Abstract

We provide here a new loss model for an optical hybrid switch that can function as an optical burst switch and/or optical circuit switch. Our model is general as it considers an implementation whereby some of the circuits have preemptive priority over bursts and others are allowed to queue their reservations. We first present an analysis based on a 3-dimension state-space Markov chain that provides exact results for the blocking probabilities of bursts and circuits, the proportion of circuits that are delayed and the mean delay of the circuits that are delayed. Because it is difficult to exactly compute the blocking probability in realistic scenarios with a large number of wavelengths, we derive computationally a scalable and accurate approximations based on reducing the 3-dimension state space into a single dimension. These scalable approximations that can produce performance results in a fraction of a second can readily enable switch dimensioning. Extensive numerical results are presented to demonstrate the accuracy and the use of the new approximations.

© 2006 Optical Society of America

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References

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  1. C. Xin, C. Qiao, Y. Ye and S. Dixit, "A hybrid optical switching approach," in Proceedings of IEEE GLOBECOM2003, 7, 3808-3812, Dec. (2003).
  2. G. M. Lee, B. Wydrowski, M. Zukerman, J. K. Choi, and C. H. Foh, "Performance Evaluation of an Optical Hybrid Switching System," in Proceedings of IEEE GLOBECOM 2003 5, 2508-2512, Dec. (2003).
  3. H. L. Vu, A. Zalesky, E.W. M. Wong, Z. Rosberg, S. M. H. Bilgrami, M. Zukerman and R. S. Tucker, "Scalable Performance Evaluation of a Hybrid Optical Switch," J. Lightwave Technol. 23, 2961-2973, Oct. (2005).
    [CrossRef]
  4. E. W. M. Wong and M. Zukerman, "Performance evaluation for an optical hybrid switch with circuit queued reservations," Opt. Express 13, 9446-9459 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-23-9446
    [CrossRef] [PubMed]
  5. E. W. M. Wong and M. Zukerman, "Analysis of an optical hybrid switch," IEEE Commun. Lett., 10, 108-110, February (2006).
    [CrossRef]
  6. M. Yoo and C. Qiao, "Just-enough-time (JET): A high speed protocol for bursty traffic in optical networks," in Proceeding of IEEE/LEOS Conf. on Technologies For a Global Information Infrastructure, 26-27, Aug. (1997).
  7. C. Qiao, and M. Yoo, "Optical Burst Switching (OBS): A New Paradigm for an Optical Internet," J. High Speed Nets. 8, 69-84, Jan. (1999).
  8. J. Turner, "Terabit Burst Switching," J. High Speed Nets. 8, 3-16, Mar. (1999).
  9. <bok>. S. Verma, H. Chaskar, and R. Ravikanth "Optical Burst Switching: A Viable Solution for Terabit IP Backbone," IEEE Network, 48-53, Nov./Dec. (2000).</bok>
  10. A. Detti, V. Eramo, and M. Listanti, "Performance evaluation of a new technique for IP support in aWDMoptical network: optical composite burst switching (OCBS)," J. Lightwave Technol. 20, 154-165, Feb. (2002).
    [CrossRef]
  11. T. Battestilli, and H. Perros, "An Introduction to Optical Burst Switching," IEEE Commun. Mag. 41, S10-S15, Aug. (2003).
    [CrossRef]
  12. <bok>. Y. Chen, C. Qiao and X. Yu, "Optical Burst Switching (OBS): A New Area in Optical Networking Research," IEEE Network Magazine 18, 16-23, May/June (2004).</bok>
    [CrossRef]
  13. <bok>. A. Zalesky, E. W. M. Wong, M. Zukerman, H. L. Vu and R. S. Tucker, "Performance Analysis of an OBS Edge Router," IEEE Photonic Technol. Lett. 16, 695-697, Feb. (2004).</bok>
