Abstract

This paper proposes an energy-saving passive optical network framework (ESPON) that aims to incorporate optical network unit (ONU) sleep/doze mode into dynamic bandwidth allocation (DBA) algorithms to reduce ONU energy consumption. In the ESPON, the optical line terminal (OLT) schedules both downstream (DS) and upstream (US) transmissions in the same slot in an online and dynamic fashion whereas the ONU enters sleep mode outside the slot. The ONU sleep time is maximized based on both DS and US traffic. Moreover, during the slot, the ONU might enter doze mode when only its transmitter is idle to further improve energy efficiency. The scheduling order of data transmission, control message exchange, sleep period, and doze period defines an energy-efficient scheme under the ESPON. Three schemes are designed and evaluated in an extensive FPGA-based evaluation. Results show that whilst all the schemes significantly save ONU energy for different evaluation scenarios, the scheduling order has great impact on their performance. In addition, the ESPON allows for a scheduling order that saves ONU energy independently of the network reach.

© 2014 Optical Society of America

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References

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  1. ITU-T G.Sup 45, GPON power conservation (2009).
  2. ITU-T G.987.x-series recommendations, 10-Gigabit-capable passive optical networks XG-PON (2010).
  3. IEEE Std 1904.1-2013, IEEE standard for service interoperability in Ethernet passive optical networks (2013).
  4. 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 Proc. of IEEE International Conference on Communications (ICC), (2010).
  5. A. R. Dhaini, P.-H. Ho, and G. Shen, “Toward green next-generation passive optical networks,” IEEE Commun. Mag. 49(11), 94–101 (2011).
    [Crossref]
  6. L. Zhang, Y. Liu, L. Guo, and X. Gong, “Energy-saving scheme based on downstream packet scheduling in Ethernet passive optical networks,” Opt. Fiber Technol. 19(2), 169–178 (2013).
    [Crossref]
  7. M. Bokhari and P. Saengudomlert, “Analysis of mean packet delay for upstream transmissions in passive optical networks with sleep mode,” Opt. Switch. Netw. 10(3), 195–210 (2013).
    [Crossref]
  8. S. H. S. Newaz, A. Cuevas, G. M. Lee, N. Crespi, and J. K. Choi, “Adaptive delay-aware energy efficient TDM-PON,” Comput. Netw. 57(7), 1577–1596 (2013).
    [Crossref]
  9. A. Dixit, B. Lannoo, D. Colle, M. Pickavet, and P. Demeester, “ONU power saving modes in next generation optical access networks: progress, efficiency and challenges,” Opt. Express 20(26), B52–B63 (2012).
    [Crossref] [PubMed]
  10. J. Kani, “Power saving techniques and mechanisms for optical access networks systems,” J. Lightwave Technol. 31(4), 563–570 (2013).
    [Crossref]
  11. A. Dixit, B. Lannoo, D. Colle, M. Pickavet, and P. Demeester, “Novel DBA algorithm for energy efficiency in TWDM-PONs,” in Proc. of Optical Communication (ECOC), (2013).
  12. E. Wong, M. Muller, M. P. I. Dias, C. A. Chan, and M. C. Amann, “Energy-efficiency of optical network units with vertical-cavity surface-emitting lasers,” Opt. Express 20(14), 14960–14970 (2012).
    [Crossref] [PubMed]
  13. IEEE Std 802.3av, 10Gb/s Ethernet passive optical network (10G-EPON) (2009).
  14. A. Mercian, M. P. McGarry, and M. Reisslein, “Impact of report message scheduling (RMS) in 1G/10G EPON and GPON,” Opt. Switch. Netw. 12(0), 1–13 (2014).
    [Crossref]
  15. D. P. Van, L. Valcarenghi, M. Chincoli, and P. Castoldi, “Experimental evaluation of a sleep-aware dynamic bandwidth allocation in a multi-ONU 10G-EPON testbed,” Opt. Switch. Netw. 14(Part 1), 11–24 (2014).
    [Crossref]
  16. D. Pham Van, M. P. I. Dias, K. Kondepu, L. Valcarenghi, P. Castoldi, and E. Wong, “Energy-efficient dynamic bandwidth allocation for long-reach passive optical networks,” in Proc. of IEEE/OSA Optoelectronics and Communications Conference/Australian Conference on Optical Fibre Technology (OECC/ACOFT), (2014).
  17. ITU-T Y.1541 recommendations, Network performance objectives for IP-based services (2011).
  18. J. R. Ferguson, M. Reisslein, and M. P. McGarry, “Online excess bandwidth distribution for Ethernet passive optical networks,” J. Opt. Netw. 8(4), 358–369 (2009).
    [Crossref]

