Abstract

The recent development of new applications and services, primarily multimedia applications, has driven the need for higher bandwidth and a faster access network, but these cannot be fully realized with the conventional single-channel Ethernet passive optical network (EPON). In such circumstances, the realization of WDM EPONs is the best solution for the implementation of converged triple-play networks. In this paper we present a novel algorithm dynamic wavelength priority bandwidth allocation with traffic class hopping for wavelength and bandwidth allocation with quality of service (QoS) support that incorporates both offline and modified online scheduling. In order to implement QoS support, we present an approach in which wavelength assignment takes place per service class and not per optical network unit, as suggested by the common approach in literature. The presented algorithm can guarantee both the priority and fairness of the differentiated traffic classes. Apart from the theoretical analysis, we studied and evaluated the performance of the presented model through detailed simulation experiments. An original network model is developed in MATLAB and incorporates all key parameters of the real network environment, such as queuing, transmission and packet processing delay, round-trip time, and framing overhead. The simulation results confirm the excellent performance of the presented model in terms of average packet delay, jitter, and packet loss.

© 2013 Optical Society of America

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References

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  1. G. Kramer and G. Pesavento, “Ethernet PON: Building a next-generation optical access network,” IEEE Commun. Mag., vol.  40, no. 2, pp. 66–73, Feb. 2002.
    [CrossRef]
  2. “Visual networking index: Forecast and methodology, 2011–2016,” Cisco White Paper, May2012 [Online]. Available: http://www.cisco.com/en/US/netsol/ns827/networking_solutions_white_papers_list.html .
  3. “National broadband plans,” OECD Telecom and Internet Reports, 2011 [Online]. Available: http://www.oecd.org/dataoecd/22/41/48459395.pdf .
  4. “Fiber access—Network developments in the OECD area,” OECD Telecom and Internet Reports, 2011 [Online]. Available: http://www.oecd.org/dataoecd/22/15/48460183.pdf .
  5. M. Radivojevic and P. Matavulj, “Implementation of intra-ONU scheduling for quality of service support in EPONs,” J. Lightwave Technol., vol.  27, no. 18, pp. 4055–4062, Sept. 2009.
    [CrossRef]
  6. K. Kwong, D. Harle, and I. Andonovic, “WDM PONs: Next step for the first mile,” in Proc. 2nd Int. Conf. on the Performance Modelling and Evaluation of Heterogeneous Networks (HET-NETs), 2004, paper P47.
  7. M. Radivojevic and P. Matavulj, “Novel wavelength and bandwidth allocation algorithms for WDM EPON with QoS support,” Photon. Netw. Commun., vol.  20, no. 2, pp. 173–182, Oct. 2010.
    [CrossRef]
  8. M. Radivojevic and P. Matavulj, “Advanced scheduling algorithm for quality of service support in WDM EPON,” Opt. Express, vol.  19, no. 26, pp. B587–B593, Dec. 2011.
    [CrossRef]
  9. K. Kwong, D. Harle, and I. Andonovic, “Dynamic bandwidth allocation algorithm for differentiated services over WDM EPONs,” in Proc. Int. Conf. on Communications Systems, Sept. 2004, pp. 116–120.
  10. A. R. Dhaini, C. M. Assi, and A. Shami, “Dynamic bandwidth allocation schemes in hybrid TDM/WDM passive optical networks,” in Proc. IEEE Consumer Communications and Networking Conf., Jan. 2006.
  11. A. R. Dhaini, C. Assi, and A. Shami, “Quality of service in TDM/WDM Ethernet passive optical networks (EPONs),” in Proc. IEEE Symp. on Computers and Communications, June 2006, pp. 616–621.
  12. A. R. Dhaini, C. Assi, M. Maier, and A. Shami, “Dynamic wavelength and bandwidth allocation in hybrid TDM/WDM EPON networks,” J. Lightwave Technol., vol.  25, no. 1, pp. 277–286, Jan. 2007.
    [CrossRef]
  13. M. P. McGarry, M. Maier, and M. Reisslein, “WDM Ethernet passive optical networks (EPONs),” IEEE Commun. Mag., vol.  44, no. 2, pp. 15–22, Feb. 2006.
    [CrossRef]
  14. J. Zheng and H. T. Mouftah, “A survey of dynamic bandwidth allocation algorithms for Ethernet passive optical networks,” Opt. Switch. Netw., vol.  6, no. 3, pp. 151–162, July 2009.
    [CrossRef]
  15. M. McGarry, M. Maier, M. Reisslein, and A. Keha, “Bandwidth management for WDM EPONs,” J. Opt. Netw., vol.  5, no. 9, pp. 637–654, Sept. 2006.
    [CrossRef]
  16. M. P. McGarry, M. Reisslein, C. J. Colbourn, M. Maier, F. Aurzada, and M. Scheutzow, “Just-in-time scheduling for multichannel EPONs,” J. Lightwave Technol., vol.  26, no. 10, pp. 1204–1216, May 2008.
    [CrossRef]
  17. S. Blake, D. Black, M. Carlson, E. Davies, Z. Wang, and W. Weiss, “An architecture for differentiated service,” , 1998.
  18. F. J. Hens and J. M. Caballero, Triple Play: Building the Converged Network for IP, VoIP and IPTV. West Sussex, UK: Wiley, 2008.
  19. W. Willinger, M. S. Taqqu, and A. Erramilli, “A bibliographical guide to self-similar traffic and performance modeling for modern high-speed networks,” in Stochastic Networks: Theory and Applications, F. P. Kelly, S. Zachary, and I. Ziedins, Eds. Oxford, U.K.: Oxford University, 1996, pp. 339–366.
  20. T. Miyazawa and H. Harai, “Optical access architecture designs based on WDM-direct toward new generation networks,” IEICE Trans. Commun., vol.  E93-B, no. 2, pp. 236–245, Feb. 2010.
    [CrossRef]
  21. H. Kimura, N. Iiyama, Y. Sakai, and K. Kumozaki, “A WDM-based future optical access network and support technologies for adapting the user demands’ diversity,” IEICE Trans. Commun., vol.  E93-B, no. 2, pp. 246–254, Feb. 2010.
    [CrossRef]
  22. M. Kiaei, K. Fouli, M. Scheutzow, M. Maier, M. Reisslein, and C. Assi, “Low-latency polling schemes for long-reach passive optical networks,” IEEE Trans. Commun., to be published.

