Abstract

The tremendous growth in high-bandwidth applications and consequent increase in power consumption has underscored the importance of energy efficient design strategies for backbone optical networks. In this paper, we exploit the knowledge of the demand holding times to obtain more power efficient grooming. We consider time-varying, periodic traffic, where the setup and teardown times of the demands may be fixed or vary within a larger time window. The problem of joint scheduling (in time) and traffic grooming, with the goal of minimizing energy consumption for sliding demands, has not been considered previously. We first present an efficient integer linear program formulation for scheduling and allocating resources to a single subwavelength traffic demand, such that incremental energy consumption due to the new demand is minimized. Next, we extend the proposed approach and present a new heuristic that jointly performs scheduling and resource allocation for a large set of periodic demands with the goal of reducing the overall energy consumption of the network for the entire demand set. Through simulations, we demonstrate that significant energy savings can be achieved by considering the demand holding time and show that joint allocation of demands yields additional improvements.

© 2013 Optical Society of America

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  1. M. Gupta and S. Singh, “Greening of the Internet,” in Proc. ACM SIGCOMM, 2003, pp. 19–26.
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  5. B. G. Bathula and J. M. H. Elmirghani, “Green networks: Energy efficient design for optical networks,” in Wireless and Optical Communications Networks, 2009, pp. 1–5.
  6. S. Huang, D. Seshadri, and R. Dutta, “Traffic grooming: A changing role in green optical networks,” in IEEE GLOBECOM, 2009, pp. 1–6.
  7. Y. Chen and A. Jaekel, “Energy efficient grooming of scheduled sub-wavelength traffic demands,” in Optical Fiber Communication Conf., 2011, paper OWI1.
  8. J. Kuri, N. Puech, M. Gagnaire, E. Dotaro, and R. Douville, “Routing and wavelength assignment of scheduled lightpath demands,” IEEE J. Sel. Areas Commun., vol.  21, pp. 1231–1240, Oct. 2003.
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  9. B. Wang, T. Li, X. Luo, Y. Fan, and C. Xin, “On service provisioning under a scheduled traffic model in reconfigurable WDM optical networks,” in BROADNETS, 2005, pp. 13–22.
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  27. A. Jaekel, A. Bari, Y. Chen, and S. Bandyopadhyay, “Strategies for optimal logical topology design and traffic grooming,” Photon. Netw. Commun., vol.  19, no. 2, pp. 223–232, 2010.
    [CrossRef]
  28. A. Jaekel, Y. Chen, and A. Bari, “Stable logical topologies for survivable traffic grooming of scheduled demands,” J. Opt. Commun. Netw., vol.  2, no. 10, pp. 793–802, 2010.
    [CrossRef]
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2012 (3)

R. Aparicio-Pardo, N. Skorin-Kapov, P. Pavon-Marino, and B. Garcia-Manrubia, “(Non-)reconfigurable virtual topology design under multihour traffic in optical networks,” IEEE/ACM Trans. Netw., vol.  20, no. 5, pp. 1567–1580, 2012.
[CrossRef]

F. Musumeci, M. Tornatore, and A. Pattavina, “A power consumption analysis for IP-over-WDM core network architectures,” J. Opt. Commun. Netw., vol.  4, no. 2, pp. 108–117, 2012.
[CrossRef]

W. V. Heddeghem, F. Idzikowski, W. Vereecken, D. Colle, M. Pickavet, and P. Demeester, “Power consumption modeling in optical multilayer networks,” Photon. Netw. Commun., vol.  24, no. 2, pp. 86–102, Oct. 2012.
[CrossRef]

2011 (2)

S. Zhang, D. Shen, and C.-K. Chan, “Energy-efficient traffic grooming in WDM networks with scheduled time traffic,” J. Lightwave Technol., vol.  29, no. 17, pp. 2577–2584, Sept. 2011.
[CrossRef]

Y. Chen, A. Jaekel, and A. Bari, “A new model for allocating resources to scheduled lightpath demands,” Comput. Netw., vol.  55, no. 13, pp. 2821–2837, 2011.
[CrossRef]

2010 (3)

2009 (3)

2006 (2)

2003 (3)

J. Kuri, N. Puech, M. Gagnaire, E. Dotaro, and R. Douville, “Routing and wavelength assignment of scheduled lightpath demands,” IEEE J. Sel. Areas Commun., vol.  21, pp. 1231–1240, Oct. 2003.
[CrossRef]

A. E. Ozdaglar and D. P. Bertsekas, “Routing and wavelength assignment in optical networks,” IEEE/ACM Trans. Netw., vol.  11, no. 2, pp. 259–272, Apr. 2003.
[CrossRef]

C. Ou, K. Zhu, H. Zang, L. H. Sahasrabuddhe, and B. Mukherjee, “Traffic grooming for survivable WDM networks: Shared protection,” IEEE J. Sel. Areas Commun., vol.  21, pp. 1367–1383, Nov. 2003.
[CrossRef]

Alresheedi, M.