    [CrossRef]
  14. M. Duser, and P. Bayvel, "Analysis of a Dynamically Wavelength Routed Optical Burst Switched Network Architecture," J. Lightwave Technol. 20, 574-585, Apr. (2002).
    [CrossRef]
  15. A. Zalesky, E. W. M. Wong, H. L. Vu, M. Zukerman, Z. Rosberg and M. S. Bilgrami, "Performance evaluation of a hybrid optical switch," in Proc. ITC19, Aug./Sep. (2005).
  16. A. Leon-Garcia, R. H. Kwong, and G. F. Williams, "Performance Evaluation Methods for an Integrated Voice/Data Link," IEEE Trans. Commun. 30, 1848-1858, August (1982).
    [CrossRef]
  17. M. Zukerman, "Circuit allocation and overload control in a hybrid switching system," Computer Networks and ISDN Systems 16, 281-298, (1989).
    [CrossRef]
  18. Z. Rosberg, H. L. Vu, M. Zukerman and J. White, "Performance analyses of optical burst-switching networks," J. Sel. Areas Commun. 21, 1187-1197, Sept. (2003).
    [CrossRef]
  19. H. L. Vu and M. Zukerman, "Blocking Probability for Priority Classes in Optical Burst Switching Networks," IEEE Commun. Lett. 6, 214-216, May (2002).
    [CrossRef]
  20. J. White, M. Zukerman and H. L. Vu, "A framework for optical burst switching network design," IEEE Commun. Lett. 6, 268-270, Jun (2002).
    [CrossRef]
  21. M. C. Yuang, P. L. Tien, and J. Shih, "QoS Scheduler/Shaper for Optical Coarse Packet Switching IP-over-WDM Networks," J. Sel. Areas Commun. 22, Nov. (2004).
    [CrossRef]
  22. N. Barakat and E. H. Sargent, "Dual-header optical burst switching: a new architecture for WDM burst-switched networks," in Proc. IEEE INFOCOM’05, March (2005).
  23. I. Baldine, G. N. Rouskas, H. G. Perros and D. Stevenson, "JumpStart: A just-in-time signaling architecture for WDM burst-switched networks," IEEE Commun. Mag., 82-89, February (2002).
    [CrossRef]
  24. N. Barakat and E. H. Sargent, "Analytical modeling of offset-induced priority in multiclass OBS networks," IEEE Trans. Commun. 53, 1343-1352, Aug. (2005).
    [CrossRef]
  25. M. Yoo, C. Qiao, and S. Dixit, "Optical burst switching for service differentiation in the next-generation optical internet," IEEE Commun. Mag. 39, 98-104, Feb. (2001).
    [CrossRef]
  26. M. Yoo and C. Qiao, "Supporting multiple classes of services in IP over WDM networks," in Proc. Globecom 1999, 1023-1027, Dec. (1999).
  27. K. Dolzer, C. Gauger, J. Sp ¨ ath, and S. Bodamer, "Evaluation of reservation mechanisms for optical burst switching," AE¨U Int. J. Electron. Commun. 55, 18-26, Jan. (2001).
    [CrossRef]
  28. P. Taylor and R. Maillardet, "Queues with reservations," Presented at the Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) 2005 meeting, Napier, New Zealand, Jan./Feb. (2005).
    [PubMed]
  29. T. Engset, "Die wahrscheinlichkeitsrechnung zur bestimmung der wahleranzahl in automatischen fernsprechamtern" Elektrotechnische zeitschrift 39, 304-306, Aug. (1918).
  30. <bok>. J. Hui, Switching and Traffic Theory for Integrated Broadband Networks, Kluwer Academic Press (1990).</bok>
  31. M. Zukerman, E. W. M. Wong, Z. Rosberg, G. M. Lee, H. L. Vu, "On Teletraffic Application to OBS," IEEE Commun. Lett. 8, 116-118, Feb. (2004).
    [CrossRef]
  32. H. Overby "Performance modelling of optical packet switched networks with the Engset traffic model," Opt. Express 13, 1685-1695 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-5-1685
    [CrossRef] [PubMed]

2005 (1)

1989 (1)

M. Zukerman, "Circuit allocation and overload control in a hybrid switching system," Computer Networks and ISDN Systems 16, 281-298, (1989).
[CrossRef]

Overby, H.

Zukerman, M.