2014 (2)

A. Mercian, M. P. McGarry, and M. Reisslein, “Impact of report message scheduling (RMS) in 1G/10G EPON and GPON,” Opt. Switch. Netw. 12(0), 1–13 (2014).
[Crossref]

D. P. Van, L. Valcarenghi, M. Chincoli, and P. Castoldi, “Experimental evaluation of a sleep-aware dynamic bandwidth allocation in a multi-ONU 10G-EPON testbed,” Opt. Switch. Netw. 14(Part 1), 11–24 (2014).
[Crossref]

2013 (4)

J. Kani, “Power saving techniques and mechanisms for optical access networks systems,” J. Lightwave Technol. 31(4), 563–570 (2013).
[Crossref]

L. Zhang, Y. Liu, L. Guo, and X. Gong, “Energy-saving scheme based on downstream packet scheduling in Ethernet passive optical networks,” Opt. Fiber Technol. 19(2), 169–178 (2013).
[Crossref]

M. Bokhari and P. Saengudomlert, “Analysis of mean packet delay for upstream transmissions in passive optical networks with sleep mode,” Opt. Switch. Netw. 10(3), 195–210 (2013).
[Crossref]

S. H. S. Newaz, A. Cuevas, G. M. Lee, N. Crespi, and J. K. Choi, “Adaptive delay-aware energy efficient TDM-PON,” Comput. Netw. 57(7), 1577–1596 (2013).
[Crossref]

2012 (2)

2011 (1)

A. R. Dhaini, P.-H. Ho, and G. Shen, “Toward green next-generation passive optical networks,” IEEE Commun. Mag. 49(11), 94–101 (2011).
[Crossref]

2009 (1)

Amann, M. C.

Bokhari, M.

M. Bokhari and P. Saengudomlert, “Analysis of mean packet delay for upstream transmissions in passive optical networks with sleep mode,” Opt. Switch. Netw. 10(3), 195–210 (2013).
[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 Proc. of IEEE International Conference on Communications (ICC), (2010).

Castoldi, P.

D. P. Van, L. Valcarenghi, M. Chincoli, and P. Castoldi, “Experimental evaluation of a sleep-aware dynamic bandwidth allocation in a multi-ONU 10G-EPON testbed,” Opt. Switch. Netw. 14(Part 1), 11–24 (2014).
[Crossref]

D. Pham Van, M. P. I. Dias, K. Kondepu, L. Valcarenghi, P. Castoldi, and E. Wong, “Energy-efficient dynamic bandwidth allocation for long-reach passive optical networks,” in Proc. of IEEE/OSA Optoelectronics and Communications Conference/Australian Conference on Optical Fibre Technology (OECC/ACOFT), (2014).

Chan, C. A.

Chincoli, M.

D. P. Van, L. Valcarenghi, M. Chincoli, and P. Castoldi, “Experimental evaluation of a sleep-aware dynamic bandwidth allocation in a multi-ONU 10G-EPON testbed,” Opt. Switch. Netw. 14(Part 1), 11–24 (2014).
[Crossref]

Choi, J. K.

