Abstract

Energy-efficient network design has recently become a very important topic because of the energy cost increases in service providers’ infrastructures. This is of particular importance in access networks because of the growing demand for digital traffic by end users. Here we address the challenge of reducing the energy consumption of fiber–wireless (FiWi) access networks, which use both optical and radio frequency technologies to provide high bandwidth and ubiquity for end-user applications, while keeping delay under a threshold. Our goal is to find optimal sleep mode schedulings that allow energy consumption to be reduced while keeping packet delay acceptable. For this purpose a mathematical formalization and an algorithm are developed. The results show that the proposed approach is able to reduce the average packet delay, with negligible energy cost increases, in many scenarios, besides being computationally efficient and scalable. The proposed approach may, therefore, serve as a basis for planning and design of quality-of-service-aware energy-efficient FiWi access networks.

© 2012 OSA

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  2. S.-W. Wong, L. Valcarenghi, S.-H. Yen, D. R. Campelo, S. Yamashita, and L. Kazovsky, “Sleep mode for energy saving PONS: Advantages and drawbacks,” in IEEE GLOBECOM Workshops, 2009.
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    [CrossRef]
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  22. F. A. Onat and I. Stojmenovic, “Generating random graphs for wireless actuator networks,” in IEEE Int. Symp. on a World of Wireless, Mobile and Multimedia Networks, June 2007, pp. 1–12.

2011 (1)

R. Bolla, R. Bruschi, F. Davoli, and F. Cucchietti, “Energy efficiency in the future Internet: a survey of existing approaches and trends in energy-aware fixed network infrastructures,” IEEE Commun. Surv. Tutorials, vol. 13, no. 2, pp. 223–244, 2011.
[CrossRef]

2010 (4)

R. Jurdak, A. G. Ruzzelli, and G. M. P. O’Har, “Radio sleep mode optimization in wireless sensor networks,” IEEE Trans. Mobile Comput., vol. 9, no. 7, pp. 955–968, July2010.
[CrossRef]

R. Gaudino, D. Cárdenas, M. Bellec, B. Charbonnier, N. Evanno, P. Guignard, S. Meyer, A. Pizzinat, I. Möllers, and D. Jäger, “Perspective in next-generation home networks: Toward optical solutions,” IEEE Commun. Mag., vol. 48, no. 2, pp. 39–47, Feb.2010.
[CrossRef]

R. Kubo, J.-i. Kani, H. Ujikawa, T. Sakamoto, Y. Fujimoto, N. Yoshimoto, and H. Hadama, “Study and demonstration of sleep and adaptive link rate control mechanisms for energy efficient 10G-EPON,” J. Lightwave Technol., vol. 2, no. 9, pp. 716–729, Sept.2010.

P. Chowdhury, M. Tornatore, S. Sarkar, and B. Mukherjee, “Building a green wireless-optical broadband access network (WOBAN),” J. Lightwave Technol., vol. 28, no. 16, pp. 2219–2229, Aug.2010.
[CrossRef]

2009 (2)

J. Baliga, R. Ayre, K. Hinton, W. V. Sorin, and R. S. Tucker, “Energy consumption in optical IP networks,” J. Lightwave Technol., vol. 27, no. 13, pp. 2391–2403, July2009.
[CrossRef]

D. Qiao, M. C. Gursoy, and S. Velipasalar, “The impact of QoS constraints on the energy efficiency of fixed-rate wireless transmissions,” IEEE Trans. Wireless Commun., vol. 8, no. 12, pp. 5957–5969, Dec.2009.
[CrossRef]

2007 (1)

2006 (1)

J. Lee, C. Rosenberg, and E. Chong, “Energy efficient schedulers in wireless networks: Design and optimization,” Mob. Netw. Appl., vol. 11, no. 3, pp. 377–389, June2006.
[CrossRef]

2001 (1)

C. E. Jones, K. M. Sivalingam, P. Agrawal, and J. C. Chen, “A survey of energy efficient network protocols for wireless networks,” Wireless Networks, vol. 7, no. 4, pp. 343–358, July2001.
[CrossRef]

1976 (1)

S. Sahni and T. Gonzalez, “P-complete approximation problems,” J. Assoc. Comput. Mach., vol. 23, pp. 555–565, 1976.
[CrossRef]

Afshar, P.

