Abstract

We investigate the issue of minimizing the cost of optical cables and arrayed waveguide gratings (AWGs) in deploying optical distribution networks using WDM passive optical networks (PONs). Generally, when deploying WDM PONs with cascaded AWGs, increasing the number of stages of cascaded AWGs decreases the optical fiber costs, but increases the AWG cost. A proper cascaded AWG structure and proper connections between AWGs and optical network units are needed to minimize the total cost of AWGs and optical cables. We decompose the network planning problem into two subproblems. One is to decide the positions of AWGs and placement of optical cables to minimize the cost of optical cables. The other one is to determine the cascaded AWG structure to minimize the total cost of AWGs and optical cables. In particular, we propose a recursive partition–combination-based algorithm to achieve the optimal trade-off between the AWG cost and the optical cable cost.

© 2009 Optical Society of America

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References

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  1. A. Banerjee, Y. Park, F. Clarke, H. Song, S. Yang, G. Kramer, K. Kim, B. Mukherjee, “Wavelength-division-multiplexed passive optical network (WDM-PON) technologies for broadband access: a review,” J. Opt. Netw., vol. 4, no. 11, pp. 737–758, Nov. 2005.
    [CrossRef]
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    [CrossRef]
  3. C.-H. Lee, S.-M. Lee, K.-M. Choi, J.-H. Moon, S.-G. Mun, K.-T. Jeong, J. H. Kim, B. Kim, “WDM-PON experiences in Korea,” J. Opt. Netw., vol. 6, no. 5, pp. 451–464, 2007.
    [CrossRef]
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    [CrossRef]
  6. G. Maier, M. Martinelli, A. Pattavina, E. Salvadori, “Design and cost performance of the multistage WDM-PON access networks,” J. Lightwave Technol., vol. 18, no. 2, pp. 125–143, Feb. 2000.
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  9. F. I. El-Nahal, R. J. Mears, “Multistage WDM access architecture employing cascaded AWGs,” Opt. Fiber Technol., vol. 15, pp. 181–186, March 2009.
    [CrossRef]
  10. S.-M. Lee, S.-G. Mun, M.-H. Kim, C.-H. Lee, “Demonstration of a long-reach DWDM-PON for consolidation of metro and access networks,” J. Lightwave Technol., vol. 25, no. 1, pp. 271–276, Jan. 2007.
    [CrossRef]
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    [CrossRef]
  12. J. Li, G. Shen, “Cost minimization planning for passive optical networks,” in Nat. Fiber Optic Engineers Conf., San Diego, CA, OSA Technical Digest (CD), Washington, DC: Optical Society of America, Feb. 24, 2008, paper NThD1.
  13. S. Khan, “Heuristics-based PON deployment,” IEEE Commun. Lett., vol. 9, no. 9, pp. 847–849, Sept. 2005.
    [CrossRef]
  14. F. K. Hwang, D. S. Richards, “Steiner tree problems,” Networks, vol. 22, no. 1, pp. 55–89, 1992.
    [CrossRef]
  15. S. Gokhale, “Deployment of fiber optic networks through underground sewers in North America,” J. Transp. Eng., vol. 132, no. 8, pp. 672–682, 2006.
    [CrossRef]
  16. J. K. Jeyapalan, “Using existing infrastructure to speed FTTH deployment,” Broadband Properties Mag., vol. 2007, no. 3, pp. 61–70, March 2007.
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  18. D. S. Johnson, K. A. Niemi, “On knapsacks, partitions, and a new dynamic programming technique for trees,” Math. Op. Res., vol. 8, no. 1, pp. 1–14, 1983.
    [CrossRef]

2009

F. I. El-Nahal, R. J. Mears, “Multistage WDM access architecture employing cascaded AWGs,” Opt. Fiber Technol., vol. 15, pp. 181–186, March 2009.
[CrossRef]

2007

2006

S. Gokhale, “Deployment of fiber optic networks through underground sewers in North America,” J. Transp. Eng., vol. 132, no. 8, pp. 672–682, 2006.
[CrossRef]