2011 (1)

2010 (3)

M. Radivojevic and P. Matavulj, “Novel wavelength and bandwidth allocation algorithms for WDM EPON with QoS support,” Photon. Netw. Commun., vol.  20, no. 2, pp. 173–182, Oct. 2010.
[CrossRef]

T. Miyazawa and H. Harai, “Optical access architecture designs based on WDM-direct toward new generation networks,” IEICE Trans. Commun., vol.  E93-B, no. 2, pp. 236–245, Feb. 2010.
[CrossRef]

H. Kimura, N. Iiyama, Y. Sakai, and K. Kumozaki, “A WDM-based future optical access network and support technologies for adapting the user demands’ diversity,” IEICE Trans. Commun., vol.  E93-B, no. 2, pp. 246–254, Feb. 2010.
[CrossRef]

2009 (2)

J. Zheng and H. T. Mouftah, “A survey of dynamic bandwidth allocation algorithms for Ethernet passive optical networks,” Opt. Switch. Netw., vol.  6, no. 3, pp. 151–162, July 2009.
[CrossRef]

M. Radivojevic and P. Matavulj, “Implementation of intra-ONU scheduling for quality of service support in EPONs,” J. Lightwave Technol., vol.  27, no. 18, pp. 4055–4062, Sept. 2009.
[CrossRef]

2008 (1)

