Abstract

We explore the problem of bandwidth management for the evolutionary upgrade of WDM EPONs. We divide the bandwidth management problem into two subproblems: (1) grant sizing and (2) grant scheduling. We then apply a scheduling theoretical approach to find a best scheduler for WDM EPONs. We show by means of extensive simulations that a multidimensional scheduling approach using results from scheduling theory can provide much better bandwidth management by means of better wavelength utilization than a static wavelength assignment. We also show that an online scheduling approach can provide lower queueing delays than a cyclical offline scheduling approach. We conclude with some specific guidance on future research on bandwidth management for WDM EPONs.

© 2006 Optical Society of America

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  1. Lucent's LambdaXtreme transport, http://www.lucent.com.
  2. A. Banerjee, Y. Park, F. Clarke, H. Song, S. Yang, G. Kramer, K. Kim, and B. Mukherjee, ''Wavelength-division-multiplexed passive optical network (WDM-PON) technologies for broadband access: a review,'' JOM 4,737-758 (2005).
  3. Y.-L. Hsueh, M. S. Rogge, S. Yamamoto, and L. G. Kazovsky, ''A highly flexible and efficient passive optical network employing dynamic wavelength allocation,'' J. Lightwave Technol. 23, 277-286 (2005)
  4. F. T. An, D. Gutierrez, K. S. Kim, J. W. Lee, and L. G. Kazovsky ''SUCESS-HPON: a next-generation optical access architecture for smooth migration from TDM-PON to WDM-PON,'' IEEE Commun. Mag. 43(11), S40-S47 (2005).
  5. K. S. Kim, D. Gutierrez, F. T. An, and L. G. Kazovsky, ''Design and performance analysis of scheduling algorithms for WDM-PON under SUCCESS-HPON architecture,'' J. Lightwave Technol. 23, 3716-3731 (2005).
  6. C. Xiao, B. Bing, and G. K. Chang, ''An efficient reservation MAC protocol with preallocation for high-speed WDM passive optical networks,'' in Proceedings of IEEE INFOCOM (IEEE, 2005), pp. 444-454.
  7. K. H. Kwong, D. Harle, and I. Andonovic, ''Dynamic bandwidth allocation algorithm for differentiated services over WDM EPONs,'' in Proceedings of the IEEE International Conference on Communications Systems (ICCS) (IEEE, 2004), pp. 116-120.
  8. G. Kramer, B. Mukherjee, and G. Pesavento, ''IPACT: A dynamic protocol for an Ethernet PON (EPON),'' IEEE Commun. Mag. 40(2), 74-80 (2002).
  9. A. R. Dhaini, C. M. Assi, and A. Shami, ''Dynamic bandwidth allocation schemes in hybrid TDM/WDM passive optical networks,'' in IEEE Consumer Communications and Networking Conference (IEEE, 2006), Vol. 1, pp. 30-34.
  10. M. Ma, Y. Zhu, and T. Cheng, ''A bandwidth guaranteed polling MAC protocol for Ethernet passive optical networks,'' in Proceedings of IEEE INFOCOM (IEEE, 2003), Vol. 1, pp. 22-31.
  11. C. M. Assi, Y. Ye, S. Dixit, and M. A. Ali, ''Dynamic bandwidth allocation for quality-of-service over Ethernet PONs,'' IEEE J. Sel. Areas Commun. 21, 1467-1477 (2003).
  12. M. P. McGarry, M. Maier, and M. Reisslein, ''Ethernet PONs: a survey of dynamic bandwidth allocation (DBA) algorithms,'' IEEE Commun. Mag. 42(8), S8-S15 (2004).
  13. H. Zang, J. Jue, and B. Mukherjee, ''A review of routing and wavelength assignment approaches for wavelength-routed optical WDM networks,'' Opt. Networks Mag. 1(1), 47-60 (2000).
  14. M. Pinedo, Scheduling: Theory, Algorithms, and Systems, 2nd ed. (Prentice-Hall, 2002).
  15. Z. L. Chen and W. B. Powell, ''Solving parallel machine scheduling problems by column generation,'' INFORMS J. Comput. 11, 78-94 (1999).
  16. J. M. Van Den Akker, J. A. Hoogeveen, and S. L. Van De Velde, ''Parallel machine scheduling by column generation,'' Oper. Res. 47, 862-872 (1999).
  17. E. Davis and J. M. Jaffe, ''Algorithms for scheduling tasks on unrelated processors,'' Acta Math. Acad. Sci. Hung. 28, 721-736 (1981).
  18. A. Fiat and G. J. Woeginger, Online Algorithms: The State of the Art (Springer, 1998).
  19. A. P. A. Vestjens, ''Online machine scheduling,'' Ph.D. thesis (Eindhoven University of Technology, 1997).
  20. R. L. Graham, ''Bounds for certain multiprocessing anomalies,'' Bell Syst. Tech. J. 45, 1563-1581 (1966).
  21. CSIM (Mesquite Software), http://www.mesquite.com.
  22. G. Kramer, ''On generating self-similar traffic using pseudo-Pareto distribution,'' UC Davis Technical Brief (University of California, Davis), http://wwwcsif.cs.ucdavis.edu/~kramer/papers/selflowbarsim.pdf.
  23. M. S. Taqqu, W. Willinger, and R. Sherman, ''Proof of a fundamental result in self-similar traffic modeling,'' ACM SIGCOMM Comput. Commun. Rev. 27, 5-23 (1997).
  24. K. Park and W. Willinger, Self-Similar Network Traffic and Performance Evaluation (Wiley-Interscience, 2000).
  25. M. P. McGarry, M. Maier, and M. Reisslein, ''WDM Ethernet Passive Optical Networks,'' IEEE Commun. Mag. 44(2), S18-S25 (2006).