B. Bathula, M. Alresheedi, and J. Elmirghani, “Energy efficient architectures for optical networks,” in Proc. London Communications Symp., 2009.

Andrei, D.

Aparicio-Pardo, R.

R. Aparicio-Pardo, N. Skorin-Kapov, P. Pavon-Marino, and B. Garcia-Manrubia, “(Non-)reconfigurable virtual topology design under multihour traffic in optical networks,” IEEE/ACM Trans. Netw., vol.  20, no. 5, pp. 1567–1580, 2012.
[CrossRef]

Ayre, R.

Baliga, J.

Bandyopadhyay, S.

A. Jaekel, A. Bari, Y. Chen, and S. Bandyopadhyay, “Strategies for optimal logical topology design and traffic grooming,” Photon. Netw. Commun., vol.  19, no. 2, pp. 223–232, 2010.
[CrossRef]

Barford, P.

J. Chabarek, J. Sommers, P. Barford, C. Estan, D. Tsiang, and S. Wright, “Power awareness in network design and routing,” in IEEE INFOCOM, 2008, pp. 457–465.

Bari, A.

Y. Chen, A. Jaekel, and A. Bari, “A new model for allocating resources to scheduled lightpath demands,” Comput. Netw., vol.  55, no. 13, pp. 2821–2837, 2011.
[CrossRef]

A. Jaekel, A. Bari, Y. Chen, and S. Bandyopadhyay, “Strategies for optimal logical topology design and traffic grooming,” Photon. Netw. Commun., vol.  19, no. 2, pp. 223–232, 2010.
[CrossRef]

A. Jaekel, Y. Chen, and A. Bari, “Stable logical topologies for survivable traffic grooming of scheduled demands,” J. Opt. Commun. Netw., vol.  2, no. 10, pp. 793–802, 2010.
[CrossRef]

Bathula, B.

B. Bathula, M. Alresheedi, and J. Elmirghani, “Energy efficient architectures for optical networks,” in Proc. London Communications Symp., 2009.

Bathula, B. G.

B. G. Bathula and J. M. H. Elmirghani, “Green networks: Energy efficient design for optical networks,” in Wireless and Optical Communications Networks, 2009, pp. 1–5.

Bertsekas, D. P.

A. E. Ozdaglar and D. P. Bertsekas, “Routing and wavelength assignment in optical networks,” IEEE/ACM Trans. Netw., vol.  11, no. 2, pp. 259–272, Apr. 2003.
[CrossRef]

Cao, X.

Chabarek, J.

J. Chabarek, J. Sommers, P. Barford, C. Estan, D. Tsiang, and S. Wright, “Power awareness in network design and routing,” in IEEE INFOCOM, 2008, pp. 457–465.

Chan, C.-K.

Chen, Y.

Y. Chen, A. Jaekel, and A. Bari, “A new model for allocating resources to scheduled lightpath demands,” Comput. Netw., vol.  55, no. 13, pp. 2821–2837, 2011.
[CrossRef]

A. Jaekel, A. Bari, Y. Chen, and S. Bandyopadhyay, “Strategies for optimal logical topology design and traffic grooming,” Photon. Netw. Commun., vol.  19, no. 2, pp. 223–232, 2010.
[CrossRef]

A. Jaekel, Y. Chen, and A. Bari, “Stable logical topologies for survivable traffic grooming of scheduled demands,” J. Opt. Commun. Netw., vol.  2, no. 10, pp. 793–802, 2010.
[CrossRef]

A. Jaekel and Y. Chen, “Resource provisioning for survivable WDM networks under a sliding scheduled traffic model,” Opt. Switching Netw., vol.  6, no. 1, pp. 44–54, Jan. 2009.
[CrossRef]

Y. Chen and A. Jaekel, “Energy efficient grooming of scheduled sub-wavelength traffic demands,” in Optical Fiber Communication Conf., 2011, paper OWI1.

