Abstract

For traditional optical network dimensioning, a plethora of algorithms exists to design the amount of network resources required to accommodate a given amount of traffic, expressed as a (source, destination)-based traffic matrix. In optical Grid dimensioning, however, the anycast principle applies: Grid users do not really care where exactly their tasks (Grid jobs) end up being executed. Thus, the destination of traffic is not known beforehand and traditional dimensioning algorithms are not applicable. In this paper we propose a mean field calculation method to analytically derive the traffic matrix for given job arrival intensities at the originating Grid sites (the sources). We also indicate how it can be integrated in a stepwise dimensioning approach to compute not only the amount of network resources, but also Grid resources (computational and/or storage). Hence it forms part of a solution for Grid dimensioning: determining how many servers to provide, where to place them, and which network to install for interconnecting server sites and users generating Grid jobs.

© 2010 Optical Society of America

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References

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  1. G. Lawton, “Moving the OS to the web,” Computer, vol. 41, no. 3, pp. 16–19, Mar. 2008.
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  3. M. De Leenheer, P. Thysebaert, B. Volckaert, F. De Turck, B. Dhoedt, P. Demeester, D. Simeonidou, R. Nejabati, G. Zervas, D. Klonidis, M. J. O’Mahony, “A view on enabling consumer-oriented grids through optical burst switching,” IEEE Commun. Mag., vol. 44, no. 3, pp. 124–131, Mar. 2006.
    [CrossRef]
  4. D. Simeonidou, R. Nejabati, G. Zervas, D. Klonidis, A. Tzanakaki, M. J. O’Mahony, “Dynamic optical-network architectures and technologies for existing and emerging grid services,” J. Lightwave Technol., vol. 23, no. 10, pp. 3347–3357, Oct. 2005.
    [CrossRef]
  5. M. De Leenheer, C. Develder, T. Stevens, B. Dhoedt, M. Pickavet, P. Demeester, “Design and control of optical grid networks (invited),” in Proc. 4th Int. Conf. on Broadband Networks (Broadnets 2007), Raleigh, NC, 2007, pp. 107–115.
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  12. B. Mukherjee, D. Banerjee, S. Ramamurthy, A. Mukherjee, “Some principles for designing a wide-area WDM optical network,” IEEE/ACM Trans. Netw., vol. 4, no. 5, pp. 684–696, Oct. 1996.
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  18. C. Develder, B. Mukherjee, B. Dhoedt, P. Demeester, “On dimensioning optical grids and the impact of scheduling,” Photonic Network Commun., vol. 17, no. 3, pp. 255–265, June 2009.
    [CrossRef]
  19. M. Telek, A. Heindl, “Matching moments for acyclic discrete and continuous phase-type distributions of second order,” Int. J. Simul. Syst., Sci. Technol., vol. 3, pp. 47–57, 2002.
  20. J. Le Boudec, D. McDonald, J. Mundinger, “A generic mean field convergence result for systems of interacting objects,” in Proc. 4th Int. Conf. on the Quantitative Evaluation of SysTems (QEST 2007), Edinburgh, UK, 2007, pp. 3–15.
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2009 (1)

C. Develder, B. Mukherjee, B. Dhoedt, P. Demeester, “On dimensioning optical grids and the impact of scheduling,” Photonic Network Commun., vol. 17, no. 3, pp. 255–265, June 2009.
[CrossRef]

2008 (1)

G. Lawton, “Moving the OS to the web,” Computer, vol. 41, no. 3, pp. 16–19, Mar. 2008.
[CrossRef]

2006 (2)

M. De Leenheer, P. Thysebaert, B. Volckaert, F. De Turck, B. Dhoedt, P. Demeester, D. Simeonidou, R. Nejabati, G. Zervas, D. Klonidis, M. J. O’Mahony, “A view on enabling consumer-oriented grids through optical burst switching,” IEEE Commun. Mag., vol. 44, no. 3, pp. 124–131, Mar. 2006.
[CrossRef]

H. Höller, S. Voß, “A heuristic approach for combined equipment-planning and routing in multi-layer SDH/WDM networks,” Eur. J. Oper. Res., vol. 171, no. 3, pp. 787–796, June 2006.
[CrossRef]

2005 (1)

2003 (1)

K. Zhu, H. Zang, B. Mukherjee, “A comprehensive study on next-generation optical grooming switches,” IEEE J. Sel. Areas Commun., vol. 21, no. 7, pp. 1173–1186, Sept. 2003.
[CrossRef]

