Design of Light-Tree Based OpticalInter-Datacenter Networks

Rongping Lin, Moshe Zukerman, Gangxiang Shen, and Wen-De Zhong

Abstract—Nowadays, people’s daily lives are increas-ingly dependent on Internet applications provided bycloud service providers that replicate their contentamong geographically distributed datacenters using inter-datacenter wide area networks to meet performance andreliability requirements. This paper provides means forefficient design of inter-datacenter networks with statictraffic scenarios, where unicast and multicast connectionrequests are known a priori along with their start andend times. Also, the optical channel setup/teardown timeis given. Integer linear programming (ILP) formulationsthat consider light-tree and lightpath connections aredeveloped to minimize the network resource consumption.Since solving ILP formulations is time consuming for largenetworks, we also propose efficient heuristic algorithms.We demonstrate by simulations an advantage in efficiencyfor a light-tree based heuristic algorithm over its lightpathcounterpart. This is due to its ability to construct and ex-tend light-trees to groom more connections. Both heuristicalgorithms perform very close to the corresponding ILPoptimal results in the case of a small network.

Index Terms—Integer linear programming (ILP); Inter-datacenter network; Light-tree; Setup/teardown time.

I. INTRODUCTION

C isco’s 2011White Paper [1] predicts that cloud serviceproviders (CSPs), such as Google, Facebook, Yahoo!,

and IBM, will generate the most Internet traffic in thecoming years. In particular, it is expected that during2016 the total CSP traffic will be 6.6 zettabytes. By com-parison, the total global IP traffic in 2016 (excludingCSP traffic) is around 1.3 zettabytes [1]. To meet the localperformance and reliability requirement, CSPs replicatetheir contents among geographically distributed datacen-ters using wavelength division multiplexing (WDM) basedinter-datacenter networks [2]. It is reported that a datacen-ter networking cost amounts to about 15% of the total cost

of the datacenter and that the cost of the wide area trans-port exceeds that of the internal network of a datacenter[3]. According to [4], global spending on datacenters willbe $143 billion in 2013 and $149 billion in 2014. Therefore,the spending on inter-datacenter networks is likely to ex-ceed $10 billion per year. Accordingly, an efficient design ofinter-datacenter networks has the potential for significantcost savings.

Efficient and cost-effective network design (and dimen-sioning) is dependent on accurate prediction of future traf-fic demand. However, due to the uncertainty of futuretraffic demand and growth trends, certain conservativeestimations may be made, keeping in mind that theymay lead to over-dimensioning, which implies excessivecost. If the actual traffic demand happens to be more thanoriginally used in the design, traffic engineering and man-agement techniques will be used to maximize throughput.However, the latter is beyond the scope of this paper.

Currently, lightpaths are established to connect datacen-ters for end-to-end connections [2], where a lightpath is anall-optical channel from a source to a destination withoutany optical–electronic–optical (O-E-O) conversion at inter-mediate nodes [5]. The use of lightpaths is justified as theyare far more efficient and energy conserving to transportthe high bitrates required between datacenters in theoptical domain than in the electronic domain [6,7].

In addition to one-to-one unicast connections, inter-datacenter networks transport many one-to-manymulticastconnections due to growing multicast applications and con-tent backup among datacenters. The light-tree is proposedto optimally support the multicast connections, where alight-tree is a generalization of a lightpath to be a tree top-ology, and traffic is sent from a root to all its associatedleaves in the optical domain [8]. Light-trees can efficientlytransmit multicast traffic without any O-E-O conversionprocess. However, to implement a light-tree in an opticalnetwork, network nodes with optical splitter deploymentsare needed. An optical splitter can split an optical signal intomultiple copies in the optical domain, and power amplifiersare also needed to compensate for the power lost during thesplitting. This implies that additional cost is incurred for anetwork to support light-trees. Fortunately, optical splittersand power amplifiers are relatively inexpensive, and it is be-lieved that the benefit obtained from light-trees significantlyoffsets the additional cost of devices used by light-trees [8].

As inter-datacenter networks transport very large vol-umes of traffic associated with content replications amonghttp://dx.doi.org/10.1364/JOCN.5.001443

Manuscript received July 12, 2013; revised September 6, 2013; acceptedSeptember 16, 2013; published November 27, 2013 (Doc. ID 193828).

R. Lin (e-mail: linr0012@e.ntu.edu.sg) was with the EE Department,City University of Hong Kong, Hong Kong SAR, China, when this workwas done, and he is now with the School of Communication and InformationEngineering, University of Electronic Science and Technology of China(UESTC), Chengdu 611731, China.

M. Zukerman is with the EE Department, City University of Hong Kong,Hong Kong SAR, China.

G. Shen is with the School of Electronic and Information Engineering,Soochow University, Suzhou, Jiangsu 215006, China.

W. D. Zhong is with the School of Electrical and Electronic Engineering,Nanyang Technological University, Singapore 639798.

Lin et al. VOL. 5, NO. 12/DECEMBER 2013/J. OPT. COMMUN. NETW. 1443

1943-0620/13/121443-13$15.00/0 © 2013 Optical Society of America

geographically distributed datacenters, they require multi-casting of very large bursts of data that distinguish themfrom traditional optical networks. This motivates the use ofa light-tree to avoid excessive cost and energy consumptionassociated with O-E-O conversions. Also, inter-datacenternetworks normally involve a smaller number of nodes thantraditional networks, which makes inter-datacenter net-works more amenable to design using mathematical pro-gramming algorithms. Moreover, a datacenter may havethe ability to obtain information on the amount of dataper connection it wishes to transport through the inter-datacenter network. Having such information enablesefficient utilization of inter-datacenter network resources.By comparison, in traditional networks, long-lived largebandwidth connections are set up to transport IP trafficgenerated by many sources between nodes/cities, and theamount of traffic is not known when the connection is setup. This may result in lower network resource utilization.This paper provides efficient algorithms for inter-datacenter network design that is based on the configura-tion involving lightpaths and light-trees, and aims tominimize the requiredWDM transmission capacity. We con-sider only all-optical single-hop architectures, where onlyone lightpath (or light-tree) is used for any given connection.