2005

2004

2000

1999

B. Kuhlow, G. Przyrembel, E. Pawlowski, M. Ferstl, W. Furst, “AWG-based device for a WDM overlay PON in the 1.5 m band,” IEEE Photon. Technol. Lett., vol. 11, no. 2, pp. 218–220, Feb. 1999.
[CrossRef]

1992

F. K. Hwang, D. S. Richards, “Steiner tree problems,” Networks, vol. 22, no. 1, pp. 55–89, 1992.
[CrossRef]

1983

D. S. Johnson, K. A. Niemi, “On knapsacks, partitions, and a new dynamic programming technique for trees,” Math. Op. Res., vol. 8, no. 1, pp. 1–14, 1983.
[CrossRef]

Banerjee, A.

Choi, K.-M.

Clarke, F.

Clearly, D.

F. Effenberger, D. Clearly, O. Haran, G. Kramer, R. D. Li, M. Oron, T. Pfeiffer, “An introduction to PON technologies [topics in optical communications],” IEEE Commun. Mag., vol. 45, no. 3, pp. S17–S25, March 2007.
[CrossRef]

da Silva, H. J.

Effenberger, F.

F. Effenberger, D. Clearly, O. Haran, G. Kramer, R. D. Li, M. Oron, T. Pfeiffer, “An introduction to PON technologies [topics in optical communications],” IEEE Commun. Mag., vol. 45, no. 3, pp. S17–S25, March 2007.
[CrossRef]

El-Nahal, F. I.

F. I. El-Nahal, R. J. Mears, “Multistage WDM access architecture employing cascaded AWGs,” Opt. Fiber Technol., vol. 15, pp. 181–186, March 2009.
[CrossRef]

Ferstl, M.

B. Kuhlow, G. Przyrembel, E. Pawlowski, M. Ferstl, W. Furst, “AWG-based device for a WDM overlay PON in the 1.5 m band,” IEEE Photon. Technol. Lett., vol. 11, no. 2, pp. 218–220, Feb. 1999.
[CrossRef]

Furst, W.

B. Kuhlow, G. Przyrembel, E. Pawlowski, M. Ferstl, W. Furst, “AWG-based device for a WDM overlay PON in the 1.5 m band,” IEEE Photon. Technol. Lett., vol. 11, no. 2, pp. 218–220, Feb. 1999.
[CrossRef]

Garey, M.

M. Garey, D. Johnson, Computers and Intractability: a Guide to the Theory of NP-Completeness. New York, NY: W. H. Freeman, 1979.

Gokhale, S.

S. Gokhale, “Deployment of fiber optic networks through underground sewers in North America,” J. Transp. Eng., vol. 132, no. 8, pp. 672–682, 2006.
[CrossRef]

Hajduczenia, M.

Haran, O.

F. Effenberger, D. Clearly, O. Haran, G. Kramer, R. D. Li, M. Oron, T. Pfeiffer, “An introduction to PON technologies [topics in optical communications],” IEEE Commun. Mag., vol. 45, no. 3, pp. S17–S25, March 2007.
[CrossRef]

Holburn, D.

Hwang, F. K.

F. K. Hwang, D. S. Richards, “Steiner tree problems,” Networks, vol. 22, no. 1, pp. 55–89, 1992.
[CrossRef]

Jeong, K.-T.

Jeyapalan, J. K.

J. K. Jeyapalan, “Using existing infrastructure to speed FTTH deployment,” Broadband Properties Mag., vol. 2007, no. 3, pp. 61–70, March 2007.

Johnson, D.

M. Garey, D. Johnson, Computers and Intractability: a Guide to the Theory of NP-Completeness. New York, NY: W. H. Freeman, 1979.

Johnson, D. S.

D. S. Johnson, K. A. Niemi, “On knapsacks, partitions, and a new dynamic programming technique for trees,” Math. Op. Res., vol. 8, no. 1, pp. 1–14, 1983.
[CrossRef]

Khan, S.

S. Khan, “Heuristics-based PON deployment,” IEEE Commun. Lett., vol. 9, no. 9, pp. 847–849, Sept. 2005.
[CrossRef]

Kim, B.

Kim, J. H.

Kim, K.