M. Zukerman, "Circuit allocation and overload control in a hybrid switching system," Computer Networks and ISDN Systems 16, 281-298, (1989).
[CrossRef]

Computer Networks and ISDN Systems (1)

M. Zukerman, "Circuit allocation and overload control in a hybrid switching system," Computer Networks and ISDN Systems 16, 281-298, (1989).
[CrossRef]

Opt. Express (1)

Other (30)

Z. Rosberg, H. L. Vu, M. Zukerman and J. White, "Performance analyses of optical burst-switching networks," J. Sel. Areas Commun. 21, 1187-1197, Sept. (2003).
[CrossRef]

H. L. Vu and M. Zukerman, "Blocking Probability for Priority Classes in Optical Burst Switching Networks," IEEE Commun. Lett. 6, 214-216, May (2002).
[CrossRef]

J. White, M. Zukerman and H. L. Vu, "A framework for optical burst switching network design," IEEE Commun. Lett. 6, 268-270, Jun (2002).
[CrossRef]

M. C. Yuang, P. L. Tien, and J. Shih, "QoS Scheduler/Shaper for Optical Coarse Packet Switching IP-over-WDM Networks," J. Sel. Areas Commun. 22, Nov. (2004).
[CrossRef]

N. Barakat and E. H. Sargent, "Dual-header optical burst switching: a new architecture for WDM burst-switched networks," in Proc. IEEE INFOCOM’05, March (2005).

I. Baldine, G. N. Rouskas, H. G. Perros and D. Stevenson, "JumpStart: A just-in-time signaling architecture for WDM burst-switched networks," IEEE Commun. Mag., 82-89, February (2002).
[CrossRef]

N. Barakat and E. H. Sargent, "Analytical modeling of offset-induced priority in multiclass OBS networks," IEEE Trans. Commun. 53, 1343-1352, Aug. (2005).
[CrossRef]

M. Yoo, C. Qiao, and S. Dixit, "Optical burst switching for service differentiation in the next-generation optical internet," IEEE Commun. Mag. 39, 98-104, Feb. (2001).
[CrossRef]

M. Yoo and C. Qiao, "Supporting multiple classes of services in IP over WDM networks," in Proc. Globecom 1999, 1023-1027, Dec. (1999).

K. Dolzer, C. Gauger, J. Sp ¨ ath, and S. Bodamer, "Evaluation of reservation mechanisms for optical burst switching," AE¨U Int. J. Electron. Commun. 55, 18-26, Jan. (2001).
[CrossRef]

P. Taylor and R. Maillardet, "Queues with reservations," Presented at the Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) 2005 meeting, Napier, New Zealand, Jan./Feb. (2005).
[PubMed]

T. Engset, "Die wahrscheinlichkeitsrechnung zur bestimmung der wahleranzahl in automatischen fernsprechamtern" Elektrotechnische zeitschrift 39, 304-306, Aug. (1918).

<bok>. J. Hui, Switching and Traffic Theory for Integrated Broadband Networks, Kluwer Academic Press (1990).</bok>

M. Zukerman, E. W. M. Wong, Z. Rosberg, G. M. Lee, H. L. Vu, "On Teletraffic Application to OBS," IEEE Commun. Lett. 8, 116-118, Feb. (2004).
[CrossRef]

C. Xin, C. Qiao, Y. Ye and S. Dixit, "A hybrid optical switching approach," in Proceedings of IEEE GLOBECOM2003, 7, 3808-3812, Dec. (2003).

G. M. Lee, B. Wydrowski, M. Zukerman, J. K. Choi, and C. H. Foh, "Performance Evaluation of an Optical Hybrid Switching System," in Proceedings of IEEE GLOBECOM 2003 5, 2508-2512, Dec. (2003).

H. L. Vu, A. Zalesky, E.W. M. Wong, Z. Rosberg, S. M. H. Bilgrami, M. Zukerman and R. S. Tucker, "Scalable Performance Evaluation of a Hybrid Optical Switch," J. Lightwave Technol. 23, 2961-2973, Oct. (2005).
[CrossRef]

E. W. M. Wong and M. Zukerman, "Performance evaluation for an optical hybrid switch with circuit queued reservations," Opt. Express 13, 9446-9459 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-23-9446
[CrossRef] [PubMed]

E. W. M. Wong and M. Zukerman, "Analysis of an optical hybrid switch," IEEE Commun. Lett., 10, 108-110, February (2006).
[CrossRef]

M. Yoo and C. Qiao, "Just-enough-time (JET): A high speed protocol for bursty traffic in optical networks," in Proceeding of IEEE/LEOS Conf. on Technologies For a Global Information Infrastructure, 26-27, Aug. (1997).