2006 (2)

A. R. Dhaini, C. M. Assi, and A. Shami, ''Dynamic bandwidth allocation schemes in hybrid TDM/WDM passive optical networks,'' in IEEE Consumer Communications and Networking Conference (IEEE, 2006), Vol. 1, pp. 30-34.

M. P. McGarry, M. Maier, and M. Reisslein, ''WDM Ethernet Passive Optical Networks,'' IEEE Commun. Mag. 44(2), S18-S25 (2006).

2005 (5)

A. Banerjee, Y. Park, F. Clarke, H. Song, S. Yang, G. Kramer, K. Kim, and B. Mukherjee, ''Wavelength-division-multiplexed passive optical network (WDM-PON) technologies for broadband access: a review,'' JOM 4,737-758 (2005).

Y.-L. Hsueh, M. S. Rogge, S. Yamamoto, and L. G. Kazovsky, ''A highly flexible and efficient passive optical network employing dynamic wavelength allocation,'' J. Lightwave Technol. 23, 277-286 (2005)

F. T. An, D. Gutierrez, K. S. Kim, J. W. Lee, and L. G. Kazovsky ''SUCESS-HPON: a next-generation optical access architecture for smooth migration from TDM-PON to WDM-PON,'' IEEE Commun. Mag. 43(11), S40-S47 (2005).

K. S. Kim, D. Gutierrez, F. T. An, and L. G. Kazovsky, ''Design and performance analysis of scheduling algorithms for WDM-PON under SUCCESS-HPON architecture,'' J. Lightwave Technol. 23, 3716-3731 (2005).

C. Xiao, B. Bing, and G. K. Chang, ''An efficient reservation MAC protocol with preallocation for high-speed WDM passive optical networks,'' in Proceedings of IEEE INFOCOM (IEEE, 2005), pp. 444-454.

2004 (1)

M. P. McGarry, M. Maier, and M. Reisslein, ''Ethernet PONs: a survey of dynamic bandwidth allocation (DBA) algorithms,'' IEEE Commun. Mag. 42(8), S8-S15 (2004).

2003 (2)

M. Ma, Y. Zhu, and T. Cheng, ''A bandwidth guaranteed polling MAC protocol for Ethernet passive optical networks,'' in Proceedings of IEEE INFOCOM (IEEE, 2003), Vol. 1, pp. 22-31.

C. M. Assi, Y. Ye, S. Dixit, and M. A. Ali, ''Dynamic bandwidth allocation for quality-of-service over Ethernet PONs,'' IEEE J. Sel. Areas Commun. 21, 1467-1477 (2003).

2002 (1)

G. Kramer, B. Mukherjee, and G. Pesavento, ''IPACT: A dynamic protocol for an Ethernet PON (EPON),'' IEEE Commun. Mag. 40(2), 74-80 (2002).