Kim, M.-H.

Kramer, G.

F. Effenberger, D. Clearly, O. Haran, G. Kramer, R. D. Li, M. Oron, T. Pfeiffer, “An introduction to PON technologies [topics in optical communications],” IEEE Commun. Mag., vol. 45, no. 3, pp. S17–S25, March 2007.
[CrossRef]

A. Banerjee, Y. Park, F. Clarke, H. Song, S. Yang, G. Kramer, K. Kim, B. Mukherjee, “Wavelength-division-multiplexed passive optical network (WDM-PON) technologies for broadband access: a review,” J. Opt. Netw., vol. 4, no. 11, pp. 737–758, Nov. 2005.
[CrossRef]

Kuhlow, B.

B. Kuhlow, G. Przyrembel, E. Pawlowski, M. Ferstl, W. Furst, “AWG-based device for a WDM overlay PON in the 1.5 m band,” IEEE Photon. Technol. Lett., vol. 11, no. 2, pp. 218–220, Feb. 1999.
[CrossRef]

Lakic, B.

Lee, C.-H.

Lee, S.-M.

Li, J.

J. Li, G. Shen, “Cost minimization planning for passive optical networks,” in Nat. Fiber Optic Engineers Conf., San Diego, CA, OSA Technical Digest (CD), Washington, DC: Optical Society of America, Feb. 24, 2008, paper NThD1.

Li, R. D.

F. Effenberger, D. Clearly, O. Haran, G. Kramer, R. D. Li, M. Oron, T. Pfeiffer, “An introduction to PON technologies [topics in optical communications],” IEEE Commun. Mag., vol. 45, no. 3, pp. S17–S25, March 2007.
[CrossRef]

Maier, G.

Martinelli, M.

Mears, R. J.

F. I. El-Nahal, R. J. Mears, “Multistage WDM access architecture employing cascaded AWGs,” Opt. Fiber Technol., vol. 15, pp. 181–186, March 2009.
[CrossRef]

Monteiro, P. P.

Moon, J.-H.

Mukherjee, B.

Mun, S.-G.

Niemi, K. A.

D. S. Johnson, K. A. Niemi, “On knapsacks, partitions, and a new dynamic programming technique for trees,” Math. Op. Res., vol. 8, no. 1, pp. 1–14, 1983.
[CrossRef]

Okamoto, K.

K. Okamoto, Fundamentals of Optical Waveguides. New York, NY: Academic, 2006.

Oron, M.

F. Effenberger, D. Clearly, O. Haran, G. Kramer, R. D. Li, M. Oron, T. Pfeiffer, “An introduction to PON technologies [topics in optical communications],” IEEE Commun. Mag., vol. 45, no. 3, pp. S17–S25, March 2007.
[CrossRef]

Park, Y.

Parker, M.

Pattavina, A.

Pawlowski, E.

B. Kuhlow, G. Przyrembel, E. Pawlowski, M. Ferstl, W. Furst, “AWG-based device for a WDM overlay PON in the 1.5 m band,” IEEE Photon. Technol. Lett., vol. 11, no. 2, pp. 218–220, Feb. 1999.
[CrossRef]

Pfeiffer, T.

F. Effenberger, D. Clearly, O. Haran, G. Kramer, R. D. Li, M. Oron, T. Pfeiffer, “An introduction to PON technologies [topics in optical communications],” IEEE Commun. Mag., vol. 45, no. 3, pp. S17–S25, March 2007.
[CrossRef]

Przyrembel, G.

B. Kuhlow, G. Przyrembel, E. Pawlowski, M. Ferstl, W. Furst, “AWG-based device for a WDM overlay PON in the 1.5 m band,” IEEE Photon. Technol. Lett., vol. 11, no. 2, pp. 218–220, Feb. 1999.
[CrossRef]

Richards, D. S.

F. K. Hwang, D. S. Richards, “Steiner tree problems,” Networks, vol. 22, no. 1, pp. 55–89, 1992.
[CrossRef]

Rochat, E.

Salvadori, E.

Shen, G.

