Abstract

Owing to environmental concerns, reducing energy consumption of optical access networks has become an important problem for network designers. This paper focuses on reducing energy consumption of optical network units (ONUs) in an Ethernet passive optical network (EPON). In an EPON, the optical line terminal (OLT) located at the central office broadcasts the downstream traffic to all ONUs, each of which checks all arriving downstream packets so as to obtain the downstream packets destined to itself. Thus, receivers at ONUs always have to stay in the awake status and consume a large amount of energy. To address the downstream challenge, we propose a novel sleep control scheme that can efficiently put ONU receivers into sleep without modifying the standardized EPON media access control protocol. The proposed scheme contains two main parts: downstream traffic scheduling rules at the OLT and sleep control schemes at ONUs. By letting ONUs be aware of the downstream traffic scheduling rules, ONUs can infer their own downstream queue status and switch into the sleep status properly; by letting the OLT know the sleep control scheme implemented at ONUs, the OLT can accurately infer the sleep status of ONUs and buffer traffic of asleep ONUs accordingly. We also theoretically analyze the impacts of different parameters in the sleep control scheme on the delay and energy-saving performances by using semi-Markov chains. It is shown that, with proper settings of sleep control parameters, the proposed scheme can save as much as 50% of the ONU receiver energy.

© 2013 Optical Society of America

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References

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  1. K. J. Christensen, B. Gunaratne, and A. D. George, “The next frontier for communications networks: Power management,” Comput. Commun., vol.  27, no. 18, pp. 1758–1770, 2004.
    [CrossRef]
  2. M. Gupta and S. Singh, “Energy conservation with low power modes in Ethernet LAN environments,” in 26th IEEE Int. Conf. on Computer Communications (INFOCOM), Anchorage, AK, 2007, pp. 2451–2455.
  3. N. Ansari and J. Zhang, Media Access Control and Resource Allocation for Next Generation Passive Optical Networks. Springer, 2013.
  4. C. Lange, M. Braune, and N. Gieschen, “On the energy consumption of FTTB and FTTH access networks,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf., San Diego, CA, 2008, paper JWA105.
  5. J. Zhang and N. Ansari, “An application-oriented resource allocation scheme for EPON,” IEEE Syst. J., vol.  4, no. 4, pp. 424–431, 2010.
    [CrossRef]
  6. Y. Zhang, P. Chowdhury, M. Tornatore, and B. Mukherjee, “Energy efficiency in telecom optical networks,” IEEE Commun. Surv. Tutorials, vol.  12, no. 4, pp. 441–458, 2010.
    [CrossRef]
  7. J. Zhang, T. Wang, and N. Ansari, “Designing energy-efficient optical line terminal for TDM passive optical networks,” in 34th IEEE Sarnoff Symp., Princeton, NJ, 2011.
  8. S. Wong, L. Valcarenghi, S. Yen, D. Campelo, S. Yamashita, and L. Kazovsky, “Sleep mode for energy saving PONs: Advantages and drawbacks,” in IEEE GLOBECOM Workshops, 2009.
  9. M. Li, “Self-similarity and long-range dependence in teletraffic,” in Proc. 9th WSEAS Int. Conf. Multimedia Systems Signal Processing, 2009, pp. 19–24.
  10. R. Kubo, J. Kani, H. Ujikawa, T. Sakamoto, Y. Fujimoto, N. Yoshimoto, and H. Hadama, “Study and demonstration of sleep and adaptive link rate control mechanism for energy efficient 1G-EPON,” J. Opt. Commun. Netw., vol.  2, no. 9, pp. 716–729, 2010.
    [CrossRef]
  11. J. Zhang and N. Ansari, “Toward energy-efficient 1G-EPON and 10G-EPON with sleep-aware MAC control and scheduling,” IEEE Commun. Mag., vol.  49, no. 2, pp. S33–S38, 2011.
    [CrossRef]
  12. Y. Luo, S. Yin, N. Ansari, and T. Wang, “Resource management for broadband access over TDM PONs,” IEEE Netw., vol.  21, no. 5, pp. 20–27, 2007.
    [CrossRef]
  13. J. Mandin, “EPON power saving via sleep mode,” in IEEE P802. 3av 10GEPON Task Force Meeting, Seoul, South Korea, 2008.
  14. Y. Yan, S. Wong, L. Valcarenghi, S. Yen, D. Campelo, S. Yamashita, L. Kazovsky, and L. Dittman, “Energy management mechanism for Ethernet passive optical networks (EPONs),” in IEEE Int. Conf. Communications (ICC), South Africa, 2010.
  15. S. Lee and A. Chen, “Design and analysis of a novel energy efficient Ethernet passive optical network,” in Ninth Int. Conf. on Netw. (ICN), Menuires, France2010, pp. 6–9.
  16. Y. Yan and L. Dittman, “Energy efficiency in Ethernet passive optical networks (EPONs): Protocol design and performance evaluation,” J. Commun., vol.  6, no. 3, pp. 249–261, 2011.
  17. J. Zhang and N. Ansari, “Standards-compliant EPON sleep control for energy efficiency: Design and analysis,” in IEEE Int. Conf. Communications (ICC), Ottawa, Canada, 2012, pp. 2994–2998.
  18. S. Wong, S. Yen, P. Afshar, S. Yamashita, and L. Kazovsky, “Demonstration of energy conserving TDM-PON with sleep mode ONU using fast clock recovery circuit,” in Optical Fiber Communication Conf., San Diego, CA, 2010, paper OThW7.
  19. G. Kramer, “Generator of self-similar traffic,” 2004 [Online]. Available: http://glenkramer.com/ucdavis/code/trf_gen3.html .