2000 (2)

H. Zang, J. Jue, and B. Mukherjee, ''A review of routing and wavelength assignment approaches for wavelength-routed optical WDM networks,'' Opt. Networks Mag. 1(1), 47-60 (2000).

K. Park and W. Willinger, Self-Similar Network Traffic and Performance Evaluation (Wiley-Interscience, 2000).

1999 (2)

Z. L. Chen and W. B. Powell, ''Solving parallel machine scheduling problems by column generation,'' INFORMS J. Comput. 11, 78-94 (1999).

J. M. Van Den Akker, J. A. Hoogeveen, and S. L. Van De Velde, ''Parallel machine scheduling by column generation,'' Oper. Res. 47, 862-872 (1999).

1998 (1)

A. Fiat and G. J. Woeginger, Online Algorithms: The State of the Art (Springer, 1998).

1997 (2)

A. P. A. Vestjens, ''Online machine scheduling,'' Ph.D. thesis (Eindhoven University of Technology, 1997).

M. S. Taqqu, W. Willinger, and R. Sherman, ''Proof of a fundamental result in self-similar traffic modeling,'' ACM SIGCOMM Comput. Commun. Rev. 27, 5-23 (1997).

1981 (1)

E. Davis and J. M. Jaffe, ''Algorithms for scheduling tasks on unrelated processors,'' Acta Math. Acad. Sci. Hung. 28, 721-736 (1981).

1966 (1)

R. L. Graham, ''Bounds for certain multiprocessing anomalies,'' Bell Syst. Tech. J. 45, 1563-1581 (1966).

Ali, M. A.

C. M. Assi, Y. Ye, S. Dixit, and M. A. Ali, ''Dynamic bandwidth allocation for quality-of-service over Ethernet PONs,'' IEEE J. Sel. Areas Commun. 21, 1467-1477 (2003).

An, F. T.

F. T. An, D. Gutierrez, K. S. Kim, J. W. Lee, and L. G. Kazovsky ''SUCESS-HPON: a next-generation optical access architecture for smooth migration from TDM-PON to WDM-PON,'' IEEE Commun. Mag. 43(11), S40-S47 (2005).

K. S. Kim, D. Gutierrez, F. T. An, and L. G. Kazovsky, ''Design and performance analysis of scheduling algorithms for WDM-PON under SUCCESS-HPON architecture,'' J. Lightwave Technol. 23, 3716-3731 (2005).

Andonovic, I.

K. H. Kwong, D. Harle, and I. Andonovic, ''Dynamic bandwidth allocation algorithm for differentiated services over WDM EPONs,'' in Proceedings of the IEEE International Conference on Communications Systems (ICCS) (IEEE, 2004), pp. 116-120.

Assi, C. M.

A. R. Dhaini, C. M. Assi, and A. Shami, ''Dynamic bandwidth allocation schemes in hybrid TDM/WDM passive optical networks,'' in IEEE Consumer Communications and Networking Conference (IEEE, 2006), Vol. 1, pp. 30-34.

C. M. Assi, Y. Ye, S. Dixit, and M. A. Ali, ''Dynamic bandwidth allocation for quality-of-service over Ethernet PONs,'' IEEE J. Sel. Areas Commun. 21, 1467-1477 (2003).

Banerjee, A.

A. Banerjee, Y. Park, F. Clarke, H. Song, S. Yang, G. Kramer, K. Kim, and B. Mukherjee, ''Wavelength-division-multiplexed passive optical network (WDM-PON) technologies for broadband access: a review,'' JOM 4,737-758 (2005).

Bing, B.

C. Xiao, B. Bing, and G. K. Chang, ''An efficient reservation MAC protocol with preallocation for high-speed WDM passive optical networks,'' in Proceedings of IEEE INFOCOM (IEEE, 2005), pp. 444-454.

Chang, G. K.

C. Xiao, B. Bing, and G. K. Chang, ''An efficient reservation MAC protocol with preallocation for high-speed WDM passive optical networks,'' in Proceedings of IEEE INFOCOM (IEEE, 2005), pp. 444-454.

Chen, Z. L.

Z. L. Chen and W. B. Powell, ''Solving parallel machine scheduling problems by column generation,'' INFORMS J. Comput. 11, 78-94 (1999).

Cheng, T.

