,simulation results for Next-generation LEO System constellation(NeLS17)show that wavelength requirements to provision requests under network topology generated by the LAS-PMM and average end-to-end delay can be reduced by 24.8%and 12.4%,respectively,in comparison to that of the regular MSN topology.

The rest of this paper is structured as follows.Section 2 presents problem statement.Section 3 presents perfect match model-based link assignment and wavelength dimensioning.Section 4 demonstrates the effectiveness of our proposed LAS-PMM through computer simulations.Finally,concluding remarks are presented in Section 5.

2.Problem statement

In WDM-OSN,there are usually N LEO satellites evenly placed in P orbits.Each orbit consists of S satellites.The jth satellite belonging to ith orbitis denoted as v=Si,j,1≤ i≤ P,1≤ j≤ S.At each time interval,two satellites are defined to be visible from each other if they are within lineof-sight,communication ability and pointing acquisition and tracking(PAT)ability during the whole time interval.The visibility graph and network topology of WDM-OSN are denoted as M=(V,E)and G=(V,E)respectively,where V(G)and V(M)are the same node set consisting of|V(G)|satellites,E(M)and E(G)are the link set consisting of|E(M)|visibility links and|E(G)|established ISLs assigned from visibility links respectively,namely V(G)=V(M)and E(G)⊆E(M).As a network node,each satellite v requires f(v)LCTs to maintain the network connectivity.Each ISL e∈E(G)has w wavelength channels with equal channel bandwidth capacity.W={1,2,...,w}is the wavelength set.A light path defined on a WDM-OSN is a route of the graph G with each link assigned a wavelength channel.It is assumed that the WDM-OSN does not have wavelength converters and so wavelength continuity constraint applies.

Each visibility link e=xy,∀e∈ E(M)represents that satellites x and y are visible from each other,while each ISL e=xy,∀e∈ E(G)represents an ISL between satellites x and y.Each ISL e=xy will occupy one LCT on satellites x and y.M and G are the matrix expression form of the visibility graph M=(V,E)and topology G=(V,E)respectively.As a result,M(x,y)=1 represents e=xy and M(x,y)=0 otherwise.Node degree dM(v)of visibility graph M represents that there are dM(v)satellites visible from satellite v,and its visible satellites are usually more than LCTs equipped,namely:

G(x,y)=1 represents e=xy,and G(x,y)=0 otherwise.Node degree dG(v)of network topology G represents that there are dG(v)active LCTs of satellite v assigned to establish ISLs and active LCTs are limited to the specified number of LCTs,namely:

The LCT utilization is defined as

Therefore,the link assignment problem of assigning LCTs to establish ISLs is to find a spanning subgraph and satisfy the node degree constraints dG(v)≤f(v).

Under the network topology G=(V,E)generated by link assignment,there is a set of requests to be accommodated.It contains N requests denoted by R.We assume that all requests ask for the same bandwidth which is the capacity of a wavelength channel.Thus,each request r∈R is represented as r=(s,d),where s and d are the source and destination satellite respectively.For practice consideration,we only consider k shortest paths for each request and the routing paths which are δ longer than the shortest one are not considered.To satisfy a request r,we should find a path prand assign a wavelength label crfor path pr.There are drhops of routing path for request r from satellite s to satellite d,therefore,the average end-to-end delay is represented as

The objective of wavelength dimensioning is to minimize the maximum wavelength channel number,i.e.

Therefore,this paper mainly focuses on minimizing the wavelength requirements to provision requests R under network topology G with all LCTs being active,which is generated by link assignment.

3.Link assignment and wavelength dimensioning

In order to minimize the wavelength requirements C on network topology G with all LCTs being active,a novel LASPMM is firstly proposed to generate a random network topology G satisfying node degree constraints dG(v)≡f(v).Then,the partition coloring model18is used to find a minimum wavelength channel label crover a wavelength conflict graph.Finally,the LAS-PMM and partition coloring model are able to be applied into aniterative method-based heuristic algorithm to optimize the wavelength requirements.For example,Fig.1(a)shows a visibility graph,where each dash line connects two satellites which are visible from each other and each satellite is equipped with four LCTs.In Fig.1(b),two wavelengths{λ1,λ2}are required to provision four requests based on MSN topology,where each satellite establishes run-back-right-left four WDM ISLs with its neighbor satellites.While in Fig.1(c),only one wavelength{λ1}is required to provision four requests based on the topology generated by LAS-PMM.

