Abstract

Many of the burst assembly algorithms employed in optical burst switching (OBS) networks preserve the IP traffic self-similarity property in the burst traffic. We introduce a mathematical model for performance evaluation of an OBS core node employing either no, a partial or a full wavelength conversion strategy. The model assumes long-range dependent (LRD) traffic arrivals to the OBS intermediate node whose inter-arrival times are accurately modeled by a Pareto distribution, whereas exponential holding times are assumed. In our proposed model, each output port in the node is modeled as a GI/M/w/w queue with partial server accessibility. An imbedded Markov chain approach is used to derive the limiting state probability distribution for the number of bursts currently served by an output port as seen by arriving bursts. Next, the average burst loss probability is evaluated from steady-state occupancy probabilities. In addition, the results of our mathematical model are validated via simulation. Furthermore, the results of the model are compared with those when assuming short-range dependent Poisson arrivals. Comparison shows that traditional Poisson traffic models yield over-optimistic performance measures compared to the LRD Pareto traffic models, especially for light traffic scenarios. Furthermore, we study the impact of varying different traffic parameters, such as the average arrival rate and the Hurst parameter, on the burst loss probability. Finally, the impact of varying the wavelength conversion capability on the burst loss probability is studied, where we compare two strategies for contention resolution: adding new channels (wavelengths) or adding wavelength converters, while taking the cost into consideration.