2007 (1)

2006 (2)

M. P. McGarry, M. Maier, and M. Reisslein, “WDM Ethernet passive optical networks (EPONs),” IEEE Commun. Mag., vol.  44, no. 2, pp. 15–22, Feb. 2006.
[CrossRef]

M. McGarry, M. Maier, M. Reisslein, and A. Keha, “Bandwidth management for WDM EPONs,” J. Opt. Netw., vol.  5, no. 9, pp. 637–654, Sept. 2006.
[CrossRef]

2002 (1)

G. Kramer and G. Pesavento, “Ethernet PON: Building a next-generation optical access network,” IEEE Commun. Mag., vol.  40, no. 2, pp. 66–73, Feb. 2002.
[CrossRef]

Andonovic, I.

K. Kwong, D. Harle, and I. Andonovic, “WDM PONs: Next step for the first mile,” in Proc. 2nd Int. Conf. on the Performance Modelling and Evaluation of Heterogeneous Networks (HET-NETs), 2004, paper P47.

K. Kwong, D. Harle, and I. Andonovic, “Dynamic bandwidth allocation algorithm for differentiated services over WDM EPONs,” in Proc. Int. Conf. on Communications Systems, Sept. 2004, pp. 116–120.

Assi, C.

A. R. Dhaini, C. Assi, M. Maier, and A. Shami, “Dynamic wavelength and bandwidth allocation in hybrid TDM/WDM EPON networks,” J. Lightwave Technol., vol.  25, no. 1, pp. 277–286, Jan. 2007.
[CrossRef]

A. R. Dhaini, C. Assi, and A. Shami, “Quality of service in TDM/WDM Ethernet passive optical networks (EPONs),” in Proc. IEEE Symp. on Computers and Communications, June 2006, pp. 616–621.

M. Kiaei, K. Fouli, M. Scheutzow, M. Maier, M. Reisslein, and C. Assi, “Low-latency polling schemes for long-reach passive optical networks,” IEEE Trans. Commun., to be published.

Assi, C. M.

A. R. Dhaini, C. M. Assi, and A. Shami, “Dynamic bandwidth allocation schemes in hybrid TDM/WDM passive optical networks,” in Proc. IEEE Consumer Communications and Networking Conf., Jan. 2006.

Aurzada, F.

Black, D.

S. Blake, D. Black, M. Carlson, E. Davies, Z. Wang, and W. Weiss, “An architecture for differentiated service,” , 1998.

Blake, S.

S. Blake, D. Black, M. Carlson, E. Davies, Z. Wang, and W. Weiss, “An architecture for differentiated service,” , 1998.

Caballero, J. M.

F. J. Hens and J. M. Caballero, Triple Play: Building the Converged Network for IP, VoIP and IPTV. West Sussex, UK: Wiley, 2008.

Carlson, M.

S. Blake, D. Black, M. Carlson, E. Davies, Z. Wang, and W. Weiss, “An architecture for differentiated service,” , 1998.

Colbourn, C. J.

Davies, E.

S. Blake, D. Black, M. Carlson, E. Davies, Z. Wang, and W. Weiss, “An architecture for differentiated service,” , 1998.

Dhaini, A. R.

A. R. Dhaini, C. Assi, M. Maier, and A. Shami, “Dynamic wavelength and bandwidth allocation in hybrid TDM/WDM EPON networks,” J. Lightwave Technol., vol.  25, no. 1, pp. 277–286, Jan. 2007.
[CrossRef]

A. R. Dhaini, C. Assi, and A. Shami, “Quality of service in TDM/WDM Ethernet passive optical networks (EPONs),” in Proc. IEEE Symp. on Computers and Communications, June 2006, pp. 616–621.

A. R. Dhaini, C. M. Assi, and A. Shami, “Dynamic bandwidth allocation schemes in hybrid TDM/WDM passive optical networks,” in Proc. IEEE Consumer Communications and Networking Conf., Jan. 2006.