3.1.LAS-PMM

Network topology G is an f-factor of visibility graph M if the node degree dG(v)satisfies dG(v)=f(v),where f(v)is a function of node v,19while network topology G is a k-factor of visibility graph M if the node degree dG(v)satisfies dG(v)=f(v)≡k.It is difficult to generate a network topology G with all the f(v)LCTs of each satellite v assigned to establish ISLs,namely the network topology G is an f-factor of visibility graph M.In order to circumvent this difficulty,a novel LAS-PMM is proposed to convert the original problem to a perfect matching problem,where a perfect matching is searched over a mixed complete bipartite graph by Edmond's Blossom algorithm.20The main idea of LAS-PMM is shown as

Step 1.Make sure∑is even,namely

Otherwise,randomly choose one satellite v and decrease its specified number of LCT by one,namely f(v)=f(v)-1.

Step 2.Get the visibility graph M.

Step 3.Generate a mixed complete bipartite graph G*=(V*,E*).

(1)Firstly,each node v∈V(M)is replaced with a complete bipartite graphwhere there areandnodes in the first node setand the second node setrespectively,namely

and

There are no common nodes betweenandnamely

The node set of complete bipartite V*(K)is equal toIn the complete bipartite graph,each nodebelonging tois connected to each nodebelonging toAs a result,there are|E*(K)|linksconnecting nodeandwhere|E*(K)|is equal to

The complete bipartite graphis also denoted as

(2)Secondly,itreplaceseach visibility link e=xy,∀e∈ E(M)with a link connecting two random nodeand random nodebelonging to node setandrespectively,where each nodeandare used only one time.The nodeis called intra-node representing an unassigned visibility link e,while the nodeis called inter-node representing a visibility link e.As a result,the intra-node degreeand inter-node degreeof the mixed bipartite graph G*are defined as

and

respectively.

As a result,there are|V*(G*)|nodes in the mixed bipartite graph G*,where|V*(G*)|is equal to

and there are|E*(G*)|links in the complete bipartite graph G*,where|E*(G*)|is equal to

Step 4.Find a perfect matching M*=(V*,E*)of the mixed complete bipartite graph G*=(V*,E*),where M*is the spanning subgraph of G*such that

Fig.1 Link assignment,routing and wavelength assignment(RWA)in WDM-OSN.

The perfect matching M*is generated by Edmond's Blossom algorithm,20which achieved a running time ofAs a result,there are|E*(M*)|links in the perfect matching M*according to Eq.(15),where|E*(M*)|is equal to

In the perfect matching M*,the intra-link is the linkconnecting nodes belonging to the same complete bipartite graph and the inter-link isconnecting two inter-nodes belonging to different complete bipartite graphs.As a result,there areintra-links andinterlinks respectively,whereandare equal to

and

Step 5.Get network topology G satisfying node degree constraints dG(v)≡f(v).

(2)Shrink each node set V*(K)of the perfect matching M*into a node v.

As a result,Step 5 will get a network topology G satisfying node degree constraints dG(v)≡f(v).There are|E(G)|ISLs in the network topology G,and|E(G)|is equal to the number of inter-linksin perfect matching M*,namely

For example,a visibility graph is shown in Fig.2(a),where each satellite(the node indexed with a,b,c,...)is equipped with an indicated number of LCTs and two satellites connected by the dash line are visible from each other.Fig.2(b)shows a network topology with all LCTs being active.In order to generate an f-factor in Fig.2(b)of visibility graph shown in Fig.2(a),Step 1 is satisfied becauseIn Fig.2(c),each node v,∀v∈ V(M) and each visibility link e=xy,∀e∈ E(M)are replaced as Step 3 does.For example,satellite a and b are replaced with K0,3and K1,3respectively and the node set A*(K)and B*(K)are surrounded by a black thick circle indexed with a and b respectively.The visibility link e=ab is replaced withconnecting two random internodesandAccording to Eqs.(11)and(12),the node degrees of inter-nodesandare 1 and 2 respectively.Furthermore,we can find that there are 26 nodes and 33 links in the mixed complete bipartite graph G*according to Eqs.(13)and(14),respectively.