2002 (2)

D. Colle, S. De Maesschalck, C. Develder, P. Van Heuven, A. Groebbens, J. Cheyns, I. Lievens, P. Lagasse, M. Pickavet, P. Demeester, “Data-centric optical networks and their survivability,” IEEE J. Sel. Areas Commun., vol. 20, no. 1, pp. 6–20, Jan. 2002.
[CrossRef]

M. Telek, A. Heindl, “Matching moments for acyclic discrete and continuous phase-type distributions of second order,” Int. J. Simul. Syst., Sci. Technol., vol. 3, pp. 47–57, 2002.

2000 (1)

O. Gerstel, R. Ramaswami, G. H. Sasaki, “Cost-effective traffic grooming in WDM rings,” IEEE/ACM Trans. Netw., vol. 8, no. 5, pp. 618–630, Oct. 2000.
[CrossRef]

1999 (1)

M. Pickavet, P. Demeester, “Long-term planning of WDM networks: a comparison between single-period and multiperiod techniques,” Photonic Network Commun., vol. 1, no. 4, pp. 331–346, Dec. 1999.
[CrossRef]

1996 (1)

B. Mukherjee, D. Banerjee, S. Ramamurthy, A. Mukherjee, “Some principles for designing a wide-area WDM optical network,” IEEE/ACM Trans. Netw., vol. 4, no. 5, pp. 684–696, Oct. 1996.
[CrossRef]

Banerjee, D.

B. Mukherjee, D. Banerjee, S. Ramamurthy, A. Mukherjee, “Some principles for designing a wide-area WDM optical network,” IEEE/ACM Trans. Netw., vol. 4, no. 5, pp. 684–696, Oct. 1996.
[CrossRef]

Barz, C.

E. Varvarigos, P. Kokkinos, K. Christodoulopoulos, M. Pilz, C. Barz, T. Stevens, J. Vermeir, C. Develder, M. De Leenheer, B. Dhoedt, “D5.2—QoS-aware resource scheduling,” IST Phosphorus project deliverable, Sept. 2007. Available: http://www.ist-phosphorus.eu/deliverables.php.

C. de Waal, U. Bornhauser, A. Willner, M. Pilz, C. Barz, E. Varvarigos, P. Kokkinos, K. Christodoulopoulos, “D5.4—Support for advance reservations in scheduling and routing,” IST Phosphorus project deliverable, June 2007. Available: http://www.ist-phosphorus.eu/deliverables.php.

Bley, A.

A. Bley, T. Koch, R. Wessäly, “Large-scale hierarchical networks: how to compute an optimal architecture?” in Proc. 11th Int. Telecommunications Network Strategy and Planning Symp. (Networks 2004), Vienna, Austria, 2004, pp. 429–434.

Bornhauser, U.

C. de Waal, U. Bornhauser, A. Willner, M. Pilz, C. Barz, E. Varvarigos, P. Kokkinos, K. Christodoulopoulos, “D5.4—Support for advance reservations in scheduling and routing,” IST Phosphorus project deliverable, June 2007. Available: http://www.ist-phosphorus.eu/deliverables.php.

Cheyns, J.

D. Colle, S. De Maesschalck, C. Develder, P. Van Heuven, A. Groebbens, J. Cheyns, I. Lievens, P. Lagasse, M. Pickavet, P. Demeester, “Data-centric optical networks and their survivability,” IEEE J. Sel. Areas Commun., vol. 20, no. 1, pp. 6–20, Jan. 2002.
[CrossRef]

Christodoulopoulos, K.

E. Varvarigos, P. Kokkinos, K. Christodoulopoulos, M. Pilz, C. Barz, T. Stevens, J. Vermeir, C. Develder, M. De Leenheer, B. Dhoedt, “D5.2—QoS-aware resource scheduling,” IST Phosphorus project deliverable, Sept. 2007. Available: http://www.ist-phosphorus.eu/deliverables.php.

C. de Waal, U. Bornhauser, A. Willner, M. Pilz, C. Barz, E. Varvarigos, P. Kokkinos, K. Christodoulopoulos, “D5.4—Support for advance reservations in scheduling and routing,” IST Phosphorus project deliverable, June 2007. Available: http://www.ist-phosphorus.eu/deliverables.php.

Colle, D.