S.-W. Wong, S.-H. Yen, P. Afshar, S. Yamashita, and L. G. Kazovsky, “Demonstration of energy conserving TDM-PON with sleep mode ONU using fast clock recovery circuit,” in IEEE OFC, 2010.

Agrawal, P.

C. E. Jones, K. M. Sivalingam, P. Agrawal, and J. C. Chen, “A survey of energy efficient network protocols for wireless networks,” Wireless Networks, vol. 7, no. 4, pp. 343–358, July2001.
[CrossRef]

Ajmone, M.

B. Rengarajan, G. Rizzo, and M. Ajmone, “Bounds on QoS-constrained energy savings in cellular access networks with sleep modes,” in 23rd Int. Teletraffic Congress, 2011, pp. 47–54.

Ayre, R.

Baliga, J.

Bellec, M.

R. Gaudino, D. Cárdenas, M. Bellec, B. Charbonnier, N. Evanno, P. Guignard, S. Meyer, A. Pizzinat, I. Möllers, and D. Jäger, “Perspective in next-generation home networks: Toward optical solutions,” IEEE Commun. Mag., vol. 48, no. 2, pp. 39–47, Feb.2010.
[CrossRef]

Bolla, R.

R. Bolla, R. Bruschi, F. Davoli, and F. Cucchietti, “Energy efficiency in the future Internet: a survey of existing approaches and trends in energy-aware fixed network infrastructures,” IEEE Commun. Surv. Tutorials, vol. 13, no. 2, pp. 223–244, 2011.
[CrossRef]

Bruschi, R.

R. Bolla, R. Bruschi, F. Davoli, and F. Cucchietti, “Energy efficiency in the future Internet: a survey of existing approaches and trends in energy-aware fixed network infrastructures,” IEEE Commun. Surv. Tutorials, vol. 13, no. 2, pp. 223–244, 2011.
[CrossRef]

Campelo, D. R.

Y. Yan, S.-W. Wong, L. Valcarenghi, S.-H. Yen, D. R. Campelo, S. Yamashita, L. Kazovsky, and L. Dittmann, “Energy management mechanism for Ethernet passive optical networks (EPONs),” in IEEE ICC, 2010.

S.-W. Wong, L. Valcarenghi, S.-H. Yen, D. R. Campelo, S. Yamashita, and L. Kazovsky, “Sleep mode for energy saving PONS: Advantages and drawbacks,” in IEEE GLOBECOM Workshops, 2009.

Cárdenas, D.

R. Gaudino, D. Cárdenas, M. Bellec, B. Charbonnier, N. Evanno, P. Guignard, S. Meyer, A. Pizzinat, I. Möllers, and D. Jäger, “Perspective in next-generation home networks: Toward optical solutions,” IEEE Commun. Mag., vol. 48, no. 2, pp. 39–47, Feb.2010.
[CrossRef]

Castoldi, P.

I. Cerutti, L. Valcarenghi, and P. Castoldi, “Power saving architectures for unidirectional WDM rings,” in IEEE OFC, 2009.

Cerutti, I.

I. Cerutti, L. Valcarenghi, and P. Castoldi, “Power saving architectures for unidirectional WDM rings,” in IEEE OFC, 2009.

Charbonnier, B.

R. Gaudino, D. Cárdenas, M. Bellec, B. Charbonnier, N. Evanno, P. Guignard, S. Meyer, A. Pizzinat, I. Möllers, and D. Jäger, “Perspective in next-generation home networks: Toward optical solutions,” IEEE Commun. Mag., vol. 48, no. 2, pp. 39–47, Feb.2010.
[CrossRef]

Chen, J. C.

C. E. Jones, K. M. Sivalingam, P. Agrawal, and J. C. Chen, “A survey of energy efficient network protocols for wireless networks,” Wireless Networks, vol. 7, no. 4, pp. 343–358, July2001.
[CrossRef]

Chiaraviglio, L.

