Abstract

An optical packet switch that shares both limited range and full range wavelength converters for contention resolution is proposed with the aim to guarantee a high conversion cost saving. To optimally dimension the number and the conversion range of the wavelength converters, an analytical model, validated by simulation, is introduced. Numerical results show that the proposed switch architecture allows for a conversion cost saving in the order of 90% with respect to a traditional architecture in which only shared full range wavelength converters are used.

©2009 Optical Society of America

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References

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  1. S. Yao, B. Mukherjee, and S. Dixit, “Advances in Photonic Packet Switching: an Overview,” IEEE Commun. Mag. 38, 84–94 (2000).
    [Crossref]
  2. S. L. Danielsen, P. B. Hansen, and K. E. Stubkjaer, “Wavelength Conversion in Optical Packet Switching,” J. Lightwave Technol. 16, 2095–2108 (1998).
    [Crossref]
  3. V. Eramo, M. Listanti, and A. Germoni, “Cost Evaluation of Optical Packet Switches Equipped With Limited-Range and Full-Range Converters for Contention Resolution,” J. Lightwave Technol. 26, 390–407 (2008).
    [Crossref]
  4. H. Li and I. Li-Jin, “Cost-Saving Two-Layer Wavelength Conversion in Optical Switching Network,” J. Lightwave Technol. 24, 705–712 (2006).
    [Crossref]
  5. V. Eramo, M. Listanti, and A. Germoni, “Cost Evaluation of Optical Packet Switches using both Limited-Range and Full-Range Converters for Contention Resolution,” in proc. IEEE Globecom, December 2007 .
  6. C. Guillemot et al., “Transparent Optical Packet Switching: The European ACTS KEOPS Project Approach,” Lasers and Electro-Optics Society 1999 12th Annual Meeting. LEOS ’99. IEEE,  vol.2, no., pp.401–402 vol.2, 1999.
  7. B. Bostica, M. Burzio, P. Gambini, and L. Zucchelli, “Synchronization issues in optical packet switched networks,” Photonic Networks, G. Prati, Sringer-Verlag, 1997.
  8. Z. Zhang and Y. Yang, “Distributed Scheduling Algorithms for Wavelength Convertible WDM Optical Interconnects,” IEEE IPDPS 2003, April 2003.
  9. Z. Zhang and Y. Yang, “Performance Modelling of Bufferless WDM Packet Switching Networks with Limited Range Wavelength Conversion,” IEEE Trans. Commun. 54, 1473–1480 (2006).
    [Crossref]
  10. V. Eramo, M. Listanti, and M. Spaziani, “Resource Sharing in Optical Packet Switches With Limited-Range Wavelength Converters,” J. Lightwave Technol. 23, 671–687 (2005).
    [Crossref]
  11. V. Eramo and M. Listanti, “Packet Loss in a Bufferless WDM Switch Employing Shared Tunable Wavelength Converters,” J. Lightwave Technol. 18, 1818–1833 (2000).
    [Crossref]

2008 (1)

2006 (2)

H. Li and I. Li-Jin, “Cost-Saving Two-Layer Wavelength Conversion in Optical Switching Network,” J. Lightwave Technol. 24, 705–712 (2006).
[Crossref]

Z. Zhang and Y. Yang, “Performance Modelling of Bufferless WDM Packet Switching Networks with Limited Range Wavelength Conversion,” IEEE Trans. Commun. 54, 1473–1480 (2006).
[Crossref]

2005 (1)

2000 (2)

V. Eramo and M. Listanti, “Packet Loss in a Bufferless WDM Switch Employing Shared Tunable Wavelength Converters,” J. Lightwave Technol. 18, 1818–1833 (2000).
[Crossref]

S. Yao, B. Mukherjee, and S. Dixit, “Advances in Photonic Packet Switching: an Overview,” IEEE Commun. Mag. 38, 84–94 (2000).
[Crossref]

1999 (1)

C. Guillemot et al., “Transparent Optical Packet Switching: The European ACTS KEOPS Project Approach,” Lasers and Electro-Optics Society 1999 12th Annual Meeting. LEOS ’99. IEEE,  vol.2, no., pp.401–402 vol.2, 1999.

