Cost Minimization Planning for Greenfield Passive Optical Networks

J. Li and G. Shen VOL. 1, NO. 1 /JUNE 2009/J. OPT. COMMUN. NETW. 17

Cost Minimization Planning forGreenfield Passive Optical Networks

Ji Li and Gangxiang Shen

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Abstract—We plan greenfield PON networks tominimize their total deployment costs. We propose anefficient heuristic called the Recursive Associationand Relocation Algorithm (RARA) to solve the optimi-zation problem. Our algorithm can significantly re-duce PON network deployment costs compared to anintuitive random-cut sectoring approach. To furthertune down the costs, we also exploit the opportunityof cable conduit sharing by proposing an extension toRARA. Our case studies show that there are saturat-ing trends for the PON deployment costs with the in-crease of the three system parameters, includingmaximal optical split ratio, maximal transmissiondistance, and maximal differential distance. Also, toreduce computation time for large PON deploymentscenarios, we propose a disintegration planningmethod to divide a large planning scenario into sev-eral small ones. The method is found to be effective toprovide close performance, but require much lesscomputation, compared to the situation without dis-integration.

Index Terms—PON deployment; Cost minimization;Sectoring approach; RARA; Disintegration.

I. INTRODUCTION

W ith the growing popularity of bandwidth-intensive services such as HDTV, VoD, peer-to-

peer, and video conferencing applications, there is anincreasing demand on broadband access. To meet thisdemand, the access networks are evolving from thetraditional DSL and cable techniques to a new genera-tion of fiber-based access techniques. Fibers are per-meating from the curb (FTTC), through the building

Manuscript received March 10, 2008; revised April 26, 2009; ac-cepted May 4, 2009; published June 1, 2009 �Doc. ID 111138�.

Part of this research has been presented at OFC/NFOEC 2008 [1].Ji Li is with the Australian Research Council Special Research

Centre for Ultra-Broadband Information Networks (CUBIN), anaffiliated program of National ICT Australia, Electrical andElectronic Engineering (EEE) Department, The University ofMelbourne, Victoria 3010, Australia (e-mail:[email protected]).

G. Shen was with the University of Melbourne. Now he is withCiena Corporation, 920 Elkridge Landing Road, Linthicum,Maryland 21090, USA (e-mail: [email protected]).

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FTTB) and the node (FTTN), eventually to the homeFTTH) [2,3]. Today there are two major types of pas-ive optical access networks (PONs), i.e., Ethernetassive optical networks (EPONs) [2,4] and gigabit-apable passive optical networks (GPONs) [5,6].PON is a type of network based on the traditionalthernet technique. An EPON can provide 1 Gb/s ca-acity in both upstream and downstream directionsnd cover a distance of up to 20 km as well as support20 km differential distance.1 In contrast, GPON is a

tandard evolved from the traditional ATM PONAPON) technique. A GPON can support higher band-idth, up to 2.5 Gb/s, in both upstream and down-

tream directions. It can cover a longer distance, up to0 km, and support a differential distance of up to0 km.Much research has been carried out for passive op-

ical networks. First, as bandwidth allocation in thepstream direction in both EPON and GPON is one ofhe most challenging issues, many investigations haveeen dedicated to efficient bandwidth allocation andoS support [2,7,8]. A range of efficient schedulingnd bandwidth allocation strategies have been devel-ped and evaluated [7,8]. Second, transmission dis-ance and capacity are also essential to passive opticaletworks. In order to support users in rural areas whore far away from a central office, the maximal trans-ission distance of a PON is being extended from

tandardized 20 km or 60 km, to up to 100 km [9].lso, to provide even higher bandwidth, a new genera-

ion of PON techniques is being developed to increasehe transmission capacity by either shortening theime duration of each data bit or increasing the num-er of parallel transmission channels. IEEE 10GPON standards are being developed to increase thePON transmission capacity from 1 Gb/s to 10 Gb/s

10]. Wavelength division multiplexing (WDM) trans-ission techniques are also being applied to upgradeON transmission capacity several times [9].On the other hand, optimal design and planning for

ON networks is important to PON deployment.1We define the coverage (also called reach) of a PON as the maxi-al transmission distance between an OLT and an ONU and theifferential distance for a PON as the difference between the fiberistances of different ONUs to a central OLT within the PON.

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18 J. OPT. COMMUN. NETW./VOL. 1, NO. 1 /JUNE 2009 J. Li and G. Shen

Little research has been performed in this direction.Only very recently, there was a study that tried tominimize the total PON network deployment cost [11].The study, however, considered several small deploy-ment scenarios. More generalized approaches are thusrequired for practical deployment with hundreds ofoptical network units (ONUs).

In this paper, we consider a generic approach forgreenfield2 PON network deployment, which is ca-pable of planning a large network scenario with hun-dreds of ONUs. We formulate the research problem ofPON network design and planning. We also developmathematical optimization models for the problem.Due to high computational complexity of solving theoptimization model, we also propose an efficient heu-ristic called the Recursive Association and RelocationAlgorithm (RARA) for suboptimal solutions. Extensivesimulation studies indicate that the proposed ap-proach RARA is much more efficient than an intuitiverandom-cut sectoring approach. In addition, we evalu-ate the impacts of PON system constraints, such asoptical split ratio, maximal PON transmission dis-tance, and maximal PON differential distance, on theoverall cost of PON deployment.

The rest of the paper is structured as follows. InSection II, we elaborate on the PON network deploy-ment problem and develop a mathematical optimiza-tion model for the problem. In Section III, we intro-duce an intuitive random-cut sectoring approach andan efficient heuristic, called the Recursive Associationand Relocation Algorithm (RARA). We also improvethe performance of RARA by combining it with an ex-tended minimum spanning tree (MST) approach to ex-ploit the benefit of cable conduit sharing among mul-tiple fiber links. In Section IV, we conduct simulationsto evaluate the performance of the proposed ap-proaches and gain insights into the factors that affectcosts of PON deployment. We conclude the paper inSection VI.