M. Ma, Y. Zhu, and T. Cheng, ''A bandwidth guaranteed polling MAC protocol for Ethernet passive optical networks,'' in Proceedings of IEEE INFOCOM (IEEE, 2003), Vol. 1, pp. 22-31.

Clarke, F.

A. Banerjee, Y. Park, F. Clarke, H. Song, S. Yang, G. Kramer, K. Kim, and B. Mukherjee, ''Wavelength-division-multiplexed passive optical network (WDM-PON) technologies for broadband access: a review,'' JOM 4,737-758 (2005).

Davis, E.

E. Davis and J. M. Jaffe, ''Algorithms for scheduling tasks on unrelated processors,'' Acta Math. Acad. Sci. Hung. 28, 721-736 (1981).

Dhaini, A. R.

A. R. Dhaini, C. M. Assi, and A. Shami, ''Dynamic bandwidth allocation schemes in hybrid TDM/WDM passive optical networks,'' in IEEE Consumer Communications and Networking Conference (IEEE, 2006), Vol. 1, pp. 30-34.

Dixit, S.

C. M. Assi, Y. Ye, S. Dixit, and M. A. Ali, ''Dynamic bandwidth allocation for quality-of-service over Ethernet PONs,'' IEEE J. Sel. Areas Commun. 21, 1467-1477 (2003).

Fiat, A.

A. Fiat and G. J. Woeginger, Online Algorithms: The State of the Art (Springer, 1998).

Graham, R. L.

R. L. Graham, ''Bounds for certain multiprocessing anomalies,'' Bell Syst. Tech. J. 45, 1563-1581 (1966).

Gutierrez, D.

K. S. Kim, D. Gutierrez, F. T. An, and L. G. Kazovsky, ''Design and performance analysis of scheduling algorithms for WDM-PON under SUCCESS-HPON architecture,'' J. Lightwave Technol. 23, 3716-3731 (2005).

F. T. An, D. Gutierrez, K. S. Kim, J. W. Lee, and L. G. Kazovsky ''SUCESS-HPON: a next-generation optical access architecture for smooth migration from TDM-PON to WDM-PON,'' IEEE Commun. Mag. 43(11), S40-S47 (2005).

Harle, D.

K. H. Kwong, D. Harle, and I. Andonovic, ''Dynamic bandwidth allocation algorithm for differentiated services over WDM EPONs,'' in Proceedings of the IEEE International Conference on Communications Systems (ICCS) (IEEE, 2004), pp. 116-120.

Hoogeveen, J. A.

J. M. Van Den Akker, J. A. Hoogeveen, and S. L. Van De Velde, ''Parallel machine scheduling by column generation,'' Oper. Res. 47, 862-872 (1999).

Hsueh, Y.-L.

Jaffe, J. M.

E. Davis and J. M. Jaffe, ''Algorithms for scheduling tasks on unrelated processors,'' Acta Math. Acad. Sci. Hung. 28, 721-736 (1981).

Jue, J.

H. Zang, J. Jue, and B. Mukherjee, ''A review of routing and wavelength assignment approaches for wavelength-routed optical WDM networks,'' Opt. Networks Mag. 1(1), 47-60 (2000).

Kazovsky, L. G.

Kim, K.

A. Banerjee, Y. Park, F. Clarke, H. Song, S. Yang, G. Kramer, K. Kim, and B. Mukherjee, ''Wavelength-division-multiplexed passive optical network (WDM-PON) technologies for broadband access: a review,'' JOM 4,737-758 (2005).

Kim, K. S.

K. S. Kim, D. Gutierrez, F. T. An, and L. G. Kazovsky, ''Design and performance analysis of scheduling algorithms for WDM-PON under SUCCESS-HPON architecture,'' J. Lightwave Technol. 23, 3716-3731 (2005).

F. T. An, D. Gutierrez, K. S. Kim, J. W. Lee, and L. G. Kazovsky ''SUCESS-HPON: a next-generation optical access architecture for smooth migration from TDM-PON to WDM-PON,'' IEEE Commun. Mag. 43(11), S40-S47 (2005).

Kramer, G.

A. Banerjee, Y. Park, F. Clarke, H. Song, S. Yang, G. Kramer, K. Kim, and B. Mukherjee, ''Wavelength-division-multiplexed passive optical network (WDM-PON) technologies for broadband access: a review,'' JOM 4,737-758 (2005).