D. Colle, S. De Maesschalck, C. Develder, P. Van Heuven, A. Groebbens, J. Cheyns, I. Lievens, P. Lagasse, M. Pickavet, P. Demeester, “Data-centric optical networks and their survivability,” IEEE J. Sel. Areas Commun., vol. 20, no. 1, pp. 6–20, Jan. 2002.
[CrossRef]

De Leenheer, M.

M. De Leenheer, P. Thysebaert, B. Volckaert, F. De Turck, B. Dhoedt, P. Demeester, D. Simeonidou, R. Nejabati, G. Zervas, D. Klonidis, M. J. O’Mahony, “A view on enabling consumer-oriented grids through optical burst switching,” IEEE Commun. Mag., vol. 44, no. 3, pp. 124–131, Mar. 2006.
[CrossRef]

M. De Leenheer, C. Develder, F. De Turck, B. Dhoedt, P. Demeester, “Erlang reduced load model for optical burst switched grids,” in Proc. 3rd Int. Conf. on Networking and Services (ICNS 2007), Athens, Greece, 2007.

M. De Leenheer, C. Develder, T. Stevens, B. Dhoedt, M. Pickavet, P. Demeester, “Design and control of optical grid networks (invited),” in Proc. 4th Int. Conf. on Broadband Networks (Broadnets 2007), Raleigh, NC, 2007, pp. 107–115.

E. Varvarigos, P. Kokkinos, K. Christodoulopoulos, M. Pilz, C. Barz, T. Stevens, J. Vermeir, C. Develder, M. De Leenheer, B. Dhoedt, “D5.2—QoS-aware resource scheduling,” IST Phosphorus project deliverable, Sept. 2007. Available: http://www.ist-phosphorus.eu/deliverables.php.

F. Farahmand, M. De Leenheer, P. Thysebaert, B. Volckaert, F. De Turck, B. Dhoedt, P. Demeester, J. P. Jue, “A multi-layered approach to optical burst-switched based grids,” in Proc. 2nd Int. Conf. on Broadband Networks (Broadnets 2005), Oct. 2005, pp. 1050–1057.

De Maesschalck, S.

D. Colle, S. De Maesschalck, C. Develder, P. Van Heuven, A. Groebbens, J. Cheyns, I. Lievens, P. Lagasse, M. Pickavet, P. Demeester, “Data-centric optical networks and their survivability,” IEEE J. Sel. Areas Commun., vol. 20, no. 1, pp. 6–20, Jan. 2002.
[CrossRef]

De Turck, F.

M. De Leenheer, P. Thysebaert, B. Volckaert, F. De Turck, B. Dhoedt, P. Demeester, D. Simeonidou, R. Nejabati, G. Zervas, D. Klonidis, M. J. O’Mahony, “A view on enabling consumer-oriented grids through optical burst switching,” IEEE Commun. Mag., vol. 44, no. 3, pp. 124–131, Mar. 2006.
[CrossRef]

M. De Leenheer, C. Develder, F. De Turck, B. Dhoedt, P. Demeester, “Erlang reduced load model for optical burst switched grids,” in Proc. 3rd Int. Conf. on Networking and Services (ICNS 2007), Athens, Greece, 2007.

F. Farahmand, M. De Leenheer, P. Thysebaert, B. Volckaert, F. De Turck, B. Dhoedt, P. Demeester, J. P. Jue, “A multi-layered approach to optical burst-switched based grids,” in Proc. 2nd Int. Conf. on Broadband Networks (Broadnets 2005), Oct. 2005, pp. 1050–1057.

P. Thysebaert, F. De Turck, B. Dhoedt, P. Demeester, “Using divisible load theory to dimension optical transport networks for grid excess load handling,” in Proc. Int. Conf. on Autonomic and Autonomous Systems & Int. Conf. on Networking and Systems (ICAS/ICNS 2005), Papeete, Tahiti, 2005.

de Waal, C.

C. de Waal, U. Bornhauser, A. Willner, M. Pilz, C. Barz, E. Varvarigos, P. Kokkinos, K. Christodoulopoulos, “D5.4—Support for advance reservations in scheduling and routing,” IST Phosphorus project deliverable, June 2007. Available: http://www.ist-phosphorus.eu/deliverables.php.

Demeester, P.