L. Chiaraviglio, M. Mellia, and F. Neri, “Reducing power consumption in backbone networks,” in IEEE ICC, 2009.

Chong, E.

J. Lee, C. Rosenberg, and E. Chong, “Energy efficient schedulers in wireless networks: Design and optimization,” Mob. Netw. Appl., vol. 11, no. 3, pp. 377–389, June2006.
[CrossRef]

Chowdhury, P.

Coimbra, J.

J. Coimbra, G. Schütz, and N. Correia, “Forwarding repeated game for end-to-end QoS support in fiber-wireless access networks,” in IEEE GLOBECOM, 2010.

Correia, N.

J. Coimbra, G. Schütz, and N. Correia, “Forwarding repeated game for end-to-end QoS support in fiber-wireless access networks,” in IEEE GLOBECOM, 2010.

Cucchietti, F.

R. Bolla, R. Bruschi, F. Davoli, and F. Cucchietti, “Energy efficiency in the future Internet: a survey of existing approaches and trends in energy-aware fixed network infrastructures,” IEEE Commun. Surv. Tutorials, vol. 13, no. 2, pp. 223–244, 2011.
[CrossRef]

Davoli, F.

R. Bolla, R. Bruschi, F. Davoli, and F. Cucchietti, “Energy efficiency in the future Internet: a survey of existing approaches and trends in energy-aware fixed network infrastructures,” IEEE Commun. Surv. Tutorials, vol. 13, no. 2, pp. 223–244, 2011.
[CrossRef]

Dittmann, L.

Y. Yan, S.-W. Wong, L. Valcarenghi, S.-H. Yen, D. R. Campelo, S. Yamashita, L. Kazovsky, and L. Dittmann, “Energy management mechanism for Ethernet passive optical networks (EPONs),” in IEEE ICC, 2010.

Dixit, D.

Evanno, N.

R. Gaudino, D. Cárdenas, M. Bellec, B. Charbonnier, N. Evanno, P. Guignard, S. Meyer, A. Pizzinat, I. Möllers, and D. Jäger, “Perspective in next-generation home networks: Toward optical solutions,” IEEE Commun. Mag., vol. 48, no. 2, pp. 39–47, Feb.2010.
[CrossRef]

Fujimoto, Y.

R. Kubo, J.-i. Kani, H. Ujikawa, T. Sakamoto, Y. Fujimoto, N. Yoshimoto, and H. Hadama, “Study and demonstration of sleep and adaptive link rate control mechanisms for energy efficient 10G-EPON,” J. Lightwave Technol., vol. 2, no. 9, pp. 716–729, Sept.2010.

Garey, M. R.

M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Co., San Francisco, 1979.

Gaudino, R.

R. Gaudino, D. Cárdenas, M. Bellec, B. Charbonnier, N. Evanno, P. Guignard, S. Meyer, A. Pizzinat, I. Möllers, and D. Jäger, “Perspective in next-generation home networks: Toward optical solutions,” IEEE Commun. Mag., vol. 48, no. 2, pp. 39–47, Feb.2010.
[CrossRef]

Gladisch, A.

C. Lange and A. Gladisch, “On the energy consumption of FTTH access networks,” in IEEE OFC, 2009.

Gonzalez, T.

S. Sahni and T. Gonzalez, “P-complete approximation problems,” J. Assoc. Comput. Mach., vol. 23, pp. 555–565, 1976.
[CrossRef]

Guignard, P.

R. Gaudino, D. Cárdenas, M. Bellec, B. Charbonnier, N. Evanno, P. Guignard, S. Meyer, A. Pizzinat, I. Möllers, and D. Jäger, “Perspective in next-generation home networks: Toward optical solutions,” IEEE Commun. Mag., vol. 48, no. 2, pp. 39–47, Feb.2010.
[CrossRef]

Gursoy, M. C.

D. Qiao, M. C. Gursoy, and S. Velipasalar, “The impact of QoS constraints on the energy efficiency of fixed-rate wireless transmissions,” IEEE Trans. Wireless Commun., vol. 8, no. 12, pp. 5957–5969, Dec.2009.
[CrossRef]

Hadama, H.