© 2012 OSA

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  1. M. Yoo and C. Qiao, “Just-enough-time (JET): A high speed protocol for bursty traffic in optical networks,” in Proc. IEEE/LEOS Summer Topical Meetings Dig. for Conf. Technologies Global Information Infrastructure, Aug. 11–15, 1997, pp. 26–27.
  2. C. Qiao and M. Yoo, “Optical burst switching (OBS)—A new paradigm for an optical Internet,” J. High Speed Netw., vol. 8, no. 1, pp. 69–84, Jan.1999.
  3. T. Battestilli and H. Perros, “An introduction to optical burst switching,” IEEE Commun. Mag., vol. 41, no. 8, pp. S10–S15, Aug.2003.
    [CrossRef]
  4. X. Yu, J. Li, X. Cao, Y. Chen, and C. Qiao, “Traffic statistics and performance evaluation in optical burst switched networks,” J. Lightwave Technol., vol. 22, no. 12, pp. 2722–2738, Dec.2004.
    [CrossRef]
  5. 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., vol. 40, no. 2, pp. 82–89, Feb.2002.
    [CrossRef]
  6. G. Wu, T. Zhang, J. Chen, X. Li, and C. Qiao, “An index-based parallel scheduler for optical burst switching networks,” J. Lightwave Technol., vol. 29, no. 18, pp. 2766–2773, Sept.2011.
    [CrossRef]
  7. L. H. Bonani, “Performance evaluation of optical burst switched mesh networks with Localized Functional Resources,” in Proc. Int. Conf. on Transparent Optical Networks (ICTON), Coventry, England, July 2–5, 2012, pp. 1–4.
  8. H. Ichikawa and K. Kamakura, “Dimensioning an scheduler buffer in OBS networks using forward resource reservation,” in Proc. Int. Conf. on Computing, Networking and Communications (ICNC), Maui, Hawaii, Jan. 30–Feb. 2, 2012, pp. 282–286.
  9. A. I. Abd El-Rahman, S. I. Rabia, and H. M. H. Shalaby, “MAC-layer performance enhancement using control packet buffering in optical burst switched networks,” J. Lightwave Technol., vol. LT-30, no. 11, pp. 1578–1586, June2012.
    [CrossRef]
  10. N. Akar, E. Karasan, and 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, Dec.2006.
    [CrossRef]
  11. M. Y. S. Sowailem, M. H. S. Morsy, and H. M. H. Shalaby, “Employing code domain for contention resolution in optical burst switched networks with detailed performance analysis,” J. Lightwave Technol., vol. LT-27, pp. 5284–5294, Dec.2009.
    [CrossRef]
  12. M. H. S. Morsy, M. Y. S. Sowailem, and H. M. H. Shalaby, “Performance analysis of a core node equipped with wavelength converter pool in an Optical Burst Switched network,” in Proc. 2010 IEEE 17th Int. Conf. on Telecommun. (ICT), Apr. 4–7, 2010, pp. 516–522.
  13. Z. Rosberg, A. Zalesky, H. L. Vu, and M. Zukerman, “Analysis of OBS networks with limited wavelength conversion,” IEEE/ACM Trans. Netw., vol. 14, no. 5, pp. 1118–1127, Oct.2006.
    [CrossRef]
  14. D. Morato, M. Izal, J. Aracil, E. Magana, and J. Miqueleiz, “Blocking time analysis of OBS routers with arbitrary burst size distribution,” in Proc. Globecom 2003, Dec. 1–5, 2003, vol. 5, pp. 2488–2492.
  15. T. Battestilli and H. G. Perros, “A performance study of an optical burst switched network with dynamic simultaneous link possession,” J. Comput. Netw., vol. 50, no. 2, pp. 219–236, Feb.2006.
    [CrossRef]
  16. L. Battestilli, H. Perros, and S. Chukova, “Burst lost probabilities in a queuing network with simultaneous resource possession: A single-node decomposition approach,” IET Commun., vol. 3, no. 3, pp. 441–453, Mar.2009.
    [CrossRef]
  17. D. Tafani, C. McArdle, and L. P. Barry, “A two-moment performance analysis of optical burst switched networks with shared fibre delay lines in a feedback configuration,” J. Opt. Switching Netw., vol. 9, no. 5, pp. 323–335, Nov.2012.
    [CrossRef]
  18. W. Leland, M. Taqqu, W. Willinger, and D. Wilson, “On the self-similar nature of Ethernet traffic (extended version),” IEEE/ACM Trans. Netw., vol. 2, no. 1, pp. 1–15, Feb.1994.
    [CrossRef]
  19. W. Leland and D. Wilson, “High time-resolution measurement and analysis of LAN traffic: Implications for LAN interconnection,” in Proc. 10th Annu. Joint Conf. of the IEEE Computers and Communications Societies, Networking in the 90s (INFOCOM), Apr. 7–11, 1991, vol. 3, pp. 1360–1366.
  20. M. H. S. Morsy, M. Y. S. Sowailem, and H. M. H. Shalaby, “Upper and lower bounds of burst loss probability for a core node in an Optical Burst Switched network with Pareto distributed arrivals,” in Proc. 2010 IEEE 17th Int. Conf. on Telecommun. (ICT), Apr. 4–7, 2010, pp. 523–527.
  21. Y. Chen, H. Wu, D. Xu, and C. Qiao, “Performance analysis of optical burst switched node with deflection routing,” in Proc. IEEE Int. Conf. on Commun. (ICC), May 2003, vol. 2, pp. 1355–1359.
  22. M. Yoo, C. Qiao, and S. Dixit, “QoS performance of optical burst switching in IP-over-WDM networks,” IEEE J. Sel. Areas Commun., vol. 18, no. 10, pp. 2062–2071, Oct.2000.
    [CrossRef]
  23. H. L. Vu and M. Zukerman, “Blocking probability for priority classes in optical burst switching networks,” IEEE Commun. Lett., vol. 6, no. 5, pp. 214–216, May2002.
    [CrossRef]
  24. S. Nadarajah and S. Kotz, “On the Laplace transform of the Pareto distribution,” IEEE Commun. Lett., vol. 10, no. 9, pp. 682–682, Sept.2006.
    [CrossRef]
  25. L. Kleinrock, Queueing Systems Volume 1: Theory. Wiley, New York, 1975.
  26. L. Takacs, Introduction to the Theory of Queues. Oxford University Press, New York, 1961.

