Contents lists available at ScienceDirectOptical Switching and Networking

Optical Switching and Networking 14 (2014) 274281http://d1573-42

n Corrmobile:

E-mshaxiaojournal homepage: www.elsevier.com/locate/osnFragmentation assessment based on-line routingand spectrum allocation for intra-data-center networkswith centralized control

Shanguo Huang n, Yu Zhou n, Shan Yin, Qian Kong, Min Zhang, Yongli Zhao,Jie Zhang, Wanyi GuState Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications,Beijing 100876, PR Chinaa r t i c l e i n f o

Article history:Received 16 March 2014Received in revised form17 April 2014Accepted 13 May 2014Available online 9 June 2014

Keywords:Elastic optical networkSoftware-defined network (SDN)On-lineRSAIntra-data-centerx.doi.org/10.1016/j.osn.2014.05.01177/& 2014 Elsevier B.V. All rights reserved.

esponding authors. Tel.: 86 10 61198106;86 10 13693578265.ail addresses: shghuang@bupt.edu.cn,ziningyi@bupt.edu.cn, shaxiaoziningyi@163.ca b s t r a c t

As is well known, elastic optical network is quite attractive due to its great spectralefficiency and flexibility, which can allocate appropriate size spectrum based on efficientmodulation modes such as Orthogonal Frequency Division Multiplexing (OFDM) modula-tion, etc. These characters are able to better meet the needs of the intra-data-centeroptical interconnection. To properly analyze and operate elastic optical networks withhighly dynamic traffic of the intra-data-center, considering the continuity constraint andthe contiguity constraint, efficient methods are required for the on-line routing andspectrum allocation (RSA) issue. In this paper, we propose two methods (AFD and CSL) forassessing the status (spectrum fragmentation) of the network, and present two algorithms(BSPR and HSR) which use the proposed assessment value to perform on-line RSA appliedto intra-data-center networks which adopt the Software-Defined Network (SDN) controlmode. Simulation results reveal that the proposed approaches allow solving the on-lineRSA problem more efficiently with lower blocking probability of the networks.

& 2014 Elsevier B.V. All rights reserved.1. Introduction

In the past few years, cloud adoption is not only anemerging technology, but also an established networkingsolution which is widely accepted and deployed by thetelecom industry. According to statistics, the traffic volumesgenerated in total are largeover 10 GB per server per day inan intra-data-center network (intra-DCN) [1]. The Ciscoglobal cloud index forecasts that global data center IP trafficwill reach 644 exabytes per month in 2017 (nearly triple ofthe traffic in 2012) [2]. The quality of service (QoS)om (S. Huang).provisioning is the users' major concern, which dependson the communication efficiency between servers. All-optical switching technique can just cater to the intra-DCN'shigh efficient transport requirement. Compared with therigid spectrum grid networks realized with the traditionalWDM technology, spectrum-efficient and scalable opticaltransport network architecture called SLICE which is basedon optical orthogonal frequency division multiplexing (O-OFDM) technology is better spectrum efficiency and flex-ibility [3,4].

In elastic optical networks, the available spectrum of afiber link is divided into a set of spectral slots with substan-tially smaller spectral width (spectral slots widths are 6.25,12.5 and 25 GHz) than a traditional wavelength (50 GHz ITU-T WDM grid). Instead of occupying a whole wavelength,connections are placed on series of contiguous subcarriers

www.sciencedirect.com/science/journal/15734277www.elsevier.com/locate/osnhttp://dx.doi.org/10.1016/j.osn.2014.05.011http://dx.doi.org/10.1016/j.osn.2014.05.011http://dx.doi.org/10.1016/j.osn.2014.05.011http://crossmark.crossref.org/dialog/?doi=10.1016/j.osn.2014.05.011&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.osn.2014.05.011&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.osn.2014.05.011&domain=pdfmailto:shghuang@bupt.edu.cnmailto:shaxiaoziningyi@bupt.edu.cnmailto:shaxiaoziningyi@163.comhttp://dx.doi.org/10.1016/j.osn.2014.05.011

S. Huang et al. / Optical Switching and Networking 14 (2014) 274281 275according to the bandwidth demand. Moreover, ultra highbit-rate super channels at 400 Gb/s sand 1 Tb/s will beallowed in future elastic optical networks.