R. Kubo, J.-i. Kani, H. Ujikawa, T. Sakamoto, Y. Fujimoto, N. Yoshimoto, and H. Hadama, “Study and demonstration of sleep and adaptive link rate control mechanisms for energy efficient 10G-EPON,” J. Lightwave Technol., vol. 2, no. 9, pp. 716–729, Sept.2010.

Hinton, K.

Jäger, D.

R. Gaudino, D. Cárdenas, M. Bellec, B. Charbonnier, N. Evanno, P. Guignard, S. Meyer, A. Pizzinat, I. Möllers, and D. Jäger, “Perspective in next-generation home networks: Toward optical solutions,” IEEE Commun. Mag., vol. 48, no. 2, pp. 39–47, Feb.2010.
[CrossRef]

Johnson, D. S.

M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Co., San Francisco, 1979.

Jones, C. E.

C. E. Jones, K. M. Sivalingam, P. Agrawal, and J. C. Chen, “A survey of energy efficient network protocols for wireless networks,” Wireless Networks, vol. 7, no. 4, pp. 343–358, July2001.
[CrossRef]

Jurdak, R.

R. Jurdak, A. G. Ruzzelli, and G. M. P. O’Har, “Radio sleep mode optimization in wireless sensor networks,” IEEE Trans. Mobile Comput., vol. 9, no. 7, pp. 955–968, July2010.
[CrossRef]

Kani, J.-i.

R. Kubo, J.-i. Kani, H. Ujikawa, T. Sakamoto, Y. Fujimoto, N. Yoshimoto, and H. Hadama, “Study and demonstration of sleep and adaptive link rate control mechanisms for energy efficient 10G-EPON,” J. Lightwave Technol., vol. 2, no. 9, pp. 716–729, Sept.2010.

Kazovsky, L.

S.-W. Wong, L. Valcarenghi, S.-H. Yen, D. R. Campelo, S. Yamashita, and L. Kazovsky, “Sleep mode for energy saving PONS: Advantages and drawbacks,” in IEEE GLOBECOM Workshops, 2009.

Y. Yan, S.-W. Wong, L. Valcarenghi, S.-H. Yen, D. R. Campelo, S. Yamashita, L. Kazovsky, and L. Dittmann, “Energy management mechanism for Ethernet passive optical networks (EPONs),” in IEEE ICC, 2010.

Kazovsky, L. G.

S.-W. Wong, S.-H. Yen, P. Afshar, S. Yamashita, and L. G. Kazovsky, “Demonstration of energy conserving TDM-PON with sleep mode ONU using fast clock recovery circuit,” in IEEE OFC, 2010.

Kubo, R.

R. Kubo, J.-i. Kani, H. Ujikawa, T. Sakamoto, Y. Fujimoto, N. Yoshimoto, and H. Hadama, “Study and demonstration of sleep and adaptive link rate control mechanisms for energy efficient 10G-EPON,” J. Lightwave Technol., vol. 2, no. 9, pp. 716–729, Sept.2010.

Lange, C.

C. Lange and A. Gladisch, “On the energy consumption of FTTH access networks,” in IEEE OFC, 2009.

Lee, J.

J. Lee, C. Rosenberg, and E. Chong, “Energy efficient schedulers in wireless networks: Design and optimization,” Mob. Netw. Appl., vol. 11, no. 3, pp. 377–389, June2006.
[CrossRef]

Mellia, M.

L. Chiaraviglio, M. Mellia, and F. Neri, “Reducing power consumption in backbone networks,” in IEEE ICC, 2009.

Meyer, S.

R. Gaudino, D. Cárdenas, M. Bellec, B. Charbonnier, N. Evanno, P. Guignard, S. Meyer, A. Pizzinat, I. Möllers, and D. Jäger, “Perspective in next-generation home networks: Toward optical solutions,” IEEE Commun. Mag., vol. 48, no. 2, pp. 39–47, Feb.2010.
[CrossRef]

Möllers, I.