S. H. S. Newaz, A. Cuevas, G. M. Lee, N. Crespi, and J. K. Choi, “Adaptive delay-aware energy efficient TDM-PON,” Comput. Netw. 57(7), 1577–1596 (2013).
[Crossref]

Colle, D.

A. Dixit, B. Lannoo, D. Colle, M. Pickavet, and P. Demeester, “ONU power saving modes in next generation optical access networks: progress, efficiency and challenges,” Opt. Express 20(26), B52–B63 (2012).
[Crossref] [PubMed]

A. Dixit, B. Lannoo, D. Colle, M. Pickavet, and P. Demeester, “Novel DBA algorithm for energy efficiency in TWDM-PONs,” in Proc. of Optical Communication (ECOC), (2013).

Crespi, N.

S. H. S. Newaz, A. Cuevas, G. M. Lee, N. Crespi, and J. K. Choi, “Adaptive delay-aware energy efficient TDM-PON,” Comput. Netw. 57(7), 1577–1596 (2013).
[Crossref]

Cuevas, A.

S. H. S. Newaz, A. Cuevas, G. M. Lee, N. Crespi, and J. K. Choi, “Adaptive delay-aware energy efficient TDM-PON,” Comput. Netw. 57(7), 1577–1596 (2013).
[Crossref]

Demeester, P.

A. Dixit, B. Lannoo, D. Colle, M. Pickavet, and P. Demeester, “ONU power saving modes in next generation optical access networks: progress, efficiency and challenges,” Opt. Express 20(26), B52–B63 (2012).
[Crossref] [PubMed]

A. Dixit, B. Lannoo, D. Colle, M. Pickavet, and P. Demeester, “Novel DBA algorithm for energy efficiency in TWDM-PONs,” in Proc. of Optical Communication (ECOC), (2013).

Dhaini, A. R.

A. R. Dhaini, P.-H. Ho, and G. Shen, “Toward green next-generation passive optical networks,” IEEE Commun. Mag. 49(11), 94–101 (2011).
[Crossref]

Dias, M. P. I.

E. Wong, M. Muller, M. P. I. Dias, C. A. Chan, and M. C. Amann, “Energy-efficiency of optical network units with vertical-cavity surface-emitting lasers,” Opt. Express 20(14), 14960–14970 (2012).
[Crossref] [PubMed]

D. Pham Van, M. P. I. Dias, K. Kondepu, L. Valcarenghi, P. Castoldi, and E. Wong, “Energy-efficient dynamic bandwidth allocation for long-reach passive optical networks,” in Proc. of IEEE/OSA Optoelectronics and Communications Conference/Australian Conference on Optical Fibre Technology (OECC/ACOFT), (2014).

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 Proc. of IEEE International Conference on Communications (ICC), (2010).

Dixit, A.

A. Dixit, B. Lannoo, D. Colle, M. Pickavet, and P. Demeester, “ONU power saving modes in next generation optical access networks: progress, efficiency and challenges,” Opt. Express 20(26), B52–B63 (2012).
[Crossref] [PubMed]

A. Dixit, B. Lannoo, D. Colle, M. Pickavet, and P. Demeester, “Novel DBA algorithm for energy efficiency in TWDM-PONs,” in Proc. of Optical Communication (ECOC), (2013).

Ferguson, J. R.

Gong, X.

L. Zhang, Y. Liu, L. Guo, and X. Gong, “Energy-saving scheme based on downstream packet scheduling in Ethernet passive optical networks,” Opt. Fiber Technol. 19(2), 169–178 (2013).
[Crossref]

Guo, L.

L. Zhang, Y. Liu, L. Guo, and X. Gong, “Energy-saving scheme based on downstream packet scheduling in Ethernet passive optical networks,” Opt. Fiber Technol. 19(2), 169–178 (2013).
[Crossref]

Ho, P.-H.