Flexible and efficient features of elastic optical network(EON) are double-edged swords. EON face some importantchallenges, although they have a great advantage thantraditional WDM networks. Due to the character of O-OFDM technology and the absence of spectrum converters,the allocated slots must be contiguous in the spectrum(contiguity constraint), and the same slots must be used inall links of the routing path (continuity constraint) [5].These two constraints let EON a main challenge beingthe so-called spectrum fragmentation effect, which refersto the condition that, as the highly dynamic set up andremove traffic over a intra-DCN, the available spectralresources become highly fragmented, potentially leadingto blocking situations.

At present, spectrum fragmentation has attracted a lotof attention in DCN. Some novel spectrum defragmenta-tion algorithm has been proposed [68]. Generally, thedefragmentation is accompanied by mass of light path orspectrum migrations, which is not a kind of suitablesolution in highly dynamic intra-DCN. Therefore, how toreduce the extent of fragmentation at first as much aspossible and choose a better way to set up a connectionwhen the network has already been fragmental, which canbe summarized as efficient on-line routing and spectrumallocation (RSA) problem is urgently needed to be solvedin the intra-DCNs.

In [9], the authors proposed two RSA methods forsuper-channels accounting for sub-carriers dynamism,which are similar to the first-fit and best-fit used in theWDM networks. The authors of [10] introduce a service-oriented spectrum assignment framework and two algo-rithms to solve the RSA problem. In [10], spectrum isdivided into some blocks for different set of servicesaccording to the chosen properties, and RSA are done inevery block just as [9]. Both of them did the RSA one stepby step without some criterion but just satisfy the band-width demand, while we may need to consider the routingand spectrum allocation together which way will makeRSA more optimal. Therefore, we need an assessmentvalue to evaluate the status (spectrum fragmentation) ofthe network, which can be used to choose differentrouting and spectrum allocation together. Also in veryrecently, the papers [11,12] focus on the static RSA pro-blem, and Integer Linear Programming (ILP) formulationsare presented to minimize the utilized spectrum.

The authors of [13] introduced a concept called Utiliza-tion Entropy (UE) to assess the degree of spectrumfragmentation in flexible grid optical networks. Theauthors of [14] presented the Spectrum Compactness(SC), which is calculated by analyzing the times of chan-ging among the occupied and vacant spectrum blocks on alink. In [15], the authors proposed an assessment methodbased the fragmentation of a set of paths between everypair of nodes in the graph. However, some influencefactors were less considered in design of the assessmentmethods in above work, such as the spectrum usage, thespectrum continuity constraint and the non-uniform sam-ple of links. In this paper, we present two fragmentationassessment schemes of the whole network, which can bemore effective and accurate to reflect the status of thenetwork, and then use them on the on-line routing andspectrum allocation.

From the perspective of intra-DCN control, the authorsof [16] describes the implemented control-plane which isconsist of GMPLS (Generalized Multi-Protocol LabelSwitching), PCE (Path Computation Engine) and a resourceallocation tool called Sub-wavelength Assignment Engine(SLAE) for the Time-Shared Optical Network (TSON). In[17], the authors demonstrate the star all-optical intra-DCN using extended OpenFlow-based software-definednetworking. Recently, in [18], a network-driven transfermode is proposed for cloud operations of data center witha Software-Defined Network (SDN) controller and anApplication-Based Network Operations (ABNO) controllerworking together. A GMPLS-enabled FBON is discussed in[19], especially its distributed reservation approach. Andfor the first time, the authors investigate the backwardreservation collision problem in an FBON, which woulddominate the blocking performance in networks with lightload or serving highly dynamic traffic. In highly dynamicintra-DCN, centralized control mode can effectively reducethe failure of the request which is because of the conflict ofresource access with distributed control mode, and it willmonitor resource of the whole network more efficientlywhich is more conductive to the inter-DCN connection. In[20] and [21], the authors respectively proposed routingalgorithm and protection algorithm for multi-layer andmulti-domain optical networks, which are playing guidingroles for the research of the connection control among thedata centers. In fact, the survivability in optical networkshould also be considered [22], which is one of our futureresearch points. We provide a feasible all-optical intra-DCN architecture based on SDN control (centralized con-trol). The architecture of the intra-DCN is based on theprevious EON based on O-OFDM. First, we need to extendthe messages between the controller and the racks. Then,an OF agent is integrated on every rack, which cantranslate the messages which are from SDN controller intocontrol orders for the O-OFDM ToR. The architecture andthe SDN control model are illustrated in Fig. 1.