II. PROBLEM DEFINITION AND MATHEMATICALOPTIMIZATION MODEL

A. Problem Definition

Figure 1 shows an example of PON network plan-ning and deployment. Given a set of disperse loca-tions, with one ONU at each location, and a central of-fice on a given position, from which passive opticalnetworks are deployed to connect to the ONUs, our ob-jective for PON network deployment is to minimize itstotal cost. Specifically, the total cost is composed ofvarious subcosts, including (i) the system cost of PON,such as the costs of optical line terminals (OLTs) and

2Here the “greenfield” that we are considering is a kind of situa-tion where central offices have been constructed, while fiber con-duits and splitter cabinets are to be planned.

ptical splitters, (ii) the labor cost for trenching andaying fibers, and (iii) the cost of fiber cables.

In general, among all the above costs, the labor costf trenching and laying fibers is the most expensive,hich overwhelms all the other costs in the whole de-loyment. In addition, for PONs with differenteaches, the costs of their OLTs are different. A long-each PON generally has a more expensive OLT thanshort-reach PON. Also, for trenching and laying fi-

ers, in addition to the labor cost there could be otherosts such as the costs for a trenching permit, trafficnterruption, and other city considerations. However,or simplicity in this study we have ignored the costifference of OLTs and also do not consider the extraosts like a trenching permit because without realata these costs are always uncertain.The optimization problem needs to consider several

ON system constraints, including (i) maximal trans-ission distance, (ii) maximal differential distance,

nd (iii) optical split ratio. Typically, the optical splitatio ranges from 1:4, 1:8, 1:16, 1:32, 1:64, to up to:128. A 1:n optical splitter means that up to n ONUsan be connected to the splitter.3

In addition to the above system constraints, thereould be other constraints, such as legacy routing/onduits, road maps, private properties, and so on.his study assumes a greenfield deployment, in whichentral offices have been constructed and fiber con-uits and splitter cabinets are to be planned. The as-umptions are practical for the PON deployment inome rural areas and developing countries, where allhe network facilities need to be built from zero. Forore complicated constraints such as legacy routing/

onduits and road maps, the current greenfield net-3Given a specific optical split ratio, each user is ensured with a

ertain average data rate. For example, in a 1:16 EPON each ONUan obtain an average 60 Mb/s data rate. Thus, by controlling theaximal split ratio, we can control the bandwidth provided to eachNU user.

Fig. 1. (Color online) Illustration of PON networks.


work is still useful. First, the solutions to the currentgreenfield design can serve as lower bounds on the de-signs that consider more constraints. Second, the ap-proach developed in the paper can function as a base-line for extensions when more specific constraints areconsidered. For example, if a fiber link of an optimiza-tion solution based on the greenfield planing needs tocross a private property, which is, however, not acces-sible, we may make a local bypass to get around theproperty.

B. Mathematical Optimization Model

We develop an optimization model for the problem,which is as follows:

• Sets:— S: set of splitters. The size of S is the maximal

number of splitters allowed for a deployment.We normally set a large size as a startingpoint though the actual required number ofsplitters is smaller in the final solution. Forexample, if there are 500 ONUs in a design,then we can set the splitter set size to be 500since each ONU can only connect to a singlesplitter.

— Ts: set of splitter types, which is based on thesplit ratios. The splitter types can range from1:4, 1:8, 1:16, 1:32, 1:64, to up to 1:128 accord-ing to the PON standards.

— U: set of ONUs. Each ONU corresponds to ageographic position in a Euclidean plane.

• Parameters:— x0 ,y0: the position coordinates of the central

office (CO).— xi

o ,yio: the position coordinates of the ith ONU,

i�U.— �: a large value, which is set to be 105 in this

study.— Tk: the total number of outlet ports of the kth

type of splitter. For example, a 1:8 splitter haseight outlet ports.

— �: the cost factor or weight of the OLT. Asmentioned, though there can be a cost differ-ence for different types of OLTs under differ-ent PON reaches, for simplicity we use asingle cost factor for all types of OLTs.

— �i: the cost factor or weight of each outlet portof the ith type of splitter. For simplicity, weassume that the cost of each outlet port ofeach type of splitter in set Ts is identical.

— �: the cost factor or weight of trenching andlaying fibers (per kilometer). In this study, weassume a uniform cost for trenching and lay-ing fibers though the cost can be increased un-der some situations at which a trenchingpermit may be required or other city consider-ations should be taken into account.

— �: the cost factor or weight of fiber cables (perkilometer).

— lmaxtotal: the maximal transmission distance of a

PON between an OLT and an ONU, which isgenerally less than 100 km.

— lmaxdiff : the maximal differential distance be-

tween different ONUs within the same PON,which is generally less than 20 km.

• Variables:— xi

s ,yis: the position coordinates of the ith split-

ter, i�S.— �i: the usage indicator function of the ith

splitter. It takes the value of one if the splitteris used; otherwise, zero.

— �ij: the connection or association indicator

function between the jth ONU and the ithsplitter. It takes the value of one if the ONU isconnected to the splitter; otherwise, zero.

— �ik: the splitter type indicator function of the

ith splitter. It takes the value of one if thesplitter is the kth type; otherwise, zero.

— lis: the distance from the ith splitter to the cen-

tral OLT.— li

j: the distance from the jth ONU to the ithsplitter.

— limax: the maximal distance from an ONU to

the OLT in the ith PON, i�S. Each PON cor-responds to a splitter.

— limin: the minimal distance from an ONU to

the OLT in the ith PON.— i ,i

j: intermediate binary variables for “if andthen” conditions in the optimization model.

• The objective is to minimize the total cost of PONdeployment that interconnects all the ONUs tothe central OLTs, subject to the PON system con-straints including maximal transmission dis-tance, maximal differential distance, and opticalsplit ratio.Objective: minimize

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In the model, the total cost is made up of threeparts. The first part is the cost of OLTs, as each split-ter corresponds to a PON, which requires an OLT. Thesecond part is the cost of splitters, and the last partincludes the cost for trenching and laying fibers andthe cost of fiber cables.