Y. Chen and A. Jaekel, “Energy aware resource allocation based on demand bandwidth and duration,” in 2nd Int. Workshop on Green Computing and Renewable Energy (GCRE), 2012.

Colle, D.

W. V. Heddeghem, F. Idzikowski, W. Vereecken, D. Colle, M. Pickavet, and P. Demeester, “Power consumption modeling in optical multilayer networks,” Photon. Netw. Commun., vol.  24, no. 2, pp. 86–102, Oct. 2012.
[CrossRef]

Demeester, P.

W. V. Heddeghem, F. Idzikowski, W. Vereecken, D. Colle, M. Pickavet, and P. Demeester, “Power consumption modeling in optical multilayer networks,” Photon. Netw. Commun., vol.  24, no. 2, pp. 86–102, Oct. 2012.
[CrossRef]

Dotaro, E.

J. Kuri, N. Puech, M. Gagnaire, E. Dotaro, and R. Douville, “Routing and wavelength assignment of scheduled lightpath demands,” IEEE J. Sel. Areas Commun., vol.  21, pp. 1231–1240, Oct. 2003.
[CrossRef]

Douville, R.

J. Kuri, N. Puech, M. Gagnaire, E. Dotaro, and R. Douville, “Routing and wavelength assignment of scheduled lightpath demands,” IEEE J. Sel. Areas Commun., vol.  21, pp. 1231–1240, Oct. 2003.
[CrossRef]

Dutta, R.

S. Huang, D. Seshadri, and R. Dutta, “Traffic grooming: A changing role in green optical networks,” in IEEE GLOBECOM, 2009, pp. 1–6.

Elmirghani, J.

B. Bathula, M. Alresheedi, and J. Elmirghani, “Energy efficient architectures for optical networks,” in Proc. London Communications Symp., 2009.

Elmirghani, J. M. H.

B. G. Bathula and J. M. H. Elmirghani, “Green networks: Energy efficient design for optical networks,” in Wireless and Optical Communications Networks, 2009, pp. 1–5.

Estan, C.

J. Chabarek, J. Sommers, P. Barford, C. Estan, D. Tsiang, and S. Wright, “Power awareness in network design and routing,” in IEEE INFOCOM, 2008, pp. 457–465.

Fan, Y.

B. Wang, T. Li, X. Luo, Y. Fan, and C. Xin, “On service provisioning under a scheduled traffic model in reconfigurable WDM optical networks,” in BROADNETS, 2005, pp. 13–22.

Gagnaire, M.

J. Kuri, N. Puech, M. Gagnaire, E. Dotaro, and R. Douville, “Routing and wavelength assignment of scheduled lightpath demands,” IEEE J. Sel. Areas Commun., vol.  21, pp. 1231–1240, Oct. 2003.
[CrossRef]

Garcia-Manrubia, B.

R. Aparicio-Pardo, N. Skorin-Kapov, P. Pavon-Marino, and B. Garcia-Manrubia, “(Non-)reconfigurable virtual topology design under multihour traffic in optical networks,” IEEE/ACM Trans. Netw., vol.  20, no. 5, pp. 1567–1580, 2012.
[CrossRef]

Ghosal, D.

Gupta, M.

M. Gupta and S. Singh, “Greening of the Internet,” in Proc. ACM SIGCOMM, 2003, pp. 19–26.

Heddeghem, W. V.

W. V. Heddeghem, F. Idzikowski, W. Vereecken, D. Colle, M. Pickavet, and P. Demeester, “Power consumption modeling in optical multilayer networks,” Photon. Netw. Commun., vol.  24, no. 2, pp. 86–102, Oct. 2012.
[CrossRef]

Hinton, K.

Huang, S.

S. Huang, D. Seshadri, and R. Dutta, “Traffic grooming: A changing role in green optical networks,” in IEEE GLOBECOM, 2009, pp. 1–6.

Idzikowski, F.

W. V. Heddeghem, F. Idzikowski, W. Vereecken, D. Colle, M. Pickavet, and P. Demeester, “Power consumption modeling in optical multilayer networks,” Photon. Netw. Commun., vol.  24, no. 2, pp. 86–102, Oct. 2012.
[CrossRef]

F. Idzikowski, S. Orlowski, C. Raack, H. Woesner, and A. Wolisz, “Saving energy in IP-over-WDM networks by switching off line cards in low-demand scenarios,” in 14th Conf. Optical Network Design and Modeling, 2010, pp. 1–6.