C. Qiao, and M. Yoo, "Optical Burst Switching (OBS): A New Paradigm for an Optical Internet," J. High Speed Nets. 8, 69-84, Jan. (1999).

J. Turner, "Terabit Burst Switching," J. High Speed Nets. 8, 3-16, Mar. (1999).

<bok>. S. Verma, H. Chaskar, and R. Ravikanth "Optical Burst Switching: A Viable Solution for Terabit IP Backbone," IEEE Network, 48-53, Nov./Dec. (2000).</bok>

A. Detti, V. Eramo, and M. Listanti, "Performance evaluation of a new technique for IP support in aWDMoptical network: optical composite burst switching (OCBS)," J. Lightwave Technol. 20, 154-165, Feb. (2002).
[CrossRef]

T. Battestilli, and H. Perros, "An Introduction to Optical Burst Switching," IEEE Commun. Mag. 41, S10-S15, Aug. (2003).
[CrossRef]

<bok>. Y. Chen, C. Qiao and X. Yu, "Optical Burst Switching (OBS): A New Area in Optical Networking Research," IEEE Network Magazine 18, 16-23, May/June (2004).</bok>
[CrossRef]

<bok>. A. Zalesky, E. W. M. Wong, M. Zukerman, H. L. Vu and R. S. Tucker, "Performance Analysis of an OBS Edge Router," IEEE Photonic Technol. Lett. 16, 695-697, Feb. (2004).</bok>
[CrossRef]

M. Duser, and P. Bayvel, "Analysis of a Dynamically Wavelength Routed Optical Burst Switched Network Architecture," J. Lightwave Technol. 20, 574-585, Apr. (2002).
[CrossRef]

A. Zalesky, E. W. M. Wong, H. L. Vu, M. Zukerman, Z. Rosberg and M. S. Bilgrami, "Performance evaluation of a hybrid optical switch," in Proc. ITC19, Aug./Sep. (2005).

A. Leon-Garcia, R. H. Kwong, and G. F. Williams, "Performance Evaluation Methods for an Integrated Voice/Data Link," IEEE Trans. Commun. 30, 1848-1858, August (1982).
[CrossRef]

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Figures (15)

Fig. 1.
Fig. 1.

Optical hybrid switching transport network architecture

Fig. 2.
Fig. 2.

Optical hybrid switch architecture

Fig. 3.
Fig. 3.

Blocking probability (left) and delay [sec.] (right) versus normalized combined traffic intensity varying PCP for BP=0.1 and µb /µc =10.

Fig. 4.
Fig. 4.

Blocking probability (left) and delay [sec.] (right) versus normalized combined traffic intensity varying PCP for BP=0.1 and µb /µc =10.

Fig. 5.
Fig. 5.

Blocking probability (left) and delay [sec.] (right) versus normalized combined traffic intensity varying PCP for BP=0.5 and µb /µc =10.

Fig. 6.
Fig. 6.

Blocking probability (left) and delay [sec.] (right) versus normalized combined traffic intensity varying PCP for BP=0.9 and µb /µc =10.

Fig. 7.
Fig. 7.

Blocking probability (left) and delay [sec.] (right) versus normalized combined traffic intensity varying N for µb /µc =10.

Fig. 8.
Fig. 8.

Blocking probability (left) and delay [sec.] (right) versus normalized combined traffic intensity varying PCP for BP=0.1 and µb /µc =100.

Fig. 9.
Fig. 9.

Blocking probability (left) and delay [sec.] (right) versus normalized combined traffic intensity varying PCP for BP=0.5 and µb /µc =100.

Fig. 10.
Fig. 10.

Blocking probability (left) and delay [sec.] (right) versus normalized combined traffic intensity varying PCP for BP=0.9 and µb /µc =100.

Fig. 11.
Fig. 11.

Blocking probability and delay [sec.] versus normalized combined traffic intensity for M=100, K=50 and µb /µc =10.