Constraint (2) says that each ONU must connect toa splitter. Constraint (3) determines whether the ithsplitter should be deployed, which depends onwhether there are any ONUs connected to the splitter.If there are any, the splitter must be deployed; other-wise, not deployed.4 Constraint (4) selects a splittertype, which ensures that the splitter has sufficientoutlet ports to connect to all the ONUs.

Constraints (5)–(7) ensure an if-then condition. Ifthe ith splitter is selected, there must be only onesplitter type associated with the splitter. More specifi-cally, if �i=1 (i.e., the ith splitter is selected), then i=0 must hold, which further leads to �k�Ts

�ik=1 due

to constraints (5) and (6) (i.e., there is a single splittertype for the ith splitter). Constraint (8) computes thedistance from a splitter to the central OLT. Constraint(9) computes the distance from a splitter to an ONU.These two constraints are nonlinear, which makes thewhole optimization model nonlinear as well.

Constraints (10)–(12) find the maximal distanceand the minimum distance between an ONU and anOLT, respectively, within each PON. The constraintsare also based on an if-then condition. If �i

j=1 (i.e.,the jth ONU is associated with the ith PON or split-

4If there is only a single ONU connected to a splitter in the opti-mization results, we will manually remove the splitter from the re-sults as no splitter is required to connect a single user to an OLT.

er), then ij=0 must hold, which thus derives con-

traints (10) and (11) into lis+ li

j limax and li

min lis+ li

j,espectively.Constraint (13) ensures that the maximal transmis-

ion distance of a PON is not exceeded. Constraint14) ensures that the maximal differential distanceetween different ONUs within the same PON net-ork is satisfied.

. Discussion

The whole optimization problem can be divided intohree subproblems, i.e., (i) determining the total num-er of required PONs (i.e., splitters); (ii) associatingNUs to splitters, which is termed the ONU-splitterssociation subproblem, i.e., clustering ONUs intoroups that connect to common splitters; and (iii) re-ocating the positions of the splitters that achieve theptimal cost, which is termed the splitter relocationubproblem. The three subproblems entangle withach other. We need to jointly solve them to obtain anptimal solution to the whole problem.In the first subproblem, the total number of re-

uired PONs or splitters cannot be determined in ad-ance. The only way to evaluate the required numberf PONs or splitters that minimizes the total cost is tonumerate all possible partition patterns of ONUsnd then determine the optimal splitter location forach ONU cluster. The computation complexity of thisrute-force search increases factorially with the totalumber of ONUs, which is prohibitive for a largeumber of ONUs.The ONU-splitter association subproblem, i.e., sub-

roblem (ii), attempts to find an optimal associationetween ONUs and splitters, providing that the loca-ions of the splitters are given, i.e., the variables xi

s, yis,

i, lis, and li

j all become given parameters. With theseiven parameters, the previous optimization modelecomes a mixed integer linear programming (MILP)odel. Though it is possible to find an optimal asso-

iation for a medium-size planning scenario, the sub-roblem is still NP-complete, which is intractable for aarge planning scenario.

The third subproblem determines splitter locationsor each PON such that the total fiber length, which ishe sum of the fiber lengths from each ONU to theplitter, is minimum.5 This relocation problem is well-nown as the Fermat–Weber point problem (FWPP)12], which is a nonlinear optimization problem andhose objective function is convex, but not every-here differentiable [13]. Several algorithms arevailable to solve the problem. One of them is the5Because the cost of trenching and laying fibers is generally muchore expensive than other costs such as OLT and splitter costs, we

onsider minimizing the fiber length as a key objective when locat-ng an optical splitter.

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Weiszfeld algorithm [12,13]. We will adopt this algo-rithm as a subroutine in our subsequent heuristic.

In addition, the current optimization problem re-lates to the well-studied classical problem, called themultifacility location-allocation problem (MLAP),which was introduced by Cooper [14] in operations re-search. The MLAP aims to select the positions of dis-tributed warehouses, such that the total cost (usuallyrepresented by a Euclidean distance) to serve a set ofgiven service centers is minimal, if each service centeris served by one and only one distributed warehouse.Despite the similarity, the fiber deployment problemthat we consider here does show major differencesfrom the classical MLAP in several aspects as follows.

First, the fiber deployment problem is subject to themaximal transmission distance and the maximal dif-ferential distance of a PON, while in the MLAP, thereare no such corresponding constraints. Second, in thefiber deployment problem, the required number ofsplitters is not given in advance, which actually is apart of the solution to be determined, while the num-ber of required distributed warehouses is given andfixed in the MLAP. Finally, the splitter capacity is lim-ited in the fiber deployment problem, while the classi-cal MLAP allows warehouses to serve any number ofservice centers. Thus, based on the above comparison,the fiber deployment problem that we attempt to solveis even more difficult than the classical MLAP.

III. HEURISTIC ALGORITHMS

We propose two heuristics to solve the above PONdeployment problem. One is based on an intuitiverandom-cut sectoring approach, which is simple andused for performance comparison. The second is calledthe Recursive Association and Relocation Algorithm(RARA), which employs a recursive process to keep onexecuting the subroutines of ONU-splitter associationand splitter relocation until an optimal (at least lo-cally minimal) solution is found. Because among allthe PON deployment costs, the cost of trenching andlaying fibers is the most expensive, which overwhelmsall the other costs in the whole deployment, in both ofthe heuristics we have taken the total distance oftrenching and laying fibers as a major minimizationobjective.

A. Random-Cut Sectoring Algorithm

Like cutting a cake, the random-cut sectoring algo-rithm partitions all the ONUs into equal-size groupsaccording to their geometric positions. The size of eachgroup is equal to the maximal optical split ratio. Afterthe partitioning, Weiszfeld’s algorithm [12,13] is then

pplied to find the optimal splitter position for eachON. Finally, all the ONUs in the same groups con-ect to common splitters.6

Figure 2 illustrates an example of the above sector-ng approach. Given a set of disperse ONUs and an op-ical split ratio 1:4. We start from the positive direc-ion of the vertical axis, which is randomly selected,nd rotate the radius line in the clockwise directionor ONU grouping. A radius line is drawn when fourNUs are included in the current section. The rota-

ion will continue until all the ONUs are grouped orlustered.