2011 (2)

J. Zhang and N. Ansari, “Toward energy-efficient 1G-EPON and 10G-EPON with sleep-aware MAC control and scheduling,” IEEE Commun. Mag., vol.  49, no. 2, pp. S33–S38, 2011.
[CrossRef]

Y. Yan and L. Dittman, “Energy efficiency in Ethernet passive optical networks (EPONs): Protocol design and performance evaluation,” J. Commun., vol.  6, no. 3, pp. 249–261, 2011.

2010 (3)

J. Zhang and N. Ansari, “An application-oriented resource allocation scheme for EPON,” IEEE Syst. J., vol.  4, no. 4, pp. 424–431, 2010.
[CrossRef]

Y. Zhang, P. Chowdhury, M. Tornatore, and B. Mukherjee, “Energy efficiency in telecom optical networks,” IEEE Commun. Surv. Tutorials, vol.  12, no. 4, pp. 441–458, 2010.
[CrossRef]

R. Kubo, J. Kani, H. Ujikawa, T. Sakamoto, Y. Fujimoto, N. Yoshimoto, and H. Hadama, “Study and demonstration of sleep and adaptive link rate control mechanism for energy efficient 1G-EPON,” J. Opt. Commun. Netw., vol.  2, no. 9, pp. 716–729, 2010.
[CrossRef]

2007 (1)

Y. Luo, S. Yin, N. Ansari, and T. Wang, “Resource management for broadband access over TDM PONs,” IEEE Netw., vol.  21, no. 5, pp. 20–27, 2007.
[CrossRef]

2004 (1)

K. J. Christensen, B. Gunaratne, and A. D. George, “The next frontier for communications networks: Power management,” Comput. Commun., vol.  27, no. 18, pp. 1758–1770, 2004.
[CrossRef]

Afshar, P.

S. Wong, S. Yen, P. Afshar, S. Yamashita, and L. Kazovsky, “Demonstration of energy conserving TDM-PON with sleep mode ONU using fast clock recovery circuit,” in Optical Fiber Communication Conf., San Diego, CA, 2010, paper OThW7.

Ansari, N.

J. Zhang and N. Ansari, “Toward energy-efficient 1G-EPON and 10G-EPON with sleep-aware MAC control and scheduling,” IEEE Commun. Mag., vol.  49, no. 2, pp. S33–S38, 2011.
[CrossRef]

J. Zhang and N. Ansari, “An application-oriented resource allocation scheme for EPON,” IEEE Syst. J., vol.  4, no. 4, pp. 424–431, 2010.
[CrossRef]

Y. Luo, S. Yin, N. Ansari, and T. Wang, “Resource management for broadband access over TDM PONs,” IEEE Netw., vol.  21, no. 5, pp. 20–27, 2007.
[CrossRef]

J. Zhang, T. Wang, and N. Ansari, “Designing energy-efficient optical line terminal for TDM passive optical networks,” in 34th IEEE Sarnoff Symp., Princeton, NJ, 2011.

