Photon Netw Commun (2012) 23:272–284DOI 10.1007/s11107-011-0358-3

A heuristic algorithm for lightpath scheduling in next-generationWDM optical networks

Goran Markovic · Vladanka Acimovic-Raspopovic ·Valentina Radojicic

Received: 26 July 2011 / Accepted: 29 November 2011 / Published online: 15 December 2011© Springer Science+Business Media, LLC 2011

Abstract We study the routing and wavelength assignment(RWA) problem of scheduled lightpath demands (SLDs) inall-optical wavelength division multiplexing networks withno wavelength conversion capability. We consider the deter-ministic lightpath scheduling problem in which the whole setof lightpath demands is completely known in advance. Theobjective is to maximize the number of established lightpathsfor a given number of wavelengths. Since this problem hasbeen shown to be NP complete, various heuristic algorithmshave been developed to solve it suboptimally. In this paper,we propose a novel heuristic RWA algorithm for SLDs basedon the bee colony optimization (BCO) metaheuristic. BCOis a newborn swarm intelligence metaheuristic approachrecently proposed to solve complex combinatorial optimi-zation problems. We compare the efficiency of the proposedalgorithm with three simple greedy algorithms for the sameproblem. Numerical results obtained by numerous simula-tions performed on the widely used realistic European Opti-cal Network topology indicate that the proposed algorithmproduces better-quality solutions compared to those obtainedby greedy algorithms. In addition, we compare the resultsof the BCO–RWA–SLD algorithm with four other heuris-tic/metaheuristic algorithms proposed in literature to solvethe RWA problem in the case of permanent (static) trafficdemands.

Keywords Bee colony optimization (BCO) · Routingand wavelength assignment (RWA) · Scheduled lightpathdemands (SLD) · Optical network

G. Markovic (B) · V. Acimovic-Raspopovic · V. RadojicicDepartment of Telecommunication Traffic and Networks,The Faculty of Transport and Traffic Engineering,University of Belgrade, Vojvode Stepe 305, 11000 Belgrade, Serbiae-mail: g.markovic@sf.bg.ac.rs

1 Introduction

Optical networks employing wavelength division multi-plexing (WDM) technique are considered as a successfuland cost-effective solution capable of providing practicallyunlimited capacities required to satisfy the enormous growthof traffic that is expected in next-generation networks. InWDM optical networks, there is need to maximize the num-ber of all-optical connections (also known the lightpaths) orto minimize the blocking probability using the limited net-work resources. One of the most important issues in WDMoptical networking is to solve the lightpath routing and wave-length assignment (RWA) problem in an efficient way. Rout-ing and wavelength assignment (RWA) procedure finds outan appropriate route for a traffic demand and assigns a wave-length among the many possible choices for each lightpathsuch that no two lightpaths using the same wavelength passthrough the same link [1]. A review of different routing andwavelengths assignment algorithms can be found in [2]. It hasbeen shown that RWA is an NP-complete problem [3] thatcould be solved optimally only in the case of small problemdimensionality [4,5]. For large size problems, different heu-ristic and metaheuristic algorithms have been developed tosolve it efficiently [2,3,6–9]. Since heuristics and metaheu-ristics explore only a fraction of the solution space associ-ated with a problem instance, the solutions obtained by suchapproaches may not be guaranteed to be optimal.

Traffic demands in WDM optical networks can be classi-fied into three categories [10]: permanent (or static) lightpathdemands (PLDs), scheduled lightpath demands (SLDs) andrandom lightpath demands (RLDs). PLDs are fully known inadvance and have unlimited durations. SLDs are also knownin advance, but they are supposed to be active only for a lim-ited period (for example, few hours, days or weeks). Durationof each SLD is specified by its starting time and ending time.

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The SLDs for which setup and tear-down times are knownin advance can take the advantage of the time schedulingproperty. That is, unless two lightpaths overlap in time, theycan be assigned the same wavelength since the paths aredisjoint in time. The lightpath scheduling problem in whichthe whole set of demands is known in advance is known asthe deterministic lightpath scheduling problem. Unlike PLDsand SLDs, random lightpath demands (RLDs) arrive sto-chastically over time and have random durations. The prob-lem where the lightpath demands have to be served withoutany knowledge of future requests is known as the dynamiclightpath scheduling problem. In this paper, we study deter-ministic lightpath scheduling problem. This problem is alsoknown as the advance lightpath reservation (ALR) problem[11,12]. For the users who desire deterministic services, net-work resources have to be reserved in advance and guaranteedfor future use.