A. Related Work

In [2], the bandwidth-on-demand (BOD) method was pro-posed tomanage CSPs’dynamic inter-datacenter connectionrequests, where end-to-end connections are set up dynami-cally according to demands in order to improve resourceutilization. In this way, telecommunications carriers suchas AT&T can provide efficient and low-cost connections tomultiple CSPs. In [9,10], to improve resource utilization,multipath and multihop strategies were employed to trans-mit traffic in inter-datacenter networks. In the multipathor multihop strategies, traffic is accommodated by multipleconcatenated lightpaths from source to destination. ThenO-E-O conversions are used to forward the traffic fromone lightpath to the next. Since a lightpath can be sharedby more connections than in the single-hop case, multihopincreases the sharing of network resources and improves ef-ficiency and performance. In addition, a multihop architec-ture enables electronic wavelength conversion, which alsoimproves efficiency and performance. However, multihopstrategies introduce prohibitively expensive and energyconsuming O-E-O conversion, especially in high-bandwidthoptical networks, and the transport over multiplelightpaths/light-trees also increases delay.

While the capacity of a terabit/second capable opticalfiber is divided into multiple parallel wavelengths by theWDM technology, where each wavelength is expected totransmit up to a 100 gigabit∕second data rate, some con-nection requests among datacenters may require onlysubwavelength bandwidth. Thus, for a better network re-source utilization, efficient traffic grooming techniques arerequired to address the disparity between the requestedconnection bandwidth and the wavelength channel band-width. We note that traffic grooming in this paper refers

to traditional electronic traffic grooming where groomingis implemented in the electronic domain. Traffic groomingcan be categorized into dynamic traffic grooming and statictraffic grooming. In the former, connection requests arrivedynamically and the target is to maintain an acceptableblocking probability of connection requests [11–17]. Inthe static traffic case, the connection requests are knowna priori, which is more like a network planning problem.An optimal solution for this type of problem is usually ob-tained [18–25] by using the integer linear programming(ILP) technique. In this paper, we focus on the static caseand provide ILP formulations for the inter-datacenternetwork design.

We find that all the existing research has not consideredoverheads associated with lightpath setup and teardowntimes. Such setup/teardown time includes signal propaga-tion delay on the links of the lightpath, and processing timeand configuration time associated with nodes on the light-path [26]. For simplicity, in this paper, we assume that for aspecific network, the lightpath/light-tree setup/teardowntime is constant. However, it can be different for differentnetworks. This setup/teardown time may compromise thenetwork efficiency if the setup/teardown time is a signifi-cant portion of the entire lightpath/light-tree holding time(which includes setup/teardown time), due to wastage ofresources during setup/teardown. In the experimentsreported in [2], the establishment of a lightpath takes60–70 s, and tearing down a lightpath takes around 10 s.However, it is also noted there that in practice the time isfar longer. It is expected that this time will be shortened asnew technologies are developed. However, it is likely thatthey will remain significant relative to flow or burst trans-mission times for the foreseeable future. We note that theduration time of a connection is between the start and endtimes of its data transmission. The setup/teardown time isassociated with establishment and teardown of a lightpathor a light-tree and not directly, but indirectly, with an indi-vidual connection. A lightpath or light-tree may accommo-date multiple subwavelength connections, and in this waythey share the setup/teardown overhead.

A technology that aims to overcome the inefficiencyintroduced by lightpath setup/teardown time overhead isoptical burst switching (OBS) [27], which is consideredas the compromise of optical circuit switching and opticalpacket switching. An OBS network will not set up a light-path (optical circuit switching) before traffic transmission.Instead, a header is sent out ahead of a data burst, to re-serve resources and to reconfigure optical cross-connects(OXCs) along the path of the burst. OBS has the advantageof avoiding end-to-end connection setup delay. However,there is no guarantee that resources will be available forthe burst along its path and the burst may be dumped. Thismay lead to loss of effective bandwidth and even to conges-tion collapse under very heavy traffic conditions [28]. Thechallenge of improving OBS performance is still a topic ofongoing research, and the jury on whether or not OBS be-comes a leading technology is still out.

The authors of [29] reduced lightpath setup time byreusing the OXC existing configuration status, which

1444 J. OPT. COMMUN. NETW./VOL. 5, NO. 12/DECEMBER 2013 Lin et al.

significantly improves network resource utilization. In[26], a signaling protocol was developed to select a wave-length for a lightpath connection with minimal setup time.

Given the ever-increasing wavelength capacity, the dura-tions of some connections in inter-datacenter networksmay be short. Therefore, to maintain a high level ofnetwork efficiency, it is important to reduce the connectionoverhead (related by lightpath/light-tree setup and tear-down) to minimum. In this paper, we propose to uselight-trees to accommodate connections, which not onlyoptimally carry multicast connections, but also mitigatethe overheads of optical connections. This benefit is gainedfrom the capability of a light-tree to carry a multiplicity ofunicast and multicast connections. For example, in Fig. 1, alight-tree rooted at node 1 and terminated at nodes 3, 4,and 6 is established for traffic transmission from datacen-ter DC a to any of the other datacenters DC b, DC c, andDC d. It can groom all unicast andmulticast traffic from itsroot to its leaves, where the traffic destination set is a sub-set of fDC b;DC c;DC dg. While these connections sharethe light-tree and the light-tree setup/teardown overheadaccounted for each individual connection is reduced, it alsoincurs the cost of transmitting traffic to unwanted leaves.We will propose methods in which the benefit from light-tree sharing significantly outweighs the cost to unwantedleaves.

In this paper, we will consider static traffic scenarioswhere connection requests are known with start and endtimes. The scenario of unicast connection was investigatedas a scheduled lightpath demand problem in [30]. Then,[31] extended the work in [30], considering the case inwhich connection requests arrive dynamically (arrivebefore start times), leading to the associated dynamicscheduling lightpath demand problem. This problem ishow to schedule the routings and resource allocationsfor connections. These routings and resource allocationsmay be modified before the connection start times in orderto achieve a lower blocking probability of the future connec-tion requests. All these publications used the informationof start and end times to increase resource sharing basedon the fact that time-disjoint (that are scheduled at differ-ent time durations) connections can share network resour-ces. A recent survey paper [32] covers most of the relatedwork in this field.

B. Contribution

The first contribution of this paper is a light-tree basedinter-datacenter network design that involves traditionaltraffic grooming as well as traffic grooming with time-disjoint connections. Next, we provide new ILP formula-tions and heuristic algorithms aiming to optimize theefficiency of wavelength transmission resources for bothlight-tree based and pure lightpath based designs. Finally,we compare the light-tree based network design with thetraditional lightpath based design and demonstrate abenefit of more than 15% transmission resource saving.

C. Organization

The remainder of this paper is organized as follows. InSection II, we illustrate the design concept and motivationsusing an example. In Section III, the problem statement ispresented. In Section IV, the ILP formulations for light-treebased and lightpath based designs are provided, and an ex-ample for theseoptimizationsmethodsapplied toa smallnet-work is presented. In Section V, the detailed steps of twoheuristic algorithms, namely, light-tree based and lightpathbased, are described. Section VI presents numerical resultsfor applying optimal and heuristic methods to test networksand compares their performance in terms of resource con-sumption. Finally, Section VII concludes this paper.