2012 (2)

A. I. Abd El-Rahman, S. I. Rabia, and H. M. H. Shalaby, “MAC-layer performance enhancement using control packet buffering in optical burst switched networks,” J. Lightwave Technol., vol. LT-30, no. 11, pp. 1578–1586, June2012.
[CrossRef]

D. Tafani, C. McArdle, and L. P. Barry, “A two-moment performance analysis of optical burst switched networks with shared fibre delay lines in a feedback configuration,” J. Opt. Switching Netw., vol. 9, no. 5, pp. 323–335, Nov.2012.
[CrossRef]

2011 (1)

2009 (2)

L. Battestilli, H. Perros, and S. Chukova, “Burst lost probabilities in a queuing network with simultaneous resource possession: A single-node decomposition approach,” IET Commun., vol. 3, no. 3, pp. 441–453, Mar.2009.
[CrossRef]

M. Y. S. Sowailem, M. H. S. Morsy, and H. M. H. Shalaby, “Employing code domain for contention resolution in optical burst switched networks with detailed performance analysis,” J. Lightwave Technol., vol. LT-27, pp. 5284–5294, Dec.2009.
[CrossRef]

2006 (4)

Z. Rosberg, A. Zalesky, H. L. Vu, and M. Zukerman, “Analysis of OBS networks with limited wavelength conversion,” IEEE/ACM Trans. Netw., vol. 14, no. 5, pp. 1118–1127, Oct.2006.
[CrossRef]

T. Battestilli and H. G. Perros, “A performance study of an optical burst switched network with dynamic simultaneous link possession,” J. Comput. Netw., vol. 50, no. 2, pp. 219–236, Feb.2006.
[CrossRef]

N. Akar, E. Karasan, and 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, Dec.2006.
[CrossRef]

S. Nadarajah and S. Kotz, “On the Laplace transform of the Pareto distribution,” IEEE Commun. Lett., vol. 10, no. 9, pp. 682–682, Sept.2006.
[CrossRef]

2004 (1)

X. Yu, J. Li, X. Cao, Y. Chen, and C. Qiao, “Traffic statistics and performance evaluation in optical burst switched networks,” J. Lightwave Technol., vol. 22, no. 12, pp. 2722–2738, Dec.2004.
[CrossRef]

2003 (1)

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

2002 (2)

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., vol. 40, no. 2, pp. 82–89, Feb.2002.
[CrossRef]

H. L. Vu and M. Zukerman, “Blocking probability for priority classes in optical burst switching networks,” IEEE Commun. Lett., vol. 6, no. 5, pp. 214–216, May2002.
[CrossRef]

2000 (1)

M. Yoo, C. Qiao, and S. Dixit, “QoS performance of optical burst switching in IP-over-WDM networks,” IEEE J. Sel. Areas Commun., vol. 18, no. 10, pp. 2062–2071, Oct.2000.
[CrossRef]

1999 (1)

C. Qiao and M. Yoo, “Optical burst switching (OBS)—A new paradigm for an optical Internet,” J. High Speed Netw., vol. 8, no. 1, pp. 69–84, Jan.1999.

1994 (1)

W. Leland, M. Taqqu, W. Willinger, and D. Wilson, “On the self-similar nature of Ethernet traffic (extended version),” IEEE/ACM Trans. Netw., vol. 2, no. 1, pp. 1–15, Feb.1994.
[CrossRef]

Abd El-Rahman, A. I.

A. I. Abd El-Rahman, S. I. Rabia, and H. M. H. Shalaby, “MAC-layer performance enhancement using control packet buffering in optical burst switched networks,” J. Lightwave Technol., vol. LT-30, no. 11, pp. 1578–1586, June2012.
[CrossRef]

Akar, N.

N. Akar, E. Karasan, and 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, Dec.2006.
[CrossRef]

Aracil, J.

D. Morato, M. Izal, J. Aracil, E. Magana, and J. Miqueleiz, “Blocking time analysis of OBS routers with arbitrary burst size distribution,” in Proc. Globecom 2003, Dec. 1–5, 2003, vol. 5, pp. 2488–2492.

Baldine, I.

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., vol. 40, no. 2, pp. 82–89, Feb.2002.
[CrossRef]

Barry, L. P.

D. Tafani, C. McArdle, and L. P. Barry, “A two-moment performance analysis of optical burst switched networks with shared fibre delay lines in a feedback configuration,” J. Opt. Switching Netw., vol. 9, no. 5, pp. 323–335, Nov.2012.
[CrossRef]

Battestilli, L.