Jaekel, A.

Y. Chen, A. Jaekel, and A. Bari, “A new model for allocating resources to scheduled lightpath demands,” Comput. Netw., vol.  55, no. 13, pp. 2821–2837, 2011.
[CrossRef]

A. Jaekel, A. Bari, Y. Chen, and S. Bandyopadhyay, “Strategies for optimal logical topology design and traffic grooming,” Photon. Netw. Commun., vol.  19, no. 2, pp. 223–232, 2010.
[CrossRef]

A. Jaekel, Y. Chen, and A. Bari, “Stable logical topologies for survivable traffic grooming of scheduled demands,” J. Opt. Commun. Netw., vol.  2, no. 10, pp. 793–802, 2010.
[CrossRef]

A. Jaekel and Y. Chen, “Resource provisioning for survivable WDM networks under a sliding scheduled traffic model,” Opt. Switching Netw., vol.  6, no. 1, pp. 44–54, Jan. 2009.
[CrossRef]

Y. Chen and A. Jaekel, “Energy efficient grooming of scheduled sub-wavelength traffic demands,” in Optical Fiber Communication Conf., 2011, paper OWI1.

Y. Chen and A. Jaekel, “Energy aware resource allocation based on demand bandwidth and duration,” in 2nd Int. Workshop on Green Computing and Renewable Energy (GCRE), 2012.

Kuri, J.

J. Kuri, N. Puech, M. Gagnaire, E. Dotaro, and R. Douville, “Routing and wavelength assignment of scheduled lightpath demands,” IEEE J. Sel. Areas Commun., vol.  21, pp. 1231–1240, Oct. 2003.
[CrossRef]

Li, J.

Li, T.

T. Li and B. Wang, “Path protection based routing and wavelength assignment in wavelength division multiplexing optical networks under a scheduled traffic model,” J. Opt. Netw., vol.  5, pp. 575–588, 2006.
[CrossRef]

T. Li and B. Wang, “On optimal survivability design in WDM optical networks under a scheduled traffic model,” in Design of Reliable Communication Networks, 2005, pp. 23–30.

B. Wang, T. Li, X. Luo, Y. Fan, and C. Xin, “On service provisioning under a scheduled traffic model in reconfigurable WDM optical networks,” in BROADNETS, 2005, pp. 13–22.

Luo, X.

B. Wang, T. Li, X. Luo, Y. Fan, and C. Xin, “On service provisioning under a scheduled traffic model in reconfigurable WDM optical networks,” in BROADNETS, 2005, pp. 13–22.

Martel, C. U.

Mukherjee, B.

D. Andrei, M. Tornatore, C. U. Martel, D. Ghosal, and B. Mukherjee, “Provisioning subwavelength multicast sessions with flexible scheduling over WDM networks,” J. Opt. Commun. Netw., vol.  2, no. 5, pp. 241–255, 2010.
[CrossRef]

C. Ou, K. Zhu, H. Zang, L. H. Sahasrabuddhe, and B. Mukherjee, “Traffic grooming for survivable WDM networks: Shared protection,” IEEE J. Sel. Areas Commun., vol.  21, pp. 1367–1383, Nov. 2003.
[CrossRef]

M. Tornatore, C. Ou, J. Zhang, A. Pattavina, and B. Mukherjee, “Efficient shared-path protection exploiting the knowledge of connection-holding time,” in Optical Fiber Communication Conf., 2005, pp. 65–72.

Musumeci, F.

Orlowski, S.

F. Idzikowski, S. Orlowski, C. Raack, H. Woesner, and A. Wolisz, “Saving energy in IP-over-WDM networks by switching off line cards in low-demand scenarios,” in 14th Conf. Optical Network Design and Modeling, 2010, pp. 1–6.

Ou, C.

C. Ou, K. Zhu, H. Zang, L. H. Sahasrabuddhe, and B. Mukherjee, “Traffic grooming for survivable WDM networks: Shared protection,” IEEE J. Sel. Areas Commun., vol.  21, pp. 1367–1383, Nov. 2003.
[CrossRef]

M. Tornatore, C. Ou, J. Zhang, A. Pattavina, and B. Mukherjee, “Efficient shared-path protection exploiting the knowledge of connection-holding time,” in Optical Fiber Communication Conf., 2005, pp. 65–72.

Ozdaglar, A. E.