G. Kramer, B. Mukherjee, and G. Pesavento, ''IPACT: A dynamic protocol for an Ethernet PON (EPON),'' IEEE Commun. Mag. 40(2), 74-80 (2002).

G. Kramer, ''On generating self-similar traffic using pseudo-Pareto distribution,'' UC Davis Technical Brief (University of California, Davis), http://wwwcsif.cs.ucdavis.edu/~kramer/papers/selflowbarsim.pdf.

Kwong, K. H.

K. H. Kwong, D. Harle, and I. Andonovic, ''Dynamic bandwidth allocation algorithm for differentiated services over WDM EPONs,'' in Proceedings of the IEEE International Conference on Communications Systems (ICCS) (IEEE, 2004), pp. 116-120.

Lee, J. W.

F. T. An, D. Gutierrez, K. S. Kim, J. W. Lee, and L. G. Kazovsky ''SUCESS-HPON: a next-generation optical access architecture for smooth migration from TDM-PON to WDM-PON,'' IEEE Commun. Mag. 43(11), S40-S47 (2005).

Ma, M.

M. Ma, Y. Zhu, and T. Cheng, ''A bandwidth guaranteed polling MAC protocol for Ethernet passive optical networks,'' in Proceedings of IEEE INFOCOM (IEEE, 2003), Vol. 1, pp. 22-31.

Maier, M.

M. P. McGarry, M. Maier, and M. Reisslein, ''WDM Ethernet Passive Optical Networks,'' IEEE Commun. Mag. 44(2), S18-S25 (2006).

M. P. McGarry, M. Maier, and M. Reisslein, ''Ethernet PONs: a survey of dynamic bandwidth allocation (DBA) algorithms,'' IEEE Commun. Mag. 42(8), S8-S15 (2004).

McGarry, M. P.

M. P. McGarry, M. Maier, and M. Reisslein, ''WDM Ethernet Passive Optical Networks,'' IEEE Commun. Mag. 44(2), S18-S25 (2006).

M. P. McGarry, M. Maier, and M. Reisslein, ''Ethernet PONs: a survey of dynamic bandwidth allocation (DBA) algorithms,'' IEEE Commun. Mag. 42(8), S8-S15 (2004).

Mukherjee, B.

A. Banerjee, Y. Park, F. Clarke, H. Song, S. Yang, G. Kramer, K. Kim, and B. Mukherjee, ''Wavelength-division-multiplexed passive optical network (WDM-PON) technologies for broadband access: a review,'' JOM 4,737-758 (2005).

G. Kramer, B. Mukherjee, and G. Pesavento, ''IPACT: A dynamic protocol for an Ethernet PON (EPON),'' IEEE Commun. Mag. 40(2), 74-80 (2002).

H. Zang, J. Jue, and B. Mukherjee, ''A review of routing and wavelength assignment approaches for wavelength-routed optical WDM networks,'' Opt. Networks Mag. 1(1), 47-60 (2000).

Park, K.

K. Park and W. Willinger, Self-Similar Network Traffic and Performance Evaluation (Wiley-Interscience, 2000).

Park, Y.

A. Banerjee, Y. Park, F. Clarke, H. Song, S. Yang, G. Kramer, K. Kim, and B. Mukherjee, ''Wavelength-division-multiplexed passive optical network (WDM-PON) technologies for broadband access: a review,'' JOM 4,737-758 (2005).

Pesavento, G.

G. Kramer, B. Mukherjee, and G. Pesavento, ''IPACT: A dynamic protocol for an Ethernet PON (EPON),'' IEEE Commun. Mag. 40(2), 74-80 (2002).

Pinedo, M.

M. Pinedo, Scheduling: Theory, Algorithms, and Systems, 2nd ed. (Prentice-Hall, 2002).

Powell, W. B.

Z. L. Chen and W. B. Powell, ''Solving parallel machine scheduling problems by column generation,'' INFORMS J. Comput. 11, 78-94 (1999).

Reisslein, M.

M. P. McGarry, M. Maier, and M. Reisslein, ''WDM Ethernet Passive Optical Networks,'' IEEE Commun. Mag. 44(2), S18-S25 (2006).

