Abstract

We present a method for analytical performance evaluation of synchronous optical packet-switched backbone networks. The proposed method is applicable to networks of any topology built of nodes of any degree with any number of wavelengths, and capable of allowing for deflections. The method provides not only general results such as fiber utilization, but also detailed results on where and at what mean rates packets travel. We analyze the steady-state performance of a network loaded with independent flows. The admission control admits in a fair way at most as many packets as there are output slots available, while the routing algorithm uses classes, distances, deflections, and wavelength conversion. We compare the results of our method with simulation results for a large set of randomly generated test cases, and conclude that the proposed method yields reasonably accurate results.

© 2011 OSA

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  1. N. Bouabdallah, "Sub-wavelength solutions for next-generation optical networks," IEEE Commun. Mag. 45, (8), 36‒43 (2007).
    [CrossRef]
  2. L. Xu, H. Perros, and G. Rouskas, "Techniques for optical packet switching and optical burst switching," IEEE Commun. Mag. 39, (1), 136‒142 (2001).
    [CrossRef]
  3. S. J. B. Yoo, "Optical packet and burst switching technologies for the future photonic Internet," J. Lightwave Technol. 24, (12), 4468‒4492 (2006).
    [CrossRef]
  4. R. Van Caenegem, D. Colle, M. Pickavet, P. Demeester, K. Christodoulopoulos, K. Vlachos, E. Varvarigos, L. Stampoulidis, D. Roccato, and R. Vilar, "The design of an all-optical packet switching network," IEEE Commun. Mag. 45, (11), 52‒61 (2007).
    [CrossRef]
  5. S. Das, G. Parulkar, and N. McKeown, "Unifying packet and circuit switched networks," 2009 IEEE GLOBECOM Workshops, Dec. 2009, pp. 1‒6.
  6. S. Yao, B. Mukherjee, S. Yoo, and S. Dixit, "A unified study of contention-resolution schemes in optical packet-switched networks," J. Lightwave Technol. 21, (3), 672‒683 (2003).
    [CrossRef]
  7. I. Szcześniak and T. Czachórski, "Performance evaluation of a bufferless packet-switched node," Proc. 9th Int. Conf. on Transparent Optical Networks (ICTON 2007), Vol. 3, July 2007, pp. 117‒120.
  8. J. Bannister, F. Borgonovo, L. Fratta, and M. Gerla, "A performance model of deflection routing in multibuffer networks with nonuniform traffic," IEEE/ACM Trans. Netw. 3, (5), 509‒520 (1995).
    [CrossRef]
  9. A. Acampora and S. Shah, "Multihop lightwave networks: a comparison of store-and-forward and hot-potato routing," IEEE Trans. Commun. 40, (6), 1082‒1090 (1992).
    [CrossRef]
  10. I. Szcześniak, T. Czachórski, and J.-M. Fourneau, "Packet loss analysis in optical packet-switched networks with limited deflection routing," Photon. Netw. Commun. 16, (3), 253‒261 (2008).
    [CrossRef]
  11. I. Szcześniak, "Analysis of a finite number of deflections in fully and uniformly loaded regular networks," Lect. Notes Comput. Sci. 3042/2004, 675‒686 (2004).
  12. S. Blake, D. Black, M. Carlson, E. Davies, Z. Wang, and W. Weiss, "An architecture for differentiated service," RFC 2475, Dec. 1998.
  13. J. Jue, "An algorithm for loopless deflection in photonic packet-switched networks," Proc. ICC 2002, Vol. 5, May 2002, pp. 2776‒2780.
  14. T. Karagiannis, M. Molle, M. Faloutsos, and A. Broido, "A nonstationary Poisson view of Internet traffic," Proc. INFOCOM 2004, Vol. 3, Mar. 2004, pp. 1558‒1569.
  15. H. Øverby, "Traffic models for slotted optical packet switched networks," Photon. Netw. Commun. 13, 183‒194 (2007).
    [CrossRef]
  16. I. Szcześniak, the website of OPUS, the optical packet switching universal solver. Apr. 2011 [Online]. Available: http://www.irkos.org/opus
  17. J. Bannister, F. Borgonovo, L. Fratta, and M. Gerla, "A versatile model for predicting the performance of deflection-routing networks," Perform. Eval. 16, (1–3), 201‒222 (1992).
    [CrossRef]