A perfect matching M*is represented as a set of black thick lines(Fig.2(d).According to Step 4,there are 8 intra-links and 5 inter-links in the perfect matching M*according to Eqs.(17)and(18),respectively.Finally,Fig.2(b)is the result of shrinking the node set V*(K)into a node v shown in Fig.2(d).According to Step 5,node degree constraints dG(v)=f(v)are satisfied in network topology G shown in Fig.2(b).

3.2.Partition coloring model

Wavelength dimensioning is to find the lowest label of wavelength channel assigned to provision request set.The partition coloring model is shown as follows.18

We use the k-shortest path algorithm to calculate k-shortest paths and δ allowable hops for R requests within a running time of O(|R||E(G)|+k|R||V(G)|lg|V(G)|).Remaining paths for the rth request are denoted as a path set Pr.Each path prin Pris denoted as a node.There is a link between the ith nodein Pxand the jth nodein Pyif and only if x≠y andnamely that the candidate paths for different requests share some common links.The node sets for all request and the links between them form the path conflict graph.The partition coloring of a path conflict graph is to find a node subset which contains only one node from each path node set Prsuch that the chromatic number of the induced graph called wavelength conflict graph is minimum.In the partition coloring model,we want to find an induced graph called wavelength conflict graph whose chromatic number is the smallest.To color a node in the wavelength conflict graph is to assign a wavelength crfor a request r,and the chromatic number of a wavelength graph is the wavelengths used to accommodate all requests.

To show how partition coloring of a path conflict graph works,use the network topology shown in Fig.1(c)and four requests shown as follows:In this example,we consider three candidate paths for each request,while the allowed additional hop is 1.As a result,the path conflict is shown in Fig.3(a).For example,for r2,three candidate paths from node S22to S32are path S22-S32,S22-S23-S32and S22-S13-S23-S32.Only paths S22-S32and S22-S23-S32are considered as feasible because the others are δ hops longer than the shortest one S22-S32.Path S22-S32for request r2and path S22-S32-S23-S24for request r3share common link e=S22S32.Thus,there is a link between the node representing S22-S32in P2and the node representing S22-S32-S23-S24in P4.Fig.3(b)shows one such wavelength conflict graph which needs one wavelength channel to provision all requests.Minimizing the number of colors offers benefit of improving resource efficiency as multiplexing can be increased.

Fig.2 An example of perfect match model-based link assignment.

Fig.3 An example of partition coloring model.

4.Simulation and evaluation

This paper mainly focuses on the network performance for NeLS constellation and its primary parameters are shown in Table 1.According to the analytical graphics,inc.systems tool kit(AGI STK which is a software for space,defense and intelligence)access analysis of each satellite in NeLS,there are altogether 2100 visibility links and we can find that 360 of them can be maintained forever and 1740 of them are maintained with time duration from the 197 s to 1462 s.As a result,the wavelength minimization could be classified into static situation and dynamic situation according to whether established ISLs in WDM-OSN could be maintained forever or not.All the visibility links' candidate for ISLs could maintain visibility permanently in static situation,while some visibility links' candidate for ISLs will be blocked out due to out of visibility in dynamic situation.Thus,wavelength dimensioning in dynamic situation can be divided into finite wavelength dimensioning in static situation during equal-length interval of the whole system period.13In each equal-length interval,the visibility links' candidate for ISLs could maintain visibility during the whole interval.As a result,the number of visibility links of visibility graph during one time interval in the dynamic situation is bigger than that in the static situation.

Fig.4 Earth zone divisions and traffic intensities.

