Abstract

We examine optical burst switching (OBS) networks with out-of-band header transmission and electronic processing. We present the first detailed analysis of the potential effects of control-plane processing limitations on the overall throughput and latency performance of OBS networks. We present an accurate analytical model that explicitly accounts for the header queuing process in core nodes, and we provide a set of design guidelines for provisioning OBS networks such that the control-plane does not become the throughput bottleneck of the system. We also estimate the minimum end-to-end latency associated with offsets and burst assembly that is required to ensure proper OBS operation. We find that ultrafast header-processing speeds (<100 ns per header) are not required for efficient OBS operation. We show that provisioning a header-offset size that corresponds to a header-processing-queue length of 50 is sufficient for a wide range of practical OBS systems. For a fully meshed network topology, a total end-to-end control latency that is 10 times longer than the duration of a single header-processing duration is required for proper network operation. By contrast, more sparsely connected networks, such as those deployed in the long haul and metro today, may require an average end-to-end control latency that is hundreds of times as large as the header-processing duration.

© 2009 Optical Society of America

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References

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  1. J. P. Jue, V. M. Vokkarane, Optical Burst Switched Networks, New York, NY: Springer, 2005.
  2. G. I. Papadimitriou, C. Papazoglou, A. S. Pomportsis, “Optical switching: switch fabrics, techniques, and architectures,” J. Lightwave Technol. vol. 21, pp. 384–405, Feb. 2003.
    [CrossRef]
  3. L. Xu, H. G. Perros, G. Rouskas, “Techniques for optical packet switching and optical burst switching,” IEEE Commun. Mag. vol. 39, no. 1, pp. 136–142, Jan. 2001.
    [CrossRef]
  4. T. Battestilli, H. Perros, “An introduction to optical burst switching,” IEEE Commun. Mag. vol. 41, no. 8, pp. S10–S15, Aug. 2003.
    [CrossRef]
  5. T. Chen, C. Qiao, X. Yu, “Optical burst switching (OBS): a new area in optical networking research,” IEEE Network, vol. 18, no. 3, pp. 16–23, May–June 2004.
    [CrossRef]
  6. F. J. Vázquez-Abad, J. A. White, L. L. H. Andrew, R. S. Tucker, “Does header length affect performance in optical burst switched networks?” J. Opt. Netw. vol. 3, no. 5, pp. 342–353, May 2004.
    [CrossRef]
  7. Y. Xiong, M. Vandenhoute, H. Cankaya, “Control architecture in optical burst-switched WDM networks,” IEEE J. Sel. Areas Commun. vol. 18, pp. 1838–1851, Oct. 2000.
    [CrossRef]
  8. J. White, M. Zukerman, H. L. Vu, “A framework for optical burst switching network design,” IEEE Commun. Lett. vol. 6, pp. 268–270, Jun. 2002.
    [CrossRef]
  9. N. Barakat, T. E. Darcie, “The control-plane stability constraint in optical burst switching networks,” IEEE Commun. Lett. vol. 11, pp. 267–269, Mar. 2007.
    [CrossRef]
  10. N. Barakat, E. H. Sargent, “Separating resource reservations from service requests to improve the performance of optical burst-switching networks,” IEEE J. Sel. Areas Commun. vol. 24, pp. 95–107, April 2006.
    [CrossRef]
  11. V. M. Vokkarane, J. P. Jue, “Prioritized burst segmentation and composite burst-assembly techniques for QoS support in optical burst-switched networks,” IEEE J. Sel. Areas Commun. vol. 21, pp. 1198–1209, Sept. 2003.
    [CrossRef]
  12. R. Rajaduray, S. Ovadia, D. Blumenthal, “Analysis of an edge router for span-constrained optical burst switched (OBS) networks,” J. Lightwave Technol. vol. 22, pp. 2693–2705, Nov. 2004.
    [CrossRef]
  13. M. Izal, J. Aracil, “On the influence of self-similarity on optical burst switching traffic,” in IEEE Global Telecommunications Conf., 2002. GLOBECOM '02, Taipei, Taiwan, Nov. 17–21, 2002, vol. 3, pp. 2308–2312.
  14. P. Hokstad, “A single server queue with constant service time and restricted accessibility,” Manage. Sci., vol. 25, pp. 205–208, Feb 1979.
    [CrossRef]
  15. X. Lu, B. Mark, “Performance modeling of optical-burst switching with fiber delay lines,” IEEE Trans. Commun. vol. 52, no. 12, pp. 2175–2183, 2004.
    [CrossRef]
  16. A. Kaheel, H. Alnuweiri, F. Gebali, “A new analytical model for computing blocking probability in optical burst switching networks,” IEEE J. Sel. Areas Commun. vol. 24, no. 12, pp. 120–128, 2006.
    [CrossRef]
  17. H. M. H. Shalaby, “A simplified performance analysis of optical burst-switched networks,” J. Lightwave Technol. vol. 25, pp. 986–995, Apr. 2007.
    [CrossRef]
  18. N. Akar, E. Karasan, K. Dogan, “Wavelength converter sharing in asynchronous optical packet/burst switching: an exact blocking analysis for Markovian arrivals,” IEEE J. Sel. Areas Commun. vol. 24, no. 12, pp. 69–80, 2006.
    [CrossRef]
  19. Z. Rosberg, H. L. Vu, M. Zukerman, J. White, “Blocking probabilities of optical burst switching networks based on reduced load fixed point approximations,” in IEEE INFOCOM 2003. 22nd Annu. Joint Conf. of the IEEE Computer and Communications Societies, San Francisco, CA, Mar. 30– Apr. 3, 2003, pp. 2008–2018.
    [CrossRef]