Fig. 12.
Fig. 12.

Network example.

Fig. 13.
Fig. 13.

End-to-end blocking probability versus normalized combined traffic intensity varying PCP for BP=0.1 and µb /µc =10.

Fig. 14.
Fig. 14.

End-to-end blocking probability versus normalized combined traffic intensity varying PCP for BP=0.5 and µb /µc =10.

Fig. 15.
Fig. 15.

End-to-end blocking probability versus normalized combined traffic intensity varying PCP for BP=0.9 and µb /µc =10.

Equations (41)

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

π i , j , k ( ( i + k ) μ b + j μ c + ( M i j k ) λ )
= π i , j , k + 1 ( k + 1 ) μ b + π i , j + 1 , k ( j + 1 ) μ c
+ π i , j 1 , k ( M ( i + j 1 + k ) ) λ c
+ π i 1 , j , k ( M ( i 1 + j + k ) ) λ b
+ π i + 1 , j , k ( i + 1 ) μ b ,
π i , j , k ( ( M K k ) ( λ b + a j λ nc + a j δ i λ pc + ( 1 δ i ) λ pc ) + ( k + i ) μ b + j μ c )
= π i , j 1 , k ( M K + 1 k ) λ c
+ π i 1 , j , k ( M K + 1 k ) λ b
+ π i , j , k 1 ( M K k + 1 ) λ b + π i , j , k + 1 ( k + 1 ) μ b
+ π i , j + 1 , k ( j μ c )
+ + π i + 1 , j , k ( i + 1 ) μ b + π i + 1 , j 1 , k 1 ( M K k + 1 ) λ pc .
π i , j , k ( ( M i j k ) ( λ b + a j λ nc + a j δ i λ pc + ( 1 δ i ) λ pc ) + ( k + i ) μ b + j μ c )
= π i , j 1 , k ( M i j k + 1 ) a j 1 ( λ nc + δ i λ pc )
+ π i + 1 , j 1 , k 1 ( M i j k + 1 ) a j 1 λ pc
+ π i , j , k 1 ( M i j k + 1 ) λ b + π i , j + 1 , k ( K i ) μ c
+ π i , j , k + 1 ( k + 1 ) μ b + π i + 1 , j , k ( i + 1 ) μ b
C pc = i + j < K , k ( M i j k ) ( λ pc μ c ) π i , j , k + i > 0 , K i + j K + N , k ( M i j k ) ( λ pc μ c ) π i , j , k
+ i = 0 , K i + j < K + N , k a j ( M i j k ) ( λ pc μ c ) π i , j , k .
Q c = D c 1 / μ c .
Q q c = Q c / D p .
1 λ = λ EPC λ eff ( 1 λ eff ) + λ b λ eff ( 1 λ eff + 1 μ b + 1 λ ) ,
λ = ( 1 B nc ) λ nc + λ pc 1 + λ b μ b .
P j = ( M j + 1 ) λ j μ c p j 1
p j = ( M j + 1 ) b j 1 λ K μ c p j 1 .
1 λ * = ( 1 B b ) 1 λ + B b ( p b μ b + 1 λ ) .
1 μ * = C c μ c C b μ b + C c μ c 1 μ c + C b μ b C b μ b + C c μ c 1 μ b
C c = C p c + C n c
C p c = ( 1 B p c ) λ p c
p i = ( M i + 1 ) λ * i μ * p i 1
p 1 = ( M i + 1 ) b i 1 p c λ * K μ * P i 1
B n c * = B n c p n c + B p c p p c .
B c = B n c * p n c + B p c p p c .
C q c = C q n c + C q p c .
N c = N n c + N p c .
Q c = D c 1 / μ u .
Q q c = Q c / D p .
( 1 B b ) ρ b = 2 ( 1 B b ) ρ b ¯ + ( 1 B b ) 2 ρ b ¯
ρ b = ρ b ¯ [ 2 + ( 1 B b ) ] .
ρ xc = ρ xc ¯ [ 1 + 2 ( 1 B xc ) ]
P b = 1 2 i = 1 2 [ 1 ( 1 B b ) i ] .
P xc = 1 2 i = 1 2 [ 1 ( 1 B xc ) i ] .

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