The traffic intensities are shown in Fig.4,where the earth was divided into 288 zones with intervals of 15°in both the latitudinal and the longitudinal directions with traffic intensity in each zone.Each zone used the satellite closet to its center as the access satellite.All source and destination satellite of requests r=(s,d)are established according to Fig.4 and Table 2,respectively,21where NA,SA,EU,AF,AS,OA represent North America,South America,Europe,Africa,Asia and Oceania respectively.We consider k=2 and δ=1 shortest paths for each request r.However,the satellite's relative position to earth changes continuously,resulting in the handover of service source and destination satellites as the major problem in Ref.22Therefore,we mainly focus on the network performances of LAS-PMM after handover has been done.The performances of LAS-PMM are compared with those of MSN LAS and greedy LAS,in terms of wavelength requirements C to provision requests R,average end-to-end delay dR(in hops),LCT utilization αG.The simulation duration is assumed to be 9000 s and the simulation results are an average over 10 runs with different request sets.

Table 1 Primary parameters for NeLS.

Table 2 Distribution of traffic.

4.1.Wavelength minimization in static situation

In the static situation,there are 360 permanent visibility links,which could be assigned to establish ISLs to consisting of the network topology.The network topology designed by MSN LAS is similar to Fig.1(b).Fig.5(a)and(b)shows the network topologies designed by greedy LAS and LAS-PMM respectively.In Fig.5,the white node with node degree dG(v)=4 represents that all the 4 LCTs of satellite v are assigned to establish ISLs;the gray node with node degree dG(v)lt;4 represents the satellites that there are 4-dG(v)LCTs of satellite v unassigned to establish ISLs.As a result,the network topology with 232 ISLs in Fig.5(a)is a subgraph of visibility graph M=(V,E)and the network topology with 240 ISLs in Fig.5(b)is the 4-factor of visibility graph M.Thus the LCT utilization αGof MSN LAS,greedy LAS and LAS-PMM are 100%,96.7%and 100%,respectively.

Figs.6(a)–6(c)shows wavelength requirements to provision 1000,2000 and 3000 requests respectively.In Fig.6(d),the performance improvements of LAS-PMM and greedy LAS compared with MSN LAS change around 24.8%and 15.3%,respectively.With the increase of requests,more wavelengths are required to provision requests under network topology designed by MSNLAS,greedy LAS and LAS-PMM respectively.

Figs.7(a)–7(c)shows average end-to-end delay dR(in hops)of 1000,2000 and 3000 requests respectively.In Fig.7(d),the performance improvements of LAS-PMM and greedy method compared with MSN method change around 12.4%and 10.0%,respectively.The average end-to-end delays of requests almost remain the same,although there are more and more requests to be provisioned.

The greedy LAS randomly assigns LCTs to maintain ISLs with other satellites until all the f(v)LCTs on this satellite are occupied.As a result,there are some LCTs unassigned shown as gray nodes in Fig.5(a).There are more ISLs in network topology shown in Fig.5(b)than those of Fig.5(a).As a result,LAS-PMM works better than greedy LAS,in terms of the wavelength requirements and average end-to-end delay.

The MSN LAS assigns four fixed run-back-right-left direction ISLs for each satellite,while the greedy LAS and LASPMM choose 4 appropriate ISLs for each satellite among its six visibility links.Therefore,greedy LAS and LAS-PMM will introduce some amounts of disorder into network topology compared with MSN LAS.Thus,LAS-PMM and greedy LAS work better than MSN LAS in terms of wavelength requirements and average end-to-end delay.Furthermore,the satellite's relative position to Earth changes continuously,so does the service source satellite and service destination satellite.As a result,the wavelength requirements to provision requests and average end-to-end delay change as time goes by.

4.2.Wavelength minimization in dynamic situation

Time interval is set to be 600 s to reduce the frequency of ISLs re-establishment.At each time interval,the visibility graph consists of the visibility links which can be maintained during the whole time interval.Due to phase deviation or imbalance symmetry of satellite constellation,two satellites may be out of their communication ability at some time during some time interval.As a result,there will be no visibility link between these two satellites during this time interval.Therefore,there are more than 360 visibility links which can be assigned to establish ISLs.For example,there are 500 visibility links which could be maintained during the first time interval 0,600[ ]s.Similar to network topology shown in Fig.5(a),there are 236 ISLs in network topology generated by greedy LAS during time interval[ 0 ,600]s.