J. Li, G. Shen, “Cost minimization planning for passive optical networks,” in Nat. Fiber Optic Engineers Conf., San Diego, CA, OSA Technical Digest (CD), Washington, DC: Optical Society of America, Feb. 24, 2008, paper NThD1.

Song, H.

Toycan, M.

I. Tsalamanis, M. Toycan, S. Walker, “Study of hybrid cascaded AWG-based access network topology,” in 2006 Int. Conf. on Transparent Optical Networks, Nottingham, UK, June 18–22, 2006, vol. 4, pp. 76–79.
[CrossRef]

Tsalamanis, I.

I. Tsalamanis, E. Rochat, S. Walker, M. Parker, D. Holburn, “Experimental demonstration of cascaded AWG access network featuring bi-directional transmission and polarization multiplexing,” Opt. Express, vol. 12, no. 5, pp. 764–769, 2004.
[CrossRef] [PubMed]

I. Tsalamanis, M. Toycan, S. Walker, “Study of hybrid cascaded AWG-based access network topology,” in 2006 Int. Conf. on Transparent Optical Networks, Nottingham, UK, June 18–22, 2006, vol. 4, pp. 76–79.
[CrossRef]

Walker, S.

I. Tsalamanis, E. Rochat, S. Walker, M. Parker, D. Holburn, “Experimental demonstration of cascaded AWG access network featuring bi-directional transmission and polarization multiplexing,” Opt. Express, vol. 12, no. 5, pp. 764–769, 2004.
[CrossRef] [PubMed]

I. Tsalamanis, M. Toycan, S. Walker, “Study of hybrid cascaded AWG-based access network topology,” in 2006 Int. Conf. on Transparent Optical Networks, Nottingham, UK, June 18–22, 2006, vol. 4, pp. 76–79.
[CrossRef]

Yang, S.

Broadband Properties Mag

J. K. Jeyapalan, “Using existing infrastructure to speed FTTH deployment,” Broadband Properties Mag., vol. 2007, no. 3, pp. 61–70, March 2007.

IEEE Commun. Lett.

S. Khan, “Heuristics-based PON deployment,” IEEE Commun. Lett., vol. 9, no. 9, pp. 847–849, Sept. 2005.
[CrossRef]

IEEE Commun. Mag.

F. Effenberger, D. Clearly, O. Haran, G. Kramer, R. D. Li, M. Oron, T. Pfeiffer, “An introduction to PON technologies [topics in optical communications],” IEEE Commun. Mag., vol. 45, no. 3, pp. S17–S25, March 2007.
[CrossRef]

IEEE Photon. Technol. Lett.

B. Kuhlow, G. Przyrembel, E. Pawlowski, M. Ferstl, W. Furst, “AWG-based device for a WDM overlay PON in the 1.5 m band,” IEEE Photon. Technol. Lett., vol. 11, no. 2, pp. 218–220, Feb. 1999.
[CrossRef]

J. Lightwave Technol.

J. Opt. Netw.

J. Transp. Eng.

S. Gokhale, “Deployment of fiber optic networks through underground sewers in North America,” J. Transp. Eng., vol. 132, no. 8, pp. 672–682, 2006.
[CrossRef]

Math. Op. Res.

D. S. Johnson, K. A. Niemi, “On knapsacks, partitions, and a new dynamic programming technique for trees,” Math. Op. Res., vol. 8, no. 1, pp. 1–14, 1983.
[CrossRef]

Networks

F. K. Hwang, D. S. Richards, “Steiner tree problems,” Networks, vol. 22, no. 1, pp. 55–89, 1992.
[CrossRef]

Opt. Express

Opt. Fiber Technol.

F. I. El-Nahal, R. J. Mears, “Multistage WDM access architecture employing cascaded AWGs,” Opt. Fiber Technol., vol. 15, pp. 181–186, March 2009.
[CrossRef]

Other

J. Li, G. Shen, “Cost minimization planning for passive optical networks,” in Nat. Fiber Optic Engineers Conf., San Diego, CA, OSA Technical Digest (CD), Washington, DC: Optical Society of America, Feb. 24, 2008, paper NThD1.