L. Battestilli, H. Perros, and S. Chukova, “Burst lost probabilities in a queuing network with simultaneous resource possession: A single-node decomposition approach,” IET Commun., vol. 3, no. 3, pp. 441–453, Mar.2009.
[CrossRef]

Battestilli, T.

T. Battestilli and H. G. Perros, “A performance study of an optical burst switched network with dynamic simultaneous link possession,” J. Comput. Netw., vol. 50, no. 2, pp. 219–236, Feb.2006.
[CrossRef]

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

Bonani, L. H.

L. H. Bonani, “Performance evaluation of optical burst switched mesh networks with Localized Functional Resources,” in Proc. Int. Conf. on Transparent Optical Networks (ICTON), Coventry, England, July 2–5, 2012, pp. 1–4.

Cao, X.

X. Yu, J. Li, X. Cao, Y. Chen, and C. Qiao, “Traffic statistics and performance evaluation in optical burst switched networks,” J. Lightwave Technol., vol. 22, no. 12, pp. 2722–2738, Dec.2004.
[CrossRef]

Chen, J.

Chen, Y.

X. Yu, J. Li, X. Cao, Y. Chen, and C. Qiao, “Traffic statistics and performance evaluation in optical burst switched networks,” J. Lightwave Technol., vol. 22, no. 12, pp. 2722–2738, Dec.2004.
[CrossRef]

Y. Chen, H. Wu, D. Xu, and C. Qiao, “Performance analysis of optical burst switched node with deflection routing,” in Proc. IEEE Int. Conf. on Commun. (ICC), May 2003, vol. 2, pp. 1355–1359.

Chukova, S.

L. Battestilli, H. Perros, and S. Chukova, “Burst lost probabilities in a queuing network with simultaneous resource possession: A single-node decomposition approach,” IET Commun., vol. 3, no. 3, pp. 441–453, Mar.2009.
[CrossRef]

Dixit, S.

M. Yoo, C. Qiao, and S. Dixit, “QoS performance of optical burst switching in IP-over-WDM networks,” IEEE J. Sel. Areas Commun., vol. 18, no. 10, pp. 2062–2071, Oct.2000.
[CrossRef]

Dogan, K.

N. Akar, E. Karasan, and 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, Dec.2006.
[CrossRef]

Ichikawa, H.

H. Ichikawa and K. Kamakura, “Dimensioning an scheduler buffer in OBS networks using forward resource reservation,” in Proc. Int. Conf. on Computing, Networking and Communications (ICNC), Maui, Hawaii, Jan. 30–Feb. 2, 2012, pp. 282–286.

Izal, M.

D. Morato, M. Izal, J. Aracil, E. Magana, and J. Miqueleiz, “Blocking time analysis of OBS routers with arbitrary burst size distribution,” in Proc. Globecom 2003, Dec. 1–5, 2003, vol. 5, pp. 2488–2492.

Kamakura, K.

H. Ichikawa and K. Kamakura, “Dimensioning an scheduler buffer in OBS networks using forward resource reservation,” in Proc. Int. Conf. on Computing, Networking and Communications (ICNC), Maui, Hawaii, Jan. 30–Feb. 2, 2012, pp. 282–286.

Karasan, E.

N. Akar, E. Karasan, and 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, Dec.2006.
[CrossRef]

Kleinrock, L.

L. Kleinrock, Queueing Systems Volume 1: Theory. Wiley, New York, 1975.

Kotz, S.

S. Nadarajah and S. Kotz, “On the Laplace transform of the Pareto distribution,” IEEE Commun. Lett., vol. 10, no. 9, pp. 682–682, Sept.2006.
[CrossRef]

Leland, W.

W. Leland, M. Taqqu, W. Willinger, and D. Wilson, “On the self-similar nature of Ethernet traffic (extended version),” IEEE/ACM Trans. Netw., vol. 2, no. 1, pp. 1–15, Feb.1994.
[CrossRef]

W. Leland and D. Wilson, “High time-resolution measurement and analysis of LAN traffic: Implications for LAN interconnection,” in Proc. 10th Annu. Joint Conf. of the IEEE Computers and Communications Societies, Networking in the 90s (INFOCOM), Apr. 7–11, 1991, vol. 3, pp. 1360–1366.