A. R. Dhaini, P.-H. Ho, and G. Shen, “Toward green next-generation passive optical networks,” IEEE Commun. Mag. 49(11), 94–101 (2011).
[Crossref]

Kani, J.

Kazovsky, 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 Proc. of IEEE International Conference on Communications (ICC), (2010).

Kondepu, K.

D. Pham Van, M. P. I. Dias, K. Kondepu, L. Valcarenghi, P. Castoldi, and E. Wong, “Energy-efficient dynamic bandwidth allocation for long-reach passive optical networks,” in Proc. of IEEE/OSA Optoelectronics and Communications Conference/Australian Conference on Optical Fibre Technology (OECC/ACOFT), (2014).

Lannoo, B.

A. Dixit, B. Lannoo, D. Colle, M. Pickavet, and P. Demeester, “ONU power saving modes in next generation optical access networks: progress, efficiency and challenges,” Opt. Express 20(26), B52–B63 (2012).
[Crossref] [PubMed]

A. Dixit, B. Lannoo, D. Colle, M. Pickavet, and P. Demeester, “Novel DBA algorithm for energy efficiency in TWDM-PONs,” in Proc. of Optical Communication (ECOC), (2013).

Lee, G. M.

S. H. S. Newaz, A. Cuevas, G. M. Lee, N. Crespi, and J. K. Choi, “Adaptive delay-aware energy efficient TDM-PON,” Comput. Netw. 57(7), 1577–1596 (2013).
[Crossref]

Liu, Y.

L. Zhang, Y. Liu, L. Guo, and X. Gong, “Energy-saving scheme based on downstream packet scheduling in Ethernet passive optical networks,” Opt. Fiber Technol. 19(2), 169–178 (2013).
[Crossref]

McGarry, M. P.

A. Mercian, M. P. McGarry, and M. Reisslein, “Impact of report message scheduling (RMS) in 1G/10G EPON and GPON,” Opt. Switch. Netw. 12(0), 1–13 (2014).
[Crossref]

J. R. Ferguson, M. Reisslein, and M. P. McGarry, “Online excess bandwidth distribution for Ethernet passive optical networks,” J. Opt. Netw. 8(4), 358–369 (2009).
[Crossref]

Mercian, A.

A. Mercian, M. P. McGarry, and M. Reisslein, “Impact of report message scheduling (RMS) in 1G/10G EPON and GPON,” Opt. Switch. Netw. 12(0), 1–13 (2014).
[Crossref]

Muller, M.

Newaz, S. H. S.

S. H. S. Newaz, A. Cuevas, G. M. Lee, N. Crespi, and J. K. Choi, “Adaptive delay-aware energy efficient TDM-PON,” Comput. Netw. 57(7), 1577–1596 (2013).
[Crossref]

Pham Van, D.

D. Pham Van, M. P. I. Dias, K. Kondepu, L. Valcarenghi, P. Castoldi, and E. Wong, “Energy-efficient dynamic bandwidth allocation for long-reach passive optical networks,” in Proc. of IEEE/OSA Optoelectronics and Communications Conference/Australian Conference on Optical Fibre Technology (OECC/ACOFT), (2014).

Pickavet, M.

A. Dixit, B. Lannoo, D. Colle, M. Pickavet, and P. Demeester, “ONU power saving modes in next generation optical access networks: progress, efficiency and challenges,” Opt. Express 20(26), B52–B63 (2012).
[Crossref] [PubMed]

A. Dixit, B. Lannoo, D. Colle, M. Pickavet, and P. Demeester, “Novel DBA algorithm for energy efficiency in TWDM-PONs,” in Proc. of Optical Communication (ECOC), (2013).

Reisslein, M.

A. Mercian, M. P. McGarry, and M. Reisslein, “Impact of report message scheduling (RMS) in 1G/10G EPON and GPON,” Opt. Switch. Netw. 12(0), 1–13 (2014).
[Crossref]

J. R. Ferguson, M. Reisslein, and M. P. McGarry, “Online excess bandwidth distribution for Ethernet passive optical networks,” J. Opt. Netw. 8(4), 358–369 (2009).
[Crossref]

Saengudomlert, P.