. Recursive Association and Relocation AlgorithmRARA)

The Recursive Association and Relocation Algo-ithm (RARA) is extended from Cooper’s algorithm15], which has been used to solve the MLAP in logis-ics studies. The flowchart of RARA is shown in Fig. 3.

The left column implements an outer loop, whichonsists of several steps. Step 1 randomly generatesn initial set of splitters, i.e., a set of locations. To findhe best design, the size of the initial splitter set s willake all the values from a minimum value, Smin, to aaximal value, Smax. Smin equals the minimum re-

uired number of splitters to connect all the �U�NUs, i.e., Smin= ��U� /n�, where 1:n is a maximal al-

owed split ratio. Smax is set to be the total number ofNUs, �U�, which corresponds to an extreme case that

ach splitter connects to a single ONU. Furthermore,6If the total number of ONUs is not an integer multiple of the split

atio, the number of ONUs in the last group is less than the splitatio. Also, no system constraints such as maximal PON reach andaximal PON differential difference are considered in this simple

lgorithm. For real deployment, a further step is required to verifyhether each of the planned PONs meets the system constraints.

ig. 2. (Color online) An example of the random-cut sectoringpproach.

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to avoid falling into a local minimum, for each specificsplitter set size s, which is a value within the rangefrom Smin to Smax, we randomly generate N differentinitial splitter sets (splitters positions). These N setsof initial splitters correspond to an i loop from i=1 toi=N in Fig. 3. In total, there are N�Smax−Smin+1� ini-tial sets of splitters that are evaluated as startingpoints in the searching algorithm. For example, if weset Smin=30, Smax=480, and N=100, then the algo-rithm evaluates a total of 45,100 initial sets of split-ters as starting points.

Step 2 validates whether the current initial set ofsplitters can meet all the PON system constraints, in-cluding maximal transmission distance, maximal dif-ferential distance, and optical split ratio, if they areused to connect all the ONUs. If the set is valid, thealgorithm calls a recursive process, i.e., Step 3, to usethe initial set of splitters as a starting point to find thebest (often a smaller) set of splitters and their corre-sponding locations. For example, the current initialsplitter set may contain 100 splitters. After the recur-sive step, i.e., Step 3, the total number of splittersmay be tuned down to 80 while all the ONUs can stillbe connected to their corresponding splitters withoutbreaking the PON system constraints.

The middle column in Fig. 3 shows the detail of therecursive (searching) process. Specifically, the processfirst calls an “ONU-splitter association and splitter re-location” step (i.e., Step 4), which is termed the A/Rstep. The detail of the A/R step is shown in the rightcolumn of Fig. 3, which employs an ONU-splitter as-sociation step (i.e., Step 7) and splitter relocationsteps (i.e., Steps 8 and 9) to find the (minimal) re-quired number of splitters and their best locations,and the association relationship between the ONUsand the splitters. We will introduce the detail of thesteps of ONU-splitter association and splitter reloca-tion later.

Based on the returned set of splitters and the asso-ciation relationship between the ONUs and the split-ters from Step 4, which essentially is a PON networkplanning, we can evaluate the optimality of the resultby calculating the total cost if the PONs are deployedin this way. This cost includes all the sub-costs de-scribed in Section II.A and is compared to the currentbest known cost in Step 5. The best known cost isbased on a previous good design. If the new cost is bet-ter than the current best known cost, then we updatethe new cost as the current best known cost andrecord the current PON network planning. Mean-while, if the two costs are very close (within a pre-defined difference range), we say the searching pro-cess is converged, and stop the recursive process andreturn the result to Step 3. Otherwise, we will repeatSteps 4 and 5 until either the total cost is eventuallyconverged or a predefined number R of iterations are

erformed. For the latter case, i.e., a non-convergedituation, we further employ a simulated annealingSA)-like process (i.e., Step 6) to finalize a (good) solu-ion. The detail of this SA-like algorithm is introducedext.We decribe the three key steps, i.e., Steps 6, 7, and

, in the RARA heuristic as follows.1) ONU-splitter association: The ONU-splitter asso-

iation step (i.e., Step 7) is important to the wholeeuristic to find an optimal association betweenNUs and splitters, subject to the PON system con-

traints. Given the location of each splitter, it is pos-ible to employ the aforementioned mixed integer lin-ar programming (MILP) model to find optimalolutions. The MILP model essentially carries out anfficient exhaustive search. However, the associationroblem itself is NP-complete, which is intractable forlarge size planning scenario. Thus, in the RARA al-

orithm we employ a heuristic subroutine to deter-ine the association.The association process first finds a pair of ONU

nd splitter, which has the shortest distance amongll the ONU-splitter pairs. Then, three PON systemonstraints including optical split ratio, maximalransmission distance, and maximal differential dis-ance, are verified for the selected ONU-splitter asso-iation. If the association is valid, we keep it and moven to the next pair of ONU and splitter that has thehortest distance among all the remaining uncon-ected ONUs, and the same verification is performed.uch a process is repeated until all the ONUs findheir associated splitters.

Particularly, if a “Calendar” data structure [16] ismployed to store the pairs of ONUs and splitters, theequired computation complexity of the above ONU-plitter association process is on the order of O�m2�,here m is the total number of ONUs, i.e., m= �U�.

Fig. 3. Flowchart of RARA [1].

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2) Splitter relocation: The ONU-splitter associationstep divides the whole group of ONUs into severalsmall groups with each corresponding to a PON.Based upon these ONU groups, the next step (i.e.,Step 8) is to find the best location of the optical split-ter for each PON. The problem is essentially to find aFemat–Weber point for a polygon with a group ofONUs and an OLT as vertices [12]. We extended thetraditional Weiszfeld’s algorithm (see Appendix A) tosearch such a splitter location in a continuous space.In particular, when applying Weiszfeld’s algorithm,we need to ensure the PON system constraints includ-ing maximal transmission distance and maximal dif-ferential distance. The output of the relocation stepwill be the best location of the splitter for the currentgroup of ONUs and the associated OLT.