Li, J.

X. Yu, J. Li, X. Cao, Y. Chen, and C. Qiao, “Traffic statistics and performance evaluation in optical burst switched networks,” J. Lightwave Technol., vol. 22, no. 12, pp. 2722–2738, Dec.2004.
[CrossRef]

Li, X.

Magana, E.

D. Morato, M. Izal, J. Aracil, E. Magana, and J. Miqueleiz, “Blocking time analysis of OBS routers with arbitrary burst size distribution,” in Proc. Globecom 2003, Dec. 1–5, 2003, vol. 5, pp. 2488–2492.

McArdle, C.

D. Tafani, C. McArdle, and L. P. Barry, “A two-moment performance analysis of optical burst switched networks with shared fibre delay lines in a feedback configuration,” J. Opt. Switching Netw., vol. 9, no. 5, pp. 323–335, Nov.2012.
[CrossRef]

Miqueleiz, J.

D. Morato, M. Izal, J. Aracil, E. Magana, and J. Miqueleiz, “Blocking time analysis of OBS routers with arbitrary burst size distribution,” in Proc. Globecom 2003, Dec. 1–5, 2003, vol. 5, pp. 2488–2492.

Morato, D.

D. Morato, M. Izal, J. Aracil, E. Magana, and J. Miqueleiz, “Blocking time analysis of OBS routers with arbitrary burst size distribution,” in Proc. Globecom 2003, Dec. 1–5, 2003, vol. 5, pp. 2488–2492.

Morsy, M. H. S.

M. Y. S. Sowailem, M. H. S. Morsy, and H. M. H. Shalaby, “Employing code domain for contention resolution in optical burst switched networks with detailed performance analysis,” J. Lightwave Technol., vol. LT-27, pp. 5284–5294, Dec.2009.
[CrossRef]

M. H. S. Morsy, M. Y. S. Sowailem, and H. M. H. Shalaby, “Performance analysis of a core node equipped with wavelength converter pool in an Optical Burst Switched network,” in Proc. 2010 IEEE 17th Int. Conf. on Telecommun. (ICT), Apr. 4–7, 2010, pp. 516–522.

M. H. S. Morsy, M. Y. S. Sowailem, and H. M. H. Shalaby, “Upper and lower bounds of burst loss probability for a core node in an Optical Burst Switched network with Pareto distributed arrivals,” in Proc. 2010 IEEE 17th Int. Conf. on Telecommun. (ICT), Apr. 4–7, 2010, pp. 523–527.

Nadarajah, S.

S. Nadarajah and S. Kotz, “On the Laplace transform of the Pareto distribution,” IEEE Commun. Lett., vol. 10, no. 9, pp. 682–682, Sept.2006.
[CrossRef]

Perros, H.

L. Battestilli, H. Perros, and S. Chukova, “Burst lost probabilities in a queuing network with simultaneous resource possession: A single-node decomposition approach,” IET Commun., vol. 3, no. 3, pp. 441–453, Mar.2009.
[CrossRef]

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

Perros, H. G.

T. Battestilli and H. G. Perros, “A performance study of an optical burst switched network with dynamic simultaneous link possession,” J. Comput. Netw., vol. 50, no. 2, pp. 219–236, Feb.2006.
[CrossRef]

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., vol. 40, no. 2, pp. 82–89, Feb.2002.
[CrossRef]

Qiao, C.

G. Wu, T. Zhang, J. Chen, X. Li, and C. Qiao, “An index-based parallel scheduler for optical burst switching networks,” J. Lightwave Technol., vol. 29, no. 18, pp. 2766–2773, Sept.2011.
[CrossRef]

X. Yu, J. Li, X. Cao, Y. Chen, and C. Qiao, “Traffic statistics and performance evaluation in optical burst switched networks,” J. Lightwave Technol., vol. 22, no. 12, pp. 2722–2738, Dec.2004.
[CrossRef]

M. Yoo, C. Qiao, and S. Dixit, “QoS performance of optical burst switching in IP-over-WDM networks,” IEEE J. Sel. Areas Commun., vol. 18, no. 10, pp. 2062–2071, Oct.2000.
[CrossRef]

C. Qiao and M. Yoo, “Optical burst switching (OBS)—A new paradigm for an optical Internet,” J. High Speed Netw., vol. 8, no. 1, pp. 69–84, Jan.1999.