In realistic optical networks, it is likely that most of thedemands would be initially of PLDs and SLDs type. Thereason is that the traffic load in core optical networks, suchas WDM networks, is quite predictable because of its peri-odic nature [13,14]. Such traffic patterns could be predictedfrom historical statistics, which repeat every day (or week)with minor variations in timing and volume. Hence, we con-sider the problem of creating the set of SLDs from periodictraffic, i.e. scheduling the lightpaths. There are various peri-odic applications, which may be serviced more efficiently byscheduled lightpath demands. For example, SLDs becomehighly attractive for service providers, which offer opticalvirtual private network (OVPN) or bandwidth on demand(BoD) services. They have to establish the set of perma-nent lightpaths (PLDs) to provide minimal network connec-tivity and capacity requirements, but some scheduled light-paths (SLDs) have to be additionally established to increasethe required capacities during certain periods of a day or aweek.

Numerous articles are devoted to solve deterministic light-path scheduling problem in WDM optical networks [10–13,15–21]. A comprehensive review of various proposed algo-rithms can be found in [22]. Both exact and approximatemethods have been considered. Integer linear programming(ILP) models have been proposed in [23], and a branch andbound algorithm has been presented in [13]. Approximatemethods relying on the tabu search metaheuristic along withtwo simple and fast greedy algorithms are described in [17]and [13]. In [11], the Lagrangean relaxation (LGR) methodhas been used for solving the SLD problem. In [24], a simu-lated annealing-based algorithm is proposed to find a solutionon predetermined k-shortest paths. Fault-tolerant routing andwavelength assignment of SLDs was also studied in [15].

In this paper, we solve the lightpath scheduling problem inWDM optical network with the mixture of PLDs and SLDsusing the bee colony optimization (BCO) metaheuristics.

BCO is a new swarm intelligence metaheuristic approachthat has been recently proposed in [25] to solve various com-plex combinatorial optimization problems in an efficient way.A review of different BCO applications can be found in[26–28]. In our previous works [9,29,30], the BCO meta-heuristic has been already used to solve the RWA problem inoptical networks, but only in the case of static (PLDs) trafficdemands. In [9], it was shown that considerable improve-ments could be achieved by applying the BCO-based RWAalgorithm compared to heuristic algorithms suggested in [31]and [32] to solve the same problem. Our motivation here is toprove that by considering a more realistic traffic scenario (thecombination of SLDs and PLDs), additional improvementsin terms of the number of established lightpaths for a givennumber of wavelengths could be achieved. Consequently, wepropose here a novel BCO-based heuristic RWA algorithm tosolve the lightpath scheduling problem in optical WDM net-works operating under the wavelength continuity constraintwith the mixture of PLDs and SLDs traffic demands. Notethat the PLD could be considered as a special case of SLD, forwhich the starting time is zero and ending times is unlimited.

The rest of the paper is organized as follows. Section 2gives the statement of the lightpath scheduling problem.In Sect. 3, the basic principles of the BCO metaheuristic,which is used here as an efficient tool to solve the consid-ered optimization problem, are given. Section 4 gives detailedexplanation of the proposed BCO–RWA–SLD algorithm forprovisioning the scheduled lightpaths in WDM optical net-works. In Sect. 5, the numerical results obtained by numeroussimulations over the realistic EON optical network topologyare given. Finally, in the last section, the concluding remarksare given.

2 Problem statement

We consider a WDM optical network composed of recon-figurable cross-connect nodes, which are linked in a meshtopology with a given number of available wavelengths oneach fiber link. We suppose that wavelength conversion is notpermitted in network nodes and that there is no limit on thenumber of transmitters and receivers at each node. We con-sider the mixture of PLDs and SLDs traffic demands withthe possibility of multiple requested lightpath demands for agiven node pair, simultaneously.

By introducing the following notations:

G− graph that represents physical topology of opticalnetwork,

N− number of nodes in given network,L− number of physical links,W− number of wavelengths available on each link

(same for each link),

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D− total number of lightpath demands (both PLDs andSLDs),

T − number of discrete time slots,k− number of candidate routes for a lightpath demand,

the considered lightpath scheduling problem can be formu-lated as follows:

For the given set of lightpath demands and a given physi-cal network topology represented by G = (N , L), the goal isto determine a routing and a wavelength assignment (RWA)schedule that maximizes the number of established lightpathsfor the given number of wavelengths, W . To establish a light-path, it is necessary to choose an available route from theset of candidates routes (with at least one same wavelengthon each link along the selected route) and assign one freewavelength to a lightpath from source node s to destinationnode d.