R. Gaudino, D. Cárdenas, M. Bellec, B. Charbonnier, N. Evanno, P. Guignard, S. Meyer, A. Pizzinat, I. Möllers, and D. Jäger, “Perspective in next-generation home networks: Toward optical solutions,” IEEE Commun. Mag., vol. 48, no. 2, pp. 39–47, Feb.2010.
[CrossRef]

Mukherjee, B.

Neri, F.

L. Chiaraviglio, M. Mellia, and F. Neri, “Reducing power consumption in backbone networks,” in IEEE ICC, 2009.

O’Har, G. M. P.

R. Jurdak, A. G. Ruzzelli, and G. M. P. O’Har, “Radio sleep mode optimization in wireless sensor networks,” IEEE Trans. Mobile Comput., vol. 9, no. 7, pp. 955–968, July2010.
[CrossRef]

Onat, F. A.

F. A. Onat and I. Stojmenovic, “Generating random graphs for wireless actuator networks,” in IEEE Int. Symp. on a World of Wireless, Mobile and Multimedia Networks, June 2007, pp. 1–12.

Pizzinat, A.

R. Gaudino, D. Cárdenas, M. Bellec, B. Charbonnier, N. Evanno, P. Guignard, S. Meyer, A. Pizzinat, I. Möllers, and D. Jäger, “Perspective in next-generation home networks: Toward optical solutions,” IEEE Commun. Mag., vol. 48, no. 2, pp. 39–47, Feb.2010.
[CrossRef]

Qiao, D.

D. Qiao, M. C. Gursoy, and S. Velipasalar, “The impact of QoS constraints on the energy efficiency of fixed-rate wireless transmissions,” IEEE Trans. Wireless Commun., vol. 8, no. 12, pp. 5957–5969, Dec.2009.
[CrossRef]

Rengarajan, B.

B. Rengarajan, G. Rizzo, and M. Ajmone, “Bounds on QoS-constrained energy savings in cellular access networks with sleep modes,” in 23rd Int. Teletraffic Congress, 2011, pp. 47–54.

Rizzo, G.

B. Rengarajan, G. Rizzo, and M. Ajmone, “Bounds on QoS-constrained energy savings in cellular access networks with sleep modes,” in 23rd Int. Teletraffic Congress, 2011, pp. 47–54.

Rosenberg, C.

J. Lee, C. Rosenberg, and E. Chong, “Energy efficient schedulers in wireless networks: Design and optimization,” Mob. Netw. Appl., vol. 11, no. 3, pp. 377–389, June2006.
[CrossRef]

Ruzzelli, A. G.

R. Jurdak, A. G. Ruzzelli, and G. M. P. O’Har, “Radio sleep mode optimization in wireless sensor networks,” IEEE Trans. Mobile Comput., vol. 9, no. 7, pp. 955–968, July2010.
[CrossRef]

Sahni, S.

S. Sahni and T. Gonzalez, “P-complete approximation problems,” J. Assoc. Comput. Mach., vol. 23, pp. 555–565, 1976.
[CrossRef]

Sakamoto, T.

R. Kubo, J.-i. Kani, H. Ujikawa, T. Sakamoto, Y. Fujimoto, N. Yoshimoto, and H. Hadama, “Study and demonstration of sleep and adaptive link rate control mechanisms for energy efficient 10G-EPON,” J. Lightwave Technol., vol. 2, no. 9, pp. 716–729, Sept.2010.

Sarkar, S.

Schütz, G.

J. Coimbra, G. Schütz, and N. Correia, “Forwarding repeated game for end-to-end QoS support in fiber-wireless access networks,” in IEEE GLOBECOM, 2010.

Sivalingam, K. M.

C. E. Jones, K. M. Sivalingam, P. Agrawal, and J. C. Chen, “A survey of energy efficient network protocols for wireless networks,” Wireless Networks, vol. 7, no. 4, pp. 343–358, July2001.
[CrossRef]

Sorin, W. V.

Stojmenovic, I.

F. A. Onat and I. Stojmenovic, “Generating random graphs for wireless actuator networks,” in IEEE Int. Symp. on a World of Wireless, Mobile and Multimedia Networks, June 2007, pp. 1–12.

Tornatore, M.

Tucker, R. S.

Ujikawa, H.