1998 (1)

Bostica, B.

B. Bostica, M. Burzio, P. Gambini, and L. Zucchelli, “Synchronization issues in optical packet switched networks,” Photonic Networks, G. Prati, Sringer-Verlag, 1997.

Burzio, M.

B. Bostica, M. Burzio, P. Gambini, and L. Zucchelli, “Synchronization issues in optical packet switched networks,” Photonic Networks, G. Prati, Sringer-Verlag, 1997.

Danielsen, S. L.

Dixit, S.

S. Yao, B. Mukherjee, and S. Dixit, “Advances in Photonic Packet Switching: an Overview,” IEEE Commun. Mag. 38, 84–94 (2000).
[Crossref]

Eramo, V.

Gambini, P.

B. Bostica, M. Burzio, P. Gambini, and L. Zucchelli, “Synchronization issues in optical packet switched networks,” Photonic Networks, G. Prati, Sringer-Verlag, 1997.

Germoni, A.

V. Eramo, M. Listanti, and A. Germoni, “Cost Evaluation of Optical Packet Switches Equipped With Limited-Range and Full-Range Converters for Contention Resolution,” J. Lightwave Technol. 26, 390–407 (2008).
[Crossref]

V. Eramo, M. Listanti, and A. Germoni, “Cost Evaluation of Optical Packet Switches using both Limited-Range and Full-Range Converters for Contention Resolution,” in proc. IEEE Globecom, December 2007 .

Guillemot, C.

C. Guillemot et al., “Transparent Optical Packet Switching: The European ACTS KEOPS Project Approach,” Lasers and Electro-Optics Society 1999 12th Annual Meeting. LEOS ’99. IEEE,  vol.2, no., pp.401–402 vol.2, 1999.

Hansen, P. B.

Li, H.

Li-Jin, I.

Listanti, M.

Mukherjee, B.

S. Yao, B. Mukherjee, and S. Dixit, “Advances in Photonic Packet Switching: an Overview,” IEEE Commun. Mag. 38, 84–94 (2000).
[Crossref]

Spaziani, M.

Stubkjaer, K. E.

Yang, Y.

Z. Zhang and Y. Yang, “Performance Modelling of Bufferless WDM Packet Switching Networks with Limited Range Wavelength Conversion,” IEEE Trans. Commun. 54, 1473–1480 (2006).
[Crossref]

Z. Zhang and Y. Yang, “Distributed Scheduling Algorithms for Wavelength Convertible WDM Optical Interconnects,” IEEE IPDPS 2003, April 2003.

Yao, S.

S. Yao, B. Mukherjee, and S. Dixit, “Advances in Photonic Packet Switching: an Overview,” IEEE Commun. Mag. 38, 84–94 (2000).
[Crossref]

Zhang, Z.

Z. Zhang and Y. Yang, “Performance Modelling of Bufferless WDM Packet Switching Networks with Limited Range Wavelength Conversion,” IEEE Trans. Commun. 54, 1473–1480 (2006).
[Crossref]

Z. Zhang and Y. Yang, “Distributed Scheduling Algorithms for Wavelength Convertible WDM Optical Interconnects,” IEEE IPDPS 2003, April 2003.

Zucchelli, L.

B. Bostica, M. Burzio, P. Gambini, and L. Zucchelli, “Synchronization issues in optical packet switched networks,” Photonic Networks, G. Prati, Sringer-Verlag, 1997.

IEEE Commun. Mag. (1)

S. Yao, B. Mukherjee, and S. Dixit, “Advances in Photonic Packet Switching: an Overview,” IEEE Commun. Mag. 38, 84–94 (2000).
[Crossref]

IEEE Trans. Commun. (1)

Z. Zhang and Y. Yang, “Performance Modelling of Bufferless WDM Packet Switching Networks with Limited Range Wavelength Conversion,” IEEE Trans. Commun. 54, 1473–1480 (2006).
[Crossref]

J. Lightwave Technol. (5)

Other (4)

V. Eramo, M. Listanti, and A. Germoni, “Cost Evaluation of Optical Packet Switches using both Limited-Range and Full-Range Converters for Contention Resolution,” in proc. IEEE Globecom, December 2007 .