Figs.8(a)–8(c)shows wavelength requirements to provision 1000,2000 and 3000 requests respectively.In Fig.8(d),the performance improvements of LAS-PMM and Greedy method compared with MSN method change around 39.9%and 30.1%,respectively.With the increase of requests,more wavelengths are required to provision requests under network topology designed by MSN LAS,greedy LAS and LASPMM respectively.Furthermore,the pattern of curve shown in Fig.8 is similar to that shown in Fig.6.

Figs.9(a)–9(c)shows average end-to-end delay dR(in hops)of 1000,2000 and 3000 requests respectively.In Fig.9(d),the performance improvements of LAS-PMM and greedy method compared with MSN method change around 21.4%and 19.0%,respectively.The average end-to-end delays of requests almost remain the same,although there are more and more requests to be provisioned.Furthermore,the pattern of curve in Fig.9 is similar to that in Fig.7.

Fig.5 Network topology of NeLS constellation designed by different LASs.

Fig.6 Wavelengths required to provision|R|requests in the static situation.

Fig.7 Average delay of|R|requests(in hops)in the static situation.

Fig.8 Wavelengths required to provision|R|requests in the dynamic situation.

Fig.9 Average delay of|R|requests(in hops)in the dynamic situation.

5.Conclusions

In WDM-OSN with wavelength routing technology,this paper studies the wavelength requirements to provision requests under the network topology generated by LAS.In order to better optimize the wavelength dimensioning for WDM-OSN,we propose a novel LAS-PMM to generate a network such that a shorter path could be routed and less wavelengths are assigned for each ISL along the path.In LAS-PMM,LCT assignment is performed based on our conversion of the original problem to a perfect matching problem,where a perfect matching is searched over a mixed complete bipartite graph.A series of simulations shows that in comparison to the regular MSN topology,wavelength requirements and average end-to-end delay based on topology generated by LAS-PMM could be reduced by 24.8%and 12.4%,respectively.Furthermore,the more visibility links candidate for ISLs establishment,the more choices network topology has to route an appropriate lightpath,resulting in better network performance on wavelength requirements and average end-to-end delay.

Acknowledgements

This work was supported by the National Natural Science Foundation of China(Nos.61471238,61433009).

1.Mukherjee J,Ramamurthy B.Communication technologies and architectures for space network and interplanetary.IEEE Commun Surv Tut 2013;15(2):881–97.

2.Satellite Industry Association.State of the industry report Internet.[Cited 2005 September 1];Available from:http://www.sia.org.

3.Emrick R,Cruz P,Carvalho NB,Gao S,Quay R,Waltereit P.The sky's the limit:key technology and market trends in satellite communications.IEEE Microwave Mag 2014;15(2):65–78.

4.Orbcomm-2(2012–2014).Internet.[Cited 2015 September 1];Available from: http://www.skyrocket.de/space/docs_dat/orbcomm-2.htm.

5.Globalstar-2(2010–2015).Internet.[Cited 2015 September 1];Available from:http://www.skyrocket.de/space/docs_dat/globalstar-2.htm.

6.Iridium-Next(2012–2014).Internet.[Cited 2015 September 1];Available from:http://www.skyrocket.de/space/docs_dat/iridiumnext.htm.

7.Karafolas N,Baroni S.Optical satellite networks.J Lightwave Technol 2000;18(12):1792–806.

8.Tan L,Yang Q,Ma J,Jiang S.Wavelength dimensioning of optical transport networks over nongeosychronous satellite constellation.J Opt Commun Networking 2010;2(4):166–74.

9.Dai LL,Chan VWS.Capacity dimensioning and routing for hybrid satellite and terrestrial systems.IEEE J Sel Areas Commun 2004;22(2):287–99.

10.Sun J,Modiano E.Routing strategies for maximizing throughput in LEO satellite networks.IEEE J Sel Areas Commun 2006;22(2):273–86.

11.Werner M,Frings J,Wauquiez F,Maral G.Topological design,routing and capacity dimensioning for ISL networks in broadband LEO satellite systems.Int J Satell Commun 2001;19:499–527.