II. ILLUSTRATION OF THE DESIGN CONCEPT

As discussed above, in this paper, we consider the designproblem of inter-datacenter networks with static trafficscenarios, where both light-trees and lightpaths are usedto support connection requests that include connectionstart and end times. We also consider lightpath and light-tree setup/teardown times. The duration of the connec-tion can be longer or shorter than the connection setup/teardown time.

For example, the light-tree in Fig. 1 can be shared in thetime domain. It can be shared by time-disjoint connections,which increases the resource sharing and further reducesthe setup/teardown time per connection and improves per-formance. In Fig. 2, an example is given to illustrate thissharing of a light-tree in the time domain, and to indicatethe advantage over the purely lightpath based method. InFig. 2, five connection requests are given with their respec-tive start and end times, and the network topology is thesame as in Fig. 1. The network time is slotted with a unitslot size, and the duration time of a connection is measuredin the number of slots. A connection request i, i � 1; 2;…; 5,is denoted by a 5-tuple of the elements �si;Di; f i;ai; bi�,where the five elements represent the source, destinationset, bandwidth required, start time, and end time, respec-tively. For example, R1�1; 3; 4; 6; 3; 3; 9�, represents thelight-tree in Fig. 1 to transmit traffic from DC a toDC b, DC c, and DC d, where 1 is the source node and3, 4, and 6 are the destinations, and the last three numbersare their required bandwidth, start time, and end time,Fig. 1. Resource sharing of a light-tree.

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respectively. (The start and end times are bolded.) In theexample, the capacity of a wavelength C is assumed tobe equal to OC-12, and the required bandwidth of connec-tions is OC-x, where only the value x is given, omitting the“OC” for brevity.

In Fig. 2, R1 starts from slot 3, and needs two slots toset up a light-tree, which are marked with crosses in thefigure (we suppose that the setup of an optical connectiontakes two slots in this example), so the first and secondslots are also occupied without traffic transmission. R2 andR3 can share the light-tree with R1 during R1’s transmis-sion time from slot 3 to slot 9. This sharing must satisfy thecondition that in each slot, the total required bandwidth isno larger thanC. However,R4 andR5 are outside the trans-mission time of R1, and are time-disjoint connections of R1.Thus, to carry R4 and R5, we can either establish newoptical channels, or extend the end time of the light-tree.If new optical channels are established, setup/teardowntime will be incurred. Finally, the solution with the leastresource consumption among all methods is selected. Inthis example, the best solution is to extend the light-tree to slot 13 to carry R4 and R5 as shown in Fig. 2 withlight gray slots. As network time is divided into slots, alightpath or light-tree of k-time-slot holding time willrequire k time slots in every wavelink (a wavelink is awavelength channel in a particular link) on its route. Thebasic resource unit used in this paper is a single time sloton a single wavelink. This resource unit will henceforth becalled a wavelink slot. In this way, a lightpath or light-treeof k-time-slot holding time that traverses n wavelinks willuse kn wavelink slots.

We here provide the detailed calculation of the examplein Fig. 2. The light-tree occupies four wavelinks, as shownin Fig. 1. If it is extended to time slot 13 from time slot 9,the resource consumption is 4 × �13 − 9� � 16 wavelinkslots. However, if a new light-tree from node 1 to nodes3 and 6 is established for R4 and R5, the new light-tree oc-cupies three wavelinks in Fig. 1, and the resource consump-tion is 3 × �2� 4� � 18wavelink slots, where two time slotsare the setup/teardown time of the new light-tree and fourtime slots are the transmission time of R4 and R5 (fromtime slot 10 to time slot 13). It is two wavelink slots morethan that obtained by extending the light-tree of R1 (whichequals 16 wavelink slots).

In another case where only lightpaths are used to sup-port all five connections, three lightpaths are required:

(1) Node 1 to node 3 (two wavelinks) from slot 1 to slot 12,used by R1 and R4.

(2) Node 1 to node 4 (one wavelink) from slot 1 to slot 9,used by R1, R2, and R3.

(3) Node 1 to node 6 (three wavelinks) from slot 1 to slot13, used by R1, R2, and R5.

Each lightpath contains two slots for setup/teardowntime, so the total resource consumption is 2 × 12� 1 × 9�3 × 13 � 72, which is significantly larger than that of thelight-tree based approach (i.e., 4 × 13 � 52). Based on theabove comparison, the benefit of using light-trees is clearbecause a light-tree can accommodate a multiplicity ofunicast and multicast connections in the time domain.Specifically, the light-tree in the example is shared by fiveconnections, and the average setup/teardown time of eachconnection is 0.4 slots.

In this paper, for a given topology and traffic demands(unicast and multicast), we optimize link dimensioningand routing and wavelength assignment (RWA) involvinglightpaths and light-trees. In the dimensioning phase, weaim to design the network so that all the connections can betransported based on optimal paths. In this phase, webegin with an unlimited number of wavelengths, and theobjective is to use the least network resources. (Actually,we preset our algorithms with very large link capacityvalues, and we end up with much smaller values.) Afterthe network is dimensioned, designed, built, and in actualoperation, the traffic demands may change relative to theoriginal prediction. Then the traffic is managed and the ob-jective is to optimize traffic engineering and management.In this phase, the number of wavelengths is fixed and can-not be changed. As mentioned in Section I, this is beyondthe scope of this paper.

III. PROBLEM STATEMENT

The problem of inter-datacenter network design for sub-wavelength connections (unicast and multicast) with startand end times can be stated as follows.

Given:

(1) A physical topology G�V;E� is a directed graph denot-ing an inter-datacenter network, where V is the set ofnodes to which datacenters are attached, and E is theset of directed edges. An edge is called a link, and itrepresents an optical cable that includes one opticalfiber connecting a pair of nodes. (The assumption ofone optical fiber per link is made for simplicity of no-tation, but the model can be generalized to the case ofmultiple fibers per link.)

(2) All the fibers in the network are identical, and eachfiber carries W wavelengths; each wavelength has acapacity of C�b∕s�.

(3) We assume that if two nodes are connected by a linkon one direction, then they are also connected by anidentical link on the opposite direction.

Fig. 2. Resource sharing of a light-tree in the bandwidth and timedomain.

1446 J. OPT. COMMUN. NETW./VOL. 5, NO. 12/DECEMBER 2013 Lin et al.

(4) There are no wavelength converters in the network,which means a lightpath or light-tree traversing multi-ple links must use the same wavelength.