C. Guillemot et al., “Transparent Optical Packet Switching: The European ACTS KEOPS Project Approach,” Lasers and Electro-Optics Society 1999 12th Annual Meeting. LEOS ’99. IEEE,  vol.2, no., pp.401–402 vol.2, 1999.

B. Bostica, M. Burzio, P. Gambini, and L. Zucchelli, “Synchronization issues in optical packet switched networks,” Photonic Networks, G. Prati, Sringer-Verlag, 1997.

Z. Zhang and Y. Yang, “Distributed Scheduling Algorithms for Wavelength Convertible WDM Optical Interconnects,” IEEE IPDPS 2003, April 2003.

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Figures (10)

Fig. 1.
Fig. 1. FLSPN OPS equipped with rl LRWC and rf FRWCs.

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Fig. 2.
Fig. 2. Scheduling algorithm for FLSPN architecture

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Fig. 3.
Fig. 3. LRWCs Assignment (LRA) sub-phase

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Fig. 4.
Fig. 4. FRWCs Assignment (FRA) sub-phase

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Fig. 5.
Fig. 5. Comparison between the analytical and simulation results for the Packet Loss Probability in the FLSPN switch as a function of the used number of FRWCs. Switch and traffic parameters are N = 8, M = 16, p = 0,4, d = 1. The used number rl of LRWCs varies from 0 to 120.

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Fig. 6.
Fig. 6. Comparison between the analytical and simulation results for the Packet Loss Probability in the FLSPN switch as a function of the used number of FRWCs. Switch and traffic parameters are N = 8, M = 32, p = 0,8, d = 2. The used number rl of LRWCs varies from 0 to 240.

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Fig. 7.
Fig. 7. Conversion cost of the FLSPN and TLWC-SPN switches as a function of the conversion range d. The switch and traffic parameters are N = 8, p = 0,8 and M varying from 16 to 64. A linear cost model (b = 1) is assumed.

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Fig. 8.
Fig. 8. Conversion cost percentage reduction of the FLSPN and TLWC-SPN switches with respect to the OLWC-SPN switch as a function of the conversion range d. The switch and traffic parameters are N = 8, p = 0,8 and M varying from 16 to 64. A linear cost model (b = 1) is assumed.

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Fig. 9.
Fig. 9. Cconversion cost of FLSPN and TLWC-SPN switches as a function of the conversion range d. The switch and traffic parameters are N = 8, p = 0,8, M = 64 and b varying from 0,5 to 2.

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Fig. 10.
Fig. 10. Conversion cost percentage reductions of the FLSPN and TLWC-SPN switches with respect to the OLWC-SPN as a function of the conversion range d. The switch and traffic parameters are N = 8, p = 0,8, M = 64 and b varying from 0,5 to 2.

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Equations (23)