K. Okamoto, Fundamentals of Optical Waveguides. New York, NY: Academic, 2006.

I. Tsalamanis, M. Toycan, S. Walker, “Study of hybrid cascaded AWG-based access network topology,” in 2006 Int. Conf. on Transparent Optical Networks, Nottingham, UK, June 18–22, 2006, vol. 4, pp. 76–79.
[CrossRef]

M. Garey, D. Johnson, Computers and Intractability: a Guide to the Theory of NP-Completeness. New York, NY: W. H. Freeman, 1979.

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Figures (15)

Fig. 1
Fig. 1

Simple example of the AWG cost and the optical cable cost.

Fig. 2
Fig. 2

Abstracted functionality of a typical AWG.

Fig. 3
Fig. 3

Equal-function cascaded AWGs.

Fig. 4
Fig. 4

Decomposition of the problem.

Fig. 5
Fig. 5

Example of construction tree, optical cable tree, and subtrees associated with AWGs.

Fig. 6
Fig. 6

Example of weights of edges and an example of tree partitioning.

Fig. 7
Fig. 7

Centroid of trees.

Fig. 8
Fig. 8

Recursive partitioning and recursive combination.

Fig. 9
Fig. 9

Case 1: the construction tree is restricted to a line.

Fig. 10
Fig. 10

Total cost versus the number of ONUs; simulation conditions: p ( x ) = 800 x 0.4 , q ( x ) = 1000 x 0.7 .

Fig. 11
Fig. 11

Total cost versus r 1 and c 1 ; simulation conditions: the construction tree forms a line, the number of ONUs is 512, and q ( x ) = 1000 x 0.7 .

Fig. 12
Fig. 12

Total cost versus r 2 and c 2 ; simulation condition: the construction tree forms a line, the number of ONUs is 512, and p ( x ) = 800 x 0.4 .

Fig. 13
Fig. 13

Case 2: the construction tree T forms a binary tree.

Fig. 14
Fig. 14

Total cost versus r 1 and c 1 ; simulation condition: the construction tree is a binary tree, the number of ONUs is 512, and q ( x ) = 1000 x 0.7 .

Fig. 15
Fig. 15

Total cost versus r 2 and c 2 ; simulation condition: the construction tree is a binary tree, the number of ONUs is 512, and p ( x ) = 800 x 0.4 .

Tables (2)