3) Simulated annealing (SA)-like subroutine: Thereis a key loop (i.e., loop a) in the middle column of Fig.3. The loop stops whenever a solution to a set of split-ters is converged. However, sometimes the loop mayfail to converge after R iterations, but enter a dead-lock between two or even more local minimum solu-tions. Under these circumstances, we need to find away to resolve the deadlock. For this purpose, we pro-pose a simulated annealing-like subroutine for theRARA algorithm, i.e., Step 6.

Specifically, when a deadlock occurs, the SA-likesubroutine is called to repeat the A/R step (i.e., Step4). The subroutine stores two variables. One is thebest solution during the whole simulated annealingprocess, and the other is the current solution. In eachiteration, if the new found solution is better than thecurrent best one, then the new solution substitutes forthe current best one, as well as the current solution;otherwise, a random number between the interval of[0, 1] is generated and compared with a temperaturefunction, which is updated in each iteration. The newsolution is also accepted as the current solution if therandom number is less than the temperature functionvalue. The whole subroutine stops when the tempera-ture function is less than a predefined small thresh-old.

C. Maximal Sharing of Cable Conduit

In RARA, an important assumption is postulatedthat an independent cable conduit is built for each fi-ber link between an ONU and a splitter. It is possibleto further tune down the deployment cost by allowinga fiber link to traverse the cable conduits that havebeen built for other fiber links, which is called sharingof cable conduits.

As shown in Fig. 4, there are three PONs in the de-ployment. We take PON 2 as an example to illustratethe concept of cable conduit sharing. Rather thanbuilding a cable conduit directly for the fiber links be-tween the splitter and ONUs B and C, respectively, we

ay build a cable conduit from A to B and from B to Cnd then use the consecutive conduits from the split-er to A and from A to B to lay fibers for the link be-ween the splitter and B. Similarly, we can use theonsecutive conduits from the splitter to A, from A to, and from B to C, to lay fibers for the link between

he splitter and C. By doing so, the trenching cost foraying fibers can be significantly reduced, compared tondependent trenching for each ONU-splitter link.

To exploit the potential benefit of conduit sharing,e develop an enhanced algorithm subsequent to theesign obtained by RARA. Specifically, for each PON,he algorithm considers each of the locations (includ-ng the splitter and each of the ONUs) as a vertex andmploys an extended minimum spanning tree algo-ithm, similar to Prim’s algorithm [17], to find a con-trained minimum spanning tree that connects all theocations. Different from a pure minimum spanningree, we need to ensure the PON system constraints,uch as maximal transmission distance, when findinghe minimum spanning tree.

IV. SIMULATION CONDITIONS AND TEST SCENARIOS

To evaluate the efficiency of the proposed ap-roaches, we conducted extensive simulation studies.he following conditions are assumed in the simula-

ions. First, the number N in the flowchart shown inig. 2 is initially set to be 500. That is, for each givenumber s of splitters, we generate 500 different in-tances of splitter set in size s. Second, the availableaximal split ratios are 1:4, 1:8, 1:16, 1:32, and 1:64.maximal split ratio constrains how many ONUs can

e connected to a common PON. For example, if theaximal split ratio is 1:32, which means that up to 32NUs can be connected to a single PON. However, it

hould be noted that the parameter of maximal split

ig. 4. (Color online) Concept of cable conduit sharing in PONetworks.

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ratio does not require us to always use the maximal-size splitter. For example, if there are only 11 ONUsconnected to a PON, then a smaller splitter with a ra-tio of 1:16, instead of 1:32, can be used for cost saving.Third, the following cost factors are assumed for thesimulations: the cost of trenching and laying fiber is$16,000/km, the cost of fiber cables is $4,000/km, thecost of each OLT is $2,500, and the cost of each split-ter port is $100.

Three PON network planning scenarios are consid-ered, including (i) a circle with a 16 km radius, (ii) anannulus with a 16 km inner circle radius and a 50 kmouter circle radius, and (iii) a circle with a 50 km ra-dius. The region of scenario (iii) is essentially made upof the regions of scenarios (i) and (ii). Within each ofthe scenario regions, we assume that all ONUs arerandomly distributed.

Practically, scenario (i) corresponds to a situationthat all the users are close to the central office, whichtherefore requires only short-reach PONs, while sce-nario (ii) represents a case that all the users are faraway from the central office, thereby requiring long-reach PONs. The last scenario corresponds to the situ-ation that we do not distinguish close or far users, butuse the same type of (long-reach) PONs to connect allthe users.

In scenario (i), we planned for the cases with differ-ent numbers of ONUs ranging from 100 to 500 ONUswith 100 ONUs for each step increase. Note that whenmaking a step increase of ONUs, the locations of theexisting ONUs are not changed. That is, based on theexisting ONUs, the new ONUs are just randomlyadded and evenly distributed. The EPON systemstandard is applied for this scenario, which is subjectto the system constraints of 20 km maximal transmis-sion distance and 20 km maximal differential dis-tance.

In scenario (ii), we considered the cases with thenumbers of ONUs ranging from 300 to 700 also with100 ONUs for each step increase. In this scenario thesystem constraints of GPON are applied, which aresubject to 60 km maximal transmission distance and20 km maximal differential distance.

Finally, the numbers of ONUs in scenario (iii)ranges from 600 to 1000 also with 100 ONUs for eachstep increase. The locations of the ONUs in scenario(iii) are actually the combinations of the previous twoscenarios. We combined the case of 300 ONUs of sce-nario (i) with all the cases ranging from 300 to 700ONUs of scenario (ii) to form all the cases of scenario(iii). For example, the case of 700 ONUs is formed by acombination of the case of 300 ONUs of scenario (i)and the case of 400 ONUs of scenario (ii). Also, for sce-nario (iii), the system constraints of GPON are ap-plied, which are subject to 60 km maximal transmis-

ion distance and 20 km maximal differentialistance.