The rest of the paper is organized as follows. In Section2, two fragmentation assessment schemes are proposed. InSection 3, two on-line RSA algorithms based on thefragmentation assessment in detail are presented. InSection 4, the performance of considered on-line RSAformulations are compared, and then the performance ofour formulation over two realistic network topologies areintroduced. Section 5 concludes the paper.

2. Proposed spectrum fragmentation assessmentschemes

In the last section, we mentioned the continuity con-straint and the contiguity constraint in elastic opticalnetworks. If the spectrum is not continuous among con-nected links in a precomputed path, it cannot be used forthe path. On the other hand, if the available slots are justenough for bandwidth demand but discrete, they also maynot be provided for set up traffic. Therefore, the status of

Fig. 1. A feasible all-optical intra-DCN architecture based on SDN control.

S. Huang et al. / Optical Switching and Networking 14 (2014) 274281276the contiguity slots in the same position among connectedlinks are importantly influence factors of the networkfragmentation in EON (Table 1).2.1. Available fragment degree

In this paper, we present a new concept called Avail-able Fragment Degree (AFD) to indicate the availability ofthe spectrum fragments among various resources. Theavailable fragment degree value is normalized between 0and 1, which can be used as an indicator for assessing andcomparing the degree of resource fragmentation. A higheravailable fragment degree indicates the spectrum frag-mentation blocks can be allocated wider and more band-width demands.

As a kind of collection of the connected links, path istaken as the foothold to calculate the AFD. Meanwhile, weconsider that the selection of path's length is of greatimportance and closely related with the size of network(the number of nodes); so we select all paths which areconsisted of Np connected links as a set, where Np can becalculated as follows:

Np round up logjV j2 1

We define the AFD_path which indicates the AFDamong Np connected links. The spectrum resource of thepath is achieved by performing bitwise AND operationamong the links. Define a network as G{V,E}, where V isthe set of bandwidth variable switching (BVS) nodes and Erepresents the set of fiber links connecting two nodes in V.Some notations and variables are introduced in Table 1,and we use |X| to represent the number of the elementsin the set of X. The calculation procedure of AFD_path isintroduced as follows.(1) Get the spectrum usage status of the pathThe spectrum occupation on a link is expressed by abits array sei s1ei ; s2ei ;; s

jSjei . By applying bitwise

AND operation among n connected links, the spec-trum usage status of a path can be calculated asfollows:

spk \ei Apk sei 2(2) Calculate the probability of provisioning availablebandwidth for bandwidth demand r among path pk.For bandwidth demand r (the number of requiredcontiguity slots), we first find out that how many startslot's position can afford r contiguity slots. Then, thevalue by dividing by the maximum number of thepositions (assuming all slots are vacant) is normalized.The probability of provisioning available bandwidthdemand r can be calculated as follows:

pk ; r Sj j r1i 1 s

i;i r1pk

Sj jr1 3(3) Update the distribution probability of bandwidthdemands after a bandwidth demand r has beenaccepted.In different networks, the probability of kinds ofbandwidth demands may be different, such as one net-work's traffic mostly request one slot but another net-work's traffics mostly request three slots. For differenthighly dynamic network, we need to base the assessedvalue on the probabilities of different bandwidth demands.With the whole traffics' number of a highly dynamicnetwork grows all the time, and for the sake of thenormalized, the probabilities of different bandwidthdemands are initialized to the same value as 1/|R|. Then,every time the network controller receives a bandwidthdemand r, probabilities are updated as follows:

Q 1 1=logjRj2

1 Pr;old=logjRj2 4

Pr;new Q Pr;old 5

Table 1Notations and variables.

Symbol Definition

V Set of nodes, index vE Set of fiber links, index eD Set of demands, index dP Set of precomputed paths, index pK Number of slots in a linkR Set of bandwidth demand, index rGc Set of connected graphs, which are consist of Np different links, index gEv Set of fiber links, which is connected with node vsd,td Source and destination of nodes of demand dS Set of frequency slots, index sse Frequency slots on the link esv Frequency slots of node v, the result by performing bitwise AND operation among frequency slots of all the links

which connect with node vsp Frequency slots of path p, the result by performing bitwise AND operation among frequency slots of all the links

which are on path psp(s,d) Frequency slots of path p (from s to d), the result by performing bitwise AND operation among frequency slots

of all the links which are on path psix The usage status of the ith slot in the collection x, if the slot is available the value equals to 1, else 0Pr The distribution probability of bandwidth demand rp;r The probability of provisioning bandwidth demand r over spv;r The probability of provisioning bandwidth demand r over svNv The degree of a node (the number of the connected links with node v)