M. Yoo and C. Qiao, “Just-enough-time (JET): A high speed protocol for bursty traffic in optical networks,” in Proc. IEEE/LEOS Summer Topical Meetings Dig. for Conf. Technologies Global Information Infrastructure, Aug. 11–15, 1997, pp. 26–27.

Y. Chen, H. Wu, D. Xu, and C. Qiao, “Performance analysis of optical burst switched node with deflection routing,” in Proc. IEEE Int. Conf. on Commun. (ICC), May 2003, vol. 2, pp. 1355–1359.

Rabia, S. I.

A. I. Abd El-Rahman, S. I. Rabia, and H. M. H. Shalaby, “MAC-layer performance enhancement using control packet buffering in optical burst switched networks,” J. Lightwave Technol., vol. LT-30, no. 11, pp. 1578–1586, June2012.
[CrossRef]

Rosberg, Z.

Z. Rosberg, A. Zalesky, H. L. Vu, and M. Zukerman, “Analysis of OBS networks with limited wavelength conversion,” IEEE/ACM Trans. Netw., vol. 14, no. 5, pp. 1118–1127, Oct.2006.
[CrossRef]

Rouskas, G. N.

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., vol. 40, no. 2, pp. 82–89, Feb.2002.
[CrossRef]

Shalaby, H. M. H.

A. I. Abd El-Rahman, S. I. Rabia, and H. M. H. Shalaby, “MAC-layer performance enhancement using control packet buffering in optical burst switched networks,” J. Lightwave Technol., vol. LT-30, no. 11, pp. 1578–1586, June2012.
[CrossRef]

M. Y. S. Sowailem, M. H. S. Morsy, and H. M. H. Shalaby, “Employing code domain for contention resolution in optical burst switched networks with detailed performance analysis,” J. Lightwave Technol., vol. LT-27, pp. 5284–5294, Dec.2009.
[CrossRef]

M. H. S. Morsy, M. Y. S. Sowailem, and H. M. H. Shalaby, “Performance analysis of a core node equipped with wavelength converter pool in an Optical Burst Switched network,” in Proc. 2010 IEEE 17th Int. Conf. on Telecommun. (ICT), Apr. 4–7, 2010, pp. 516–522.

M. H. S. Morsy, M. Y. S. Sowailem, and H. M. H. Shalaby, “Upper and lower bounds of burst loss probability for a core node in an Optical Burst Switched network with Pareto distributed arrivals,” in Proc. 2010 IEEE 17th Int. Conf. on Telecommun. (ICT), Apr. 4–7, 2010, pp. 523–527.

Sowailem, M. Y. S.

M. Y. S. Sowailem, M. H. S. Morsy, and H. M. H. Shalaby, “Employing code domain for contention resolution in optical burst switched networks with detailed performance analysis,” J. Lightwave Technol., vol. LT-27, pp. 5284–5294, Dec.2009.
[CrossRef]

M. H. S. Morsy, M. Y. S. Sowailem, and H. M. H. Shalaby, “Performance analysis of a core node equipped with wavelength converter pool in an Optical Burst Switched network,” in Proc. 2010 IEEE 17th Int. Conf. on Telecommun. (ICT), Apr. 4–7, 2010, pp. 516–522.

M. H. S. Morsy, M. Y. S. Sowailem, and H. M. H. Shalaby, “Upper and lower bounds of burst loss probability for a core node in an Optical Burst Switched network with Pareto distributed arrivals,” in Proc. 2010 IEEE 17th Int. Conf. on Telecommun. (ICT), Apr. 4–7, 2010, pp. 523–527.

Stevenson, D.

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., vol. 40, no. 2, pp. 82–89, Feb.2002.
[CrossRef]

Tafani, D.