2007 (2)

N. Barakat, T. E. Darcie, “The control-plane stability constraint in optical burst switching networks,” IEEE Commun. Lett. vol. 11, pp. 267–269, Mar. 2007.
[CrossRef]

H. M. H. Shalaby, “A simplified performance analysis of optical burst-switched networks,” J. Lightwave Technol. vol. 25, pp. 986–995, Apr. 2007.
[CrossRef]

2006 (3)

A. Kaheel, H. Alnuweiri, F. Gebali, “A new analytical model for computing blocking probability in optical burst switching networks,” IEEE J. Sel. Areas Commun. vol. 24, no. 12, pp. 120–128, 2006.
[CrossRef]

N. Akar, E. Karasan, K. Dogan, “Wavelength converter sharing in asynchronous optical packet/burst switching: an exact blocking analysis for Markovian arrivals,” IEEE J. Sel. Areas Commun. vol. 24, no. 12, pp. 69–80, 2006.
[CrossRef]

N. Barakat, E. H. Sargent, “Separating resource reservations from service requests to improve the performance of optical burst-switching networks,” IEEE J. Sel. Areas Commun. vol. 24, pp. 95–107, April 2006.
[CrossRef]

2004 (4)

T. Chen, C. Qiao, X. Yu, “Optical burst switching (OBS): a new area in optical networking research,” IEEE Network, vol. 18, no. 3, pp. 16–23, May–June 2004.
[CrossRef]

X. Lu, B. Mark, “Performance modeling of optical-burst switching with fiber delay lines,” IEEE Trans. Commun. vol. 52, no. 12, pp. 2175–2183, 2004.
[CrossRef]

F. J. Vázquez-Abad, J. A. White, L. L. H. Andrew, R. S. Tucker, “Does header length affect performance in optical burst switched networks?” J. Opt. Netw. vol. 3, no. 5, pp. 342–353, May 2004.
[CrossRef]

R. Rajaduray, S. Ovadia, D. Blumenthal, “Analysis of an edge router for span-constrained optical burst switched (OBS) networks,” J. Lightwave Technol. vol. 22, pp. 2693–2705, Nov. 2004.
[CrossRef]