The set of traffic demands is composed of PLDs and SLDswith various percentages in total demand D. A PLD i can berepresented by a triple (si , di , qi ), where si and di are thesource the destination nodes of the PLD, respectively, andqi is an integer number representing the number of light-paths required to be established between nodes si and di .Note that a demand for which qi > 1 lightpaths may exist ifthe requested rate is greater than the nominal rate of a light-path (that is typically 2.5, 10, or 40 Gbit/s). As well, an SLDi could be represented by a quintuple (si , di , qi , t start

i , tendi ),

where t starti and tend

i are starting time and ending time ofdemand i , respectively. Lightpaths are scheduled to be setup at the beginning of their starting time slots t start

i and betorn down at the end of their ending time slots tend

i . Notethat if we set all SLDs with the same starting and endingtimes, such problem is reduced to the RWA with PLDs,only.

To make possible lightpath scheduling, the time is slotted.Let T be the total number of time slots for which the trafficis defined. Each time slot t = 1, 2, . . . , T is assumed to havethe same (fixed) length. The wavelength availability in a timeslot is independent of its availability in other time slots. As aresult, a wavelength can be reused over different links as wellas multiple time slots. Since scheduled lightpath demands arenot commonly simultaneous, some network resources can bereused by different lightpaths, provided that these lightpathsdo not overlap in time. By improving the utilization of net-work resources, number of established lightpaths could beincreased [33].

The deterministic lightpath scheduling problem can beformulated as an ILP problem. Since such problem has beenshown to be NP complete, it is unlikely to obtain an exactsolution for the realistic size networks. Due to the high com-plexity of the problem, to make possible to find a solutionin an efficient way, we propose here a new BCO-based heu-ristic algorithm for routing and wavelength assignment of

scheduled lightpath demands (RWA-SLD) in optical WDMnetworks. In the following section, we firstly describe in shortthe basic principles of the BCO metaheuristic.

3 BCO metaheuristic—the basic principles

The BCO is stochastic swarm intelligence metaheuristicapproach capable of solving various complex combinato-rial optimization problems [26,27]. Swarm intelligence isthe part of artificial intelligence based on studying actions ofindividuals in various decentralized systems. BCO is inspiredby the foraging habits of bees in the nature while lookingfor a food. The communication systems between individ-ual insects contribute to the configuration of the “collectiveintelligence” of the social insect colonies. The artificial beecolony behaves partially alike and partially differently frombee colonies in nature.

The central idea behind the BCO is to create an artifi-cial multiagent system or the colony of artificial bees thatcollaboratively searches for the optimal solution of a prob-lem. They explore the search space looking for the feasi-ble solutions. Each artificial bee generates one solution tothe problem. During the search process, artificial bees com-municate directly. Every bee performs the so-called forwardand backward passes throughout the artificial network. Dur-ing each forward pass, every bee is exploring the searchspace (tries to find a feasible solution of the problem). Dur-ing the backward pass, bees are “flying” back to the hiveand exchange the information about the qualities of the cre-ated partial solutions. In the hive, bees participate in a deci-sion-making process. Based on the quality of the generatedpartial solutions, some bees abandon from its solutions andsome of them continue to expand the same partial solu-tion with or without recruiting the other bees. This proce-dure is performed iteratively until some stopping conditionis met. The more detailed description of the BCO princi-ples could be found in [25–28]. In the following section,we suggest a BCO-based deterministic lightpath schedul-ing algorithm tailored to solve the RWA problem of SLDsin WDM optical networks. We shortly named it the BCO–RWA–SLD algorithm. This algorithm represents the exten-sion of the basic BCO-RWA algorithm previously proposedin [9] to solve the RWA problem of PLDs. The central mod-ifications include its upgrading to provide temporal featurerequired for SLDs with the goal to utilize the wavelengths ina more efficient way. In addition, the algorithm is modifiedin terms of lightpath demands ordering and the mechanismof its selection based on the new proposed bee’s utilities aswell as by the applied method for route selection and thewavelength assignment strategy. In the following section,we describe in more detail the proposed BCO–RWA–SLDalgorithm.

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4 BCO-RWA algorithm for scheduled lightpathdemands

To explain the search process performed by bees, we createa multistage artificial network throughout the bees that are“flying”, which is given by Fig. 1 [9].