2008 (1)

I. Szcześniak, T. Czachórski, and J.-M. Fourneau, "Packet loss analysis in optical packet-switched networks with limited deflection routing," Photon. Netw. Commun. 16, (3), 253‒261 (2008).
[CrossRef]

2007 (3)

H. Øverby, "Traffic models for slotted optical packet switched networks," Photon. Netw. Commun. 13, 183‒194 (2007).
[CrossRef]

N. Bouabdallah, "Sub-wavelength solutions for next-generation optical networks," IEEE Commun. Mag. 45, (8), 36‒43 (2007).
[CrossRef]

R. Van Caenegem, D. Colle, M. Pickavet, P. Demeester, K. Christodoulopoulos, K. Vlachos, E. Varvarigos, L. Stampoulidis, D. Roccato, and R. Vilar, "The design of an all-optical packet switching network," IEEE Commun. Mag. 45, (11), 52‒61 (2007).
[CrossRef]

2006 (1)

2004 (1)

I. Szcześniak, "Analysis of a finite number of deflections in fully and uniformly loaded regular networks," Lect. Notes Comput. Sci. 3042/2004, 675‒686 (2004).

2003 (1)

2001 (1)

L. Xu, H. Perros, and G. Rouskas, "Techniques for optical packet switching and optical burst switching," IEEE Commun. Mag. 39, (1), 136‒142 (2001).
[CrossRef]

1995 (1)

J. Bannister, F. Borgonovo, L. Fratta, and M. Gerla, "A performance model of deflection routing in multibuffer networks with nonuniform traffic," IEEE/ACM Trans. Netw. 3, (5), 509‒520 (1995).
[CrossRef]

1992 (2)

A. Acampora and S. Shah, "Multihop lightwave networks: a comparison of store-and-forward and hot-potato routing," IEEE Trans. Commun. 40, (6), 1082‒1090 (1992).
[CrossRef]

J. Bannister, F. Borgonovo, L. Fratta, and M. Gerla, "A versatile model for predicting the performance of deflection-routing networks," Perform. Eval. 16, (1–3), 201‒222 (1992).
[CrossRef]

Acampora, A.

A. Acampora and S. Shah, "Multihop lightwave networks: a comparison of store-and-forward and hot-potato routing," IEEE Trans. Commun. 40, (6), 1082‒1090 (1992).
[CrossRef]

Bannister, J.

J. Bannister, F. Borgonovo, L. Fratta, and M. Gerla, "A performance model of deflection routing in multibuffer networks with nonuniform traffic," IEEE/ACM Trans. Netw. 3, (5), 509‒520 (1995).
[CrossRef]

J. Bannister, F. Borgonovo, L. Fratta, and M. Gerla, "A versatile model for predicting the performance of deflection-routing networks," Perform. Eval. 16, (1–3), 201‒222 (1992).
[CrossRef]

Black, D.

S. Blake, D. Black, M. Carlson, E. Davies, Z. Wang, and W. Weiss, "An architecture for differentiated service," RFC 2475, Dec. 1998.

Blake, S.

S. Blake, D. Black, M. Carlson, E. Davies, Z. Wang, and W. Weiss, "An architecture for differentiated service," RFC 2475, Dec. 1998.

Borgonovo, F.

J. Bannister, F. Borgonovo, L. Fratta, and M. Gerla, "A performance model of deflection routing in multibuffer networks with nonuniform traffic," IEEE/ACM Trans. Netw. 3, (5), 509‒520 (1995).
[CrossRef]

J. Bannister, F. Borgonovo, L. Fratta, and M. Gerla, "A versatile model for predicting the performance of deflection-routing networks," Perform. Eval. 16, (1–3), 201‒222 (1992).
[CrossRef]

Bouabdallah, N.

N. Bouabdallah, "Sub-wavelength solutions for next-generation optical networks," IEEE Commun. Mag. 45, (8), 36‒43 (2007).
[CrossRef]

Broido, A.

T. Karagiannis, M. Molle, M. Faloutsos, and A. Broido, "A nonstationary Poisson view of Internet traffic," Proc. INFOCOM 2004, Vol. 3, Mar. 2004, pp. 1558‒1569.

Carlson, M.