(5) All nodes are capable of splitting an incoming opticalsignal into multiple ones to be transmitted through theoutgoing ports to form a light-tree.

(6) A set of connection requests with start and end times ofsubwavelength or wavelength capacity demands.

Our goal is to design the network with minimal wave-link resource consumption. In particular, we provide thefollowing:

(1) A set of light-trees and lightpaths. In a light-tree or alightpath, the transmission from the source to the des-tination(s) is all-optical, which provides a transmissionchannel for connection requests.

(2) Traffic routing. For each connection, we assign one light-tree or lightpath, which provides single-hop routing forits traffic. This can be extended to the case in whichconnections traverse multiple lightpaths or light-treesas in our earlier work [22]. Meanwhile, the connectionduration time (from start to end) where the traffic is con-veyed in the light-tree or lightpath is also allocated.

(3) Physical RWA. We find routes and assign wavelengthsfor all the light-trees and lightpaths. The RWAs havetime constraints, where the start and end times of thelight-trees and lightpaths are determined (the starttime begins from the time of setting up the light-treeor lightpath).

IV. ILP FORMULATIONS

In our formulations, a light-tree (or a lightpath) isdenoted by �i; w; k; p; q�, where i is the source node, w isthe particular wavelength used, k is the index of the com-bination of adjacent links (the outgoing branches of a light-tree from a node can extend to any set of its adjacent links),p is the start time, which begins from the setup time of thelight-tree or lightpath, and q is the end time, which termi-nates at the teardown time of the light-tree or lightpath.The variable k has different ranges for the light-tree andthe lightpath: for the light-tree 1 ≤ k ≤ 2Deg�i� − 1, as thereare 2Deg�i� − 1 combinations of adjacent links of node i,where Deg�i� is the nodal degree of node i. Recall that nodei is the source node of the light-tree (or lightpath). In thecase of a lightpath, we have Deg�i� combinations. As in anycombination, the lightpath can traverse only one branch ofthe tree (one adjacent link), 1 ≤ k ≤ Deg�i�. For any node xin light-tree �i; w; k; p; q�, let a Boolean parameter Tx

iwk;p;qtake the value of 1 if node x is a destination of light-tree�i; w; k; p; q�, and 0 otherwise. For a lightpath, there is onlyone destination for light-tree �i; w; k; p; q�, which requiresP

xTxiwk;p;q � 1, and the outgoing branch from a node is

no larger than 1. Both light-tree and lightpath basedILP formulations are provided in this section. They sharethe same input parameters, variables, and ILP objectivefunction. Thus, we present them first. Next, we provideseparate constraints for each of the formulations.

Given:V : set of nodes in the network.E: set of edges in the network.W: number of wavelengths per fiber, which

is preset for optimization. Usually, theoptimal value is lower than this value.

C: capacity of a wavelength.Pmn: indicator of interconnecting nodes m

and n. As we assume that there are twofibers in the opposite directions, ifm andn are connected, then Pmn � Pnm � 1.

e: setup/teardown time of a lightpath or alight-tree.

T: total number of slots. The network timeis slotted from 1 to T with a unit slotsize.

R: maximal index of connection request.�sr;Dr; f r;ar;br�: r � 1;2;…; R, a 5-tuple of the elements

denoting connection request r, wherefive elements represent the source, des-tination set, bandwidth required, starttime, and end time, respectively. Accord-ingly, the total duration time of theconnection is br − ar � 1 slots.

Variables:Tx

iwk;p;q: a Boolean variable. It takes the value of 1 if nodex is a destination of the light-tree �i; w; k; p; q�;otherwise 0.

Fmniwk;p;q: an integer commodity-flow variable [33], denot-

ing the number of units of commodity flowingon link �m;n� for light-tree �i; w; k; p; q�. Eachdestination of a light-tree needs one unit ofcommodity. Thus, a total of

PxT

xiwk;p;q units of

commodity flow out of the source i for light-tree�i; w; k; p; q�. The variable Fmn

iwk;p;q is equal to thenumber of destinations in the downstream oflink �m;n�.

Mmniwk;p;q: a Boolean variable. It takes the value of 1 when

light-tree �i; w; k; p; q� traverses link �m;n�;otherwise 0.

λriwk;p;q: a Boolean variable. It takes the value of 1 if con-nection request r traverses light-tree �i; w; k; p; q�;otherwise 0.

Qr;xiwk;p;q: a Boolean variable. It takes the value of 1 if

node x is a destination of light-tree�i; w; k; p; q� that is occupied by connection re-quest r; otherwise 0. This variable should beset to λriwk;p;q × Tx

iwk;p;q.

Objective:

MinimizeX

m;n;i;w;k;p;q

�q − p� 1� ·Mmniwk;p;q: (1)

The objective is to minimize the total number ofwavelink slots used. This minimization is achieved bysharing the setup/teardown overheads among multipleconnections. In this way, the overhead per connection isreduced and a more efficient operation is achieved, because

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this implies using fewer wavelinks for the same traffic de-mands or accommodating more traffic in a given network.

A. Light-Tree Based Formulation

As discussed before, a light-tree can not only optimallysupport multicast connections, but also support unicastconnections with improved resource sharing. As the setup/teardown time of a light-tree or a lightpath is assumed tobe e slots, a light-tree or a lightpath would consume at leaste� 1 slots.

Constraints:

Physical RWA of light-tree

X

n∈adj�i�Fin

iwk;p;q �X

x

Txiwk;p;q

∀ i; w; k; p ≤ T − e; q ≥ p� e; (2)

X

m∈adj�x�Fmx

iwk;p;q −X

n∈adj�x�Fxn

iwk;p;q � Txiwk;p;q

∀ i; w; k; ∀ x ≠ i; p ≤ T − e; q ≥ p� e; (3)

Fmniwk;p;q ≥ Mmn

iwk;p;q

∀ i; w; k; p ≤ T − e; q ≥ p� e; mn ∈ E; (4)

Fmniwk;p;q ≤ jVj ·Mmn

iwk;p;q

∀ i; w; k; p ≤ T − e; q ≥ p� e; mn ∈ E; (5)

X

i;k;p≤t≤qMmn

iwk;p;q ≤ Pmn ∀ w; t ≤ T; mn ∈ E: (6)

Equations (2)–(6) are the commodity-flow conservationconstraints for creating physical routing of light-tree�i; w; k; p; q�. According to the definitions at the beginningof this section, the ranges of i, w, and k are i ∈ V, w ∈ W,and 1 ≤ k ≤ 2Deg�i� − 1. These ranges are also applied to theequations below if no specific ranges for i, w, and k aregiven. Equation (2) ensures that, for the source node i,the number of units of the outgoing commodity is equalto the number of destinations. Equation (3) ensures thatfor light-tree �i; w; k; p; q�, if node x is a destination, thenumber of units of incoming commodity is larger than thatof outgoing commodity by 1; otherwise, they are equal.Equations (4) and (5) ensure that if link �m;n� carriesthe commodity of light-tree �i; w; k; p; q�, then this link istraversed by the light-tree; otherwise, it is not traversed.Equation (6) ensures that at any slot, the wavelength wof a fiber link �m;n� can be occupied by at most onelight-tree.