N. Ansari and J. Zhang, Media Access Control and Resource Allocation for Next Generation Passive Optical Networks. Springer, 2013.

J. Zhang and N. Ansari, “Standards-compliant EPON sleep control for energy efficiency: Design and analysis,” in IEEE Int. Conf. Communications (ICC), Ottawa, Canada, 2012, pp. 2994–2998.

Braune, M.

C. Lange, M. Braune, and N. Gieschen, “On the energy consumption of FTTB and FTTH access networks,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf., San Diego, CA, 2008, paper JWA105.

Campelo, D.

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

Y. Yan, S. Wong, L. Valcarenghi, S. Yen, D. Campelo, S. Yamashita, L. Kazovsky, and L. Dittman, “Energy management mechanism for Ethernet passive optical networks (EPONs),” in IEEE Int. Conf. Communications (ICC), South Africa, 2010.

Chen, A.

S. Lee and A. Chen, “Design and analysis of a novel energy efficient Ethernet passive optical network,” in Ninth Int. Conf. on Netw. (ICN), Menuires, France2010, pp. 6–9.

Chowdhury, P.

Y. Zhang, P. Chowdhury, M. Tornatore, and B. Mukherjee, “Energy efficiency in telecom optical networks,” IEEE Commun. Surv. Tutorials, vol.  12, no. 4, pp. 441–458, 2010.
[CrossRef]

Christensen, K. J.

K. J. Christensen, B. Gunaratne, and A. D. George, “The next frontier for communications networks: Power management,” Comput. Commun., vol.  27, no. 18, pp. 1758–1770, 2004.
[CrossRef]

Dittman, L.

Y. Yan and L. Dittman, “Energy efficiency in Ethernet passive optical networks (EPONs): Protocol design and performance evaluation,” J. Commun., vol.  6, no. 3, pp. 249–261, 2011.

Y. Yan, S. Wong, L. Valcarenghi, S. Yen, D. Campelo, S. Yamashita, L. Kazovsky, and L. Dittman, “Energy management mechanism for Ethernet passive optical networks (EPONs),” in IEEE Int. Conf. Communications (ICC), South Africa, 2010.

Fujimoto, Y.

George, A. D.

K. J. Christensen, B. Gunaratne, and A. D. George, “The next frontier for communications networks: Power management,” Comput. Commun., vol.  27, no. 18, pp. 1758–1770, 2004.
[CrossRef]

Gieschen, N.

C. Lange, M. Braune, and N. Gieschen, “On the energy consumption of FTTB and FTTH access networks,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf., San Diego, CA, 2008, paper JWA105.

Gunaratne, B.

K. J. Christensen, B. Gunaratne, and A. D. George, “The next frontier for communications networks: Power management,” Comput. Commun., vol.  27, no. 18, pp. 1758–1770, 2004.
[CrossRef]

Gupta, M.

M. Gupta and S. Singh, “Energy conservation with low power modes in Ethernet LAN environments,” in 26th IEEE Int. Conf. on Computer Communications (INFOCOM), Anchorage, AK, 2007, pp. 2451–2455.

Hadama, H.

Kani, J.

Kazovsky, L.

Y. Yan, S. Wong, L. Valcarenghi, S. Yen, D. Campelo, S. Yamashita, L. Kazovsky, and L. Dittman, “Energy management mechanism for Ethernet passive optical networks (EPONs),” in IEEE Int. Conf. Communications (ICC), South Africa, 2010.

S. Wong, S. Yen, P. Afshar, S. Yamashita, and L. Kazovsky, “Demonstration of energy conserving TDM-PON with sleep mode ONU using fast clock recovery circuit,” in Optical Fiber Communication Conf., San Diego, CA, 2010, paper OThW7.

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

Kubo, R.

Lange, C.

C. Lange, M. Braune, and N. Gieschen, “On the energy consumption of FTTB and FTTH access networks,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf., San Diego, CA, 2008, paper JWA105.

Lee, S.

S. Lee and A. Chen, “Design and analysis of a novel energy efficient Ethernet passive optical network,” in Ninth Int. Conf. on Netw. (ICN), Menuires, France2010, pp. 6–9.