Let us represent every requested lightpath by an artifi-cial node in a given network. Each artificial node representsa part of the physical optical network topology. More pre-cisely, each artificial node represents small network that con-tains all candidate routes for the considered lightpath demandbetween given source and given destination, which are spec-ified in advance.

The artificial network is organized throughout stages.Each stage (represented by one column of artificial nodes)contains D nodes, where D represents the total number ofrequested lightpath demands (PLDs and SLDs) in a givenoptical network. Additionally, the artificial network consistsof D stages. Hence, there is totally D × D nodes in a givenartificial network.

Let the total number of bees engaged in the search processbe B. All artificial bees are located in the hive at the beginningof the search process. When flying through the space, beesperform forward pass and backward pass. Figure 2 illustratesthe first forward and backward pass of the search process.During a forward pass, every bee visits n unvisited artificial

Fig. 2 First forward and backward pass [9]

nodes (bee tries to establish n new lightpaths). The number ofnodes n to be visited during each forward pass is prescribedby the analyst at the beginning of the search process. After

Fig. 1 Artificial network [9]

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that, all bees perform backward pass, i.e. they return to thehive. In the hive, all bees participate in a decision-makingprocess.

We assume that every artificial bee can obtain the infor-mation about solutions’ quality generated by all other bees.In this way, bees exchange information about the quality ofpartial solutions created. Bees compare all generated partialsolutions. Based on the quality of the partial solutions, everybee decides whether to abandon the created partial solutionand become again uncommitted follower, continue to expandthe same partial solution without recruiting the nestmatesor dance and thus recruit the nestmates before returning tothe created partial solution. Depending on the quality of thepartial solutions generated, every bee possesses certain levelof loyalty to the path leading to the previously discoveredpartial solution. When they reach the end of the path, bees arefree to make individual decision about next artificial node(s)to be visited. Sequence of the artificial nodes visited by abee represents one partial solution of the problem consid-ered.

After the first pass throughout the network is finished, thesecond forward pass is started. During the second forwardpass (Fig. 3), by visiting n more unvisited nodes, bees expandcreated partial solutions (try to establish additional n newlightpaths) and after that perform again the backward pass(return to the hive). In the hive, bees will again participate ina decision-making process, make a decision, perform thirdforward pass, etc. The iteration ends when each bee visits allartificial nodes (D) in a given network. The best discoveredsolution during the first iteration is saved, and then, the sec-ond iteration begins. Within the second iteration, bees againincrementally construct solutions of the problem, etc. At the

end of iterations, one or more feasible solutions of the RWAproblem are created.

4.1 Bee’s node choice mechanism

A bee is choosing artificial nodes (lightpath demands) in arandom manner, but with the probability proportional to theduration of a demand. The main idea behind that is to forcethe bees to choose firstly those demands with longer dura-tion for which it is more difficult to provide free wavelengths(throughout more number of continuous time slots) in a net-work. In addition, lightpaths with longer durations could bepreferable for a service provider because of higher proba-ble revenues they would offer to him. For that reason, alllightpath demands are sorted according to its durations, withthe PLDs located on the top of the list. We define the util-ity V b

i that the bee b has to select a SLD i by the followingequation:

V bi = tend

i − t starti = T service

i (1)

where T servicei is the service time (duration) of a requested

demand i . For the PLDs, the same durations T servicei = T are

assumed, where T is the total number of time slots duringthe considered period. Longer the duration of a demand, thegreater is the utility for a bee to choose it. Based on the bee’sutility, we define the probability pb

i that a bee b will choosea demand i , given by the following equation:

pbi = V b

iJ∑

j=1V b

j

(2)

Fig. 3 Bee’s flight throughout the artificial network during the first and second pass [9]

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where J is the number of demands not previously cho-sen by bee b. Using the Eq. (2) and a random numbergenerator, a lightpath demand i that will be tested by thebee b is chosen. In this way, bees are favoured to choosefirstly longer demands, but also the demands with shorterdurations have a chance to be chosen firstly by a bee, butwith smaller probability. Consequently, different bees willchoose lightpath demands in different order.