C. Develder, B. Mukherjee, B. Dhoedt, P. Demeester, “On dimensioning optical grids and the impact of scheduling,” Photonic Network Commun., vol. 17, no. 3, pp. 255–265, June 2009.
[CrossRef]

M. De Leenheer, P. Thysebaert, B. Volckaert, F. De Turck, B. Dhoedt, P. Demeester, D. Simeonidou, R. Nejabati, G. Zervas, D. Klonidis, M. J. O’Mahony, “A view on enabling consumer-oriented grids through optical burst switching,” IEEE Commun. Mag., vol. 44, no. 3, pp. 124–131, Mar. 2006.
[CrossRef]

D. Colle, S. De Maesschalck, C. Develder, P. Van Heuven, A. Groebbens, J. Cheyns, I. Lievens, P. Lagasse, M. Pickavet, P. Demeester, “Data-centric optical networks and their survivability,” IEEE J. Sel. Areas Commun., vol. 20, no. 1, pp. 6–20, Jan. 2002.
[CrossRef]

M. Pickavet, P. Demeester, “Long-term planning of WDM networks: a comparison between single-period and multiperiod techniques,” Photonic Network Commun., vol. 1, no. 4, pp. 331–346, Dec. 1999.
[CrossRef]

M. De Leenheer, C. Develder, F. De Turck, B. Dhoedt, P. Demeester, “Erlang reduced load model for optical burst switched grids,” in Proc. 3rd Int. Conf. on Networking and Services (ICNS 2007), Athens, Greece, 2007.

M. De Leenheer, C. Develder, T. Stevens, B. Dhoedt, M. Pickavet, P. Demeester, “Design and control of optical grid networks (invited),” in Proc. 4th Int. Conf. on Broadband Networks (Broadnets 2007), Raleigh, NC, 2007, pp. 107–115.

P. Thysebaert, F. De Turck, B. Dhoedt, P. Demeester, “Using divisible load theory to dimension optical transport networks for grid excess load handling,” in Proc. Int. Conf. on Autonomic and Autonomous Systems & Int. Conf. on Networking and Systems (ICAS/ICNS 2005), Papeete, Tahiti, 2005.

F. Farahmand, M. De Leenheer, P. Thysebaert, B. Volckaert, F. De Turck, B. Dhoedt, P. Demeester, J. P. Jue, “A multi-layered approach to optical burst-switched based grids,” in Proc. 2nd Int. Conf. on Broadband Networks (Broadnets 2005), Oct. 2005, pp. 1050–1057.

Develder, C.

C. Develder, B. Mukherjee, B. Dhoedt, P. Demeester, “On dimensioning optical grids and the impact of scheduling,” Photonic Network Commun., vol. 17, no. 3, pp. 255–265, June 2009.
[CrossRef]

D. Colle, S. De Maesschalck, C. Develder, P. Van Heuven, A. Groebbens, J. Cheyns, I. Lievens, P. Lagasse, M. Pickavet, P. Demeester, “Data-centric optical networks and their survivability,” IEEE J. Sel. Areas Commun., vol. 20, no. 1, pp. 6–20, Jan. 2002.
[CrossRef]

M. De Leenheer, C. Develder, T. Stevens, B. Dhoedt, M. Pickavet, P. Demeester, “Design and control of optical grid networks (invited),” in Proc. 4th Int. Conf. on Broadband Networks (Broadnets 2007), Raleigh, NC, 2007, pp. 107–115.

E. Varvarigos, P. Kokkinos, K. Christodoulopoulos, M. Pilz, C. Barz, T. Stevens, J. Vermeir, C. Develder, M. De Leenheer, B. Dhoedt, “D5.2—QoS-aware resource scheduling,” IST Phosphorus project deliverable, Sept. 2007. Available: http://www.ist-phosphorus.eu/deliverables.php.

M. De Leenheer, C. Develder, F. De Turck, B. Dhoedt, P. Demeester, “Erlang reduced load model for optical burst switched grids,” in Proc. 3rd Int. Conf. on Networking and Services (ICNS 2007), Athens, Greece, 2007.

Dhoedt, B.