S. Blake, D. Black, M. Carlson, E. Davies, Z. Wang, and W. Weiss, "An architecture for differentiated service," RFC 2475, Dec. 1998.

Christodoulopoulos, K.

R. Van Caenegem, D. Colle, M. Pickavet, P. Demeester, K. Christodoulopoulos, K. Vlachos, E. Varvarigos, L. Stampoulidis, D. Roccato, and R. Vilar, "The design of an all-optical packet switching network," IEEE Commun. Mag. 45, (11), 52‒61 (2007).
[CrossRef]

Colle, D.

R. Van Caenegem, D. Colle, M. Pickavet, P. Demeester, K. Christodoulopoulos, K. Vlachos, E. Varvarigos, L. Stampoulidis, D. Roccato, and R. Vilar, "The design of an all-optical packet switching network," IEEE Commun. Mag. 45, (11), 52‒61 (2007).
[CrossRef]

Czachórski, T.

I. Szcześniak, T. Czachórski, and J.-M. Fourneau, "Packet loss analysis in optical packet-switched networks with limited deflection routing," Photon. Netw. Commun. 16, (3), 253‒261 (2008).
[CrossRef]

I. Szcześniak and T. Czachórski, "Performance evaluation of a bufferless packet-switched node," Proc. 9th Int. Conf. on Transparent Optical Networks (ICTON 2007), Vol. 3, July 2007, pp. 117‒120.

Das, S.

S. Das, G. Parulkar, and N. McKeown, "Unifying packet and circuit switched networks," 2009 IEEE GLOBECOM Workshops, Dec. 2009, pp. 1‒6.

Davies, E.

S. Blake, D. Black, M. Carlson, E. Davies, Z. Wang, and W. Weiss, "An architecture for differentiated service," RFC 2475, Dec. 1998.

Demeester, P.

R. Van Caenegem, D. Colle, M. Pickavet, P. Demeester, K. Christodoulopoulos, K. Vlachos, E. Varvarigos, L. Stampoulidis, D. Roccato, and R. Vilar, "The design of an all-optical packet switching network," IEEE Commun. Mag. 45, (11), 52‒61 (2007).
[CrossRef]

Dixit, S.

Faloutsos, M.

T. Karagiannis, M. Molle, M. Faloutsos, and A. Broido, "A nonstationary Poisson view of Internet traffic," Proc. INFOCOM 2004, Vol. 3, Mar. 2004, pp. 1558‒1569.

Fourneau, J.-M.

I. Szcześniak, T. Czachórski, and J.-M. Fourneau, "Packet loss analysis in optical packet-switched networks with limited deflection routing," Photon. Netw. Commun. 16, (3), 253‒261 (2008).
[CrossRef]

Fratta, L.

J. Bannister, F. Borgonovo, L. Fratta, and M. Gerla, "A performance model of deflection routing in multibuffer networks with nonuniform traffic," IEEE/ACM Trans. Netw. 3, (5), 509‒520 (1995).
[CrossRef]

J. Bannister, F. Borgonovo, L. Fratta, and M. Gerla, "A versatile model for predicting the performance of deflection-routing networks," Perform. Eval. 16, (1–3), 201‒222 (1992).
[CrossRef]

Gerla, M.

J. Bannister, F. Borgonovo, L. Fratta, and M. Gerla, "A performance model of deflection routing in multibuffer networks with nonuniform traffic," IEEE/ACM Trans. Netw. 3, (5), 509‒520 (1995).
[CrossRef]

J. Bannister, F. Borgonovo, L. Fratta, and M. Gerla, "A versatile model for predicting the performance of deflection-routing networks," Perform. Eval. 16, (1–3), 201‒222 (1992).
[CrossRef]

Jue, J.

J. Jue, "An algorithm for loopless deflection in photonic packet-switched networks," Proc. ICC 2002, Vol. 5, May 2002, pp. 2776‒2780.

Karagiannis, T.

T. Karagiannis, M. Molle, M. Faloutsos, and A. Broido, "A nonstationary Poisson view of Internet traffic," Proc. INFOCOM 2004, Vol. 3, Mar. 2004, pp. 1558‒1569.

McKeown, N.

S. Das, G. Parulkar, and N. McKeown, "Unifying packet and circuit switched networks," 2009 IEEE GLOBECOM Workshops, Dec. 2009, pp. 1‒6.