Traffic routing of connection request

λrsrwk;p;q � Txsrwk;p;q ≥ 2Qr;x

srwk;p;q

∀ w; k; r; ∀ x ≠ sr; p ≤ T − e; q ≥ p� e; (7)

λrsrwk;p;q � Txsrwk;p;q ≤ Qr;x

srwk;p;q � 1

∀ w; k; r; ∀ x ≠ sr; p ≤ T − e; q ≥ p� e: (8)

As Qr;xiwk;p;q is set to be λriwk;p;q times Tx

iwk;p;q, we useEqs. (7) and (8) to assign value to Qr;x

iwk;p;q. These equationsensure that if a connection request r traverses light-tree�i; w; k; p; q�, and node x is a destination of the light-tree,then Qr;x

iwk;p;q will be set to 1; otherwise 0.

X

w;k;ar≥p�e&br≤qλrsrwk;p;q � 1 ∀ r; (9)

X

w;k;p;q

Qr;xsrwk;p;q � 1 ∀ r; ∀ x ∈ Dr: (10)

Equation (9) ensures that a connection request has onelight-tree to transmit its traffic, where the start time ofthe connection is no earlier than the start time of thelight-tree plus the setup/teardown time, and the end timeof the connection is no later than the end time of thelight-tree. This is because during the setup/teardown time,even resources are reserved, but cannot transmit traffic,so traffic can only start after it. Equation (10) ensures thateach destination of a connection request must be reached.X

r�ar≤t≤br�f r · λrsrwk;p;q ≤ C

∀ w; k; ∀ t ∈ �p; q�; p ≤ T − e; q ≥ p� e: (11)

Equation (11) ensures that at any time slot, the totalbandwidth required by the connection requests in alight-tree �i; w; k; p; q� must be no larger than the wave-length capacity.

B. Lightpath Based Formulation

If lightpaths are established to support connectionrequests, only one destination can be reached for eachlightpath. For a multicast request, multiple lightpathsare established from the source to each of the destinations.These lightpaths can also groom traffic of other connectionswith the same source and destination.

Constraints:

Physical RWA of lightpath

X

n∈adj�i�Min

iwk;p;q �X

x

Txiwk;p;q

∀ i; w; k; p ≤ T − e; q ≥ p� e; (12)

X

m∈adj�x�Mmx

iwk;p;q −X

n∈adj�x�Mxn

iwk;p;q � Txiwk;p;q

∀ i; w; k; ∀ x ≠ i; p ≤ T − e; q ≥ p� e; (13)

X

x

Txiwk;p;q ≤ 1 ∀ i; w; k; p ≤ T − e; q ≥ p� e; (14)

1448 J. OPT. COMMUN. NETW./VOL. 5, NO. 12/DECEMBER 2013 Lin et al.

X

i;k;p≤t≤qMmn

iwk;p;q ≤ Pmn ∀ w; t ≤ T; mn ∈ E: (15)

Equations (12)–(15) are the constraints for creatingphysical routing of lightpath �i; w; k; p; q�. Accordingly,the ranges of i, w, and k are i ∈ V, w ∈ W, and1 ≤ k ≤ Deg�i�, where only the last one is different fromthe light-tree case (1 ≤ k ≤ 2Deg�i� − 1). The explanationsof these equations are similar to their light-tree counter-parts, except that they consider only one destination, whiletheir counterparts consider multiple destinations.

Traffic routing of connection request

X

w;k;ar≥p�e&br≤qλrsrwk;p;q � jDrj ∀ r: (16)

Equation (16) ensures that the number of lightpathsused to transmit traffic for a connection request is the sameas the number of destinations of the connection request.The other constraints are similar to those provided inthe light-tree case, which are given by Eqs. (7), (8), (10),and (11). The only difference is in the lightpath case therange of k is 1 ≤ k ≤ Deg�i�.

C. Numbers of Variables and Constraints

We check the numbers of variables and constraints ofthe two formulations to gain insight into the complexitiesof the ILP problems. For the light-tree based formulation,the number of variables is O�jVjjEjW2gT2 � RjVj2W2gT2�,where g is the maximal nodal degree in the net-work. The number of constraints is O�jVj2W2gT2�jVjjEjW2gT2 � RjVjW2gT2�. Both grow quadratically withthe number of nodes. For the lightpath based formulation,they are O�gjVjjEjWT2 � gRjVj2WT2� and O�gjVj2WT2�gjVjjEjWT2 � gRjVjWT2�. They also grow quadraticallywith the number of nodes, but they are lower than theircounterparts in the light-tree based case. As network sizegrows, solving the ILP problem becomes prohibitivelytime consuming. Thus, heuristic algorithms are neededfor scalability.

D. Example for the ILP Formulations

An example of a small network that uses the ILP formu-lations to find an optimal solution is given below. The testnetwork has six nodes as shown in Fig. 1. We assume thatthe network time is divided into six slots with a unit slotsize for simplicity and the setup/teardown time is two slotsfor a light-tree or a lightpath. Accordingly, the maximallightpath/light-tree holding time is six slots (includingtwo slots overhead associated with the establishment/teardown of lightpath or light-tree) in this network. Wenote that the unit of network time slot is a normalized unit.In other words, the slot time is arbitrary. Ten randomlygenerated connection requests, including two multicastrequests as shown in Table I, are given as the input to

the formulations. The source and the destination(s) of aconnection request are randomly selected from the networknodes. We assume that the capacity C of a wavelength isOC-12, and the required bandwidth of a connection requestis a random integer with uniform distribution from 1 to12 (an integer i denotes a bandwidth of OC-i). We used acommercial ILP solver, CPLEX [34], to solve the ILPformulations.

The traffic routing of 10 connection requests is obtainedfrom the ILP solution, where Table I is for the light-treebased solution and Table II is for the lightpath based sol-ution. In Table I, we see that two light-trees are establishedfor two multicast connections with different source nodes.These two light-trees are also shared by other connectionrequests, grooming traffic of other connection requests. Forexample, light-tree �4 → 1;2;3;5� <1,6> (where 4 is thesource; 1, 2, 3, and 5 are the destinations; and <1,6> de-notes the start and end times) is used to carry the first con-nection request (multicast request), and this light-tree alsogrooms connection requests 3 and 4 during its holding time.This on average decreases the resource consumption andsetup/teardown time of each connection request.