Tables Icon

Table 1 Algorithm 1. Recursive Partition

Tables Icon

Table 2 Algorithm 2. Recursive Combination

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

in 1 × n 1 = F ;
out k × n k = in k + 1 × n k + 1 ;
out K × n K N , where 2 N F × W .
p ( x ) > p ( y ) , x > y .
p ( x ) x < p ( y ) y , x > y .
n K × out K × k = 1 K ( k + 1 K in i out i × p ( out k ) out k ) .
( u , v ) E ( t ) q ( w ( u , v ) ) | ( u , v ) | .
i = 1 m ( u , v ) E ( st i ) q ( w ( u , v ) ) | ( u , v ) | .
i = 1 m ( u , v ) E ( st i ) | ( u , v ) | .
( u , v ) E ( st i ) q ( w ( u , v ) ) | ( u , v ) | i .
Δ = p ( 2 ) + 2 p ( m 2 ) p ( m ) + 4 0 l 4 q ( a ( l 4 x ) ) d x 2 0 l 2 q ( a ( l 2 x ) ) d x + q ( 1 ) l 2.
Δ ( l 2 ) = c 1 2 r 1 + c 1 a r 1 ( 2 1 r 1 ) l r 1 2 r 1 + c 2 l 4 ( 2 r 2 4 r 2 ) c 2 a r 2 l r 2 + 1 [ ( r 2 + 1 ) 2 r 2 + 1 ] = 1 2 r 2 + 1 [ c 1 2 r 1 + r 2 + 1 + c 1 a r 1 ( 2 1 r 1 ) l r 1 2 r 2 + 1 r 1 + c 2 l 2 r 2 1 c 2 ( 2 r 2 4 r 2 ) a r 2 l r 2 + 1 ( r 2 + 1 ) ] > 1 2 r 2 + 1 [ c 1 2 r 1 + c 1 a r 1 ( 2 1 r 1 ) l r 1 + c 2 l 2 1 ( 2 r 2 4 r 2 ) c 2 a r 2 l r 2 + 1 ( r 2 + 1 ) ] = 1 2 r 2 + 1 Δ ( l ) = 0.
Δ = p ( 2 ) + 2 p ( m 2 ) p ( m ) + ( q ( 1 ) q ( m 2 ) ) ( | ( a , b ) | + | ( a , c ) | ) .
Δ = p ( 2 ) + 2 p ( m 2 ) p ( m ) + 2 ( q ( 1 ) q ( m 2 ) ) | ( a , b ) | = p ( 2 ) + 2 p ( M 2 k + 1 ) p ( M 2 k ) + 2 ( q ( 1 ) q ( M 2 k + 1 ) ) R k sin ( π 2 k + 1 ) sin ( θ 2 π 2 k + 1 ) = c 1 2 r 1 + c 1 ( 2 1 r 1 1 ) ( M 2 k ) r 1 c 2 ( ( M 2 k + 1 ) r 2 1 ) R k sin ( π 2 k + 1 ) sin ( θ 2 π 2 k + 1 ) .
Δ ( k ) 0 c 1 c 2 ( ( M 2 k + 1 ) r 2 1 ) R k sin ( π 2 k + 1 ) [ 2 r 1 + ( 2 1 r 1 1 ) ( M 2 k ) r 1 ] sin ( θ 2 π 2 k + 1 ) .
R k sin ( π 2 k + 1 ) sin ( θ 2 π 2 k + 1 ) R k + 1 sin ( π 2 k + 2 ) sin ( θ 2 π 2 k + 2 ) ,
( M 2 k + 1 ) r 2 1 2 r 1 + ( 2 1 r 1 1 ) ( M 2 k ) r 1 ( M 2 k + 2 ) r 2 1 2 r 1 + ( 2 1 r 1 1 ) ( M 2 k + 1 ) r 1 :
R k sin ( π 2 k + 1 ) sin ( θ 2 π 2 k + 1 ) = R k + 1 sin ( π 2 k + 1 ) sin ( θ 2 ) = R k + 1 sin ( π 2 k + 2 ) 2 cos ( π 2 k + 2 ) sin ( θ 2 ) = R k + 1 sin ( π 2 k + 2 ) sin ( θ 2 π 2 k + 2 ) 2 cos ( π 2 k + 1 ) sin ( θ 2 π 2 k + 1 ) sin ( θ 2 ) = R k + 1 sin ( π 2 k + 2 ) sin ( θ 2 π 2 k + 2 ) sin ( θ 2 ) + sin ( θ 2 π 2 k ) sin ( θ 2 ) > R k + 1 sin ( π 2 k + 2 ) sin ( θ 2 π 2 k + 2 ) .
( M 2 k ) r 2 2 r 1 r 2 + ( 2 1 r 1 1 ) ( M 2 k + 1 ) r 1 + r 2 ( 2 1 r 1 1 ) ( M 2 k ) r 1 > ( M 2 k ) r 2 2 r 1 2 r 2 + ( 2 1 r 1 1 ) ( M 2 k ) r 1 + r 2 2 2 r 2 ( 2 1 r 1 1 ) ( M 2 k + 1 ) r 1 ( M 2 k + 1 ) r 2 1 2 r 1 + ( 2 1 r 1 1 ) ( M 2 k ) r 1 > ( M 2 k + 2 ) r 2 1 2 r 1 + ( 2 1 r 1 1 ) ( M 2 k + 1 ) r 1
R k + 1 sin ( π 2 k + 2 ) sin ( θ 2 π 2 k + 2 ) ( M 2 k + 2 ) r 2 1 2 r 1 + ( 2 1 r 1 1 ) ( M 2 k + 1 ) r 1 < R k sin ( π 2 k + 1 ) sin ( θ 2 π 2 k + 1 ) ( M 2 k + 1 ) r 2 1 2 r 1 + ( 2 1 r 1 1 ) ( M 2 k ) r 1 c 1 c 2 Δ ( k + 1 ) > 0.