PON Network Designing Algorithm for Suboptimal ...

PON Network Designing Algorithm for Suboptimal Deployment of Optical Fiber Cables Akira Agata, and Yukio Horiuchi KDDI R&D Laboratories Inc., 2-1-15 Ohara, Fujimino-shi, Saitama 356-8502, Japan [email protected] ABSTRACT A passive double star (PDS) network, which shares one optical fiber with multiple subscribers by using a power splitter, is being deployed as an infrastructure for the passive optical network (PON) systems. One of the main focuses for PON network planning is to determine the optical cable route of a point-to-multipoint network that connects every subscriber to the central offices (COs) through the power splitter(s) within a limited deployment cost under realistic restrictions, such as possible fiber paths, the splitting ratio of optical splitters and locations, when the locations of COs and subscribers are given. In this paper, we propose a novel suboptimal design algorithm for PON outside plant deployment. Under the realistic restrictions, the algorithm can automatically generate a suboptimal PON network that connects every subscriber to the COs in terms of total fiber length. Keywords: PON, Network Architecture, Network Planning

1. INTRODUCTION With the increasing demand for broadband services, passive optical networks (PONs), such as Ethernet PON (EPON) or gigabit PON (GPON), have been widely deployed as primary optical access networks. PON is a point-to-multipoint fiber optical network with no active components in the optical distribution networks (ODNs). Although PON is considered as a reliable and cost-effective solution, it becomes much more difficult to design an optimal fiber network, compared to a point-to-point system. There have been only a few studies on the suboptimal point-to-multipoint network planning algorithm [1,2]. However, these algorithms assumed that it is possible to establish additional optical fiber routes other than the given possible paths when connecting any pair of nodes [1], or when avoiding obstacles [2]. In realistic cases, a PON network should be designed based on the set of given possible paths. This is due to the fact that most of the paths where the optical fiber could be deployed are restricted, such as the path between existing power poles or along a road, especially in urban areas of many Asian countries. In this paper, we propose a novel PON network planning algorithm that can overcome this issue. The proposed algorithm automatically generates a suboptimal point-to-multipoint network that connects every subscriber (ONU) to the Optical Line Terminal (OLT) through the power splitter with the sum of the optical fiber length close to the shortest value, when the locations of the central offices (COs), subscribers, and set of paths where the optical fiber cable could be placed are given.

2. PROPOSED PON NETWORK PLANNING ALGORITHM In many cases, a network designer of PON systems has to design the point-to-multipoint optical fiber network under many restrictions such as locations of COs (i.e. the location of OLTs), subscribers, and paths where the optical fiber cable could be placed. In this section, we propose a PON network planning algorithm that can overcome this issue. The proposed algorithm uses two graph related algorithms as key elemental techniques. One is the construction method of a network Voronoi diagram. The other is the graph clustering algorithm.

Network Architectures, Management, and Applications VII, edited by Ken-ichi Sato, Yuefeng Ji, Lena Wosinska, Jing Wu, Proc. of SPIE-OSA-IEEE Asia Communications and Photonics, SPIE Vol. 7633, 76330L © 2009 SPIE-OSA-IEEE · CCC code: 0277-786X/09/$18 · doi: 10.1117/12.852150 SPIE-OSA-IEEE/ Vol. 7633 76330L-1

2.1 The Network Voronoi Diagram A construction algorithm of a Voronoi diagram is a powerful tool in computational geometry that is dedicated to the algorithmic study of geometric problems [3]. Suppose that N points (p1, p2,…,pN), which we call generators, are given in a two-dimensional plane. If we allocate all points in this plane with the generator that the Euclidean distance becomes minimum, the result is a partition of the plane into N areas. Such a partition is called a Voronoi diagram and each area is called a Voronoi region. The i-th Voronoi region, which corresponds to the generator pi, can be defined as follows:

V ( pi ) = { p | d ( p, pi ) ≤ d ( p, p j ) , i ≠ j , j = 1,2,L, N }

(1)

where p represents a point in the two-dimensional plane, { p | condition} represents a set of points that satisfy the condition, and the function d(u,v) calculates the Euclidean distance between the two points u and v, respectively. The network Voronoi diagram is an extension of the Voronoi diagram to the graph consisting of a set of nodes and edges [4]. It is obtained from replacing a plane and Euclidean distance with a graph and the shortest-path distance. A modification of the Dijkstra algorithm [5] is presented that allows calculation of the network Voronoi diagram. 2.2 The Graph Clustering Algorithm Cluster analysis is the assignment of a large number of data into multiple groups (called clusters) so that data in the same cluster are similar in some sense. Clustering is a method of unsupervised learning, and a common technique for statistical data analysis used in many fields. Among many clustering techniques, k-means and k-medoids, which aims to classify n data into k clusters (k Nsplitter or Li > Lmax, then increment the Nc and go back to Step 2. Step 4: Set the cluster medoid as the location of the optical splitter, and define the route of the aerial lead-in line to the subscribers. Step 5: Calculate the shortest paths between the central office and every optical splitter in the subgraph by the shortest path search algorithm, such as the Dijkstra method, and determine the route to each splitter.

