Drop Points Placement Algorithms for Layered Network Planning

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International Journal of Information and Computer Science (IJICS) Volume 4, 2015 doi: 10.14355/ijics.2015.04.006

Drop Points Placement Algorithms for Layered Network Planning K. W. Peng Department of Risk Management and Insurance, Ming Chuan University, Taiwan kwpeng@mail.mcu.edu.tw Abstract Planning a network with hundreds of thousands nodes, multilayered approach is generally applied. It is natural to divide a large network, like nation-wide network into several county networks or smaller networks. It is not only for network planning, but also for managerial purposes. In such a way, multilayered networks are planned and constructed. In each smaller network, we must decide the location of hub, or drop point from upper layer view, for this smaller network. In order to reduce the cost of networks and enhance the signal quality, better placement of drop points means better network planning. In this paper, we proposed two placement algorithms for drop point placements in multilayer network planning. By comparing different placement algorithms, we proposed PA and GA placement algorithms for drop point placements. In computational experiments, the results show that adaptive placement algorithms, GA and PA, are better than Centroid and Near-HE algorithms unsurprisingly. Furthermore, comparing two adaptive placement algorithms, the computing time of PA algorithm is 61.5% less than GA algorithm in average. On the other hand, the network costs for PA algorithm is 5.42% higher than GA algorithm. By compromising the network cost and computing time of planning, we can get cost-efficient network planning in a reasonable time for multilayered networks.

Keywords Network Planning; Clustering Algorithms

Introduction Multilayered approach is generally applied when we design a network with hundreds of thousands nodes. It is natural to divide a state network into several county networks or smaller networks (Herroelen & Rand 2013). It is not only for network planning, but also for managerial purposes. In such a way, multi-layered network approaches are frequently used. In each smaller network, we must decide the location of hub, or drop point of upper layer, for this smaller network. In order to reduce the cost of networks and enhance the signal quality, better placement of drop points means lower cost and better quality.

There are several approaches to decide the placement of drop points. For example, the central position of sub network can be a good choice since the link cost of intranet can be reduced (Dymarsky & Nourmiyeva 2001).

However, it may not be a good choice for upper layer network. For upper layer network, the node which is the nearest to head-end should be the best one to reduce the cost form drop point to head-end. In this paper, we proposed two placement algorithms for drop placements in multilayer network planning problems. By comparing several placement algorithms, we found it is not so critical for each small network. If we regard a network as a tree structure, the position of drop points in leaf nodes would be critical to network planning. Therefore, different placement for drop placements should have impacts on network cost.

However, computing time is another issue when we optimize the network planning. With unlimited planning time, we can do the best network plan by exhaust searching. Therefore, how to compromise the network construction cost and computing time of planning is critical to designing of multilayered network.

Placement Problems in Multilayered Network Planning In the description of CATV network design problem, we have to determine the routing configuration. By given number and positions of end users, we have to construct a minimum cost tree to connect head end and all users.

This is called the Steiner tree problem. Steiner tree problem is known to be NP-complete. When the network size is small enough, it can be solved by algorithms in reasonable computing time (Takahashi & Matsuyama 1980).

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International Journal of Information and Computer Science (IJICS) Volume 4, 2015

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Therefore, in order to solve a larger network planning problem, the concept of “layering� can be used to describe the network planning procedure. For example, from the point view of CATV operators, the entire network can be seen as a tree network with many branch networks (Hsieh & Lin 1999). There are ten smaller branches in a city, serving the subscribers in this city, as shown in Figure 1, upper layer. An easy way to comply with the journal paper formatting requirements is to use this document as a template and simply type your text into it.

In a branch, the positions of the local branch box (triangle 1) and subscribers are shown in Figure 2, lower layer.

FIG. 1 LOCATION MAP OF SUBSCRIBERS FOR A CATV NETWORK: UPPER LAYER

FIG. 2 LOCATION MAP OF SUBSCRIBERS FOR A CATV NETWORK: LOWER LAYER

After the clusters are constructed, we place some networking equipments to connect subscribers in cluster and head end of a CATV network. It is intuitive to apply two kinds of placements, Centroid and Near-HE, as shown in Figure 3. In Centroid placements, drop points (DP) are placed in the centers of each cluster. On the other hand, for Near-HE placements, drop points are placed in the point nearest Head-End inside each cluster. In general, it would be the nearest point to Head-End in a cluster.

FIG. 3 PLACEMENTS FOR DROP POINTS

Different placement policies change the costs for networks intra-cluster and inter-cluster (Peng et al. 2006). In Figure 3, the centroid policy, placing the drop points on the centroid points of clusters, should reduce the intracluster network costs but may increase inter-cluster network costs. On the other hand, the near-HE policy, placing the drop points on the boundaries closest to the Head-End, may reduce the inter-cluster costs. If we can place drop points properly, the network cost should be reduced.

Proposed Algorithms and Computational Experiment Results Here a sample of placement policies is shown. Consider the network graph after clustering in Figure 4.