There is another light-tree �6 → 1; 4� <2,6>, which isestablished for multicast connection request 2, but withonly one more slot extension, it can also support connectionrequest 7. This demonstrates the ability of the light-treeto carry additional connections at relatively low marginalcost. Such savings are also achievable by the lightpathbased solution, as illustrated in Table II, where two light-paths are established for connection request 2 with differ-ent holding times in order to also carry connection 7. Theend time of lightpath �6 → 4� <2,6> is one slot later thanthe end time of request 2. This extension enables the trans-mission of the traffic of connection request 7. We can seethat this extension of the light-tree or lightpath consumesfewer resources than establishing a new light-tree or light-path, and a light-tree is more likely to be shared comparedto a lightpath as there are multiple destinations in alight-tree.

With the information of light-tree routings and theirrespective holding times, we can calculate the total net-work resource usage by Eq. (1). The physical routings oflight-tree and lightpath are not given here as they canbe easily derived from Fig. 1 with minimal physical links.

TABLE ILIGHT-TREE BASED TRAFFIC ROUTING

Index Request Traffic Routing

1 (4; 1, 2, 3, 5; 3; 3, 6) �4 → 1;2;3; 5� <1,6>2 (6; 1, 4; 7; 4, 5) �6 → 1;4� <2,6>3 (4; 1; 2; 4, 6) �4 → 1;2;3; 5� <1,6>4 (4; 2; 1; 5, 6) �4 → 1;2;3; 5� <1,6>5 (5; 1; 12; 3, 3) �5 → 1� <1,3>6 (2; 4; 3; 4, 5) �2 → 4� <2,5>7 (6; 4; 10; 6, 6) �6 → 1;4� <2,6>8 (1; 3; 5; 3, 5) �1 → 3� <1,6>9 (2; 4; 4; 5, 5) �2 → 4� <2,5>10 (1; 3; 6; 4, 6) �1 → 3� <1,6>

Lin et al. VOL. 5, NO. 12/DECEMBER 2013/J. OPT. COMMUN. NETW. 1449

Thus, the total resource consumption of the light-treebased case and the lightpath based case is 61 and 74,respectively, where the light-tree based approach showsa significant smaller resource consumption value. This isbecause in the lightpath based formulation, a lightpathcan only reach one destination, which limits resource shar-ing and further leads the setup/teardown time to be lessefficient than in the light-tree case. We can see that thereare nine optical connections (correspondingly, nine setup/teardown times) in Table II, while there are only fiveoptical connections (correspondingly, five setup/teardowntimes) in Table I.

In the above example, it took several hours to solvethe ILP formulation running on a PC with a 2.8 GHz CPUand 1024MB RAM. The ILP approach cannot scale to largenetworks, so heuristic algorithms are needed. In thedevelopment of heuristic algorithms, we incorporate thefollowing observations from the optimal solution obtainedby the ILP method.

(1) A light-tree can be used to groom many connectionsto reduce the average setup/teardown time of a connec-tion request.

(2) A light-tree should be extended in the time domain toaccommodate time-disjoint connections if the resourceincurred by extension is less than that used by estab-lishing a new light-tree.

V. HEURISTIC ALGORITHMS

Motivated by the above observations, we propose a light-tree based heuristic algorithm for inter-datacenter networkdesign with static connection requests. In the algorithm,a light-tree may be selected to groom traffic of other con-nection requests. When this grooming happens betweentime-disjoint requests, i.e., the start and/or end timesof light-tree need to be extended to include the durationof the connection, additional resources are consumed. Wedefine the resource used by the extension of thelight-tree as an extension resource (the unit is wavelinkslot), which is defined as

extension resource � no: of light-tree wavelinks

× no: of slots extended: (17)

There are six scenarios for grooming a connection re-quest onto an existing light-tree in the time domain, whichare illustrated in Fig. 3. Suppose that the existing light-tree has its start time at a slot and its end time at b slot,and the setup/teardown time is e, so traffic can be transmit-ted from slot a� e. If the start time of the connectionis before slot a� e, then additional resourcesare needed, as the establishment of the light-tree will beearlier than the start time of the connection. Similarly, ifthe end time of the connection is larger than b, then addi-tional resources are required as the end time of the light-tree is delayed. The total numbers of extended slots in thesix scenarios of Fig. 3 are (a) a� e − x, (b) a� e − x, (c) 0,(d) y − b, (e) y − b, and (f) a� e − x� y − b, respectively.According to Eq. (17), the product of the number of slotsextended and the number of wavelinks of the light-treegives the value of the extension resource. The proposedheuristic algorithm, Algorithm 1, would select a light-tree to groom traffic according to the extensionresource value.

In Algorithm 1, the connection requests are first sortedin descending order of destination set size. The algorithmgives preference to larger connection requests becauselarger light-trees can be shared by more connectionrequests with traditional traffic grooming and in the timedomain with time-disjoint connections, so as to increasethe resource sharing and reduce the setup/teardown timeof each connection request. The complexity of sorting isO�R2�. The loop from command 2 to command 4 in thealgorithm is to select an existing light-tree to groom the con-nection request. Except the requirements (1) Di ⊆Dj and(2) f i ≤ uk, where k is in the overlap time, there are twoother requirements (3) and (4), which incorporate the obser-vations from the optimal solution of the ILP. Requirement(3) says that the selected light-tree should have the minimalextension resource among all other light-trees. This require-ment is to groom traffic in the time domain while keepinglow resource consumption. Requirement (4) says that underrequirement (3), the minimal waste light-tree will be se-lected, where the waste is defined as the number of destina-tions of the light-tree that are not the destinations of theconnection (equal to jDjj − jDij). Requirements (3) and (4)aim to achieve high light-tree sharing and reduce the re-source wasted to unwanted leaves. At command 4, if the ex-tension resource of the selected light-tree is smaller than theresource of establishing a new light-tree (the number ofwavelinks of the new light-tree times the holding time), thisrequest is groomed onto the selected light-tree with (or with-out) extending the light-tree. Accordingly, in the time slotswhere the new traffic is groomed with the existing traffic,the available bandwidth of the light-tree is updated touk − f i, where k is in the overlap time, and in the time slotsthat are extended only for new traffic, the available band-width of light-tree is set to C − f i. Otherwise, a new light-tree will be established. The complexity of this loop isO�R2 � RjVj2 log jVj� as the upper bound of the number