A. E. Ozdaglar and D. P. Bertsekas, “Routing and wavelength assignment in optical networks,” IEEE/ACM Trans. Netw., vol.  11, no. 2, pp. 259–272, Apr. 2003.
[CrossRef]

Pattavina, A.

F. Musumeci, M. Tornatore, and A. Pattavina, “A power consumption analysis for IP-over-WDM core network architectures,” J. Opt. Commun. Netw., vol.  4, no. 2, pp. 108–117, 2012.
[CrossRef]

M. Tornatore, C. Ou, J. Zhang, A. Pattavina, and B. Mukherjee, “Efficient shared-path protection exploiting the knowledge of connection-holding time,” in Optical Fiber Communication Conf., 2005, pp. 65–72.

Pavon-Marino, P.

R. Aparicio-Pardo, N. Skorin-Kapov, P. Pavon-Marino, and B. Garcia-Manrubia, “(Non-)reconfigurable virtual topology design under multihour traffic in optical networks,” IEEE/ACM Trans. Netw., vol.  20, no. 5, pp. 1567–1580, 2012.
[CrossRef]

Pickavet, M.

W. V. Heddeghem, F. Idzikowski, W. Vereecken, D. Colle, M. Pickavet, and P. Demeester, “Power consumption modeling in optical multilayer networks,” Photon. Netw. Commun., vol.  24, no. 2, pp. 86–102, Oct. 2012.
[CrossRef]

Puech, N.

J. Kuri, N. Puech, M. Gagnaire, E. Dotaro, and R. Douville, “Routing and wavelength assignment of scheduled lightpath demands,” IEEE J. Sel. Areas Commun., vol.  21, pp. 1231–1240, Oct. 2003.
[CrossRef]

Raack, C.

F. Idzikowski, S. Orlowski, C. Raack, H. Woesner, and A. Wolisz, “Saving energy in IP-over-WDM networks by switching off line cards in low-demand scenarios,” in 14th Conf. Optical Network Design and Modeling, 2010, pp. 1–6.

Rouskas, G.

E. Yetginer and G. Rouskas, “Power efficient traffic grooming in optical WDM networks,” in IEEE GLOBECOM, 2009, pp. 1–6.

Sahasrabuddhe, L. H.

C. Ou, K. Zhu, H. Zang, L. H. Sahasrabuddhe, and B. Mukherjee, “Traffic grooming for survivable WDM networks: Shared protection,” IEEE J. Sel. Areas Commun., vol.  21, pp. 1367–1383, Nov. 2003.
[CrossRef]

Seshadri, D.

S. Huang, D. Seshadri, and R. Dutta, “Traffic grooming: A changing role in green optical networks,” in IEEE GLOBECOM, 2009, pp. 1–6.

Shen, D.

Shen, G.

Singh, S.

M. Gupta and S. Singh, “Greening of the Internet,” in Proc. ACM SIGCOMM, 2003, pp. 19–26.

Skorin-Kapov, N.

R. Aparicio-Pardo, N. Skorin-Kapov, P. Pavon-Marino, and B. Garcia-Manrubia, “(Non-)reconfigurable virtual topology design under multihour traffic in optical networks,” IEEE/ACM Trans. Netw., vol.  20, no. 5, pp. 1567–1580, 2012.
[CrossRef]

Sommers, J.

J. Chabarek, J. Sommers, P. Barford, C. Estan, D. Tsiang, and S. Wright, “Power awareness in network design and routing,” in IEEE INFOCOM, 2008, pp. 457–465.

Sorin, W.

Tornatore, M.

Tsiang, D.

J. Chabarek, J. Sommers, P. Barford, C. Estan, D. Tsiang, and S. Wright, “Power awareness in network design and routing,” in IEEE INFOCOM, 2008, pp. 457–465.

Tucker, R.

Vereecken, W.

W. V. Heddeghem, F. Idzikowski, W. Vereecken, D. Colle, M. Pickavet, and P. Demeester, “Power consumption modeling in optical multilayer networks,” Photon. Netw. Commun., vol.  24, no. 2, pp. 86–102, Oct. 2012.
[CrossRef]

Wang, B.

C. Xin, B. Wang, X. Cao, and J. Li, “Logical topology design for dynamic traffic grooming in WDM optical networks,” J. Lightwave Technol., vol.  24, no. 6, pp. 2267–2275, June 2006.
[CrossRef]

T. Li and B. Wang, “Path protection based routing and wavelength assignment in wavelength division multiplexing optical networks under a scheduled traffic model,” J. Opt. Netw., vol.  5, pp. 575–588, 2006.
[CrossRef]

T. Li and B. Wang, “On optimal survivability design in WDM optical networks under a scheduled traffic model,” in Design of Reliable Communication Networks, 2005, pp. 23–30.