4.2 Routing and wavelength assignment

Our RWA algorithm uses fixed-alternate routing and a first-fit (FF) wavelength assignment strategy. In fixed-alternaterouting, a set of k− alternate shortest routes are computed inadvance for each source/destination pair in the network, andthey are used as the candidate routes for the demand. Thesek-shortest paths should also satisfy the path length constraint.If multiple lightpath demands are requested for a node pair,they could be established over different routes, i.e. bifurcatedrouting is used. The first available route from the set of can-didate routes is chosen. If such a route exists, the consideredlightpath is established, and the network resources are beingreserved for its duration. Otherwise, a lightpath demand isrejected. For the wavelength assignment problem, the first-fit(FF) strategy is used. In the FF wavelength selection strat-egy, the wavelengths are numbered in ascending order. Whensearching for an available wavelength, a lower numbered isconsidered before a higher-numbered one.

4.3 Bee’s partial solutions comparison

When all the bees visit n artificial nodes, they perform back-ward pass and return to the hive to compare the quality ofpartial solutions generated. Based on this information, beesmake decisions about the future “flying” throughout the arti-ficial network.

The probability that bth bee at the beginning of the newforward pass is loyal to its previously generated partial solu-tion is expressed as follows:

pb = e− Cmax−Cbu (3)

where Cb total number of demands satisfied by the bth beefrom the beginning of the search process; Cmax maximalnumber of demands satisfied by any bee from the beginningof the search process; u ordinary number of forward pass.

We can see from the Eq. (3) that if a bee has discovered thebest partial solution in forward pass u(Cb = Cmax), the beeb will continue to fly along the same partial tour in the u + 1forward pass with the probability pb = 1. Better-generatedpartial solutions (greater values of Cb) implies higher prob-ability that the bee b will be loyal to the previously discov-ered partial solution. At the beginning of the search process

(smaller values of u), bees are “more brave” to search thesolution space. Greater the ordinary number of the forwardpass u, the smaller is the bees’ “freedom of flight”. In otherwords, the more approaching to the end of the search pro-cess, bees are more focused on the already discovered partialsolutions. Using the relation (3) and a random number gen-erator, for each artificial bee, it is decided whether to becomeuncommitted follower or to continue flight along the previ-ously generated path.

4.4 Bees recruiting process

For each uncommitted bee with a certain probability, it isdecided which recruiter it would follow. In such a way, withineach backward pass, all bees are divided into two groups(R recruiters and remaining B − R uncommitted bees). Val-ues for R and B − R are changing from one backward passto another one. The probability pb that b’s partial solutionwould be chosen by any uncommitted bee is equal to

pb = Cb∑R

i=1 Ci, b = 1, 2, . . . , R (4)

where Ci is the objective function value of the i th advertisedpartial solution and; R is the number of recruiters.

The random number is generated from the interval [0, 1]for every uncommitted follower. Using these random num-bers and the relation (4), every uncommitted follower is“assigned” to one of the dancing bees. In this way, the numberof bees flying along specific path is changed before beginningof the new forward pass. Using collective knowledge andsharing information among themselves, bees concentrate onmore promising search paths and slowly abandon less prom-ising paths. Based on the described algorithm, we developeda particular program code to make simulation tests.

5 Experimental results

In this section, we evaluate the performance of the proposedBCO–RWA–SLD algorithm by performing numerous sim-ulation experiments for the optical WDM network exam-ple under randomly generated traffic demands. The programcode was implemented using the MATLAB software pack-age. Developed software application enables us to find out thesolution of the considered RWA problem in an efficient wayfor various traffic scenarios and different network topologies.For illustration, we provide here the results obtained for real-istic backbone EON (European Optical Network) topologywith N = 20 nodes and L = 39 bidirectional links, shown byFig. 4. We assumed that each physical link consists of a pairof unidirectional optical fibers, one for each direction, withthe same number of wavelengths W over each fiber link andthat there is no wavelength conversion in nodes. It requires

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2

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Fig. 4 EON (European optical network) topology [34]

that the same wavelength have to be available on each linktraversed by a lightpath. We have run the simulator for severaltraffic scenarios. In each case, lightpath demands are madefor a period of one day (24 h).

The following input parameters are assumed in all simu-lation experiments: the number of bees engaged in the searchprocess B = 10, the number of algorithm iterations I = 10,the number of artificial nodes visited during each forwardpass n = 1, maximal number of candidate routes for a nodepair k = 5 and duration of each time slot �t = 15 min.Note that decreasing the duration of the time slot directlyaffects the complexity of the problem as well as the effi-ciency of the algorithm. With a shorter time slot, there arefewer requests per time slot and consequently more lightpathscould be established. The SLDs are generated randomly withthe start time and durations following the uniform distribu-tion. If the requested start time of a lightpath is occurred atany time within a time slot, it is assumed that entire slot t