S. Huang et al. / Optical Switching and Networking 14 (2014) 274281 277Pr0 ;new 1 Pr;new1 Pr;oldPr0 ;old 6

Above all, the available fragment degree of a path canbe achieved as follows:

AFD_path k 8 rpk ;rPr 7

The available fragment degree of the network (AFD_-network) is presented to indicate the AFD of the networkand it can be calculated by expression (8).

AFD_network 1jKj8 kAFD_path k 82.2. Continuity of spectrum among links

Although the AFD assessment scheme proposed isreasonable and scientific, because of that |P| is about thesquare of the |E|, the cost (CPU instructions) of the calcula-tion may be high. It may greatly suit a small-scale network,and it will bring much cost for a large-scale network.Actually, the cost can be greatly reduced by doing precom-putation such as just updating the AFD_paths which arerelated to the RSA. However, we proposed another quickassessment scheme to indicate the continuity of the spec-trum between links, which is called Continuity of Spec-trum among Links (CSL). As the intersection of links, nodeis taken as the foothold to calculate the CSL. The calculationprocedure of CSL_node is great similar with AFD_path, so itis introduced as follows in brief.

First, the conjunct spectrum usage status of the linksaround a node can be calculated as follows:

svk \ei A Ev sei 9Second, the probability of provisioning available band-

width for bandwidth demand r over svk is calculated asfollows:

vk ; r Sj j r1i 1 s

i;i r1vk

Sj jr1 10

Third, update the distribution probability of bandwidthdemands after a bandwidth demand r being accepted, andthe calculation method of the probability is same to theAFD's.

Finally, the continuity of spectrum between links whichis linked node v can be achieved as follows:

CSL_node k 8 rvk ;rPr 11

The available fragment degree of the network (AFD_-network) is presented to indicate the AFD of the networkand calculated as follows:

CSL_network 1jV j8kCSL_node k 123. On-line RSA algorithms

In this section, two on-line RSA algorithms are pro-posed based on fragmentation assessment (AFD and CSL,we adopt AFD in the description of algorithms). The aim ofthe algorithms is trying to make the network accept moredemands (keep the network in an optimal status) bychoosing the route and the allocation position of thespectrum in the light path together. In order to simplifythe expression of the algorithm, the concept of channel isintroduced in [23]. The definition of channels can bedescribed as contiguous n slots, and the value of them are,

cix;n \n ik iskxThe above formula shows that in a collection x (se, sp or

sv), if the contiguous n slots from the position i are

Table 2BSPR algorithm.

1: While receive a demand for r slots do2: Get all nodes and the links which can afford enough contiguous slots for the demand, then

create a new graph3: Find at most k shortest paths according to the K-shortest paths algorithm4: For each calculated path Do5: Initialize the data containers Vc and Vt (container of values which is consist of the value of AFD_network, start

slot position and path point. The subscript c for compare, t for tempThe initialize value for both containers is {1, 0, NULL})

6: For each channel with exact r slots do7: Calculate the AFD_network assuming the channel among the path has been located,

and use Vt record the value of AFD_network, the start slot position and path point8: Compare the data containers Vt with Vc9: If the value of AFD_network in Vt is bigger10: Use the three data in Vt to replace the corresponding data in Vc11: Else if the values of AFD_network in Vt and Vc are equal12: Compare the start slot position. If the start slot position in Vt is farthest away from

the slots center (the value is equal to half of the number of possible start slotsposition in a link), use the three data in Vt to replace the corresponding data in Vc

13: End for14: End for15: Compare every final Vc for different calculated path as above method, the final result with

biggest value of AFD_network and start slot position which is farthest away from theslots center, is used to response to the demand

16: End do

Table 3HSR algorithm.