TABLE IILIGHTPATH BASED TRAFFIC ROUTING

Index Request Traffic Routing

1 (4; 1, 2, 3, 5; 3; 3, 6) �4 → 1� <1,6>�4 → 2� <1,6>�4 → 3� <1,6>�4 → 5� <1,6>

2 (6; 1, 4; 7; 4, 5) �6 → 1� <2,5>�6 → 4� <2,6>

3 (4; 1; 2; 4, 6) �4 → 1� <1,6>4 (4; 2; 1; 5, 6) �4 → 2� <1,6>5 (5; 1; 12; 3, 3) �5 → 1� <1,3>6 (2; 4; 3; 4, 5) �2 → 4� <2,5>7 (6; 4; 10; 6, 6) �6 → 4� <2,6>8 (1; 3; 5; 3, 5) �1 → 3� <1,6>9 (2; 4; 4; 5, 5) �2 → 4� <2,5>10 (1; 3; 6; 4, 6) �1 → 3� <1,6>

1450 J. OPT. COMMUN. NETW./VOL. 5, NO. 12/DECEMBER 2013 Lin et al.

of existing light-trees is R, and for establishing a light-tree,it isO�jVj2 log jVj�. Theminimum-cost path heuristic (MPH)algorithm [35] is applied to derive the minimum-cost light-tree, which is known to be an NP-complete problem.

After grooming traffic and establishing light-trees, thealgorithm tries to merge multiple light-trees or lightpathsto one light-tree if the merging operation can further re-duce the resources used. This merging process has thecomplexity of O�R2jVj�. Thus, the overall complexity ofthe whole heuristic algorithm is O�R2jVj �RjVj2 log jVj�.

We also consider the heuristic algorithm based on thelightpath, which is quite similar to the light-tree basedalgorithm, except that in the lightpath based algorithm,there is no light-tree-merging operation from command 5to command 9, and instead of establishing a light-tree,multiple lightpaths from the source to each destination areestablished. The overall complexity of the lightpath basedalgorithm is O�R2jVj �RjVj log jVj�.

VI. NUMERICAL RESULTS

In this section, the performance of the four methods, in-cluding (1) the light-tree based ILP formulation, (2) thelightpath based ILP formulation, (3) the light-tree basedheuristic algorithm, and (4) the lightpath based heuristicalgorithm, is compared in terms of resource consumptionin the six-node network of Fig. 1. Here resource consump-tion is calculated as the total number of wavelink slots usedby all the established light-trees as defined by the objectivefunction of Eq. (1). We then study the performance of light-tree based and lightpath based heuristic algorithms in alarger network, namely, NSFNET, in Fig. 4.

A. Six-Node Network

Ten requests are generated in each simulation experi-ment. As before, the network time is divided into six slots,and the setup/teardown time is two slots, where the maxi-mal lightpath/light-tree holding time is six slots (includingtwo slots overhead associated with the establishment/teardown of a lightpath or light-tree). Although the ILP

has its limitation as it is not scalable, it can provide optimalsolutions for problems of small dimensionality that canserve as a benchmark to test the performance of the heu-ristic algorithm. Then we use the validated heuristics forproblems of large dimensionality that are computationallyprohibitive for the ILP.

The source and the destination nodes of connectionrequests are randomly selected from the network nodes. Thesize of a multicast destination set is randomly chosen be-tween 1 and 5. We still assume that the capacity C isOC-12, and the required bandwidth is randomly chosenbetween 1 and 12. The start time of a connection israndomly selected from 3 (two slots for setup) to 6, andthe end time is larger than the start time by 0, 1, 2, and3 for the results in Figs. 5–8, respectively. If the end timeexceeds the last slot (i.e., the sixth slot), the last slot willbe used. Accordingly, each scenario has the maximal dura-tion time (with traffic transmission), 1, 2, 3, and 4 slots, re-spectively. Figures 5–8 compare the resource consumption ofdifferent methods under different multicast ratios (a ratio 0implies that all connection requests are unicast). Each ofthe result points in Figs. 5–9 is the average over 20 simula-tion runs.

In Fig. 5, when the multicast ratio is increased from 0to 0.4, the numbers of wavelink slots of all methods growsince a multicast connection request usually occupies morewavelinks than a unicast request. Thus, an increasein the multicast ratio consumes more resources. It is clearthat in the example considered, the light-tree basedmethods outperform the lightpath based methods, and

Fig. 3. Time relationship for six traffic grooming scenarios where the lower part of each graph shows the start and end times of thelight-tree, and the upper part shows the start and end times of the connection.

Fig. 4. 14-node 21-link NSFNET topology.

Lin et al. VOL. 5, NO. 12/DECEMBER 2013/J. OPT. COMMUN. NETW. 1451

the light-tree based heuristic algorithm performs almost thesame as the light-tree based optimal method, and so doesthe lightpath based heuristic algorithm as compared tothe lightpath based optimal method. We observe from thefigure that the light-tree based methods consume on aver-age 14% fewer resources than the lightpath based methods.As the multicast ratio increases, the difference between thelight-tree based and lightpath based methods increases.This is because when the multicast ratio increases, moreunicast connections can be groomed onto light-trees, whichincreases the grooming gain of the light-tree. Similar resultsare observed in other scenarios with different maximalduration times as in Figs. 6–8, and the average resourcesavings of the light-tree based methods over the lightpathbased methods are 16%, 15%, and 17%, respectively.

Algorithm 1 Light-tree based heuristic algorithm

Input: A network G�V;E� with capacity C of each wave-length, optical connection setup/teardown time, and a setof connection requests.Output: (a) RWA of light-trees with start and end times,(b) traffic routings and time allocations of the connectionrequests in the light-trees, and (c) resource consumption(the number of wavelink slots).Algorithm BEGIN:1. Sort connection requests in descending order of destina-tion set size and label them from 1 to R; the ith request isdenoted as �si;Di; f i;ai;bi�.2. for i � 1 to R do

//select existing light-trees to groom request i,Ex containsall existing light-trees, each is denoted as fsj;Dj;u;aj;bjg,where u � fuk; aj ≤ k ≤ bjg is the set of available bandwidthsof light-tree j at its holding time3. Select the light-tree j from Ex with the satisfactionof all four conditions: (1) Di ⊆Dj, (2) f i ≤ uk, where k is inthe overlap time, (3) can carry request i with the minimalextension resource, and (4) if multiple light-trees have thesame minimal extension resource, select the one with min-imal waste. If such a light-tree is not feasible, establish anew light-tree for request i, then Continue to next i.4. If the minimal extension resource of the selectedlight-tree is smaller than the resource of establishing anew light-tree, extend the holding time of the light-treeaccordingly, and then groom request i onto the selectedlight-tree; otherwise, establish a new light-tree for request i.