2003 (3)

G. I. Papadimitriou, C. Papazoglou, A. S. Pomportsis, “Optical switching: switch fabrics, techniques, and architectures,” J. Lightwave Technol. vol. 21, pp. 384–405, Feb. 2003.
[CrossRef]

T. Battestilli, H. Perros, “An introduction to optical burst switching,” IEEE Commun. Mag. vol. 41, no. 8, pp. S10–S15, Aug. 2003.
[CrossRef]

V. M. Vokkarane, J. P. Jue, “Prioritized burst segmentation and composite burst-assembly techniques for QoS support in optical burst-switched networks,” IEEE J. Sel. Areas Commun. vol. 21, pp. 1198–1209, Sept. 2003.
[CrossRef]

2002 (1)

J. White, M. Zukerman, H. L. Vu, “A framework for optical burst switching network design,” IEEE Commun. Lett. vol. 6, pp. 268–270, Jun. 2002.
[CrossRef]

2001 (1)

L. Xu, H. G. Perros, G. Rouskas, “Techniques for optical packet switching and optical burst switching,” IEEE Commun. Mag. vol. 39, no. 1, pp. 136–142, Jan. 2001.
[CrossRef]

2000 (1)

Y. Xiong, M. Vandenhoute, H. Cankaya, “Control architecture in optical burst-switched WDM networks,” IEEE J. Sel. Areas Commun. vol. 18, pp. 1838–1851, Oct. 2000.
[CrossRef]

1979 (1)

P. Hokstad, “A single server queue with constant service time and restricted accessibility,” Manage. Sci., vol. 25, pp. 205–208, Feb 1979.
[CrossRef]

Akar, N.

N. Akar, E. Karasan, K. Dogan, “Wavelength converter sharing in asynchronous optical packet/burst switching: an exact blocking analysis for Markovian arrivals,” IEEE J. Sel. Areas Commun. vol. 24, no. 12, pp. 69–80, 2006.
[CrossRef]

Alnuweiri, H.

A. Kaheel, H. Alnuweiri, F. Gebali, “A new analytical model for computing blocking probability in optical burst switching networks,” IEEE J. Sel. Areas Commun. vol. 24, no. 12, pp. 120–128, 2006.
[CrossRef]

Andrew, L. L. H.

Aracil, J.

M. Izal, J. Aracil, “On the influence of self-similarity on optical burst switching traffic,” in IEEE Global Telecommunications Conf., 2002. GLOBECOM '02, Taipei, Taiwan, Nov. 17–21, 2002, vol. 3, pp. 2308–2312.

Barakat, N.

N. Barakat, T. E. Darcie, “The control-plane stability constraint in optical burst switching networks,” IEEE Commun. Lett. vol. 11, pp. 267–269, Mar. 2007.
[CrossRef]

N. Barakat, E. H. Sargent, “Separating resource reservations from service requests to improve the performance of optical burst-switching networks,” IEEE J. Sel. Areas Commun. vol. 24, pp. 95–107, April 2006.
[CrossRef]

Battestilli, T.

T. Battestilli, H. Perros, “An introduction to optical burst switching,” IEEE Commun. Mag. vol. 41, no. 8, pp. S10–S15, Aug. 2003.
[CrossRef]

Blumenthal, D.

Cankaya, H.

Y. Xiong, M. Vandenhoute, H. Cankaya, “Control architecture in optical burst-switched WDM networks,” IEEE J. Sel. Areas Commun. vol. 18, pp. 1838–1851, Oct. 2000.
[CrossRef]

Chen, T.

T. Chen, C. Qiao, X. Yu, “Optical burst switching (OBS): a new area in optical networking research,” IEEE Network, vol. 18, no. 3, pp. 16–23, May–June 2004.
[CrossRef]

Darcie, T. E.