1: While receive a demand for r slots do2: For each channel with exact r slots do3: Get all nodes and the links which each has the available corresponding channel, then

create a new graph4: Find at most k shortest paths according to the K-shortest paths algorithm5: Initialize the data containers Vc and Vt (container of values which is consist of the value

of AFD_network, start slot position and path point. The subscript c for compare, t fortemp. The initialize value for both containers is {1, 0, NULL})

6: For each calculated path Do7: Calculate the AFD_network assuming the channel among the path has been located,

and use Vt record the value of AFD_network, the start slot position and path point8: Compare the data containers Vt with Vc9: If the value of AFD_network in Vt is bigger10: Use the three data in Vt to replace the corresponding data in Vc11: Else if the values of AFD_network in Vt and Vc are equal12: Compare the length of paths, if the length of the path in Vt is shorter than the

length of the path in Vc, Use the three data in Vt to replace the corresponding datain Vc

13: End for14: End for15: Compare every final Vc with different start slot position, leave the one which meet the

conditions as follow: First, it has the biggest value of AFD_network; Furthermore, itsstart slot position is farthest away from the slots center (the value is equal to half of thenumber of possible start slots position in a link), the final result is used to response tothe demand

16: End do

S. Huang et al. / Optical Switching and Networking 14 (2014) 274281278all available, the channel cix;n is available otherwise it isequal to 0.

3.1. Best spectrum position routing (BSPR) algorithm

RSA should be considered together to optimize thecarrying capacity of the network. When the networkcontroller receives a demand d, first it gets informationfor all nodes and the links which can afford enoughcontiguous slots for the demand to constitute a new graph(topology), which way can increase the success probabilityof the spectrum allocation (without by this way, althoughthe routing is successful, the spectrum allocation on theroute may be failed). The details of the BSPR algorithm areshown in Table 2.

3.2. Hierarchical spectrum routing (HSR) algorithm

When the spectrum fragmentation degree is high, thespectrum of the traditional k shortest paths we used in thealgorithms may be unable to afford enough resource. Toreduce the blocking probability of the networks, we first

Fig. 2. Network topologies for the simulations.

Fig. 3. Calculated values of different assessment schemes.

Table 4All kinds of assessment schemes.

Timecomplexity

Problems

UE O(|S|n|E|) Only care the change of adjacent slots, butignore the spectrum usage

SC O(|S|n|E|) The spectrum continuity between links has notbeen considered

AFD O(|S|n|E|2) More computation time is spent in large-scalenetworks

CSL O(|S|n|V|) Cannot be used to reflect the spectrumfragmentation among long path

S. Huang et al. / Optical Switching and Networking 14 (2014) 274281 279get the links which can afford available channel at thesame position to constitute a new graph, after that therouting of the traffic is implemented. The above methodoperates at every reasonable layer (contiguity spectrumblock), and the procedure of HSR algorithm is shown inTable 3.4. Numerical simulation

The NSFNET network (14 nodes and 21 links) and theCOST239 network (11 nodes and 26 links) are chosen forthe simulations to evaluate the performance of the pro-posed algorithms in this paper (as shown in the Fig. 2). Inthe simulations, each link has 80 slots spectrum resourcewith equal bandwidth and the bandwidth demands(required slots for connection, R{1, 2, 3, 4}) followPoisson distribution (the mean of Poisson distribution2.5, and ignore the value bigger than 4 and smallerthan 1). Meanwhile the traffic time model also followsPoisson distribution. In this paper, we assume that theguard-band has been included in the bandwidth demandin its forming for simplicity.4.1. Effectiveness of the spectrum fragmentation assessmentschemes

Fig. 3 shows the calculated values of different spectrumfragmentation assessment schemes (UE, SC, AFD and CSL)under different resource utilization in the above two topol-ogies. Although these four assessment schemes have certainrelevance to the resource utilization, they have differenceand characteristics. The value of UE scheme has a prominentchange when the resource utilization reaches 50%, which isbecause that UE scheme mainly counts the changing fre-quency of the slots' state but ignores the utilization of theslots. In terms of normalized, the values of UE scheme aresmall, and SC scheme has no normalized processing. Simula-tion results demonstrate that AFD and CSL can effectively

Fig. 4. Impact of proposed algorithms. (a) Compares the performance ofthe proposed on-line RSA algorithms with KRFS algorithm in terms ofblocking probability in NSFNET network. (b) Compares the performanceof the proposed on-line RSA algorithms with KRFS algorithm in terms ofblocking probability in COST239 network.

Table 5Average running time of the algorithms.