Erramilli, A.

W. Willinger, M. S. Taqqu, and A. Erramilli, “A bibliographical guide to self-similar traffic and performance modeling for modern high-speed networks,” in Stochastic Networks: Theory and Applications, F. P. Kelly, S. Zachary, and I. Ziedins, Eds. Oxford, U.K.: Oxford University, 1996, pp. 339–366.

Fouli, K.

M. Kiaei, K. Fouli, M. Scheutzow, M. Maier, M. Reisslein, and C. Assi, “Low-latency polling schemes for long-reach passive optical networks,” IEEE Trans. Commun., to be published.

Harai, H.

T. Miyazawa and H. Harai, “Optical access architecture designs based on WDM-direct toward new generation networks,” IEICE Trans. Commun., vol.  E93-B, no. 2, pp. 236–245, Feb. 2010.
[CrossRef]

Harle, D.

K. Kwong, D. Harle, and I. Andonovic, “WDM PONs: Next step for the first mile,” in Proc. 2nd Int. Conf. on the Performance Modelling and Evaluation of Heterogeneous Networks (HET-NETs), 2004, paper P47.

K. Kwong, D. Harle, and I. Andonovic, “Dynamic bandwidth allocation algorithm for differentiated services over WDM EPONs,” in Proc. Int. Conf. on Communications Systems, Sept. 2004, pp. 116–120.

Hens, F. J.

F. J. Hens and J. M. Caballero, Triple Play: Building the Converged Network for IP, VoIP and IPTV. West Sussex, UK: Wiley, 2008.

Iiyama, N.

H. Kimura, N. Iiyama, Y. Sakai, and K. Kumozaki, “A WDM-based future optical access network and support technologies for adapting the user demands’ diversity,” IEICE Trans. Commun., vol.  E93-B, no. 2, pp. 246–254, Feb. 2010.
[CrossRef]

Keha, A.

Kiaei, M.

M. Kiaei, K. Fouli, M. Scheutzow, M. Maier, M. Reisslein, and C. Assi, “Low-latency polling schemes for long-reach passive optical networks,” IEEE Trans. Commun., to be published.

Kimura, H.

H. Kimura, N. Iiyama, Y. Sakai, and K. Kumozaki, “A WDM-based future optical access network and support technologies for adapting the user demands’ diversity,” IEICE Trans. Commun., vol.  E93-B, no. 2, pp. 246–254, Feb. 2010.
[CrossRef]

Kramer, G.

G. Kramer and G. Pesavento, “Ethernet PON: Building a next-generation optical access network,” IEEE Commun. Mag., vol.  40, no. 2, pp. 66–73, Feb. 2002.
[CrossRef]

Kumozaki, K.

H. Kimura, N. Iiyama, Y. Sakai, and K. Kumozaki, “A WDM-based future optical access network and support technologies for adapting the user demands’ diversity,” IEICE Trans. Commun., vol.  E93-B, no. 2, pp. 246–254, Feb. 2010.
[CrossRef]

Kwong, K.

K. Kwong, D. Harle, and I. Andonovic, “WDM PONs: Next step for the first mile,” in Proc. 2nd Int. Conf. on the Performance Modelling and Evaluation of Heterogeneous Networks (HET-NETs), 2004, paper P47.

K. Kwong, D. Harle, and I. Andonovic, “Dynamic bandwidth allocation algorithm for differentiated services over WDM EPONs,” in Proc. Int. Conf. on Communications Systems, Sept. 2004, pp. 116–120.

Maier, M.

Matavulj, P.

McGarry, M.

McGarry, M. P.