is required for that lightpath. In other words, a lightpath canonly be scheduled at the beginning of a time slot. Duration(service time) of each SLD is fixed and could be specifiedas the integer multiple of one time slot duration �t . Suchinteger numbers were generated from the range [1,T ], wherethe total number of time slots is assumed to be T = 96. Thisvalue corresponds to the maximal number of (15-min) timeslots during 24 h. The source and destination nodes for boththe PLDs and the SLDs are chosen according to a randomuniform distribution of integer numbers in the interval [1,20].On any source–destination pair, we assume that there can bemultiple demands. The generated traffic demand matrix rep-resents the number of lightpath demands required betweenany two nodes. We generated various traffic scenarios forsimulation experiments, with the total number of lightpathdemands, D, ranging from 100 to 1,000 and various propor-tions between PLDs and SLDs. We assumed the absolutepriority of PLDs, which means that all PLDs are consideredfirstly (before any SLD), while establishing the lightpaths ingiven network.

First, we give the results for a particular traffic pattern ofD = 500 required lightpath demands (Fig. 5). The resultsare obtained by numerous test cases performed with differ-ent number of wavelengths (for boundary values of PLDsand SLDs percents), with the number of alternate routes kvaried between 1 and 5.

For each discrete result shown in Fig. 5, a separate simu-lation is performed by running developed software applica-tion. Given results are the best values obtained throughoutI = 10 algorithm iterations. It could be seen that the num-ber of established lightpaths greatly depends on the numberof available wavelengths over fiber links, W , the number ofcandidate routes, k, between end nodes as well as the percentof SLDs. It can be seen that significantly fewer number ofwavelengths is required to establish all lightpath demands

SLD=0%

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path

s k= 1

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k= 1 47 134 229 302 364 418 459 489 500

k= 2 46 135 231 317 385 439 477 496 500

k= 3 44 127 233 321 389 442 481 498 500

k= 4 43 127 228 314 389 443 482 498 500

k= 5 42 130 227 323 387 445 486 498 500

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k= 1 71 211 335 371 472 498

k= 2 75 224 357 423 484 500

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k= 4 79 229 364 450 491 500

k= 5 77 223 367 454 493 500

1 4 8 12 16 20

Fig. 5 Number of established lightpaths versus number of wavelengths when D = 500 demands in the cases of completely permanent demands(SLD = 0%) and completely scheduled demands (SLD = 100%)

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when SLD = 100%. In addition, when the number of alter-nate routes is increased (up to k = 5), more lightpaths couldbe established for a given number of wavelengths (Fig. 6).However, the most improvements are achieved between thecase of fixed routing (k = 1) and the case of fixed-alternaterouting for k = 2. If the number of alternate routes is furtherincreased (k > 2), longer routes could be used to estab-lish the lightpaths, which yields to ineffective utilization ofresources. Hence, the number of established lightpaths couldnot be significantly increased by using more candidate routes.In addition, the number of established lightpaths is increasedif the percent of SLD demands in total demand is greater. Itis illustrated by Fig. 6.

Based on the performed simulations, it is able to obtainthe results of the maximal number of established lightpaths

W=16

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% of scheduled demands

# of

est

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path

s k = 1k = 2k = 3k = 4k = 5

Fig. 6 Percent of established lightpaths for different proportions ofSLDs in total demand D and various number of candidate routes k(W =16, D = 500)

for various percentages of SLDs in total demand, differentnumber of candidate routes k (between 1 and 5) and numberof available wavelengths, W . Figure 7 directly shows how thetype of traffic demands affects the efficiency of the algorithm.As it could be seen, greater the percent of SLDs is, morelightpaths could be established (note that PLDs + SLDs =100%).

We also performed numerous simulations for differenttraffic scenarios in the considered EON network by chang-ing the total number of requested lightpath demands between100 and 1,000. We assumed the uniform distribution ofthe requested number of demands between node pairs. Theobtained results are given by Fig. 8 (in the cases of W = 16and W = 32), which validate the fact that the number ofestablished lightpaths is decreased by increasing the trafficload in a network.

This fact stands for all percentages of SLDs, but the differ-ences between boundary values of SLDs (that correspond tofully permanent and fully scheduled demands) are more sig-nificant at higher network loads. It can be seen (for W = 16)that up to 26% more demands could be satisfied in the caseof SLD = 100% compared to the case of fully permanentdemands (SLD = 0%). If the number of wavelengths is small(W = 16), the percent of established lightpaths is decreasedsignificantly faster compared to the case when the numberof wavelengths is better scaled (W = 32). In addition, thedifferences between various percents of SLDs are reducedif the number available of wavelengths is dimensioned moreproperly for given traffic scenarios.