Molle, M.

T. Karagiannis, M. Molle, M. Faloutsos, and A. Broido, "A nonstationary Poisson view of Internet traffic," Proc. INFOCOM 2004, Vol. 3, Mar. 2004, pp. 1558‒1569.

Mukherjee, B.

Øverby, H.

H. Øverby, "Traffic models for slotted optical packet switched networks," Photon. Netw. Commun. 13, 183‒194 (2007).
[CrossRef]

Parulkar, G.

S. Das, G. Parulkar, and N. McKeown, "Unifying packet and circuit switched networks," 2009 IEEE GLOBECOM Workshops, Dec. 2009, pp. 1‒6.

Perros, H.

L. Xu, H. Perros, and G. Rouskas, "Techniques for optical packet switching and optical burst switching," IEEE Commun. Mag. 39, (1), 136‒142 (2001).
[CrossRef]

Pickavet, M.

R. Van Caenegem, D. Colle, M. Pickavet, P. Demeester, K. Christodoulopoulos, K. Vlachos, E. Varvarigos, L. Stampoulidis, D. Roccato, and R. Vilar, "The design of an all-optical packet switching network," IEEE Commun. Mag. 45, (11), 52‒61 (2007).
[CrossRef]

Roccato, D.

R. Van Caenegem, D. Colle, M. Pickavet, P. Demeester, K. Christodoulopoulos, K. Vlachos, E. Varvarigos, L. Stampoulidis, D. Roccato, and R. Vilar, "The design of an all-optical packet switching network," IEEE Commun. Mag. 45, (11), 52‒61 (2007).
[CrossRef]

Rouskas, G.

L. Xu, H. Perros, and G. Rouskas, "Techniques for optical packet switching and optical burst switching," IEEE Commun. Mag. 39, (1), 136‒142 (2001).
[CrossRef]

Shah, S.

A. Acampora and S. Shah, "Multihop lightwave networks: a comparison of store-and-forward and hot-potato routing," IEEE Trans. Commun. 40, (6), 1082‒1090 (1992).
[CrossRef]

Stampoulidis, L.

R. Van Caenegem, D. Colle, M. Pickavet, P. Demeester, K. Christodoulopoulos, K. Vlachos, E. Varvarigos, L. Stampoulidis, D. Roccato, and R. Vilar, "The design of an all-optical packet switching network," IEEE Commun. Mag. 45, (11), 52‒61 (2007).
[CrossRef]

Szczesniak, I.

I. Szcześniak, T. Czachórski, and J.-M. Fourneau, "Packet loss analysis in optical packet-switched networks with limited deflection routing," Photon. Netw. Commun. 16, (3), 253‒261 (2008).
[CrossRef]

I. Szcześniak, "Analysis of a finite number of deflections in fully and uniformly loaded regular networks," Lect. Notes Comput. Sci. 3042/2004, 675‒686 (2004).

I. Szcześniak and T. Czachórski, "Performance evaluation of a bufferless packet-switched node," Proc. 9th Int. Conf. on Transparent Optical Networks (ICTON 2007), Vol. 3, July 2007, pp. 117‒120.

Van Caenegem, R.

R. Van Caenegem, D. Colle, M. Pickavet, P. Demeester, K. Christodoulopoulos, K. Vlachos, E. Varvarigos, L. Stampoulidis, D. Roccato, and R. Vilar, "The design of an all-optical packet switching network," IEEE Commun. Mag. 45, (11), 52‒61 (2007).
[CrossRef]

Varvarigos, E.

R. Van Caenegem, D. Colle, M. Pickavet, P. Demeester, K. Christodoulopoulos, K. Vlachos, E. Varvarigos, L. Stampoulidis, D. Roccato, and R. Vilar, "The design of an all-optical packet switching network," IEEE Commun. Mag. 45, (11), 52‒61 (2007).
[CrossRef]

Vilar, R.

R. Van Caenegem, D. Colle, M. Pickavet, P. Demeester, K. Christodoulopoulos, K. Vlachos, E. Varvarigos, L. Stampoulidis, D. Roccato, and R. Vilar, "The design of an all-optical packet switching network," IEEE Commun. Mag. 45, (11), 52‒61 (2007).
[CrossRef]

Vlachos, K.