M. P. McGarry, M. Maier, and M. Reisslein, ''Ethernet PONs: a survey of dynamic bandwidth allocation (DBA) algorithms,'' IEEE Commun. Mag. 42(8), S8-S15 (2004).

Rogge, M. S.

Shami, A.

A. R. Dhaini, C. M. Assi, and A. Shami, ''Dynamic bandwidth allocation schemes in hybrid TDM/WDM passive optical networks,'' in IEEE Consumer Communications and Networking Conference (IEEE, 2006), Vol. 1, pp. 30-34.

Sherman, R.

M. S. Taqqu, W. Willinger, and R. Sherman, ''Proof of a fundamental result in self-similar traffic modeling,'' ACM SIGCOMM Comput. Commun. Rev. 27, 5-23 (1997).

Song, H.

A. Banerjee, Y. Park, F. Clarke, H. Song, S. Yang, G. Kramer, K. Kim, and B. Mukherjee, ''Wavelength-division-multiplexed passive optical network (WDM-PON) technologies for broadband access: a review,'' JOM 4,737-758 (2005).

Taqqu, M. S.

M. S. Taqqu, W. Willinger, and R. Sherman, ''Proof of a fundamental result in self-similar traffic modeling,'' ACM SIGCOMM Comput. Commun. Rev. 27, 5-23 (1997).

Van De Velde, S. L.

J. M. Van Den Akker, J. A. Hoogeveen, and S. L. Van De Velde, ''Parallel machine scheduling by column generation,'' Oper. Res. 47, 862-872 (1999).

Van Den Akker, J. M.

J. M. Van Den Akker, J. A. Hoogeveen, and S. L. Van De Velde, ''Parallel machine scheduling by column generation,'' Oper. Res. 47, 862-872 (1999).

Vestjens, A. P. A.

A. P. A. Vestjens, ''Online machine scheduling,'' Ph.D. thesis (Eindhoven University of Technology, 1997).

Willinger, W.

K. Park and W. Willinger, Self-Similar Network Traffic and Performance Evaluation (Wiley-Interscience, 2000).

M. S. Taqqu, W. Willinger, and R. Sherman, ''Proof of a fundamental result in self-similar traffic modeling,'' ACM SIGCOMM Comput. Commun. Rev. 27, 5-23 (1997).

Woeginger, G. J.

A. Fiat and G. J. Woeginger, Online Algorithms: The State of the Art (Springer, 1998).

Xiao, C.

C. Xiao, B. Bing, and G. K. Chang, ''An efficient reservation MAC protocol with preallocation for high-speed WDM passive optical networks,'' in Proceedings of IEEE INFOCOM (IEEE, 2005), pp. 444-454.

Yamamoto, S.

Yang, S.

A. Banerjee, Y. Park, F. Clarke, H. Song, S. Yang, G. Kramer, K. Kim, and B. Mukherjee, ''Wavelength-division-multiplexed passive optical network (WDM-PON) technologies for broadband access: a review,'' JOM 4,737-758 (2005).

Ye, Y.

C. M. Assi, Y. Ye, S. Dixit, and M. A. Ali, ''Dynamic bandwidth allocation for quality-of-service over Ethernet PONs,'' IEEE J. Sel. Areas Commun. 21, 1467-1477 (2003).

Zang, H.

H. Zang, J. Jue, and B. Mukherjee, ''A review of routing and wavelength assignment approaches for wavelength-routed optical WDM networks,'' Opt. Networks Mag. 1(1), 47-60 (2000).

Zhu, Y.

M. Ma, Y. Zhu, and T. Cheng, ''A bandwidth guaranteed polling MAC protocol for Ethernet passive optical networks,'' in Proceedings of IEEE INFOCOM (IEEE, 2003), Vol. 1, pp. 22-31.

ACM SIGCOMM Comput. Commun. Rev. (1)

M. S. Taqqu, W. Willinger, and R. Sherman, ''Proof of a fundamental result in self-similar traffic modeling,'' ACM SIGCOMM Comput. Commun. Rev. 27, 5-23 (1997).

Acta Math. Acad. Sci. Hung. (1)

E. Davis and J. M. Jaffe, ''Algorithms for scheduling tasks on unrelated processors,'' Acta Math. Acad. Sci. Hung. 28, 721-736 (1981).