To evaluate the quality of the solution obtained by theproposed BCO–RWA–SLD algorithm, we compare it withthree simple greedy heuristics that we called LDF (longerduration first), ESF (earlier started first) and EFF (earlier fin-

Fig. 7 Maximal number ofestablished lightpaths fordifferent number of availablewavelengths and proportions ofSLDs in total demand(D = 500)

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Fig. 8 Percent of establishedlightpaths for different numberof requested demands (W = 16and W = 32)

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SLD=50%

SLD=100%

ished first). These heuristics differs according to the orderby which the lightpath demands are tried to be established.In the LDF heuristic, all SLDs are sorted in the list accord-ing to the durations of individual demands, with the longestdemand on the top. If two or more SLDs have the same dura-tions, they are located randomly in the sorted list. For othertwo heuristics (ESF and EFF), the lightpath demands aresorted in the list according to the starting and ending timesof the lightpath demands, respectively. Again, all of the SLDsare positioned in the lists after the PLDs (if they exist). ThePLDs are sorted randomly with uniform probability distribu-tion of node pair selection. To begin with, we compare theresults of the proposed BCO algorithm with the LDF heuristic

(Fig. 9) for different number of requested lightpath demands.We can see that BCO always outperforms LDF heuristic orat worst gives the same results (for lower values of trafficdemands).

In Fig. 10, the BCO is compared to all considered greedyheuristics. From the obtained results, we can see that whensorting traffic demands differently (i.e., by applying LDF,ESF or EFF), the BCO algorithm provides superior perfor-mances in terms of number of established lightpaths at highervolumes of offered traffic. The equal solutions obtained forlower number of requested lightpath demands are the resultsof over-dimensioning of network resources for such traffic

W=16, SLD=0%

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LDF 100 200 293 334 356 380 393 413 424 445

BCO 100 200 300 360 387 405 429 430 440 448

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LDF 100 200 300 391 482 541 599 575 595 597

BCO 100 200 300 394 486 543 621 647 674 712

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LDF 100 200 300 400 498 571 633 669 684 720

BCO 100 200 300 400 500 594 669 709 732 766

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LDF 100 200 300 400 500 600 700 796 872 951

BCO 100 200 300 400 500 600 700 800 891 968

100 200 300 400 500 600 700 800 900 1000

Fig. 9 Comparison of the results for BCO and LDF heuristic

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W=16, SLD=100%

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LDF 100 200 300 391 482 541 599 575 595 597

ESF 100 200 300 391 468 524 589 623 603 672

EFF 100 200 300 390 474 521 601 631 647 701

BCO 100 200 300 394 486 543 621 647 674 712

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LDF 500 600 700 796 872 951

ESF 500 600 700 795 870 937

EEF 500 600 700 796 874 939

BCO 500 600 700 800 891 968

500 600 700 800 900 1000

LDFESFEEFBCO

Fig. 10 Comparison of the BCO with LDF, EFF and EFF heuristics

demands. Hence, the order in which the lightpath demandsare arranged is not relevant in such cases.

Finally, we compare the results of the proposed BCO–RWA–SLD algorithm with four other heuristic/metaheuris-tic algorithms, for which the results of the same consideredproblem in EON network (for the case of D = 374 light-path demands) could be found in literature. These are thealgorithm A and algorithm B, which are proposed in [31],Tabu metaheuristic algorithm proposed in [32] and BCO-based metaheuristic algorithm proposed in [9] for solvingthe RWA problem in the case of fully permanent lightpathdemands (PLDs). The comparative results obtained by vari-ous considered algorithms are given in Fig. 11. As it could be

seen, the results obtained by the proposed BCO–RWA–SLDalgorithm (for completely scheduled lightpath demands, i.e.SLD = 100%) significantly outperform all other algorithms.In other words, the number of wavelengths required to satisfyall requested demands in given network could be consider-ably reduced by applying our proposed BCO-based algo-rithm for scheduled lightpath demands.