end//Merge light-trees to save resources

5. for t � 1 to jVj do6. Sort light-trees rooted at t in a descending order ofsize of light-tree destinations and label them from 1 to n.7. for i � 1 to n do8. for j � i� 1 to n do9. Merge two light-trees i and j to be a larger one ifresource can be saved. If the merging is successful, go backto command 6 to start over again until no more mergingcan happen.

endend

endEND

We also extract the data that have the multicast ratio0 in the four scenarios of Figs. 5–8, and show them inFig. 9. The multicast ratio 0 indicates that all connectionrequests are unicast. These data illustrate the performanceadvantage of light-tree based methods over lightpathbased methods with only unicast connection requests.From Fig. 9, we see that even without multicast connectionrequests, the light-tree based methods can still outperformthe lightpath based methods. This savings is due to thefact that a light-tree can support more unicast connectionswith different destinations, which increases the resourcesharing and reduces the setup/teardown time per connec-tion. On average, the overall resource consumption is re-duced by 5% over lightpath based methods.

B. NSFNET Network

Because ILP is not scalable, in this section, we comparethe light-tree based heuristic algorithm with the lightpath

Fig. 5. Comparison of resource consumption when maximalduration time is one slot.

Fig. 6. Comparison of resource consumption when maximalduration time is two slots.

1452 J. OPT. COMMUN. NETW./VOL. 5, NO. 12/DECEMBER 2013 Lin et al.

based heuristic algorithm in a larger network, i.e., theNSFNET network as shown in Fig. 4. We assume that thebandwidth required by a connection request is still ran-domly chosen between 1 and C, where C equals OC-48.The setup/teardown time is four slots, and the networktime is divided into 100 slots, where the maximallightpath/light-tree holding time is 100 slots (includingfour slots overhead associated with the setup/teardown ofthe lightpath or light-tree). In the six-node network, theshortest connection duration time is one slot, and it cannotbe less than 50% of the lightpath/light-tree setup/teardownoverhead, which is equal to two slots. As this overhead is onthe order of minutes, we want to consider a shorter connec-tion duration time relative to the lightpath/light-tree over-head, so we considered a four-slot setup/teardown time inthe NSFNET case. We need to emphasize that the unit ofnetwork time slot is a normalized unit and the slot time isarbitrary. An interesting measure is the ratio ofthe connection duration to the lightpath/light-tree setup/teardown overhead. In the NSFNET network, where the

lightpath/light-tree setup/teardown time is four slots, thesubwavelength connection duration times are between 1and 96 slots, allowing for a wide range of scenarios of ratiovalues. In many cases, the setup/teardown time is negli-gible, but in others it is nonnegligible. The number ofconnection requests generated in each experiment is1000, and 20 experiments are simulated to obtain the aver-age value as shown in Fig. 10 and Table III.

In Fig. 10, three multicast ratios are considered, includ-ing 0%, 10%, and 30%. It is clear that the light-tree basedheuristic algorithm, which implements the light-tree basednetwork design, achieves better performance than itslightpath counterpart, which implements the lightpathbased design for all of the three multicast ratios. It is notedthat when the connection duration time is smaller thanthe setup/teardown time (four slots), the light-tree basedalgorithm also shows better performance than the light-path based one, and this better performance remainswhen the duration time increases. This is relevant to

Fig. 7. Comparison of resource consumption when maximalduration time is three slots.

Fig. 8. Comparison of resource consumption when maximalduration time is four slots.

Fig. 9. Comparison of resource consumption whenmulticast ratiois 0 (unicast case).

Fig. 10. Comparison of resource consumptions for three differentmulticast ratios (NSFNET).

Lin et al. VOL. 5, NO. 12/DECEMBER 2013/J. OPT. COMMUN. NETW. 1453

inter-datacenter networks that need multicast for datareplications and backup, and where some high bitrate con-nections require duration shorter than the optical channelsetup/teardown time.

Next, we simulate three scenarios in which the durationtimes of connections are short, medium, and long, whichare from 1 to 20, from 21 to 60, and from 61 to 96 slots,respectively. The short, medium, and long connectionsare of different proportions as 10∶5∶1, 20∶5∶1, and40∶5∶1 in each scenario, and the duration times in eachcategory are randomly distributed. The multicast ratio is0.1 in all three scenarios. We can see that connections withshort durations are dominant. In Table III, the light-treebased heuristic algorithm performs significantly betterthan the lightpath based case, consuming about 18.2%,18.6%, and 18.7% less resources in the three scenariosof 10∶5∶1, 20∶5∶1, and 40∶5∶1, respectively. Also, as ex-pected, we can see that when the portion of the connectionwith short duration time increases, the resource consump-tion of the two algorithms is reduced. We have tested otherexperiments with even larger network sizes, and withhundreds of time slots, similar results are observed. Forthe sake of brevity, they are not shown in this paper.

VII. CONCLUSION

In this paper, we have considered the inter-datacenternetwork design problem with static traffic scenarios wherethe connection requests are known a priori with additionalinformation of start and end times. The optical channelsetup/teardown time is also taken into consideration,which may be comparable to the holding time of lightpathor light-tree in inter-datacenter networks. We have pro-posed light-tree and lightpath based network design meth-ods that rely on ILP formulations and heuristic algorithms.The results reveal that the light-tree based design achieveslower resource consumption than its lightpath counterpart.This is because the light-tree can optimally support multi-cast connection requests, and using the light-tree tosupport unicast connections increases resource sharingby traditional traffic grooming and traffic grooming amongtime-disjoint connections. This will largely decrease theaverage setup/teardown time per connection. Our heuris-tics that have been developed based on insights from theILP formulations can achieve near optimal results com-pared to the ILP benchmark for small networks. Thebenefit of more than 15% resource efficiency improvementby the light-tree based design over its lightpath counter-part has been demonstrated for the network examplestudied.

ACKNOWLEDGMENT

This work was supported by a grant from the ResearchGrants Council of the Hong Kong Special AdministrativeRegion, China [CityU 123012], by a grant from City Uni-versity of Hong Kong (Project No. 7004063), and by grantsfrom the National Natural Science Foundation of China(NSFC) (61322109) and the Natural Science Foundationof Jiangsu Province (BK20130003).

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TABLE IIIRESOURCE CONSUMPTION (WAVELINK SLOTS)

Traffic proportion(short:medium:long)

10∶5∶1 20∶5∶1 40∶5∶1

Lightpath based algorithm 75779.9 62131.9 53069.9Light-tree based algorithm 61998.4 50547.8 43120.6

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