N. Barakat, T. E. Darcie, “The control-plane stability constraint in optical burst switching networks,” IEEE Commun. Lett. vol. 11, pp. 267–269, Mar. 2007.
[CrossRef]

Dogan, K.

N. Akar, E. Karasan, K. Dogan, “Wavelength converter sharing in asynchronous optical packet/burst switching: an exact blocking analysis for Markovian arrivals,” IEEE J. Sel. Areas Commun. vol. 24, no. 12, pp. 69–80, 2006.
[CrossRef]

Gebali, F.

A. Kaheel, H. Alnuweiri, F. Gebali, “A new analytical model for computing blocking probability in optical burst switching networks,” IEEE J. Sel. Areas Commun. vol. 24, no. 12, pp. 120–128, 2006.
[CrossRef]

Hokstad, P.

P. Hokstad, “A single server queue with constant service time and restricted accessibility,” Manage. Sci., vol. 25, pp. 205–208, Feb 1979.
[CrossRef]

Izal, M.

M. Izal, J. Aracil, “On the influence of self-similarity on optical burst switching traffic,” in IEEE Global Telecommunications Conf., 2002. GLOBECOM '02, Taipei, Taiwan, Nov. 17–21, 2002, vol. 3, pp. 2308–2312.

Jue, J. P.

V. M. Vokkarane, J. P. Jue, “Prioritized burst segmentation and composite burst-assembly techniques for QoS support in optical burst-switched networks,” IEEE J. Sel. Areas Commun. vol. 21, pp. 1198–1209, Sept. 2003.
[CrossRef]

J. P. Jue, V. M. Vokkarane, Optical Burst Switched Networks, New York, NY: Springer, 2005.

Kaheel, A.

A. Kaheel, H. Alnuweiri, F. Gebali, “A new analytical model for computing blocking probability in optical burst switching networks,” IEEE J. Sel. Areas Commun. vol. 24, no. 12, pp. 120–128, 2006.
[CrossRef]

Karasan, E.

N. Akar, E. Karasan, K. Dogan, “Wavelength converter sharing in asynchronous optical packet/burst switching: an exact blocking analysis for Markovian arrivals,” IEEE J. Sel. Areas Commun. vol. 24, no. 12, pp. 69–80, 2006.
[CrossRef]

Lu, X.

X. Lu, B. Mark, “Performance modeling of optical-burst switching with fiber delay lines,” IEEE Trans. Commun. vol. 52, no. 12, pp. 2175–2183, 2004.
[CrossRef]

Mark, B.

X. Lu, B. Mark, “Performance modeling of optical-burst switching with fiber delay lines,” IEEE Trans. Commun. vol. 52, no. 12, pp. 2175–2183, 2004.
[CrossRef]

Ovadia, S.

Papadimitriou, G. I.

Papazoglou, C.

Perros, H.

T. Battestilli, H. Perros, “An introduction to optical burst switching,” IEEE Commun. Mag. vol. 41, no. 8, pp. S10–S15, Aug. 2003.
[CrossRef]

Perros, H. G.

L. Xu, H. G. Perros, G. Rouskas, “Techniques for optical packet switching and optical burst switching,” IEEE Commun. Mag. vol. 39, no. 1, pp. 136–142, Jan. 2001.
[CrossRef]

Pomportsis, A. S.

Qiao, C.

T. Chen, C. Qiao, X. Yu, “Optical burst switching (OBS): a new area in optical networking research,” IEEE Network, vol. 18, no. 3, pp. 16–23, May–June 2004.
[CrossRef]

Rajaduray, R.

Rosberg, Z.

Z. Rosberg, H. L. Vu, M. Zukerman, J. White, “Blocking probabilities of optical burst switching networks based on reduced load fixed point approximations,” in IEEE INFOCOM 2003. 22nd Annu. Joint Conf. of the IEEE Computer and Communications Societies, San Francisco, CA, Mar. 30– Apr. 3, 2003, pp. 2008–2018.
[CrossRef]

Rouskas, G.