12.Harathi K,Krishna P,Newman-Wolfe RE,Chow Randy YC.A fast link assignment algorithm for satellite communication networks.1993 twelfth annual international phoenix conference on computers and communications;1993 Mar.23-26;Tempe,AZ,USA.Piscataway,NJ:IEEE Press,1993.p.401–8.

13.Chang HS,Kim BW,Lee CG,Min SL,Choi Y,Yang HS,et al.FSA-based link assignment and routing in low-Earth orbit satellite networks.IEEE Trans Veh Technol 1998;47(3):1037–48.

14.Noakes MD,Cain JB,Nieto JW,Althouse EL.An adaptive link assignment algorithm for dynamically changing topologies.IEEE Trans Commun 1993;41(5):694–706.

15.Czygrinow A,Hanckowiak M,Szymanska E,Wawrzyniak M.Distributed computing.Berlin:Springer Berlin Heidelberg;2012.p.210–22.

16.Schmid S,Suomela J.Exploiting locality in distributed SDN control.2013 second ACM SIGCOMM workshop on hot topics in software defined networking;2013 Aug 12–16;HK,China.2013.p.121–6.

17.Suzuki R,Yasuda Y.Study on ISL network structure in LEO satellite communication systems.Acta Astronaut2007;61(7–8):648–58.

18.Liu Z,Shi Q,Guo W,Hu W,Xia M.Sliding scheduled light path provisioning by mixed partition coloring in WDM optical networks.Opt Switch Networking 2013;10(1):44–53.

19.Tutte WT.A short proof of the factor theorem for finite graphs.Can J Math 1954;6(3):347–52.

20.Kolmogorov V.Blossom V a new implementation of a minimum cost perfect matching algorithm.Math Program Comput 2009;1(1):43–67.

21.Nishiyama H,Kudoh D,Kato N,Kadowaki N.Load balancing and QoS provisioning based on congestion prediction for GEO/LEO hybrid satellite networks.Proc IEEE 2011;9(11):1998–2007.

22.Chowdhury PK,Atiquzzaman M,Ivancic W.Handover schemes in satellite networks:state-of-the-art and future research directions.IEEE Commun Surv Tut 2006;8(4):2–14.

Liu Zhereceived the B.S.degree in optical and Electronic Information Engineering from Huazhong University of Science and Technology in 2010.He is currently working towards the Ph.D.degree in Electronic Engineering at Shanghai Jiao Tong University,China.His research interests include the application of the graph theory in network resource optimization.

Guo Weireceived the bachelor,master and Ph.D.degrees in Computer Science from Wuhan University in 1985,1990,and 1998,respectively.She is a professor at the State Key Lab of Advanced Optical Communication System and Network in Shanghai Jiao Tong University.She has over 50 publications published in technical journals and conferences.Her primary research interests include architecture of automatically switch optical network,network management system,network planning,and optimization algorithm.

Deng Changlinreceived the B.S.degree in communication engineering from University of Electronic Science and Technology of China in 2010.He is currently a Ph.D.candidate in Electronic Engineering at Shanghai Jiao Tong University,China.His research interests include the routing protocol and algorithm of the interplanetary network.

Hu Weishengreceived the B.S.,M.S.,and Ph.D.degrees from Tsinghua University,Beijing University of Science and Technology and Nanjing University in 1986,1989,and 1997,respectively.He is the director of the State Key Laboratory of Advanced Optical Communication Systems and Networks,Shanghai Jiao Tong University,China.He serves for four journals and 12 conferences,including IEEE JLT,OFC and APOC.His interests are on the optical transport network with GMPLS controlled,and optical packet switching.He is the co-author of over 200 peer journal and conference papers.

14 October 2015;revised 16 November 2015;accepted 25 November 2015

Available online 9 May 2016

LAS;

LAS-PMM;

Routing;

Wavelength assignment;

Wavelength dimensioning;

WDM-OSN

Ⓒ2016 Chinese Society of Aeronautics and Astronautics.Production and hosting by Elsevier Ltd.This is an open access article under the CCBY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

*Corresponding author.Tel.:+86 21 34205359.

E-mail address:wguo@sjtu.edu.cn(W.Guo).

Peer review under responsibility of Editorial Committee of CJA.