V. RESULTS AND ANALYSES

. Comparison of Different Approaches

In this section, we compare the performance of dif-erent planning approaches. Figure 5 shows how theotal cost changes with the total number of ONUs un-er a maximal split ratio of 1:16 for scenario (i). Wean see that the RARA approach can achieve a muchetter performance, i.e., lower cost, than the random-ut sectoring approach. Moreover, RARA shows betterfficiency with the increase of the total number ofNUs. Also, comparing the results of cable conduit

haring and non-sharing (i.e., with MST and withoutST in the legends), we can see that cable conduit

haring can help to significantly reduce the cost ofON deployment. The cost reduction also increasesith the increase of the total number of ONUs. Welso conducted similar simulations for other maximalplit ratios, and similar results were observed.To highlight the significance of the RARA and cable

onduit sharing, we also compare two extreme cases,.e., the sectoring approach without cable conduitharing, i.e., Sectoring, and the RARA approach withable conduit sharing, i.e., RARA+MST. It can beound that the RARA approach and the effort of con-uit sharing can jointly bring about 50% cost reduc-ion for a network design with 500 ONUs.

Figures 6 and 7 show the results for the annuluscenario, i.e., scenario (ii), and the large circular sce-ario, i.e., scenario (iii), respectively. Similar observa-ions are made to those of the small circular scenario.pecifically, the sectoring approach without MST per-

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ig. 5. Total cost vs. number of ONUs, circular scenario, radius16 km, maximal split ratio=1:16.

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forms worst, and the RARA approach with MST andwithout PON system constraints (i.e., allowing anymaximal transmission distance and maximal differen-tial distance) performs best.

In particular, for the annulus scenario, it seems ab-normal (actually not abnormal) that the approach ofSectoring+MST outperforms the approach of RARA+MST. This is because the sectoring approach doesnot consider the PON system constraints (includingmaximal transmission distance and maximal differen-tial distance), while the RARA approach always takesthese constraints into account. To evaluate the effec-tiveness of the RARA approach, we also show the re-sults of RARA+MST without considering the systemconstraints, i.e., RARA+MST (unconstrained), whichas shown significantly outperforms the approach ofSectoring+MST.

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Fig. 6. Total cost vs. number of ONUs, annulus scenario, maximalsplit ratio=1:16.

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Fig. 7. Total cost vs. number of ONUs, circular scenario, radius=50 km, maximal split ratio=1:16.

. Impact of Maximal Optical Split Ratio

Maximal optical split ratio is an important systemarameter that affects the deployment cost of PONs.igures 8 and 9 show how the average PON deploy-ent cost per user changes with different maximal op-

ical split ratios under the small circular scenario, i.e.,cenario (i), and the annulus scenario, i.e., scenarioii). As shown in Fig. 8, in addition to the similar per-ormance ranks of the curves as reported in Section.A, we can see that the average cost per user de-reases with the increase of maximal optical split ra-io. This is because a larger optical split ratio enablessingle splitter to accommodate more ONUs, therebyore efficiently sharing the feeder fiber from a centralLT to the splitter.On the other hand, it is interesting to see that there

s a saturating trend with the increase of maximal op-ical split ratio. When the split ratio is small, an in-rease of the split ratio can significantly reduce theeployment cost per user, e.g., up to 40% from a ratiof 1:4 to a ratio of 1:16. However, if the split ratio haseached a certain level, a further increase does notring much reduction to the deployment cost. Ashown in Fig. 8, the cost reduction from the split ratiof 1:16 to 1:32 is marginal. Similar observations cane found for the annulus scenario as shown in Fig. 9,n which the cost per user decreases with the increasef split ratio, until it approaches a saturation split ra-io of 1:32. It should be noted that the saturatinghreshold value changes with the ONU density. Ineneral, a higher optimal split ratio can be expectedor a higher ONU density.

. Impact of Maximal PON Transmission Distance

The maximal transmission distance of a PON is an-ther important system constraint that shows impact

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ig. 8. Average cost per user vs. split ratio, circular scenario,adius=16 km, number of ONUs=500.

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on the total deployment cost. To evaluate the impact,the following test conditions were assumed. We con-sider the small circular scenario with radius=16 km.400 ONUs are assumed to be uniformly randomly dis-tributed within the circle. The allowed maximal opti-cal split ratios include 1:4, 1:16, and 1:64. The maxi-mal differential distance is 20 km. The maximal PONtransmission distances are configured to changeamong 16, 18, 20, 24, and 30 km.

Figure 10 shows how the total PON deployment costchanges with the increase of the PON maximal trans-mission distance under the RARA approach with cableconduit sharing. It is not surprising to see that the to-tal cost decreases with the increase of the maximaltransmission distance, as a longer maximal transmis-sion distance provides more flexibility and optimiza-tion opportunities for the design. Also, it is interesting

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Fig. 9. Average cost per user vs. split ratio, annulus scenario,number of ONUs=700.

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Fig. 10. Total cost vs. maximal PON transmission distance, circu-lar scenario, radius=16 km, ONU number=400.

o see that there is a saturating trend, which shows aarginal total cost reduction after the maximal trans-ission distance has been extended to a certain

ange. Specifically, for the current design scenario,uch a saturation distance is around 20 km, which im-lies that after 20 km, a further increase of maximalransmission distance will not bring much reductionn the total cost. It is reasonable since once a trans-

ission distance is sufficient to cover all the users, itould not bring any benefit even if the maximal

ransmission distance is further increased.

. Impact of Maximal Differential Distance

The maximal differential distance of a PON can alsoffect the total deployment cost. To evaluate this ef-ect, we again design the test scenarios as follows. Weonsider the smaller circle scenario, i.e., scenario (i),ith 400 ONUs uniformly randomly distributed. Theaximal PON transmission distance is set to be

0 km. The maximal optical split ratio is assumed tohange among 1:4, 1:16, and 1:64. Finally, the maxi-al differential distance is assumed to range from

rom 4 km to 20 km with 4 km increase for each step.

Figure 11 shows how the total network costs changeith the increase of maximal differential distance un-er the RARA+MST approach. It can be found thathe increase of maximum differential distance canring some reduction of the total deployment cost,hich is, however, very marginal. The result thus im-lies that the total PON deployment cost seems not toe sensitive to the change of the maximal differentialistance. This is reasonable because all the ONU us-rs that are connected to a common splitter are oftenlose to each other, which does not require a largeaximal differential distance.