B. Wang, T. Li, X. Luo, Y. Fan, and C. Xin, “On service provisioning under a scheduled traffic model in reconfigurable WDM optical networks,” in BROADNETS, 2005, pp. 13–22.

Woesner, H.

F. Idzikowski, S. Orlowski, C. Raack, H. Woesner, and A. Wolisz, “Saving energy in IP-over-WDM networks by switching off line cards in low-demand scenarios,” in 14th Conf. Optical Network Design and Modeling, 2010, pp. 1–6.

Wolisz, A.

F. Idzikowski, S. Orlowski, C. Raack, H. Woesner, and A. Wolisz, “Saving energy in IP-over-WDM networks by switching off line cards in low-demand scenarios,” in 14th Conf. Optical Network Design and Modeling, 2010, pp. 1–6.

Wright, S.

J. Chabarek, J. Sommers, P. Barford, C. Estan, D. Tsiang, and S. Wright, “Power awareness in network design and routing,” in IEEE INFOCOM, 2008, pp. 457–465.

Xin, C.

C. Xin, B. Wang, X. Cao, and J. Li, “Logical topology design for dynamic traffic grooming in WDM optical networks,” J. Lightwave Technol., vol.  24, no. 6, pp. 2267–2275, June 2006.
[CrossRef]

B. Wang, T. Li, X. Luo, Y. Fan, and C. Xin, “On service provisioning under a scheduled traffic model in reconfigurable WDM optical networks,” in BROADNETS, 2005, pp. 13–22.

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C. Ou, K. Zhu, H. Zang, L. H. Sahasrabuddhe, and B. Mukherjee, “Traffic grooming for survivable WDM networks: Shared protection,” IEEE J. Sel. Areas Commun., vol.  21, pp. 1367–1383, Nov. 2003.
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T. Li and B. Wang, “On optimal survivability design in WDM optical networks under a scheduled traffic model,” in Design of Reliable Communication Networks, 2005, pp. 23–30.

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Figures (11)

Fig. 1.
Fig. 1.

Logical topology and traffic routing.

Fig. 2.
Fig. 2.

Overlapping demands under the fixed window model.

Fig. 3.
Fig. 3.

Demand scheduling under the sliding window model.

Fig. 4.
Fig. 4.

Comparison of the average number of active lightpaths used for single and joint demand allocation.

Fig. 5.
Fig. 5.

Percentage reduction in total power consumption and the average number of active lightpaths compared with the energy-aware HTU case for a 10-node network.

Fig. 6.
Fig. 6.

Comparison of total power consumption for the FDO case, traditional traffic grooming and H-EER for a 10-node network.

Fig. 7.
Fig. 7.

Comparison of the average number of active lightpaths used for different topologies.

Fig. 8.
Fig. 8.

Comparison of the average number of active lightpaths used for different sorting criteria.

Fig. 9.
Fig. 9.

Percentage reduction in total power consumption compared with the fixed scheduled traffic model.

Fig. 10.
Fig. 10.

Effect of increasing window size for different topologies.

Fig. 11.
Fig. 11.

Comparison of traffic dropped under the different scheduled traffic models.

Equations (18)

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

Ptotal=lLP0+pt·tl,
i = α q ω q P i · T i
l:o(l)=jxll:e(l)=jxl={1ifj=sq,1ifj=dq,0otherwise.
γl,i=1lLi,i,αqiωq,
tq·xl·rq,i+qQalloctq·xq,l·rq,ig·γl,i.
xlγl,ilL,i,αqiωq,
Pi=lLLiγl,i.P0+lLtq.rq,i.pt.xl.
i = α q ω q P i · T i
l:o(l)=jxll:e(l)=jxl={1ifj=sq,1ifj=dq,0otherwise.
tq·zl,i+qQalloctq·xq,l·rq,ig·γl,i
i=αqωqsti=1
ri+jstii,0j<τq
i=αqωqri=τq
ri+xlzl,i1
xlzl,i
rizl,i
Pi=lLγl,i·P0+lLtq·zl,i·pt+lLqQalloctq·xq,l·rq,i·pt
δ=ilmaxj=1n1k=j+1nTj,ki0.5·lmax·n(n1).