M. Bokhari and P. Saengudomlert, “Analysis of mean packet delay for upstream transmissions in passive optical networks with sleep mode,” Opt. Switch. Netw. 10(3), 195–210 (2013).
[Crossref]

Shen, G.

A. R. Dhaini, P.-H. Ho, and G. Shen, “Toward green next-generation passive optical networks,” IEEE Commun. Mag. 49(11), 94–101 (2011).
[Crossref]

Valcarenghi, L.

D. P. Van, L. Valcarenghi, M. Chincoli, and P. Castoldi, “Experimental evaluation of a sleep-aware dynamic bandwidth allocation in a multi-ONU 10G-EPON testbed,” Opt. Switch. Netw. 14(Part 1), 11–24 (2014).
[Crossref]

D. Pham Van, M. P. I. Dias, K. Kondepu, L. Valcarenghi, P. Castoldi, and E. Wong, “Energy-efficient dynamic bandwidth allocation for long-reach passive optical networks,” in Proc. of IEEE/OSA Optoelectronics and Communications Conference/Australian Conference on Optical Fibre Technology (OECC/ACOFT), (2014).

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 Proc. of IEEE International Conference on Communications (ICC), (2010).

Van, D. P.

D. P. Van, L. Valcarenghi, M. Chincoli, and P. Castoldi, “Experimental evaluation of a sleep-aware dynamic bandwidth allocation in a multi-ONU 10G-EPON testbed,” Opt. Switch. Netw. 14(Part 1), 11–24 (2014).
[Crossref]

Wong, E.

E. Wong, M. Muller, M. P. I. Dias, C. A. Chan, and M. C. Amann, “Energy-efficiency of optical network units with vertical-cavity surface-emitting lasers,” Opt. Express 20(14), 14960–14970 (2012).
[Crossref] [PubMed]

D. Pham Van, M. P. I. Dias, K. Kondepu, L. Valcarenghi, P. Castoldi, and E. Wong, “Energy-efficient dynamic bandwidth allocation for long-reach passive optical networks,” in Proc. of IEEE/OSA Optoelectronics and Communications Conference/Australian Conference on Optical Fibre Technology (OECC/ACOFT), (2014).

Wong, S. W.

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 Proc. of IEEE International Conference on Communications (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 Proc. of IEEE International Conference on Communications (ICC), (2010).

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 Proc. of IEEE International Conference on Communications (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 Proc. of IEEE International Conference on Communications (ICC), (2010).

Zhang, L.

L. Zhang, Y. Liu, L. Guo, and X. Gong, “Energy-saving scheme based on downstream packet scheduling in Ethernet passive optical networks,” Opt. Fiber Technol. 19(2), 169–178 (2013).
[Crossref]

Comput. Netw. (1)

S. H. S. Newaz, A. Cuevas, G. M. Lee, N. Crespi, and J. K. Choi, “Adaptive delay-aware energy efficient TDM-PON,” Comput. Netw. 57(7), 1577–1596 (2013).
[Crossref]

IEEE Commun. Mag. (1)

A. R. Dhaini, P.-H. Ho, and G. Shen, “Toward green next-generation passive optical networks,” IEEE Commun. Mag. 49(11), 94–101 (2011).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Netw. (1)

Opt. Express (2)

Opt. Fiber Technol. (1)

L. Zhang, Y. Liu, L. Guo, and X. Gong, “Energy-saving scheme based on downstream packet scheduling in Ethernet passive optical networks,” Opt. Fiber Technol. 19(2), 169–178 (2013).
[Crossref]

Opt. Switch. Netw. (3)