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ig. 11. Total cost vs. maximal differential distance, circular sce-ario, radius=16 km, ONU number=400.

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E. Effectiveness of ONU-Splitter AssociationAlgorithm

In the RARA approach, there is an important stepthat associates ONUs to splitters given a specific setof splitters. For the association, in addition to the heu-ristic subroutine as proposed in RARA, we employ theMILP model described in Section II.B (ignoring con-straints (8) and (9)) to find an optimal solution for amedium-size planning scenario, e.g., with up to hun-dreds of ONUs. This posterior MILP optimization istermed RARA+MILP. It is carried out based on theresults found by the RARA heuristic, in which a list ofsplitters have been found. We used the commercialsoftware package AMPL/CPLEX to solve the MILP op-timization model. We consider the small circular sce-nario, i.e., scenario (i), as a study case, in which thetotal number of ONUs is no greater than 500 and themaximal split ratio is 1:64.

Figure 12 compares the total costs of the two de-signs, i.e., pure RARA vs. RARA with the posteriorMILP optimization �RARA+MILP�. It is found thatwithout considering the PON system constraints in-cluding maximal transmission distance and maximaldifferential distance, the pure RARA algorithm canachieve almost the same performance as that ofRARA+MILP. Their relative performance differenceis less than 1%. When the PON system constraints areconsidered, the pure RARA algorithm still performswell, close to that of RARA+MILP. Their relative dif-ference is consistently less than 10%. These resultsthus verify that the ONU-splitter association algo-rithm used in RARA is efficient, which can achievegood solutions, close to the optimal results obtained bythe MILP optimization.

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Fig. 12. Comparison of the ONU-splitter association algorithm inRARA and the MILP model for the circular planning scenario withradius=16 km, split ratio=1:64.

. Disintegrating Large PON Planning Scenarios

RARA+MST is efficient and fast for the design sce-arios containing several hundreds of ONUs. How-ver, for a very large planning scenario with thou-ands or several thousands of ONUs, the computationime of RARA+MST is prohibitive. To shorten theomputation time, one effective way is to divide aarge planning scenario into several smaller ones. Forxample, given a large circle containing 1400 ONUs,e may divide this large circle into two parts, includ-

ng one small circle containing 700 ONUs and oneuter annulus containing the remaining 700 ONUs.hen we apply the approaches proposed in the study

o solve the two smaller scenarios and sum them up tond an overall solution to the large circular scenario.y doing this, we expect that the overall computation

ime can be significantly reduced, while the designerformance is still close to the design without suchisintegration.In our study, scenario (iii) is essentially made up of

he combinations of the cases of the small circularrea, i.e., scenario (i), and the cases of the outer annu-us, i.e., scenario (ii). To evaluate the effectiveness ofhe proposed disintegration method, we compare theolutions to scenario (iii) with the sums of the solu-ions to scenarios (i) and (ii).

Under the RARA+MST approach, Fig. 13 shows theotal costs of the designs without disintegration, i.e.,cenario (iii), and the designs with disintegration, i.e.,he sums of scenarios (i) and (ii). We can see that theesults without disintegration and with disintegrationre very close, while the latter requires much shorteromputation times. As shown in Table I, the approachith disintegration requires only 20% of the time of

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ig. 13. Total cost of the planning with disintegration and withoutisintegration, SR, split ratio

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that required by the approach without disintegrationwhen planning a PON network with 600 ONUs. Theresults therefore verify that the disintegration methodis effective for large-size PON deployment.

VI. CONCLUSION

We plan greenfield PON networks to minimize theirtotal deployment costs. A mathematical optimizationmodel is developed, which is intractable due to itsnonlinearity and NP-complete feature. Thus, we pro-pose an efficient heuristic called RARA to find sub-optimal solutions to the problem. Due to the dominantcost of trenching and laying fibers, we also exploit thebenefit of cable conduit sharing among different fiberlinks to further tune down the deployment cost. Thesimulation studies indicate that the RARA approachis efficient to significantly reduce PON deploymentcost compared to a random-cut sectoring approach.The simulation studies also show that the effort ofcable conduit sharing can bring up to 20% cost savingcompared to the pure RARA approach.

We also evaluate the effects of PON system con-straints, including maximal optical split ratio, maxi-mal transmission distance, and maximal differentialdistance. Saturating trends of the PON deploymentcost are observed in PON network planning when in-creasing the three system parameters. In addition,the efficiency of the ONU-splitter association subrou-tine in RARA is evaluated. It is found that the pro-posed association heuristic is efficient to performclosely to the MILP approach.

Finally, to shorten the computation time of a large-PON network design, we develop an approach to dis-integrate a large size planning scenario into severalsmall scenarios. It is found that the disintegration ef-fort can significantly reduce the planning time whileno significant performance is sacrificed.

As a limitation, the current study has considered asimplified greenfield PON network deployment, inwhich only PON system constraints were taken intoaccount. A more comprehensive future study can alsoconsider other constraints such as existing routing/conduits. Moreover, while a single-stage splitter perPON is a valid assumption, multi-stage PONs are an-

TABLE ICOMPARISON OF COMPUTATION TIMES (HOURS) OF THE

APPROACHES WITH DISINTEGRATION AND WITHOUT DISINTE-GRATION (600 ONUS)

Computation Times (hours)

Optical split ratio 1:4 1:8 1:16 1:32 1:64With disintegration 4.93 6.16 7.06 7.93 8Without disintegration 23.33 31.05 32.77 37.17 34.21

ther interesting topic that shows practice in realON deployment. As a first-cut of PON network plan-ing, we hope this article will spark new research in-erest in the field.

ACKNOWLEDGMENT

he authors would like to thank Marcus Voltz for theiscussion of Weiszfeld’s Algorithm, and the Austra-ian Research Council (ARC) for supporting this re-earch.