M. P. McGarry, M. Reisslein, C. J. Colbourn, M. Maier, F. Aurzada, and M. Scheutzow, “Just-in-time scheduling for multichannel EPONs,” J. Lightwave Technol., vol.  26, no. 10, pp. 1204–1216, May 2008.
[CrossRef]

M. P. McGarry, M. Maier, and M. Reisslein, “WDM Ethernet passive optical networks (EPONs),” IEEE Commun. Mag., vol.  44, no. 2, pp. 15–22, Feb. 2006.
[CrossRef]

Miyazawa, T.

T. Miyazawa and H. Harai, “Optical access architecture designs based on WDM-direct toward new generation networks,” IEICE Trans. Commun., vol.  E93-B, no. 2, pp. 236–245, Feb. 2010.
[CrossRef]

Mouftah, H. T.

J. Zheng and H. T. Mouftah, “A survey of dynamic bandwidth allocation algorithms for Ethernet passive optical networks,” Opt. Switch. Netw., vol.  6, no. 3, pp. 151–162, July 2009.
[CrossRef]

Pesavento, G.

G. Kramer and G. Pesavento, “Ethernet PON: Building a next-generation optical access network,” IEEE Commun. Mag., vol.  40, no. 2, pp. 66–73, Feb. 2002.
[CrossRef]

Radivojevic, M.

Reisslein, M.

M. P. McGarry, M. Reisslein, C. J. Colbourn, M. Maier, F. Aurzada, and M. Scheutzow, “Just-in-time scheduling for multichannel EPONs,” J. Lightwave Technol., vol.  26, no. 10, pp. 1204–1216, May 2008.
[CrossRef]

M. McGarry, M. Maier, M. Reisslein, and A. Keha, “Bandwidth management for WDM EPONs,” J. Opt. Netw., vol.  5, no. 9, pp. 637–654, Sept. 2006.
[CrossRef]

M. P. McGarry, M. Maier, and M. Reisslein, “WDM Ethernet passive optical networks (EPONs),” IEEE Commun. Mag., vol.  44, no. 2, pp. 15–22, Feb. 2006.
[CrossRef]

M. Kiaei, K. Fouli, M. Scheutzow, M. Maier, M. Reisslein, and C. Assi, “Low-latency polling schemes for long-reach passive optical networks,” IEEE Trans. Commun., to be published.

Sakai, Y.

H. Kimura, N. Iiyama, Y. Sakai, and K. Kumozaki, “A WDM-based future optical access network and support technologies for adapting the user demands’ diversity,” IEICE Trans. Commun., vol.  E93-B, no. 2, pp. 246–254, Feb. 2010.
[CrossRef]

Scheutzow, M.

M. P. McGarry, M. Reisslein, C. J. Colbourn, M. Maier, F. Aurzada, and M. Scheutzow, “Just-in-time scheduling for multichannel EPONs,” J. Lightwave Technol., vol.  26, no. 10, pp. 1204–1216, May 2008.
[CrossRef]

M. Kiaei, K. Fouli, M. Scheutzow, M. Maier, M. Reisslein, and C. Assi, “Low-latency polling schemes for long-reach passive optical networks,” IEEE Trans. Commun., to be published.

Shami, A.

A. R. Dhaini, C. Assi, M. Maier, and A. Shami, “Dynamic wavelength and bandwidth allocation in hybrid TDM/WDM EPON networks,” J. Lightwave Technol., vol.  25, no. 1, pp. 277–286, Jan. 2007.
[CrossRef]

A. R. Dhaini, C. Assi, and A. Shami, “Quality of service in TDM/WDM Ethernet passive optical networks (EPONs),” in Proc. IEEE Symp. on Computers and Communications, June 2006, pp. 616–621.

A. R. Dhaini, C. M. Assi, and A. Shami, “Dynamic bandwidth allocation schemes in hybrid TDM/WDM passive optical networks,” in Proc. IEEE Consumer Communications and Networking Conf., Jan. 2006.

Taqqu, M. S.