L. Xu, H. G. Perros, G. Rouskas, “Techniques for optical packet switching and optical burst switching,” IEEE Commun. Mag. vol. 39, no. 1, pp. 136–142, Jan. 2001.
[CrossRef]

Sargent, E. H.

N. Barakat, E. H. Sargent, “Separating resource reservations from service requests to improve the performance of optical burst-switching networks,” IEEE J. Sel. Areas Commun. vol. 24, pp. 95–107, April 2006.
[CrossRef]

Shalaby, H. M. H.

Tucker, R. S.

Vandenhoute, M.

Y. Xiong, M. Vandenhoute, H. Cankaya, “Control architecture in optical burst-switched WDM networks,” IEEE J. Sel. Areas Commun. vol. 18, pp. 1838–1851, Oct. 2000.
[CrossRef]

Vázquez-Abad, F. J.

Vokkarane, V. M.

V. M. Vokkarane, J. P. Jue, “Prioritized burst segmentation and composite burst-assembly techniques for QoS support in optical burst-switched networks,” IEEE J. Sel. Areas Commun. vol. 21, pp. 1198–1209, Sept. 2003.
[CrossRef]

J. P. Jue, V. M. Vokkarane, Optical Burst Switched Networks, New York, NY: Springer, 2005.

Vu, H. L.

J. White, M. Zukerman, H. L. Vu, “A framework for optical burst switching network design,” IEEE Commun. Lett. vol. 6, pp. 268–270, Jun. 2002.
[CrossRef]

Z. Rosberg, H. L. Vu, M. Zukerman, J. White, “Blocking probabilities of optical burst switching networks based on reduced load fixed point approximations,” in IEEE INFOCOM 2003. 22nd Annu. Joint Conf. of the IEEE Computer and Communications Societies, San Francisco, CA, Mar. 30– Apr. 3, 2003, pp. 2008–2018.
[CrossRef]

White, J.

J. White, M. Zukerman, H. L. Vu, “A framework for optical burst switching network design,” IEEE Commun. Lett. vol. 6, pp. 268–270, Jun. 2002.
[CrossRef]

Z. Rosberg, H. L. Vu, M. Zukerman, J. White, “Blocking probabilities of optical burst switching networks based on reduced load fixed point approximations,” in IEEE INFOCOM 2003. 22nd Annu. Joint Conf. of the IEEE Computer and Communications Societies, San Francisco, CA, Mar. 30– Apr. 3, 2003, pp. 2008–2018.
[CrossRef]

White, J. A.

Xiong, Y.

Y. Xiong, M. Vandenhoute, H. Cankaya, “Control architecture in optical burst-switched WDM networks,” IEEE J. Sel. Areas Commun. vol. 18, pp. 1838–1851, Oct. 2000.
[CrossRef]

Xu, L.

L. Xu, H. G. Perros, G. Rouskas, “Techniques for optical packet switching and optical burst switching,” IEEE Commun. Mag. vol. 39, no. 1, pp. 136–142, Jan. 2001.
[CrossRef]

Yu, X.

T. Chen, C. Qiao, X. Yu, “Optical burst switching (OBS): a new area in optical networking research,” IEEE Network, vol. 18, no. 3, pp. 16–23, May–June 2004.
[CrossRef]

Zukerman, M.