C. Develder, B. Mukherjee, B. Dhoedt, P. Demeester, “On dimensioning optical grids and the impact of scheduling,” Photonic Network Commun., vol. 17, no. 3, pp. 255–265, June 2009.
[CrossRef]

M. De Leenheer, P. Thysebaert, B. Volckaert, F. De Turck, B. Dhoedt, P. Demeester, D. Simeonidou, R. Nejabati, G. Zervas, D. Klonidis, M. J. O’Mahony, “A view on enabling consumer-oriented grids through optical burst switching,” IEEE Commun. Mag., vol. 44, no. 3, pp. 124–131, Mar. 2006.
[CrossRef]

M. De Leenheer, C. Develder, F. De Turck, B. Dhoedt, P. Demeester, “Erlang reduced load model for optical burst switched grids,” in Proc. 3rd Int. Conf. on Networking and Services (ICNS 2007), Athens, Greece, 2007.

E. Varvarigos, P. Kokkinos, K. Christodoulopoulos, M. Pilz, C. Barz, T. Stevens, J. Vermeir, C. Develder, M. De Leenheer, B. Dhoedt, “D5.2—QoS-aware resource scheduling,” IST Phosphorus project deliverable, Sept. 2007. Available: http://www.ist-phosphorus.eu/deliverables.php.

P. Thysebaert, F. De Turck, B. Dhoedt, P. Demeester, “Using divisible load theory to dimension optical transport networks for grid excess load handling,” in Proc. Int. Conf. on Autonomic and Autonomous Systems & Int. Conf. on Networking and Systems (ICAS/ICNS 2005), Papeete, Tahiti, 2005.

F. Farahmand, M. De Leenheer, P. Thysebaert, B. Volckaert, F. De Turck, B. Dhoedt, P. Demeester, J. P. Jue, “A multi-layered approach to optical burst-switched based grids,” in Proc. 2nd Int. Conf. on Broadband Networks (Broadnets 2005), Oct. 2005, pp. 1050–1057.

M. De Leenheer, C. Develder, T. Stevens, B. Dhoedt, M. Pickavet, P. Demeester, “Design and control of optical grid networks (invited),” in Proc. 4th Int. Conf. on Broadband Networks (Broadnets 2007), Raleigh, NC, 2007, pp. 107–115.

Farahmand, F.

F. Farahmand, M. De Leenheer, P. Thysebaert, B. Volckaert, F. De Turck, B. Dhoedt, P. Demeester, J. P. Jue, “A multi-layered approach to optical burst-switched based grids,” in Proc. 2nd Int. Conf. on Broadband Networks (Broadnets 2005), Oct. 2005, pp. 1050–1057.

Gerstel, O.

O. Gerstel, R. Ramaswami, G. H. Sasaki, “Cost-effective traffic grooming in WDM rings,” IEEE/ACM Trans. Netw., vol. 8, no. 5, pp. 618–630, Oct. 2000.
[CrossRef]

Groebbens, A.

D. Colle, S. De Maesschalck, C. Develder, P. Van Heuven, A. Groebbens, J. Cheyns, I. Lievens, P. Lagasse, M. Pickavet, P. Demeester, “Data-centric optical networks and their survivability,” IEEE J. Sel. Areas Commun., vol. 20, no. 1, pp. 6–20, Jan. 2002.
[CrossRef]

Heindl, A.

M. Telek, A. Heindl, “Matching moments for acyclic discrete and continuous phase-type distributions of second order,” Int. J. Simul. Syst., Sci. Technol., vol. 3, pp. 47–57, 2002.

Höller, H.

H. Höller, S. Voß, “A heuristic approach for combined equipment-planning and routing in multi-layer SDH/WDM networks,” Eur. J. Oper. Res., vol. 171, no. 3, pp. 787–796, June 2006.
[CrossRef]

Johnson, R.

R. Johnson, D. Wichern, Applied Multivariate Statistical Analysis. Prentice-Hall, 1998.

Jue, J. P.

F. Farahmand, M. De Leenheer, P. Thysebaert, B. Volckaert, F. De Turck, B. Dhoedt, P. Demeester, J. P. Jue, “A multi-layered approach to optical burst-switched based grids,” in Proc. 2nd Int. Conf. on Broadband Networks (Broadnets 2005), Oct. 2005, pp. 1050–1057.

Klonidis, D.

M. De Leenheer, P. Thysebaert, B. Volckaert, F. De Turck, B. Dhoedt, P. Demeester, D. Simeonidou, R. Nejabati, G. Zervas, D. Klonidis, M. J. O’Mahony, “A view on enabling consumer-oriented grids through optical burst switching,” IEEE Commun. Mag., vol. 44, no. 3, pp. 124–131, Mar. 2006.
[CrossRef]

D. Simeonidou, R. Nejabati, G. Zervas, D. Klonidis, A. Tzanakaki, M. J. O’Mahony, “Dynamic optical-network architectures and technologies for existing and emerging grid services,” J. Lightwave Technol., vol. 23, no. 10, pp. 3347–3357, Oct. 2005.
[CrossRef]

Koch, T.