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C LRWC = a d b , C FRWC = a ( M − 1 ) b
a = C norm ∑ d = 1 M − 1 d b .
C FLSPN = r l C LRWC + r f C FRWC .
P loss FLSPN ( r l , r f ) = ∑ i = 0 N ( M − 1 ) ∑ j = 0 N ( M − 1 ) p R l av , R f av ( i , j ) P loss FLSPN , OF ( r l av , r f av ) ∣ r l av = i r f av = j
P loss FLSPN , OF ( r l av , r f av ) = E [ N l , WB ] + E [ N l , CB ] E [ N O ]
E [ N l , WB ] = ∑ j = M + 1 NM ( j − M ) ( NM j ) ( P N ) j ( 1 − P N ) NM − j
E [ N l , CB ] = ∑ i = 0 M − 1 ∑ j = 0 M − i E [ N l , CB / d = i , w = j ] p D , W ( i , j )
E [ N l , CB / d = i , w = j ] = { j − r f av i ≤ r l av , j > r f av i − ( r l av + r f av ) + j i > r l av + r f av min ( 0 , j − ( r l av + r f av − i ) ) r l av < i ≤ r l av + r f av 0 otherwise
p D , W ( i , j ) = ∑ k = j M p α , β , γ ( j , k , i ) + ∑ h = j + 1 NM p α , β , γ ( h , j , i )
p r ( i ) = ( N i ) ( p N ) i ( 1 − p N ) N − i i = 0,1 , … , N ;
p A ( k ) ( i ) = ( Nk i ) ( p N ) i ( 1 − p N ) N − i i = 0,1 , … , N ;
p α , β , γ ( 1 , q , i , j , h ) = { p r ( q + i ) i ≤ N − q , j = 0 , h = q − 1 p r ( q − j ) i = 0 , 1 ≤ j ≤ q , h = q − j 0 otherwise
p α , β , γ ( 1 , d + 2 , i , j , h ) = { p α , β , γ ( 1 , d + 1 , i , j − 1 , h ) j ≠ 0 0 j = 0
p α , β , γ ( p , q , i , j , h ) = ∑ k = 0 N Prob ( α p , q = i , β p , q = j , γ p , q = h / r M − p = k ) Prob ( r M − p = k )
p α , β , γ ( p , q , i , j , h ) = { ∑ k = 0 q − 1 p r ( k ) p α , β , γ ( p − 1 , q − k , i , 0 , min ( 0 , h − k ) ) + ∑ k = q min ( N , i + q ) p A ( p - 1 ) ( i − ( k − q ) ) δ ( h − q ) j = 0 ∑ k = 0 q − 1 p r ( k ) p α , β , γ ( p − 1 , q − k , i , 0 , min ( 0 , h − k ) ) j ≠ 0
where :
δ ( i ) = { 1 if i = 0 0 otherwise
p α , β , γ ( p , q , i , j , h ) = { ∑ k = 0 q − p − 1 p r ( k ) p α , β , γ ( p − 1 , q − k , i , 0 , min ( 0 , h − k ) ) + + ∑ k = q − p q − 1 p r ( k ) p α , β , γ ( p − 1 , q − k , i , 0 , min ( 0 , h − ( k − 1 ) ) ) + + ∑ k = q min ( N , i + q ) p r ( k ) p A ( p − 1 ) ( i − ( k − q ) ) δ ( h − ( q − 1 ) ) j = 0 ∑ k = 0 q − p − 1 p r ( k ) p α , β , γ ( p − 1 , q − k , i , j , min ( 0 , h − k ) ) + + ∑ k = q − p q − 1 p r ( k ) p α , β , γ ( p − 1 , q − k , i , j , min ( 0 , h − ( k − 1 ) ) ) j ≠ 0
p α , β , γ ( p , p + d + 1 , i , j , h ) = { p α , β , γ ( p − 1 , p + d , i , j − 1 , h ) j ≠ 0 0 j = 0
p D s , W s ( k , h ) = 1 N ∑ i = 1 N p D i , W i ( k , h )
p D 1 , W 1 = { 1 k = 0 ; h = 0 0 k ≠ 0 ; h ≠ 0
p D i , w i ( k , h ) = p D , W ( k , h ) ⊗ p D , W ( k , h ) ⋯⋯ ⊗ p D , W ( k , h ) ︷ ( i − 1 ) times ,
p R l av , R f av ( i , j ) = { p D s , W s ( r l − i , r f − j ) i ≠ 0 ; j ≠ 0 ∑ k = r l r l + r f − j p D s , W s ( k , r f − ( k − r l ) − j ) i = 0 ; j ≠ 0 ∑ h = r f N ( M − 1 ) p D s , W s ( r l − i , h ) i ≠ 0 ; j = 0 ∑ k = r l N ( M − 1 ) ∑ h = r f − ( k − r l ) N ( M − 1 ) p D s , W s ( k , h ) i = 0 ; j = 0

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