J. White, M. Zukerman, H. L. Vu, “A framework for optical burst switching network design,” IEEE Commun. Lett. vol. 6, pp. 268–270, Jun. 2002.
[CrossRef]

Z. Rosberg, H. L. Vu, M. Zukerman, J. White, “Blocking probabilities of optical burst switching networks based on reduced load fixed point approximations,” in IEEE INFOCOM 2003. 22nd Annu. Joint Conf. of the IEEE Computer and Communications Societies, San Francisco, CA, Mar. 30– Apr. 3, 2003, pp. 2008–2018.
[CrossRef]

IEEE Commun. Lett. (2)

J. White, M. Zukerman, H. L. Vu, “A framework for optical burst switching network design,” IEEE Commun. Lett. vol. 6, pp. 268–270, Jun. 2002.
[CrossRef]

N. Barakat, T. E. Darcie, “The control-plane stability constraint in optical burst switching networks,” IEEE Commun. Lett. vol. 11, pp. 267–269, Mar. 2007.
[CrossRef]

IEEE Commun. Mag. (2)

L. Xu, H. G. Perros, G. Rouskas, “Techniques for optical packet switching and optical burst switching,” IEEE Commun. Mag. vol. 39, no. 1, pp. 136–142, Jan. 2001.
[CrossRef]

T. Battestilli, H. Perros, “An introduction to optical burst switching,” IEEE Commun. Mag. vol. 41, no. 8, pp. S10–S15, Aug. 2003.
[CrossRef]

IEEE J. Sel. Areas Commun. (5)

Y. Xiong, M. Vandenhoute, H. Cankaya, “Control architecture in optical burst-switched WDM networks,” IEEE J. Sel. Areas Commun. vol. 18, pp. 1838–1851, Oct. 2000.
[CrossRef]

N. Barakat, E. H. Sargent, “Separating resource reservations from service requests to improve the performance of optical burst-switching networks,” IEEE J. Sel. Areas Commun. vol. 24, pp. 95–107, April 2006.
[CrossRef]

V. M. Vokkarane, J. P. Jue, “Prioritized burst segmentation and composite burst-assembly techniques for QoS support in optical burst-switched networks,” IEEE J. Sel. Areas Commun. vol. 21, pp. 1198–1209, Sept. 2003.
[CrossRef]

A. Kaheel, H. Alnuweiri, F. Gebali, “A new analytical model for computing blocking probability in optical burst switching networks,” IEEE J. Sel. Areas Commun. vol. 24, no. 12, pp. 120–128, 2006.
[CrossRef]

N. Akar, E. Karasan, K. Dogan, “Wavelength converter sharing in asynchronous optical packet/burst switching: an exact blocking analysis for Markovian arrivals,” IEEE J. Sel. Areas Commun. vol. 24, no. 12, pp. 69–80, 2006.
[CrossRef]

IEEE Network (1)

T. Chen, C. Qiao, X. Yu, “Optical burst switching (OBS): a new area in optical networking research,” IEEE Network, vol. 18, no. 3, pp. 16–23, May–June 2004.
[CrossRef]

IEEE Trans. Commun. (1)

X. Lu, B. Mark, “Performance modeling of optical-burst switching with fiber delay lines,” IEEE Trans. Commun. vol. 52, no. 12, pp. 2175–2183, 2004.
[CrossRef]

J. Lightwave Technol. (3)

J. Opt. Netw. (1)

Manage. Sci. (1)

P. Hokstad, “A single server queue with constant service time and restricted accessibility,” Manage. Sci., vol. 25, pp. 205–208, Feb 1979.
[CrossRef]

Other (3)

M. Izal, J. Aracil, “On the influence of self-similarity on optical burst switching traffic,” in IEEE Global Telecommunications Conf., 2002. GLOBECOM '02, Taipei, Taiwan, Nov. 17–21, 2002, vol. 3, pp. 2308–2312.

Z. Rosberg, H. L. Vu, M. Zukerman, J. White, “Blocking probabilities of optical burst switching networks based on reduced load fixed point approximations,” in IEEE INFOCOM 2003. 22nd Annu. Joint Conf. of the IEEE Computer and Communications Societies, San Francisco, CA, Mar. 30– Apr. 3, 2003, pp. 2008–2018.
[CrossRef]

J. P. Jue, V. M. Vokkarane, Optical Burst Switched Networks, New York, NY: Springer, 2005.

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Figures (9)

Fig. 1
Fig. 1

Core-node, constant-offset OBS architecture that uses fixed FDLs to insert an offset between headers and bursts. As an alternative to using input FDLs, one can also realize constant-offset operation by using the dual-header OBS architecture described in [10]. The presence of constant (as opposed to variable) offsets dramatically simplifies scheduling and therefore significantly increases the maximum control-plane throughput capacity.