D. Tafani, C. McArdle, and L. P. Barry, “A two-moment performance analysis of optical burst switched networks with shared fibre delay lines in a feedback configuration,” J. Opt. Switching Netw., vol. 9, no. 5, pp. 323–335, Nov.2012.
[CrossRef]

Takacs, L.

L. Takacs, Introduction to the Theory of Queues. Oxford University Press, New York, 1961.

Taqqu, M.

W. Leland, M. Taqqu, W. Willinger, and D. Wilson, “On the self-similar nature of Ethernet traffic (extended version),” IEEE/ACM Trans. Netw., vol. 2, no. 1, pp. 1–15, Feb.1994.
[CrossRef]

Vu, H. L.

Z. Rosberg, A. Zalesky, H. L. Vu, and M. Zukerman, “Analysis of OBS networks with limited wavelength conversion,” IEEE/ACM Trans. Netw., vol. 14, no. 5, pp. 1118–1127, Oct.2006.
[CrossRef]

H. L. Vu and M. Zukerman, “Blocking probability for priority classes in optical burst switching networks,” IEEE Commun. Lett., vol. 6, no. 5, pp. 214–216, May2002.
[CrossRef]

Willinger, W.

W. Leland, M. Taqqu, W. Willinger, and D. Wilson, “On the self-similar nature of Ethernet traffic (extended version),” IEEE/ACM Trans. Netw., vol. 2, no. 1, pp. 1–15, Feb.1994.
[CrossRef]

Wilson, D.

W. Leland, M. Taqqu, W. Willinger, and D. Wilson, “On the self-similar nature of Ethernet traffic (extended version),” IEEE/ACM Trans. Netw., vol. 2, no. 1, pp. 1–15, Feb.1994.
[CrossRef]

W. Leland and D. Wilson, “High time-resolution measurement and analysis of LAN traffic: Implications for LAN interconnection,” in Proc. 10th Annu. Joint Conf. of the IEEE Computers and Communications Societies, Networking in the 90s (INFOCOM), Apr. 7–11, 1991, vol. 3, pp. 1360–1366.

Wu, G.

Wu, H.

Y. Chen, H. Wu, D. Xu, and C. Qiao, “Performance analysis of optical burst switched node with deflection routing,” in Proc. IEEE Int. Conf. on Commun. (ICC), May 2003, vol. 2, pp. 1355–1359.

Xu, D.

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Figures (6)

Fig. 1
Fig. 1

Arrival scenario to the GI/M/w/w queue showing imbedded Markov points.

Fig. 2
Fig. 2

State transition probability diagram of the imbedded DTMC for GI/M/w/w showing transitions out of state i.

Fig. 3
Fig. 3

(Color online) Average burst loss probability versus mean arrival rate for both the mathematical model and the simulation in the NWC, PWC and FWC cases assuming Pareto arrivals.

Fig. 4
Fig. 4

(Color online) Comparison of the average burst loss probability versus the mean arrival rate for Pareto and Poisson arrivals in the NWC, PWC and FWC cases.

Fig. 5
Fig. 5

Semi-log plot for average burst loss probability versus node conversion capability for Pareto arrivals at different values of the Hurst parameter.

Fig. 6
Fig. 6

Average burst loss probability versus node conversion capability, taking the overall cost of resources into consideration, for Pareto arrivals at different values of the Hurst parameter and the cost ratio parameter.

Equations (44)