Li, M.

M. Li, “Self-similarity and long-range dependence in teletraffic,” in Proc. 9th WSEAS Int. Conf. Multimedia Systems Signal Processing, 2009, pp. 19–24.

Luo, Y.

Y. Luo, S. Yin, N. Ansari, and T. Wang, “Resource management for broadband access over TDM PONs,” IEEE Netw., vol.  21, no. 5, pp. 20–27, 2007.
[CrossRef]

Mandin, J.

J. Mandin, “EPON power saving via sleep mode,” in IEEE P802. 3av 10GEPON Task Force Meeting, Seoul, South Korea, 2008.

Mukherjee, B.

Y. Zhang, P. Chowdhury, M. Tornatore, and B. Mukherjee, “Energy efficiency in telecom optical networks,” IEEE Commun. Surv. Tutorials, vol.  12, no. 4, pp. 441–458, 2010.
[CrossRef]

Sakamoto, T.

Singh, S.

M. Gupta and S. Singh, “Energy conservation with low power modes in Ethernet LAN environments,” in 26th IEEE Int. Conf. on Computer Communications (INFOCOM), Anchorage, AK, 2007, pp. 2451–2455.

Tornatore, M.

Y. Zhang, P. Chowdhury, M. Tornatore, and B. Mukherjee, “Energy efficiency in telecom optical networks,” IEEE Commun. Surv. Tutorials, vol.  12, no. 4, pp. 441–458, 2010.
[CrossRef]

Ujikawa, H.

Valcarenghi, L.

Y. Yan, S. Wong, L. Valcarenghi, S. Yen, D. Campelo, S. Yamashita, L. Kazovsky, and L. Dittman, “Energy management mechanism for Ethernet passive optical networks (EPONs),” in IEEE Int. Conf. Communications (ICC), South Africa, 2010.

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

Wang, T.

Y. Luo, S. Yin, N. Ansari, and T. Wang, “Resource management for broadband access over TDM PONs,” IEEE Netw., vol.  21, no. 5, pp. 20–27, 2007.
[CrossRef]

J. Zhang, T. Wang, and N. Ansari, “Designing energy-efficient optical line terminal for TDM passive optical networks,” in 34th IEEE Sarnoff Symp., Princeton, NJ, 2011.

Wong, S.

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

Y. Yan, S. Wong, L. Valcarenghi, S. Yen, D. Campelo, S. Yamashita, L. Kazovsky, and L. Dittman, “Energy management mechanism for Ethernet passive optical networks (EPONs),” in IEEE Int. Conf. Communications (ICC), South Africa, 2010.

S. Wong, S. Yen, P. Afshar, S. Yamashita, and L. Kazovsky, “Demonstration of energy conserving TDM-PON with sleep mode ONU using fast clock recovery circuit,” in Optical Fiber Communication Conf., San Diego, CA, 2010, paper OThW7.

Yamashita, S.

S. Wong, S. Yen, P. Afshar, S. Yamashita, and L. Kazovsky, “Demonstration of energy conserving TDM-PON with sleep mode ONU using fast clock recovery circuit,” in Optical Fiber Communication Conf., San Diego, CA, 2010, paper OThW7.

Y. Yan, S. Wong, L. Valcarenghi, S. Yen, D. Campelo, S. Yamashita, L. Kazovsky, and L. Dittman, “Energy management mechanism for Ethernet passive optical networks (EPONs),” in IEEE Int. Conf. Communications (ICC), South Africa, 2010.

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

Yan, Y.

Y. Yan and L. Dittman, “Energy efficiency in Ethernet passive optical networks (EPONs): Protocol design and performance evaluation,” J. Commun., vol.  6, no. 3, pp. 249–261, 2011.

Y. Yan, S. Wong, L. Valcarenghi, S. Yen, D. Campelo, S. Yamashita, L. Kazovsky, and L. Dittman, “Energy management mechanism for Ethernet passive optical networks (EPONs),” in IEEE Int. Conf. Communications (ICC), South Africa, 2010.

Yen, S.

Y. Yan, S. Wong, L. Valcarenghi, S. Yen, D. Campelo, S. Yamashita, L. Kazovsky, and L. Dittman, “Energy management mechanism for Ethernet passive optical networks (EPONs),” in IEEE Int. Conf. Communications (ICC), South Africa, 2010.