M. Bokhari and P. Saengudomlert, “Analysis of mean packet delay for upstream transmissions in passive optical networks with sleep mode,” Opt. Switch. Netw. 10(3), 195–210 (2013).
[Crossref]

A. Mercian, M. P. McGarry, and M. Reisslein, “Impact of report message scheduling (RMS) in 1G/10G EPON and GPON,” Opt. Switch. Netw. 12(0), 1–13 (2014).
[Crossref]

D. P. Van, L. Valcarenghi, M. Chincoli, and P. Castoldi, “Experimental evaluation of a sleep-aware dynamic bandwidth allocation in a multi-ONU 10G-EPON testbed,” Opt. Switch. Netw. 14(Part 1), 11–24 (2014).
[Crossref]

Other (8)

D. Pham Van, M. P. I. Dias, K. Kondepu, L. Valcarenghi, P. Castoldi, and E. Wong, “Energy-efficient dynamic bandwidth allocation for long-reach passive optical networks,” in Proc. of IEEE/OSA Optoelectronics and Communications Conference/Australian Conference on Optical Fibre Technology (OECC/ACOFT), (2014).

ITU-T Y.1541 recommendations, Network performance objectives for IP-based services (2011).

A. Dixit, B. Lannoo, D. Colle, M. Pickavet, and P. Demeester, “Novel DBA algorithm for energy efficiency in TWDM-PONs,” in Proc. of Optical Communication (ECOC), (2013).

IEEE Std 802.3av, 10Gb/s Ethernet passive optical network (10G-EPON) (2009).

ITU-T G.Sup 45, GPON power conservation (2009).

ITU-T G.987.x-series recommendations, 10-Gigabit-capable passive optical networks XG-PON (2010).

IEEE Std 1904.1-2013, IEEE standard for service interoperability in Ethernet passive optical networks (2013).

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 Proc. of IEEE International Conference on Communications (ICC), (2010).

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Figures (9)

Fig. 1
Fig. 1 Illustration of energy-saving PON framework where the number of ONUs is 4.
Fig. 2
Fig. 2 Illustration of SDBA scheme operation.
Fig. 3
Fig. 3 Illustration of EDBA scheme operation.
Fig. 4
Fig. 4 Illustration of ASDBA scheme operation.
Fig. 5
Fig. 5 Waveform demonstration of 10G-EPON featuring ESPON schemes in ModelSim.
Fig. 6
Fig. 6 Energy-savings with varying network reach (Tc = 10 ms, DS aggr. load = 0.6).
Fig. 7
Fig. 7 DS frame delay with varying network reach (Tc = 10 ms, DS aggr. load = 0.6).
Fig. 8
Fig. 8 US frame delay with varying network reach (Tc = 10 ms, DS aggr. load = 0.6).
Fig. 9
Fig. 9 EDBA vs ASDBA with varying Tc (DS aggr. load = 0.6, US aggr. load = 0.4).

Tables (2)

Tables Icon

Table 1 Summary of energy-efficient schemes under ESPON framework

Tables Icon

Table 2 Values of evaluation parameters

Equations (7)

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

Tx len = { B ds + RTT + T msg , if B ds B us B us + RTT + T msg , otherwise
{ Len ds = Tx len T msg = max { B ds , B us } + RTT Len us = Tx len RTT T msg = max { B ds , B us }
Tx len = { B ds + T msg , if B ds B us + RTT B us + RTT + T msg , otherwise
{ Len ds = Tx len T msg = max { B ds , B us + RTT } Len us = Tx len RTT T msg = max { B ds RTT , B us }
Tx len = { B ds + RTT + T msg , if B ds B us B us + RTT + T msg , otherwise
{ Len ds = Tx len RTT T msg = max { B ds , B us } Len us = Tx len RTT T msg = max { B ds , B us }
η = 1 P a T a + P s T s + P d T d P a ( T a + T s + T d ) = ( P a P s ) T s + ( P a P d ) T d P a T c ,

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