R. Van Caenegem, D. Colle, M. Pickavet, P. Demeester, K. Christodoulopoulos, K. Vlachos, E. Varvarigos, L. Stampoulidis, D. Roccato, and R. Vilar, "The design of an all-optical packet switching network," IEEE Commun. Mag. 45, (11), 52‒61 (2007).
[CrossRef]

Wang, Z.

S. Blake, D. Black, M. Carlson, E. Davies, Z. Wang, and W. Weiss, "An architecture for differentiated service," RFC 2475, Dec. 1998.

Weiss, W.

S. Blake, D. Black, M. Carlson, E. Davies, Z. Wang, and W. Weiss, "An architecture for differentiated service," RFC 2475, Dec. 1998.

Xu, L.

L. Xu, H. Perros, and G. Rouskas, "Techniques for optical packet switching and optical burst switching," IEEE Commun. Mag. 39, (1), 136‒142 (2001).
[CrossRef]

Yao, S.

Yoo, S.

Yoo, S. J. B.

IEEE Commun. Mag. (3)

N. Bouabdallah, "Sub-wavelength solutions for next-generation optical networks," IEEE Commun. Mag. 45, (8), 36‒43 (2007).
[CrossRef]

L. Xu, H. Perros, and G. Rouskas, "Techniques for optical packet switching and optical burst switching," IEEE Commun. Mag. 39, (1), 136‒142 (2001).
[CrossRef]

R. Van Caenegem, D. Colle, M. Pickavet, P. Demeester, K. Christodoulopoulos, K. Vlachos, E. Varvarigos, L. Stampoulidis, D. Roccato, and R. Vilar, "The design of an all-optical packet switching network," IEEE Commun. Mag. 45, (11), 52‒61 (2007).
[CrossRef]

IEEE Trans. Commun. (1)

A. Acampora and S. Shah, "Multihop lightwave networks: a comparison of store-and-forward and hot-potato routing," IEEE Trans. Commun. 40, (6), 1082‒1090 (1992).
[CrossRef]

IEEE/ACM Trans. Netw. (1)

J. Bannister, F. Borgonovo, L. Fratta, and M. Gerla, "A performance model of deflection routing in multibuffer networks with nonuniform traffic," IEEE/ACM Trans. Netw. 3, (5), 509‒520 (1995).
[CrossRef]

J. Lightwave Technol. (2)

Lect. Notes Comput. Sci. (1)

I. Szcześniak, "Analysis of a finite number of deflections in fully and uniformly loaded regular networks," Lect. Notes Comput. Sci. 3042/2004, 675‒686 (2004).

Perform. Eval. (1)

J. Bannister, F. Borgonovo, L. Fratta, and M. Gerla, "A versatile model for predicting the performance of deflection-routing networks," Perform. Eval. 16, (1–3), 201‒222 (1992).
[CrossRef]

Photon. Netw. Commun. (2)

I. Szcześniak, T. Czachórski, and J.-M. Fourneau, "Packet loss analysis in optical packet-switched networks with limited deflection routing," Photon. Netw. Commun. 16, (3), 253‒261 (2008).
[CrossRef]

H. Øverby, "Traffic models for slotted optical packet switched networks," Photon. Netw. Commun. 13, 183‒194 (2007).
[CrossRef]

Other (6)

I. Szcześniak, the website of OPUS, the optical packet switching universal solver. Apr. 2011 [Online]. Available: http://www.irkos.org/opus

S. Das, G. Parulkar, and N. McKeown, "Unifying packet and circuit switched networks," 2009 IEEE GLOBECOM Workshops, Dec. 2009, pp. 1‒6.

I. Szcześniak and T. Czachórski, "Performance evaluation of a bufferless packet-switched node," Proc. 9th Int. Conf. on Transparent Optical Networks (ICTON 2007), Vol. 3, July 2007, pp. 117‒120.

S. Blake, D. Black, M. Carlson, E. Davies, Z. Wang, and W. Weiss, "An architecture for differentiated service," RFC 2475, Dec. 1998.

J. Jue, "An algorithm for loopless deflection in photonic packet-switched networks," Proc. ICC 2002, Vol. 5, May 2002, pp. 2776‒2780.