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

S. Wong, S. Yen, P. Afshar, S. Yamashita, and L. Kazovsky, “Demonstration of energy conserving TDM-PON with sleep mode ONU using fast clock recovery circuit,” in Optical Fiber Communication Conf., San Diego, CA, 2010, paper OThW7.

Yin, S.

Y. Luo, S. Yin, N. Ansari, and T. Wang, “Resource management for broadband access over TDM PONs,” IEEE Netw., vol.  21, no. 5, pp. 20–27, 2007.
[CrossRef]

Yoshimoto, N.

Zhang, J.

J. Zhang and N. Ansari, “Toward energy-efficient 1G-EPON and 10G-EPON with sleep-aware MAC control and scheduling,” IEEE Commun. Mag., vol.  49, no. 2, pp. S33–S38, 2011.
[CrossRef]

J. Zhang and N. Ansari, “An application-oriented resource allocation scheme for EPON,” IEEE Syst. J., vol.  4, no. 4, pp. 424–431, 2010.
[CrossRef]

N. Ansari and J. Zhang, Media Access Control and Resource Allocation for Next Generation Passive Optical Networks. Springer, 2013.

J. Zhang, T. Wang, and N. Ansari, “Designing energy-efficient optical line terminal for TDM passive optical networks,” in 34th IEEE Sarnoff Symp., Princeton, NJ, 2011.

J. Zhang and N. Ansari, “Standards-compliant EPON sleep control for energy efficiency: Design and analysis,” in IEEE Int. Conf. Communications (ICC), Ottawa, Canada, 2012, pp. 2994–2998.

Zhang, Y.

Y. Zhang, P. Chowdhury, M. Tornatore, and B. Mukherjee, “Energy efficiency in telecom optical networks,” IEEE Commun. Surv. Tutorials, vol.  12, no. 4, pp. 441–458, 2010.
[CrossRef]

Comput. Commun. (1)

K. J. Christensen, B. Gunaratne, and A. D. George, “The next frontier for communications networks: Power management,” Comput. Commun., vol.  27, no. 18, pp. 1758–1770, 2004.
[CrossRef]

IEEE Commun. Mag. (1)

J. Zhang and N. Ansari, “Toward energy-efficient 1G-EPON and 10G-EPON with sleep-aware MAC control and scheduling,” IEEE Commun. Mag., vol.  49, no. 2, pp. S33–S38, 2011.
[CrossRef]

IEEE Commun. Surv. Tutorials (1)

Y. Zhang, P. Chowdhury, M. Tornatore, and B. Mukherjee, “Energy efficiency in telecom optical networks,” IEEE Commun. Surv. Tutorials, vol.  12, no. 4, pp. 441–458, 2010.
[CrossRef]

IEEE Netw. (1)

Y. Luo, S. Yin, N. Ansari, and T. Wang, “Resource management for broadband access over TDM PONs,” IEEE Netw., vol.  21, no. 5, pp. 20–27, 2007.
[CrossRef]

IEEE Syst. J. (1)

J. Zhang and N. Ansari, “An application-oriented resource allocation scheme for EPON,” IEEE Syst. J., vol.  4, no. 4, pp. 424–431, 2010.
[CrossRef]

J. Commun. (1)

Y. Yan and L. Dittman, “Energy efficiency in Ethernet passive optical networks (EPONs): Protocol design and performance evaluation,” J. Commun., vol.  6, no. 3, pp. 249–261, 2011.

J. Opt. Commun. Netw. (1)

Other (12)

J. Zhang and N. Ansari, “Standards-compliant EPON sleep control for energy efficiency: Design and analysis,” in IEEE Int. Conf. Communications (ICC), Ottawa, Canada, 2012, pp. 2994–2998.

S. Wong, S. Yen, P. Afshar, S. Yamashita, and L. Kazovsky, “Demonstration of energy conserving TDM-PON with sleep mode ONU using fast clock recovery circuit,” in Optical Fiber Communication Conf., San Diego, CA, 2010, paper OThW7.

G. Kramer, “Generator of self-similar traffic,” 2004 [Online]. Available: http://glenkramer.com/ucdavis/code/trf_gen3.html .