APPENDIX A. WEISZFELD’S ALGORITHM

Weiszfeld’s algorithm is an iterative reweight leastquare method, which computes the position of theeometric median, also known as the Fermat–Weberoint, for a convex polygon. Though the complexity ofhe Fermat–Weber problem itself is not known [12],he Weiszfeld algorithm is proved to be efficient inractice, especially for a small-scale problem. The al-orithm is proved to be convergent in linear time. Theesudo-code of Weiszfeld’s algorithm is given below:

lgorithm 1 Weiszfeld Algorithm [12]nput: Set of ONUs U;

1: for i=1 to �U� do2:

if ��v��U\v�i

v� −v� i

�v� −v� i�� 1 then

3: return v� i

4: Select initial solution x0 inside the convex hullform by U.

5: repeat6:

x�k+1=�v��Uv�

�v� −x�k�/�v��U

1�v� −x�k�

7: Until �x�k−x�k+1 � �

8: return x�k+1

In the algorithm, �U� stands for the cardinality ofet U. v� corresponds to an ONU in U, which is a two-imensional vector embedding the coordinates of theNU. The for loop (i.e., lines 1–3) is a procedure to

heck whether the Fermat–Weber point coincides withny of the ONU positions. The procedure of theepeat-until loop (i.e., lines 5–7) is an iterative stepo find the Fermat–Weber point, providing that theoint does not coincide with any of the ONU positions.he subscript k of x�k is an iteration counter.

REFERENCES

[1] J. Li and G. Shen, “Cost minimization planning for passive op-tical networks,” in Proc. OFC/NFOEC 2008, Feb 2008.

[2] G. Kramer, B. Mukherjee, and G. Pesavento, “IPACT: a dy-namic protocol for an Ethernet PON (EPON),” IEEE Commun.Mag., vol. 40, no. 2, pp. 74–80, Feb. 2002.

[3] F. Effenberger, D. C. Calix, G. Kramer, R. Li, M. Oron, and T.Pfeiffer, “An introduction to PON technologies,” IEEE Com-mun. Mag., vol. 45, no. 3, pp. S17–S25, Mar. 2007.

[4] “Ethernet in the First Mile,” IEEE 802.3ah, June 2004.

b

cgra4ICU


[5] ITU-T G.984.1, SG 15, “Gigabit-capable Passive Optical Net-works (G-PON): General Characteristics,” March 2003.

[6] ITU-T G.984.4, SG 15, “Gigabit-capable Passive Optical Net-works (G-PON): Transmission Convergence Layer Specifica-tion,” July 2005.

[7] C. M. Assi, Y. Ye, S. Dixit, and M. A. Ali, “Dynamic bandwidthallocation for quality-of-service over Ethernet PONs,” IEEE J.Sel. Areas Commun., vol. 3, no. 9, pp. 1467–1477, Nov. 2003.

[8] C. H. Foh, L. Andrew, E. Wong, and M. Zukerman, “FULL-RCMA: a high utilization EPON,” IEEE J. Sel. Areas Com-mun., vol. 22, no. 8, pp. 1514–1524, 2004.

[9] G. C. Gupta, M. Kashima, H. Iwamura, H. Tamai, T. Ushikubo,and T. Kamijoh, “Over 100 km bidirectional, multi-channelsCOF-PON without optical amplifier,” in OFC 2006, paperPDP51.

[10] “10 GEPON IEEE Working Group,” http://www.ieee802.org/3/av/index.html, online on September 18, 2007.

[11] M. Hajduczenia, B. Lakic, H. J. A. Da Silva, and P. P. Monteiro,“Optimized passive optical network deployment,” J. Opt.Netw., vol. 6, no. 9, pp. 1079–1104, 2007.

[12] D. Cieslik, Steiner Minimal Trees, Kluwer Academic Publish-ers, 1998.

[13] H. W. Kuhn and R. E. Kuenne, “An efficient algorithm for thenumerical solution of the generalized Weber problem in spatialeconomics,” J. Regional Sci., vol. 4, no. 2, pp. 21–33, 1962.

[14] L. Cooper, “Location-allocation problems,” Oper. Res., vol. 11,no. 3, pp. 331–343, 1963.

[15] L. Cooper, “Heuristic methods for location-allocation prob-lems,” SIAM Rev., vol. 6, no. 1, pp. 37–53, 1964.

[16] R. Brown, “Calendar queues: a fast 0(1) priority queue imple-mentation for the simulation event set problem,” Commun.ACM, vol. 31, no. 10, pp. 1220–1227, Oct. 1988.

[17] C. H. Papadimitriou and K. Steiglitz, Combinatorial Optimiza-

tion: Algorithms and Complexity, Prentice-Hall, 1982.

Ji Li (S’04) received the B.Eng. degree inelectrical engineering from South ChinaUniversity of Technology, Guangzhou, P. R.China, and the Ph.D. degree recently fromARC Special Research Center for Ultra-Broadband Information Networks, Depart-ment of Electrical Engineering, Universityof Melbourne, Australia. His research inter-ests include network dimensioning andplanning, teletraffic theory, stochastic pro-cesses, wireless sensor networks, and mo-

ile wireless networking.

Gangxiang Shen (S’98-M’99) is a Lead En-gineer with Ciena US. Before he joinedCiena, he was an Australian PostdoctoralFellow (APD) and ARC Research Fellowwith ARC Special Research Center forUltra-Broadband Information Networks,Department of Electrical Engineering, Uni-versity of Melbourne, Australia. He receivedhis Ph.D. from the Department of Electricaland Computer Engineering, University ofAlberta, Canada, in January 2006. He re-

eived his M.Sc. from Nanyang Technological University in Sin-apore and his B.Eng. from Zhejiang University in P. R. China. Hisesearch interests are in network survivability, optical networks,nd wireless networks. He has authored and co-authored more than0 peer-reviewed technical papers. He is also a recipient of thezaak Walton Killam Memorial Award of University of Alberta, theanadian NSERC Industrial R&D Fellowship, etc. His personalRL is http://www.gangxiang-shen.com/.

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Cost Minimization Planning for Greenfield Passive Optical Networks