T. Karagiannis, M. Molle, M. Faloutsos, and A. Broido, "A nonstationary Poisson view of Internet traffic," Proc. INFOCOM 2004, Vol. 3, Mar. 2004, pp. 1558‒1569.

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Figures (4)

Fig. 1
Fig. 1

Inputs and outputs of node i.

Fig. 2
Fig. 2

Mean rates of packets at node i.

Fig. 3
Fig. 3

Sample network, where the first number of the fiber label gives the fiber length, while the second gives the number of wavelengths.

Fig. 4
Fig. 4

Simulation and analysis results.

Tables (3)

Tables Icon

Table I The Seven Most Probable Arrangements for Λ = ( 3 , 11 )

Tables Icon

Table II Description of Packet Visits for Flow (5, 1)

Tables Icon

Table III Description of Packet Hops for Flow (5, 1)

Equations (30)

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

f ( l , λ ) = e λ λ l l ! .
p ( x ) = d = 0 δ λ d x d .
P ( x ) = r = 1 R f ( x r , λ r ) .
Ξ ( Λ ) = max e N | P ( x e ) P ( x 1 ) > ξ .
f ( Γ ( y , λ ) , λ ) f ( Γ ( y + 1 , λ ) , λ ) for  y = 1 , 2 , .
ρ i = P ( A i | B i ) = P ( A i B i ) P ( B i ) .
P ( A i B i ) = e = 1 Ξ ( Λ adm,i ) P ( B i , e ) P ( D i , e ) .
P ( B i , e ) = P ( x adm,i,e ) P ( E i , e ) .
P ( D i , e ) = C b i , e 1 b i , e 1 C b i , e b i , e = b i , e b i , e .
P ( E i , e ) = C b i , e 1 Z 1 C b i , e Z = b i , e Z .
P ( B i ) = e = 1 Ξ ( Λ adm,i ) P ( B i , e ) .
ρ i = e = 1 Ξ ( Λ adm,i ) P ( x adm,i,e ) b i , e e = 1 Ξ ( Λ adm,i ) P ( x adm,i,e ) b i , e .
β i , n = ρ i β i , n .
ϕ i , j , n = P ( H i , j , n | L i , n ) = P ( H i , j , n L i , n ) P ( L i , n ) .
P ( H i , j , n L i , n ) = e = 1 Ξ ( Λ rou,i ) P ( L i , n , e ) ϕ i , e , j , n .
P ( L i , n , e ) = P ( x rou,i,e ) P ( R i , n , e ) .
P ( R i , n , e ) = C x i , n , e 1 Z n 1 C x i , n , e Z n = x i , n , e Z n .
P ( H i , j , n L i , n ) = 1 Z n e = 1 Ξ ( Λ rou,i ) P ( x rou,i,e ) x i , n , e ϕ i , e , j , n .
P ( L i , n ) = e = 1 Ξ ( Λ rou,i ) P ( L i , n , e ) .
P ( L i , n ) = 1 Z n e = 1 Ξ ( Λ rou,i ) P ( x rou,i,e ) x i , n , e .
ϕ i , j , n = e = 1 Ξ ( Λ rou,i ) P ( x rou,i,e ) x i , n , e ϕ i , e , j , n e = 1 Ξ ( Λ rou,i ) P ( x rou,i,e ) x i , n , e .
ϕ i , e , j , n = x i , e , j , n x i , n , e .
P a,b,v = p a , b , v , 1 ( x ) , , p a , b , v , n ( x ) , , p a , b , v , N ( x ) .
P a,b,v = P a,b,v 1 T b for v > 1 .
t i , j , b = ϕ i , j , b x d i , j .
q a , b , h , i , j ( x ) = t i , j , b p a , b , h , i ( x ) .
T 1 = 0 0 0 0 0 0 x 100 0 0 0 0 0 0 x 200 0 0 0 0 0 0 x 80 0 0 0 0 . 05 x 210 0 . 95 x 40 0 0 0 0 0 0 x 100 0 0 0 .
α i , n = a = 1 N h = 1 η j = 1 N q a , n , h , j , i ( x = 1 ) ( s ) .
ψ i , j ( S ) = a = 1 N b = 1 N h = 1 η q a , b , h , i , j ( x = 1 ) ( S ) w i , j .
ξ = 1 10 log ( N ) .