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τ n = def  arrival time of  DB n
T a n = def inter-arrival time between  DB n 1  and  DB n = τ n τ n 1 .
f T a n ( t ) = a b a ( b + t ) a + 1 , where  t > 0 , a > 0  and  b > 0 ,
T a = def lim n T a n ,
f T a = def lim n f T a n = f T a n .
F T a ( s ) = a ( b s ) a e b s Γ ( a , b s ) ,
Γ ( a , x ) = x t a 1 e t d t .
E ( T a ) = 1 λ = b a 1 .
H = ( 3 a ) / 2 .
X n = def  service time of  DB n ,
f X n ( x ) = μ e μ x , where  x > 0 .
X = def lim n X n ,
f X ( x ) = lim n f X n ( x ) = μ e μ x , where  x > 0 ,
q n = def number of customers in the system immediately  prior to arrival of  DB n = N ( τ n ) .
p i j = Pr { q n + 1 = j | q n = i } .
q n + 1 = { q n + 1 v n + 1 , 0 q n < w , q n v n + 1 , q n = w .
p i j = Pr { i + 1 j  DBs are served during  T a n + 1 } = Pr { v n + 1 = i + 1 j } = 0 Pr { v n + 1 = i + 1 j | T a n + 1 = t } f T a ( t ) d t .
p i j = 0 ( i + 1 i + 1 j ) ( 1 e μ t ) i + 1 j e j μ t f T a ( t ) d t ,
( i + 1 i + 1 j ) = ( i + 1 j ) .
p i j = p w j = Pr { w j  DBs are served during  T a n + 1 } = 0 ( w j ) ( 1 e μ t ) w j e j μ t f T a ( t ) d t .
π k = lim n Pr { q n = k } .
Π = Π P ,
Π ( z ) = k = 0 w π k z k .
Π ( z ) = k = 0 w π k 0 ( 1 e μ t + z e μ t ) k + 1 f T a ( t ) d t + ( 1 z ) π w 0 e μ t ( 1 e μ t + z e μ t ) w f T a ( t ) d t .
Π ( z ) = r = 0 w B r ( z 1 ) r ,
B r = 1 r ! d r Π ( z ) d z r | z = 1 , r W .
π k = 1 k ! d k Π ( z ) d z k | z = 0 = 1 k ! r = 0 w B r d k d z k { ( z 1 ) r } | z = 0 = r = k k ( r k ) ( 1 ) r k B r .
B r = α r [ B r + B r 1 ] α r ( w r 1 ) B w ,
α r = F T a ( r μ ) = 0 f T a ( t ) e r μ t d t .
B r = C r k = r w ( w k ) 1 c k k = 0 w ( w k ) 1 c k ,
C r = l = 1 r α l 1 α l .
P L = Pr { Incoming DB sees  w  customers in the system } = lim n Pr { q n = w } = π w ,
β i = Pr { incoming DB is accepted } = Pr { incoming DB rides on a free wavelength} + Pr { incoming DB rides on a busy wavelength } × Pr { busy wavelength of incoming DB is convertible } = w i w + i w × γ .
p i j = Pr { incoming DB is accepted } × Pr { i + 1 j  DBs are served during  T a n + 1 } + Pr { incoming DB is rejected } × Pr { i j  DBs are served during  T a n + 1 } = β i 0 ( i + 1 j ) ( 1 e μ t ) i + 1 j e j μ t f T a ( t ) d t + ( 1 β i ) 0 ( i j ) ( 1 e μ t ) i j e j μ t f T a ( t ) d t ,
p i j = p i , i + 1 = β i 0 e ( i + 1 ) μ t f T a ( t ) d t .
Π ( z ) = k = 0 w π k 0 ( 1 e μ t + z e μ t ) k + 1 f T a ( t ) d t + γ ( 1 z ) π w 0 e μ t ( 1 e μ t + z e μ t ) w f T a ( t ) d t + ( 1 γ ) ( 1 z ) w k = 0 w k π k 0 e μ t ( 1 e μ t + z e μ t ) k f T a ( t ) d t .
B r = α r [ B r + B r 1 ] γ α r ( w r 1 ) B w ( 1 γ ) w α r [ r B r + ( r 1 ) B r 1 ] ,
B r = C r l = r w ( w l ) 1 c l ( 1 k l ) l = 0 w ( w l ) 1 c l ( 1 k l ) ,
C r = i = 1 r α i ( 1 k i 1 ) 1 α i 1 ( 1 k i )
k i = ( 1 γ ) i w .
P L = Pr { incoming DB finds  w  customers in system } + i = 1 w 1 ( Pr { incoming DB finds  i  customers in system } × Pr { incoming DB rides on busy wavelength } × Pr { its wavelength is nonconvertible } ) = π w + i = 1 w 1 π i × i w × ( 1 γ ) ,
Overall Cost = c 1 w + c 2 u ,
Overall Cost / c 1 = w ( 1 + r c γ ) ,
w ( 1 + r c γ ) = const = w NWC ,