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Figure 1. Flow chart of the proposed PON network designing algorithm.

3. NUMERICAL SIMULATION To evaluate the feasibility of the proposed algorithm, we conducted a numerical simulation. In this evaluation, we used a Delaunay triangulation graph of 100 randomly deployed nodes to approximate a network consisting of power poles and possible optical fiber paths in an urban area [9]. The total number of edges is calculated to be 277. Since no two edges intersect each other in Delaunay triangulation, the graph is assumed to represent a realistic set of power poles and paths where the optical fiber could be deployed. The input parameters in the numerical simulation are listed in Table 2.

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First, we randomly selected two nodes in the network as the location of the central offices. Next, we applied our algorithm to the network, assuming each power pole has a subscriber around it. The given conditions are shown in Fig. 2(a). The two squares in the graph G represent the COs. At the first step, the graph is separated into the subgraphs by Voronoi technique, as shown in Fig. 2(b). Each subgraph is a set of nodes and edges closer to the CO. Next, by applying Step 2 through 4 in the algorithm, the power poles with subscribers are clustered and the location of optical splitters are determined in each subgraph, as shown in Fig. 2(c). In order to reduce the complexity of the figure, clusters and optical splitters in one subgraph are shown in the figure. Finally, the optical fiber route between the CO and each optical splitter is determined by applying the shortest path search technique, such as the Dijkstra method, and the suboptimal PON network in terms of the total optical fiber length is designed, as shown in Fig. 2(d).

(a)

(b)

(c)

(d)

Figure 2. Designing process of PON network: (a) Given restrictions, (b) Make the subgraphs by Voronoi technique, (c) Determining the location of the optical splitters, (d) Designing the path between CO and optical splitters.

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Table 2. Input parameters in the numerical simulation.

Parameter

Values used in the evaluation

G(N,E)

Delaunay triangulation graph of 100 randomly deployed nodes in a square 2 km on a side. The total number of edges is 277.

PCO_j

Randomly selected in the graph G(N,E).

NCO

2

NC_j

3 (for all j)

Nsplitter Lmax

8 400 m

4. SUMMARY We proposed a novel PON network planning algorithm. The proposed algorithm automatically generates a suboptimal point-to-multipoint network that connects every subscriber (ONU) to the OLT(s) through the power splitter(s), when the locations of OLT(s), subscribers, power poles, and paths where the optical fiber could be placed are given. Moreover, the splitting ratio of the optical splitter and the maximum allowable length of an optical drop cable that connects the optical splitter and subscriber are also considered. Through the numerical simulations, we confirmed that the algorithm can design the suboptimal PON network in terms of total optical fiber length.

REFERENCES [1] E. Bonsma, N. Karunatillake, R. Shipman, M. Shackleton and D. Mortimore, “Evolving Greenfield Passive Optical Networks,” BT Technical Journal, Vol. 21, No. 4, pp. 44-49, (2003). [2] B. Lakic, M. Hajduczenia, H. da Silva and P. P. Monteiro1, “Using Adapted Visibility Graphs for Network Planning,” in Proc. IEEE Symposium on Computers and Communications 2008 (ISCC’08), (2008). [3] F, Aurenhammer, “Voronoi Diagrams - A Survey of a Fundamental Geometric Data Structure,” ACM Computing Surveys, Vol. 23, No. 3, pp.345-405, (1991). [4] M. Erwig, “The Graph Voronoi Diagram with Applications,” Networks, vol. 36, no. 3, pp. 156-163, (2000). [5] E. W. Dijkstra, "A note on two problems in connection with graphs," Numerische Mathematik, Vol. 1, pp. 269-271, (1959). [6] J. MacQueen, “Some methods for classification and analysis of multivariate observations,” in Proc. of the 5th Berkeley Symposium on Math., pp. 281-296, (1967). [7] S. Garg and R. C. Jain, “Variation of k-mean Algorithm: A Study for High-Dimensional Large Data Set,” Information Technology Journal, Vol. 5, pp. 1132-1135, (2006). [8] M.J. Rattigan, M. Maier, and D. Jensen, “Graph Clustering with Network Structure Indices,” in Proc. 24th Annual International Conference on Machine Learning (ICML'07), (2007). [9] J. R. Shewchuk, “Tetrahedral Mesh Generation by Delaunay Refinement,” In Proc. of the 14th Annual ACM Symposium on Computational Geometry, pp. 86-95, (1998).

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