W. Willinger, M. S. Taqqu, and A. Erramilli, “A bibliographical guide to self-similar traffic and performance modeling for modern high-speed networks,” in Stochastic Networks: Theory and Applications, F. P. Kelly, S. Zachary, and I. Ziedins, Eds. Oxford, U.K.: Oxford University, 1996, pp. 339–366.

Wang, Z.

S. Blake, D. Black, M. Carlson, E. Davies, Z. Wang, and W. Weiss, “An architecture for differentiated service,” , 1998.

Weiss, W.

S. Blake, D. Black, M. Carlson, E. Davies, Z. Wang, and W. Weiss, “An architecture for differentiated service,” , 1998.

Willinger, W.

W. Willinger, M. S. Taqqu, and A. Erramilli, “A bibliographical guide to self-similar traffic and performance modeling for modern high-speed networks,” in Stochastic Networks: Theory and Applications, F. P. Kelly, S. Zachary, and I. Ziedins, Eds. Oxford, U.K.: Oxford University, 1996, pp. 339–366.

Zheng, J.

J. Zheng and H. T. Mouftah, “A survey of dynamic bandwidth allocation algorithms for Ethernet passive optical networks,” Opt. Switch. Netw., vol.  6, no. 3, pp. 151–162, July 2009.
[CrossRef]

IEEE Commun. Mag. (2)

G. Kramer and G. Pesavento, “Ethernet PON: Building a next-generation optical access network,” IEEE Commun. Mag., vol.  40, no. 2, pp. 66–73, Feb. 2002.
[CrossRef]

M. P. McGarry, M. Maier, and M. Reisslein, “WDM Ethernet passive optical networks (EPONs),” IEEE Commun. Mag., vol.  44, no. 2, pp. 15–22, Feb. 2006.
[CrossRef]

IEICE Trans. Commun. (2)

T. Miyazawa and H. Harai, “Optical access architecture designs based on WDM-direct toward new generation networks,” IEICE Trans. Commun., vol.  E93-B, no. 2, pp. 236–245, Feb. 2010.
[CrossRef]

H. Kimura, N. Iiyama, Y. Sakai, and K. Kumozaki, “A WDM-based future optical access network and support technologies for adapting the user demands’ diversity,” IEICE Trans. Commun., vol.  E93-B, no. 2, pp. 246–254, Feb. 2010.
[CrossRef]

J. Lightwave Technol. (3)

J. Opt. Netw. (1)

Opt. Express (1)

Opt. Switch. Netw. (1)

J. Zheng and H. T. Mouftah, “A survey of dynamic bandwidth allocation algorithms for Ethernet passive optical networks,” Opt. Switch. Netw., vol.  6, no. 3, pp. 151–162, July 2009.
[CrossRef]

Photon. Netw. Commun. (1)

M. Radivojevic and P. Matavulj, “Novel wavelength and bandwidth allocation algorithms for WDM EPON with QoS support,” Photon. Netw. Commun., vol.  20, no. 2, pp. 173–182, Oct. 2010.
[CrossRef]

Other (11)

K. Kwong, D. Harle, and I. Andonovic, “WDM PONs: Next step for the first mile,” in Proc. 2nd Int. Conf. on the Performance Modelling and Evaluation of Heterogeneous Networks (HET-NETs), 2004, paper P47.

S. Blake, D. Black, M. Carlson, E. Davies, Z. Wang, and W. Weiss, “An architecture for differentiated service,” , 1998.

F. J. Hens and J. M. Caballero, Triple Play: Building the Converged Network for IP, VoIP and IPTV. West Sussex, UK: Wiley, 2008.

W. Willinger, M. S. Taqqu, and A. Erramilli, “A bibliographical guide to self-similar traffic and performance modeling for modern high-speed networks,” in Stochastic Networks: Theory and Applications, F. P. Kelly, S. Zachary, and I. Ziedins, Eds. Oxford, U.K.: Oxford University, 1996, pp. 339–366.