J. Mandin, “EPON power saving via sleep mode,” in IEEE P802. 3av 10GEPON Task Force Meeting, Seoul, South Korea, 2008.

Y. Yan, S. Wong, L. Valcarenghi, S. Yen, D. Campelo, S. Yamashita, L. Kazovsky, and L. Dittman, “Energy management mechanism for Ethernet passive optical networks (EPONs),” in IEEE Int. Conf. Communications (ICC), South Africa, 2010.

S. Lee and A. Chen, “Design and analysis of a novel energy efficient Ethernet passive optical network,” in Ninth Int. Conf. on Netw. (ICN), Menuires, France2010, pp. 6–9.

J. Zhang, T. Wang, and N. Ansari, “Designing energy-efficient optical line terminal for TDM passive optical networks,” in 34th IEEE Sarnoff Symp., Princeton, NJ, 2011.

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

M. Li, “Self-similarity and long-range dependence in teletraffic,” in Proc. 9th WSEAS Int. Conf. Multimedia Systems Signal Processing, 2009, pp. 19–24.

M. Gupta and S. Singh, “Energy conservation with low power modes in Ethernet LAN environments,” in 26th IEEE Int. Conf. on Computer Communications (INFOCOM), Anchorage, AK, 2007, pp. 2451–2455.

N. Ansari and J. Zhang, Media Access Control and Resource Allocation for Next Generation Passive Optical Networks. Springer, 2013.

C. Lange, M. Braune, and N. Gieschen, “On the energy consumption of FTTB and FTTH access networks,” in Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf., San Diego, CA, 2008, paper JWA105.

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Figures (10)

Fig. 1.
Fig. 1.

Downstream transmission in EPON.

Fig. 2.
Fig. 2.

Sleep control at ONU 1.

Fig. 3.
Fig. 3.

Flow chart of the sleep control scheme implemented at both the OLT and ONUs.

Fig. 4.
Fig. 4.

State transitions in the Markov chain.

Fig. 5.
Fig. 5.

Energy saving and delay versus traffic arrival rate for Poisson traffic.

Fig. 6.
Fig. 6.

Energy saving and delay versus the number of listening cycles for Poisson traffic.

Fig. 7.
Fig. 7.

Energy saving and delay versus the number of sleep cycles for Poisson traffic.

Fig. 8.
Fig. 8.

Energy saving and delay versus traffic arrival rate for self-similar traffic.

Fig. 9.
Fig. 9.

Energy saving and delay versus the number of listening cycles for self-similar traffic.

Fig. 10.
Fig. 10.

Energy saving and delay versus the number of sleep cycles for self-similar traffic.

Equations (14)

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

pa(β,γ)=eλγT·(λ·γT)β/β!,
pd(β,γ)=eμγT·(μ·γT)β/β!,
P(S)[i=1pr{SA(i)}+pr{SL(1)}]=P(L(x))pr{L(x)S}.
P(L(x))[i=0pr{L(x)A(i)}+pr{L(x)S}]=P(L(x1))pr{L(x1)L(x)}.
P(L(j))[i=0pr{L(j)A(i)}+pr{L(j)L(j+1)}]=P(L(j1))pr{L(j1)L(j)}(1<j<x),
P(L(1))[i=0pr{L(1)A(i)}+pr{L(1)L(2)}]=P(A(0))pr{A(0)L(1)}+P(S)pr{SL(1)},
P(A(i))jipr{A(i)A(j)}=jiP(A(j))pr{A(j)A(i)}+jiP(L(j))pr{L(j)A(i)}+P(S)pr{SA(i)},
P(A(0))[i0pr{A(0)A(i)}+pr{A(0)L(1)}]=i0P(A(i))pr{A(i)A(0)}+jiP(L(j))pr{L(j)A(0)}.
P(S)+i=0+P(A(i))+j=1xP(L(j))=1.
W(A)·i=0P(A(i))+W(L)·j=1xP(L(j))+y·W(S)·P(S).
E[δ|S]·P(S)+E[δ|L]·j=1P(L(j))+E[δ|A]·i=0P(A(i)).
E[δ|S]=y/2·T+i=1[pa(i,y)(i1)·1/μ].
E[δ|L]=i=1[pa(i,x)(i1)·1/μ],
E[δ|A]=i=1[pa(i,z)(i1)·1/μ].