Bell Syst. Tech. J. (1)

R. L. Graham, ''Bounds for certain multiprocessing anomalies,'' Bell Syst. Tech. J. 45, 1563-1581 (1966).

IEEE Commun. Mag. (4)

M. P. McGarry, M. Maier, and M. Reisslein, ''WDM Ethernet Passive Optical Networks,'' IEEE Commun. Mag. 44(2), S18-S25 (2006).

M. P. McGarry, M. Maier, and M. Reisslein, ''Ethernet PONs: a survey of dynamic bandwidth allocation (DBA) algorithms,'' IEEE Commun. Mag. 42(8), S8-S15 (2004).

F. T. An, D. Gutierrez, K. S. Kim, J. W. Lee, and L. G. Kazovsky ''SUCESS-HPON: a next-generation optical access architecture for smooth migration from TDM-PON to WDM-PON,'' IEEE Commun. Mag. 43(11), S40-S47 (2005).

G. Kramer, B. Mukherjee, and G. Pesavento, ''IPACT: A dynamic protocol for an Ethernet PON (EPON),'' IEEE Commun. Mag. 40(2), 74-80 (2002).

IEEE J. Sel. Areas Commun. (1)

C. M. Assi, Y. Ye, S. Dixit, and M. A. Ali, ''Dynamic bandwidth allocation for quality-of-service over Ethernet PONs,'' IEEE J. Sel. Areas Commun. 21, 1467-1477 (2003).

INFORMS J. Comput. (1)

Z. L. Chen and W. B. Powell, ''Solving parallel machine scheduling problems by column generation,'' INFORMS J. Comput. 11, 78-94 (1999).

J. Lightwave Technol. (2)

JOM (1)

A. Banerjee, Y. Park, F. Clarke, H. Song, S. Yang, G. Kramer, K. Kim, and B. Mukherjee, ''Wavelength-division-multiplexed passive optical network (WDM-PON) technologies for broadband access: a review,'' JOM 4,737-758 (2005).

Oper. Res. (1)

J. M. Van Den Akker, J. A. Hoogeveen, and S. L. Van De Velde, ''Parallel machine scheduling by column generation,'' Oper. Res. 47, 862-872 (1999).

Opt. Networks Mag. (1)

H. Zang, J. Jue, and B. Mukherjee, ''A review of routing and wavelength assignment approaches for wavelength-routed optical WDM networks,'' Opt. Networks Mag. 1(1), 47-60 (2000).

Other (11)

M. Pinedo, Scheduling: Theory, Algorithms, and Systems, 2nd ed. (Prentice-Hall, 2002).

A. Fiat and G. J. Woeginger, Online Algorithms: The State of the Art (Springer, 1998).

A. P. A. Vestjens, ''Online machine scheduling,'' Ph.D. thesis (Eindhoven University of Technology, 1997).

Lucent's LambdaXtreme transport, http://www.lucent.com.

A. R. Dhaini, C. M. Assi, and A. Shami, ''Dynamic bandwidth allocation schemes in hybrid TDM/WDM passive optical networks,'' in IEEE Consumer Communications and Networking Conference (IEEE, 2006), Vol. 1, pp. 30-34.

M. Ma, Y. Zhu, and T. Cheng, ''A bandwidth guaranteed polling MAC protocol for Ethernet passive optical networks,'' in Proceedings of IEEE INFOCOM (IEEE, 2003), Vol. 1, pp. 22-31.

C. Xiao, B. Bing, and G. K. Chang, ''An efficient reservation MAC protocol with preallocation for high-speed WDM passive optical networks,'' in Proceedings of IEEE INFOCOM (IEEE, 2005), pp. 444-454.

K. H. Kwong, D. Harle, and I. Andonovic, ''Dynamic bandwidth allocation algorithm for differentiated services over WDM EPONs,'' in Proceedings of the IEEE International Conference on Communications Systems (ICCS) (IEEE, 2004), pp. 116-120.

CSIM (Mesquite Software), http://www.mesquite.com.

G. Kramer, ''On generating self-similar traffic using pseudo-Pareto distribution,'' UC Davis Technical Brief (University of California, Davis), http://wwwcsif.cs.ucdavis.edu/~kramer/papers/selflowbarsim.pdf.

K. Park and W. Willinger, Self-Similar Network Traffic and Performance Evaluation (Wiley-Interscience, 2000).

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