By applying Centroid and Near-He placements, we can get different network topology as shown in Figure 5. The network topology in dotted line is the Near-He placement. Meanwhile, the network topology in solid line is the Centroid placement. The graph shows some hints for us to reduce the cost for multilayer network planning. First, the cost of each cluster generated by centroid policy is usually lower than near-HE policy. It is not surprised since

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International Journal of Information and Computer Science (IJICS) Volume 4, 2015

the centroid policy should reduce the length of wire in each cluster. On the other hand, the near-HE policy should reduce the cost for upper layers.

FIG. 4 NETWORK CLUSTERS GRAPH

FIG. 5 LAYER 1 NETWORK TOPOLOGY FOR DIFFERENT PLACEMENT OF DROP POINTS

For some clusters, like clusters c03 and c08, the costs of upper layers were not changed to put the drop points near head end. However, the intra-cluster costs increased. Therefore we could choose different polices in each cluster according to the differences of costs. The algorithm to adjust placement policies, named as Globally Adaptive Placement algorithm for drop points, is proposed as follow: GA(Globally Adaptive) placement algorithm for drop points, Step 1: Clusters subscribers by modified agglomerative clustering algorithm.

Step 2: Compute the total cost of network by centroid placement policy.

Step 3: Consider every cluster, change different placement policy, and compare the total cost newly generated. If new placement policy can decrease the total cost, change the placement for this cluster.

Step 4: Repeat step 3 until all clusters are considered.

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International Journal of Information and Computer Science (IJICS) Volume 4, 2015

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However, when we consider about the computing time for placement adjustment algorithms, it is possible to improve this algorithm from another perspective. Let us look at Figure 5 again. For those clusters on the leaf of trees, like clusters c04 and c06, different placements would change costs for inter- and intra-clusters. On the other hand, for those clusters are not leaf nodes in Steiner trees of upper layers, the network costs change very few when the placement policies change. Therefore, it should be more time conserving to adjust placements only for those clusters on leaf nodes of Steiner trees of upper layers. We propose another adjustment algorithm described as follow: PA(Partially Adaptive) placement algorithm for drop points Step 1: Clusters subscribers by modified agglomerative clustering algorithm.

Step 2: Compute the total cost of network by centroid placement policy.

Step 3: Consider those clusters on the leaf nodes of Steiner tree in upper layer, change different placement policies, and compare the total cost newly generated. If new placement policy can decrease the total cost, change the placement for this cluster.

Step 4: Repeat step 3 until all clusters on the leaf nodes are considered.

Here we randomly generate 13 networks with different amount of subscribers and applying Centroid, Near-HE, GA and PA placement algorithms. Nodes are randomly placed in a 35x35 area. By applying clustering algorithm (Imperl et al. 2000), these nodes are grouped into sub networks with diameters no more than 10. After that, the drop points are decided by placement algorithms. The network costs and computing time of all phases are computed based on the methods in (Gillete 1995). The comparison of Network costs for placement policies are listed in Table 1.

TABLE 1 COMPARISON OF NETWORK COSTS FOR PLACEMENT POLICIES

Network # N01

Centroid 707

Near-HE 707

PA 707

GA 707

N02

456

456

456

456

N03

1662

1755

1662

1662

N04

1450

1126

1450

1126

N05

1241

1245

1241

1241

N06

1443

1509

1443

1443

N07

1331

1324

1324

1324

N08

1690

1353

1690

1353

N09

3535

2300

2300

2300

N10

3432

2396

3432

2396

N11

2855

3173

2855

2855

N12

3300

3560

3300

3300

N13

13554

17028

13005

12929

Average

2820

2918

2682

2544

For sparse network with only 1 subscriber in each cluster, like N1 or N2, the drop points are all the same no matter which method is chosen. With more and more subscribers added, the costs may different by these placement algorithms. The results show that adaptive placement algorithms, GA and PA, are better than Centroid and NearHE generally. Furthermore, comparing two adaptive placement algorithms, the computing time of PA algorithm is 61.5% less than GA algorithm in average. On the other hand, the network costs for PA algorithm is 5.42% higher than GA algorithm. Therefore, the choice between these two algorithms should depend on how much computing time allowed.

Conclusions In this paper, we proposed two placement algorithms for drop point placements in multilayer network planning problems. By comparing different placement algorithms, we proposed PA and GA placement algorithms for drop point placements. In computational experiments, the network costs for PA al-gorithm are slightly higher than GA

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International Journal of Information and Computer Science (IJICS) Volume 4, 2015

algorithm. However, the computing time of PA algorithm is significantly reduced. By compromising the network construction cost and computing time of planning, we can get cost-efficient network planning in a reasonable time for the multilayered network.

REFERENCES

[1]

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[2]

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[3]

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[4]

Hsieh, H. J. and Lin, Y. S., “Planning and Management of CATV Networks,” ISCOM, 1999.

[5]

Imperl, B.; Kacic, Z.; Horvat, B.; Zgank, A., “Agglomerative vs. tree-based clustering for the definition of multilingual set of triphones,” IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP '00, Volume 3, 5-9 June 2000.

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Peng, K. W., Kwang, J. F., Lin, Y. S., “An Optimization-based Design Algorithm for CATV Networks,” IASTED The International Conference on Networks and Communication systems, 2006.

[8]

Takahashi, H. and Matsuyama, A., "An approximate solution for the Steiner problem in graphs," Math. Japon., pp. 573-577, 1980.

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