K. Kwong, D. Harle, and I. Andonovic, “Dynamic bandwidth allocation algorithm for differentiated services over WDM EPONs,” in Proc. Int. Conf. on Communications Systems, Sept. 2004, pp. 116–120.

A. R. Dhaini, C. M. Assi, and A. Shami, “Dynamic bandwidth allocation schemes in hybrid TDM/WDM passive optical networks,” in Proc. IEEE Consumer Communications and Networking Conf., Jan. 2006.

A. R. Dhaini, C. Assi, and A. Shami, “Quality of service in TDM/WDM Ethernet passive optical networks (EPONs),” in Proc. IEEE Symp. on Computers and Communications, June 2006, pp. 616–621.

“Visual networking index: Forecast and methodology, 2011–2016,” Cisco White Paper, May2012 [Online]. Available: http://www.cisco.com/en/US/netsol/ns827/networking_solutions_white_papers_list.html .

“National broadband plans,” OECD Telecom and Internet Reports, 2011 [Online]. Available: http://www.oecd.org/dataoecd/22/41/48459395.pdf .

“Fiber access—Network developments in the OECD area,” OECD Telecom and Internet Reports, 2011 [Online]. Available: http://www.oecd.org/dataoecd/22/15/48460183.pdf .

M. Kiaei, K. Fouli, M. Scheutzow, M. Maier, M. Reisslein, and C. Assi, “Low-latency polling schemes for long-reach passive optical networks,” IEEE Trans. Commun., to be published.

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Figures (9)

Fig. 1.
Fig. 1.

WDM EPON architecture. Txi, transceivers; Rxi receivers ( i = 1 , 2 , 3 ).

Fig. 2.
Fig. 2.

Fixed and dynamic subcycles on λ i .

Fig. 3.
Fig. 3.

Upstream communication on λ i .

Fig. 4.
Fig. 4.

Example of OLT–ONU communication.

Fig. 5.
Fig. 5.

Average packet delay of the EF traffic class.

Fig. 6.
Fig. 6.

Average packet delay of the AF traffic class.

Fig. 7.
Fig. 7.

Average packet delay of the BE traffic class.

Fig. 8.
Fig. 8.

Jitter performance.

Fig. 9.
Fig. 9.

Packet loss rate.

Tables (1)

Tables Icon

Table I Parameters of the Mathematical Model

Equations (12)

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

W total = R * ( T cycle max N * T g ) .
w i tc = W i tc _ req i N W i tc _ req , tc { EF , AF , BE } ,
W i tc _ all = { w i tc * W total , W i tc _ req < W queue W queue , W i tc _ req W queue , tc { EF , AF , BE } .
T cycle = { max { i N W i tc _ all R } , max { i N W i tc _ all R } < T cycle max T cycle max , otherwise .
T FWA - CL ( λ i ) = j N W j tc _ all / R .
T FWA - CL ( λ i ) < T FWA - CL ( λ j ) , i j & ( i , j ) { 1 , 2 , 3 } ,
T DWA - CL ( λ i ) = T cycle - T FWA - CL ( λ i ) ,
W total add = R * i { 1 , 2 , 3 } T DWA - CL ( λ i ) , ( λ i , tc ) { ( λ 1 , EF ) , ( λ 2 , AF ) , ( λ 3 , BE ) } .
W total EF _ add = { { i N ( W i EF _ req W i EF _ all } , i N ( W i EF _ req W i EF _ all ) < W total add W total add , otherwise ,
W total AF _ add = { { i N ( W i AF _ req W i AF _ all } , i N ( W i AF _ req W i AF _ all ) < W total add W total EF _ add W total add W total EF _ add , otherwise ,
W total BE _ add = { { i N ( W i BE _ req W i BE _ all } , { i N ( W i BE _ req W i BE _ all } < W total add W total EF _ add W total AF _ add , W total add W total EF _ add W total AF _ add , otherwise .
W i tc _ add = w i tc * W total add , tc { EF , AF , BE } .