All simulation experiments were performed using thePC with the Intel(R) Core(TM)2 Duo 3 GHz processor and3.49GB of RAM. The required CPU run times for various rel-evant input parameters values are given in appendix. Keepin mind that the proposed algorithm is not supposed to beexecuted in a real-time environment, but as a batch process

Fig. 11 Comparison of theBCO–RWA–SLD withBCO-RWA-PLD, Tabu and twoLP- relaxations basedalgorithms (A and B)

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Tabu

Algorithm A

Algorithm B

BCO_RWA_SLD 353 363 369 372 374 374 374 374 374 374 374 374 374 374 374

BCO_RWA_PLD 264 285 301 315 326 338 348 354 361 365 370 372 374 374 374

Tabu 281 294 307 318 328 338 345 352 356 361 366 370 372 374 374

Algorithm A 262 274 284 295 310 316 319 333 339 340 343 347 355 361 367

Algorithm B 250 265 278 290 308 314 318 325 334 337 340 347 352 361 364

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

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that could be carried out over a long time (for instance, up tofew hours or even more).

6 Conclusion

Lightpath scheduling is an important capability in next-generation WDM optical networks to reserve resources inadvance for a specified time period while provisioning end-to-end lightpaths. In this paper, we studied the determinis-tic lightpath scheduling problem, which implies solving therouting and wavelength assignment (RWA) problem of light-path demands whose setup and tear-down times are knownin advance. Since this problem is highly complex, its solu-tion for larger instances by using exact methods is infeasible.To solve the RWA problem of scheduled lightpath demands(SLDs) in an efficient way, we suggested the BCO-basedmetaheuristic algorithm (BCO–RWA–SLD). It was shownthat by applying the proposed algorithm significant improve-ments (more than 25%) in terms of the number of establishedlightpaths could be achieved by taking into account temporalinformation of lightpath demands compared to the case whenthis information is not considered. The gain is achieved by

exploiting the time disjointness among demands such that asame wavelength channel can be re-used by several lightpathsat different times. We considered three timing-related greedyheuristics in our experiments to compare the performancesof the BCO–RWA–SLD algorithm in terms of the number ofestablished lightpaths. Experimental results obtained over thewidely used EON network have shown that our BCO algo-rithm achieves better-quality solutions compared to greedyalgorithms, which have shorter execution times. However,the BCO–RWA–SLD heuristic algorithm is robust and highlytractable and thus could be used to solve sizeable probleminstances in reasonable computation time.

Acknowledgments This paper was supported by the Serbian Ministryof Education and Science (project # TR-32025).

Appendix

The computer execution time to find the solutions by BCOalgorithm depends mainly on the number of algorithm itera-tions, I , the number of bees engaged, B, the number of light-path demands, D, the number of wavelengths, W, as wellas the number of time slots T and the number of candidate

Fig. 12 CPU times for various problem dimensionalities

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routes k. Figure 12 illustrates the required CPU run times forsome of the mentioned algorithm’s parameters. It can be seenthat the number of bees significantly affects the required CPUtimes, but the solutions quality (number of established light-paths) are not improved if it is increased. Thus, we limitedthe number of bees to B = 10 in all simulation experiments.

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Author Biographies

Goran Markovic received his B.Sc., M.Sc.and Ph.D. degrees in telecommunication traf-fic engineering from the University of Bel-grade, Serbia, in 1996, 2002 and 2007,respectively. Since 1997, he has been with theDepartment of Telecommunication Traffic atThe Faculty of Transport and Traffic Engi-neering, University of Belgrade, where he iscurrently an Assistant Professor. His researchinterests are concerned with traffic routing in

communication networks, optical networking and application of swarmintelligence for solving the optimization problems in telecommunica-tion network design.

Vladanka Acimovic-Raspopovic receivedher B.Sc. (1976), M.Sc. (1984) and Ph.D.(1995) degrees in electrical engineering fromthe University of Belgrade. She is a Profes-sor at the University of Belgrade, Telecom-munication Networks Department—Facultyof Transport and Traffic Engineering. Shehas over 100 research publications mostly onoptical transmission systems design and opti-cal networking. Her current research interests

are in the field of performance evaluation, QoS routing and traffic engi-neering in next-generation broadband networks.

Valentina Radojicic Ph.D., is an Associ-ate Professor at University of Belgrade, TheFaculty of Transport and Traffic EngineeringDepartment of Telecommunication Trafficand Networks. She received her first degreein telecommunication engineering (1986),M.Sc. (1996) and Ph.D. (2002) at The Fac-ulty of Transport and Traffic Engineering,University of Belgrade. Currently, she isemployed as vice-dean of The Faculty of

Transport and Traffic Engineering. Her research interests are optimi-zation problems in telecommunication network design and planning,development of services, strategic modeling of telecommunication andforecasting of new telecommunication product/services.

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