Fig. 2
Fig. 2

Approximate model of the overall blocking process in an OBS core node. The model assumes that the burst arrival process to the data-plane scheduler is randomly thinned out by an amount proportional to the control-plane blocking probability P B cp .

Fig. 3
Fig. 3

Graphical depiction of optimal-parameter selection procedure for minimizing the control latency over an OBS burst-switched path. The solid curve represents the set of operating points that satisfy the overall blocking and control-plane blocking requirements. The dotted curve represents the control latency associated with points on the solid curve. Minimal end-to end latency occurs at the point labeled ( Ω h * , Δ h * ) , where an equal-delay (dashed) curve is tangent to the solid curve.

Fig. 4
Fig. 4

Data-plane, control-plane, and overall burst loss probability versus normalized offset size for a 32-wavelength OBS system.

Fig. 5
Fig. 5

Overall burst-loss probability as a function of the offset size for different values of average burst length. Control-plane blocking can be reduced by increasing the offset size or the average length of bursts.

Fig. 6
Fig. 6

Combinations of minimum burst duration and minimum offset duration required for reducing control-plane blocking to less than 1% of overall blocking for a 32-wavelength system. The offered load of the control processor depends on the amount of traffic that is carried in the data plane, which is directly determined by the target overall blocking probability P B total . Valid control-plane operation requires operating above the corresponding curve.

Fig. 7
Fig. 7

Combinations of minimum burst duration and minimum offset duration required to reduce control-plane blocking to to less than 1% of overall blocking when P B target = 10 4 . Each solid curve corresponds to a different number of data wavelengths as indicated. Each dashed curve indicates the operating point that corresponds to minimum average end-to-end delay for different values of network-topology parameter ( n 1 ) d as labeled.

Fig. 8
Fig. 8

Required control latency, which consists of burst-assembly latency and offset latency, as a function of number of data channels for a burst-switched path with P B target = 10 4 and ε = 0.1 % . Each subgraph corresponds to a different level of network-topology density ( n 1 ) d as indicated.

Fig. 9
Fig. 9

Required normalized control latency per hop versus network-connectivity metric ( n 1 ) d . The regions corresponding to full-mesh, ring, and typical long-haul mesh networks are indicated.

Tables (1)

Tables Icon

Table 1 Achieving Negligible Control-Plane Blocking a

Equations (11)

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

ρ cp = Δ h ρ dp W B dp L b ,
PB cp = 1 ρ cp [ ρ cp 1 + ( 1 + ρ cp j = 1 Ω h Δ h [ ρ cp ( j Ω h Δ h ) ] j 1 ( j 1 ) ! e ρ cp ( Ω h Δ h j ) ) 1 ] ,
P B total = P [ B cdp | B cp ] P [ B cp ] + P [ B cdp | B cp ¯ ] P [ B cp ¯ ] = ( 1 ) ( P B cp ) + P [ B cdp | B cp ¯ ] ( 1 P B cp ) = P B cp + ( 1 P B cp ) P B dp ,
P B total path 1 i P ( 1 P B total i ) i P P B total i .
D asm = L b γ .
D Ω = n p Ω h .
γ ¯ = ρ ¯ dp l W B dp n ¯ p n ( n 1 ) ,
D ¯ ctrl = D ¯ Ω + D ¯ asm = n ¯ p Ω h + n ¯ p n ( n 1 ) ρ ¯ dp l W B dp L b ,
P B total P B total min 1 + ε .
ρ ¯ dp W Ω h + ( n 1 ) d ¯ Δ b
P B total = ( 1 + ε ) P B total min ,