R. Kubo, J.-i. Kani, H. Ujikawa, T. Sakamoto, Y. Fujimoto, N. Yoshimoto, and H. Hadama, “Study and demonstration of sleep and adaptive link rate control mechanisms for energy efficient 10G-EPON,” J. Lightwave Technol., vol. 2, no. 9, pp. 716–729, Sept.2010.

Valcarenghi, L.

S.-W. Wong, L. Valcarenghi, S.-H. Yen, D. R. Campelo, S. Yamashita, and L. Kazovsky, “Sleep mode for energy saving PONS: Advantages and drawbacks,” in IEEE GLOBECOM Workshops, 2009.

Y. Yan, S.-W. Wong, L. Valcarenghi, S.-H. Yen, D. R. Campelo, S. Yamashita, L. Kazovsky, and L. Dittmann, “Energy management mechanism for Ethernet passive optical networks (EPONs),” in IEEE ICC, 2010.

I. Cerutti, L. Valcarenghi, and P. Castoldi, “Power saving architectures for unidirectional WDM rings,” in IEEE OFC, 2009.

Velipasalar, S.

D. Qiao, M. C. Gursoy, and S. Velipasalar, “The impact of QoS constraints on the energy efficiency of fixed-rate wireless transmissions,” IEEE Trans. Wireless Commun., vol. 8, no. 12, pp. 5957–5969, Dec.2009.
[CrossRef]

Wang, L.

Z. Wang, W. Yu, and L. Wang, “Energy saving mechanism based on double-way polling DBA algorithm and ONU sleep mode for EPON,” in Int. Conf. on Electronic and Mechanical Engineering and Information Technology (EMEIT), 2011.

Wang, Z.

Z. Wang, W. Yu, and L. Wang, “Energy saving mechanism based on double-way polling DBA algorithm and ONU sleep mode for EPON,” in Int. Conf. on Electronic and Mechanical Engineering and Information Technology (EMEIT), 2011.

Wong, S.-W.

S.-W. Wong, L. Valcarenghi, S.-H. Yen, D. R. Campelo, S. Yamashita, and L. Kazovsky, “Sleep mode for energy saving PONS: Advantages and drawbacks,” in IEEE GLOBECOM Workshops, 2009.

S.-W. Wong, S.-H. Yen, P. Afshar, S. Yamashita, and L. G. Kazovsky, “Demonstration of energy conserving TDM-PON with sleep mode ONU using fast clock recovery circuit,” in IEEE OFC, 2010.

Y. Yan, S.-W. Wong, L. Valcarenghi, S.-H. Yen, D. R. Campelo, S. Yamashita, L. Kazovsky, and L. Dittmann, “Energy management mechanism for Ethernet passive optical networks (EPONs),” in IEEE ICC, 2010.

Yamashita, S.

Y. Yan, S.-W. Wong, L. Valcarenghi, S.-H. Yen, D. R. Campelo, S. Yamashita, L. Kazovsky, and L. Dittmann, “Energy management mechanism for Ethernet passive optical networks (EPONs),” in IEEE ICC, 2010.

S.-W. Wong, S.-H. Yen, P. Afshar, S. Yamashita, and L. G. Kazovsky, “Demonstration of energy conserving TDM-PON with sleep mode ONU using fast clock recovery circuit,” in IEEE OFC, 2010.

S.-W. Wong, L. Valcarenghi, S.-H. Yen, D. R. Campelo, S. Yamashita, and L. Kazovsky, “Sleep mode for energy saving PONS: Advantages and drawbacks,” in IEEE GLOBECOM Workshops, 2009.

Yan, Y.

Y. Yan, S.-W. Wong, L. Valcarenghi, S.-H. Yen, D. R. Campelo, S. Yamashita, L. Kazovsky, and L. Dittmann, “Energy management mechanism for Ethernet passive optical networks (EPONs),” in IEEE ICC, 2010.

Yen, S.-H.

Y. Yan, S.-W. Wong, L. Valcarenghi, S.-H. Yen, D. R. Campelo, S. Yamashita, L. Kazovsky, and L. Dittmann, “Energy management mechanism for Ethernet passive optical networks (EPONs),” in IEEE ICC, 2010.