Traffic load(Erlang)

Networktopology

Average running time of thealgorithms (ms)

KRFS BSPR HSR

20 NSFNET 0.195 1.19 5.792COST239 0.205 1.126 5.789

240 NSFNET 0.187 0.365 0.852COST239 0.175 0.637 1.358

Time complexity O(TkkCTf)

O(TkkCTcsl)

O(CTkkCTcsl)

S. Huang et al. / Optical Switching and Networking 14 (2014) 274281280indicate both the spectrum fragmentation and the change ofthe resource utilization in elastic optical networks.

In highly dynamic network, the time complexity is alsoa point needed to be paid attention to when we build aspectrum fragmentation assessment schemes. As morecomprehensive factors are considered in AFD scheme,AFD scheme has a high time complexity. Different fromAFD scheme which considers the spectrum fragmentationon paths, CSL pays more attention on the spectrumfragmentation of the link pairs around nodes. The timecomplexity and existing problems of all mentioned assess-ment schemes are shown in Table 4.

4.2. Performance of the BSPR and HSR Algorithms

The simulations are designed to evaluate the proposed on-line RSA algorithms with CSL assessment. First-fit slot assign-ment with K-shortest paths routing (KRFS, KNp as in theproposed algorithms in this paper) is used for evaluation ofon-line RSA algorithms. Fig. 4 compares the performance ofthe proposed on-line RSA algorithms with KRFS algorithm interms of blocking probability in NSFNET network andCOST239 network. As shown, using the algorithms proposedin this paper reduce the blocking probability, in which BSPR isbetter than KRFS, and HSR algorithm outperforms than others.The load capacity of the COST239 is better than NSFNET justbecause that the average of the former's nodes degree ishigher than the latter's.

In above two networks, the efficiency of HSR algorithm isbetter than that of BSPR algorithm, which is because thatHSR algorithm more considers of the contribution of spec-trum allocation than routing. Because BSRP algorithm a littlemore considers the routing attribute when choose a route,the blocking probability is only reduced a little than the KRFSalgorithm in a network which the average of nodes degree ishigh (such as COST239). Meanwhile, for HSR algorithm, thehigh average of nodes degree means more routing choices,which leads to lower blocking probability.

In addition to the influences of the algorithms for theblocking probability, the time efficiencies of the algorithmsare also what we are concerned with, which are shown inTable 5. Tk is the time cost to running K-shortest pathsrouting; k is the path number of the K-shortest pathsresult; C represents the number of possible channel; Tf isthe time cost to make sure the path and channel can beused for the demand; Tcsl stands for the time cost torunning the CSL spectrum fragmentation AssessmentSchemes. We run the Java Project with Eclipse on a PC(3.0 GHz dual-core processor, 4 GB RAM). From the result,we can draw conclusions as follows:(1) The algorithms spend main time for running K-short-est paths routing, which means that the more times torunning K-shortest paths routing the more time thealgorithms will spend.(2) Although BSPR and HSR algorithms spend more timethan KRFS algorithm, the time cost of them isacceptable.(3) In the different stages of the network traffic load state,the different algorithms can be used for improving thenetwork performance.5. Conclusions

In this paper, two assessment concepts called AFD andCSL are proposed to represent the availability of the

S. Huang et al. / Optical Switching and Networking 14 (2014) 274281 281spectrum fragments in EON. Then two algorithms whichuse the assessment value to perform on-line RSA arepresented. The simulation results reveal that the proposedalgorithms can solve the on-line RSA problem moreefficiently with lower blocking probability, especially forthe network with high average of nodes degree such as theintra-data-center networks.Acknowledgments

This work is supported partly by the National BasicResearch Program of China (973 Program) (Nos.2010CB328204 and 2010CB328202), the National NaturalScience Foundation of China (Nos. 61331008 and61205058), the Hi-Tech Research and Development Pro-gram of China (863 Program) (No. 2012AA011302), theProgram for New Century Excellent Talents in University(NCET-120793), the Beijing Nova Program (No. 2011065),and the Fundamental Research Funds for the CentralUniversities.

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Fragmentation assessment based on-line routing and spectrum allocation for intra-data-center networks with centralized...IntroductionProposed spectrum fragmentation assessment schemesAvailable fragment degreeContinuity of spectrum among links

On-line RSA algorithmsBest spectrum position routing (BSPR) algorithmHierarchical spectrum routing (HSR) algorithm

Numerical simulationEffectiveness of the spectrum fragmentation assessment schemesPerformance of the BSPR and HSR Algorithms

ConclusionsAcknowledgmentsReferences