S.-W. Wong, L. Valcarenghi, S.-H. Yen, D. R. Campelo, S. Yamashita, and L. Kazovsky, “Sleep mode for energy saving PONS: Advantages and drawbacks,” in IEEE GLOBECOM Workshops, 2009.

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Figures (8)

Fig. 1
Fig. 1

A fiber–wireless access architecture.

Fig. 2
Fig. 2

The sleep mode scheduling scheme.

Fig. 3
Fig. 3

Plot of packet delay assuming a router capacity of 100 Mbps.

Fig. 4
Fig. 4

The randomly generated networks used in the simulations.

Fig. 5
Fig. 5

Average network energy costs.

Fig. 6
Fig. 6

Average network packet delays.

Fig. 7
Fig. 7

Minimum and maximum network energy costs among all topology and gateway scenarios generated.

Fig. 8
Fig. 8

Minimum and maximum network packet delays among all topology and gateway scenarios generated.

Tables (3)

Tables Icon

Table I Average Cumulative Frequencies of Sleep Mode Schedulings Involved in the Solutions (%).

Tables Icon

Table II Average, Minimum and Maximum Network Energy Costs Obtained by the Two-Step Heuristic Approach (Joules).

Tables Icon

Table III Average, Minimum and Maximum Network Packet Delays Obtained by the Two-Step Heuristic Approach (seconds).

Equations (29)

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Minimize s v V { OLT } ρ v ( s ) .
l L : s ( l ) = v δ r , l l L : d ( l ) = v δ r , l = D r , if v = OLT , D r , if v = r , 0 , otherwise , r R , v V ,
l L : s ( l ) = v μ r , l l L : d ( l ) = v μ r , l = U r , if v = r , U r , if v = OLT , 0 , otherwise , r R , v V ,
γ o = max l L : s ( l ) = o r R δ r , l , l L : s ( l ) = o r R μ r , l , o O .
γ r = l L : s ( l ) = r d ( l ) = r r R ( μ r , l + δ r , l ) , r R .
v V { OLT } Δ v s ( s ) Δ T h , s S .
Δ v s ( s ) = 1 C v γ v , if s = 0 , 1 C v γ v + γ v C v C v γ v C v 1 s , otherwise , v V { OLT } ,
ω r ( s ) = s r × E R Wake × W R ,
ω o ( s ) = s o × E O Wake × W O ,
ρ r ( s ) = C R × P × E R Wake , if s r = 0 , or γ r C R , γ r × P × E R Wake + ω r ( s ) + P C R γ r s r × W R P E R Standby , otherwise , r R ,
ρ o ( s ) = C O × P × E O Wake , if s o = 0 , or γ o C O , γ o × P × E O Wake + ω o ( s ) + P C O γ o s o × W O P E O Sleep , otherwise , o O .
s , γ v , δ r , l , μ r , l 0 .
Minimize s v V OLT ρ v , s x v , s ,
s S x v , s = 1 , v V { OLT } ,
v V { OLT } Δ v , s x v , s Δ T h , s S ,
C R × P × E R Wake > γ r × P × E R Wake + ω r ( s r ) + C R γ r s r × W R P × P × E R Standby
γ r < C R s r × W R P .
C O × P × E O Wake > γ o × P × E O Wake + ω o ( s r ) + C O γ o s o × W O P × P × E O Sleep
γ o < C O s o × W O P .
Minimize: T R + α × T O ,
Subject to: γ r T R , r R ,
γ o T O , o O ,
r R l L δ r , l D r H × | R | ,
r R l L μ r , l U r H × | R | ,
T R , T O 0 ,
E O Wake = 30 . 8 × 1 0 9 J , E R Wake = 1 . 0 × 1 0 7 J , E O Sleep = 6 . 0 × 1 0 9 J , E R Standby = 8 . 0 × 1 0 10 J .
Byte time for wireless routers = 1 C R × P s ,
Byte time for ONUs = 1 C O × P s .
D max = v V { OLT } 1 C v γ v + γ v C v × C v γ v C v | S | .