A. Bley, T. Koch, R. Wessäly, “Large-scale hierarchical networks: how to compute an optimal architecture?” in Proc. 11th Int. Telecommunications Network Strategy and Planning Symp. (Networks 2004), Vienna, Austria, 2004, pp. 429–434.

Kokkinos, P.

E. Varvarigos, P. Kokkinos, K. Christodoulopoulos, M. Pilz, C. Barz, T. Stevens, J. Vermeir, C. Develder, M. De Leenheer, B. Dhoedt, “D5.2—QoS-aware resource scheduling,” IST Phosphorus project deliverable, Sept. 2007. Available: http://www.ist-phosphorus.eu/deliverables.php.

C. de Waal, U. Bornhauser, A. Willner, M. Pilz, C. Barz, E. Varvarigos, P. Kokkinos, K. Christodoulopoulos, “D5.4—Support for advance reservations in scheduling and routing,” IST Phosphorus project deliverable, June 2007. Available: http://www.ist-phosphorus.eu/deliverables.php.

Lagasse, P.

D. Colle, S. De Maesschalck, C. Develder, P. Van Heuven, A. Groebbens, J. Cheyns, I. Lievens, P. Lagasse, M. Pickavet, P. Demeester, “Data-centric optical networks and their survivability,” IEEE J. Sel. Areas Commun., vol. 20, no. 1, pp. 6–20, Jan. 2002.
[CrossRef]

Lawton, G.

G. Lawton, “Moving the OS to the web,” Computer, vol. 41, no. 3, pp. 16–19, Mar. 2008.
[CrossRef]

Le Boudec, J.

J. Le Boudec, D. McDonald, J. Mundinger, “A generic mean field convergence result for systems of interacting objects,” in Proc. 4th Int. Conf. on the Quantitative Evaluation of SysTems (QEST 2007), Edinburgh, UK, 2007, pp. 3–15.

Lievens, I.

D. Colle, S. De Maesschalck, C. Develder, P. Van Heuven, A. Groebbens, J. Cheyns, I. Lievens, P. Lagasse, M. Pickavet, P. Demeester, “Data-centric optical networks and their survivability,” IEEE J. Sel. Areas Commun., vol. 20, no. 1, pp. 6–20, Jan. 2002.
[CrossRef]

McDonald, D.

J. Le Boudec, D. McDonald, J. Mundinger, “A generic mean field convergence result for systems of interacting objects,” in Proc. 4th Int. Conf. on the Quantitative Evaluation of SysTems (QEST 2007), Edinburgh, UK, 2007, pp. 3–15.

Mukherjee, A.

B. Mukherjee, D. Banerjee, S. Ramamurthy, A. Mukherjee, “Some principles for designing a wide-area WDM optical network,” IEEE/ACM Trans. Netw., vol. 4, no. 5, pp. 684–696, Oct. 1996.
[CrossRef]

Mukherjee, B.

C. Develder, B. Mukherjee, B. Dhoedt, P. Demeester, “On dimensioning optical grids and the impact of scheduling,” Photonic Network Commun., vol. 17, no. 3, pp. 255–265, June 2009.
[CrossRef]

K. Zhu, H. Zang, B. Mukherjee, “A comprehensive study on next-generation optical grooming switches,” IEEE J. Sel. Areas Commun., vol. 21, no. 7, pp. 1173–1186, Sept. 2003.
[CrossRef]

B. Mukherjee, D. Banerjee, S. Ramamurthy, A. Mukherjee, “Some principles for designing a wide-area WDM optical network,” IEEE/ACM Trans. Netw., vol. 4, no. 5, pp. 684–696, Oct. 1996.
[CrossRef]

Mundinger, J.

J. Le Boudec, D. McDonald, J. Mundinger, “A generic mean field convergence result for systems of interacting objects,” in Proc. 4th Int. Conf. on the Quantitative Evaluation of SysTems (QEST 2007), Edinburgh, UK, 2007, pp. 3–15.

Nejabati, R.

M. De Leenheer, P. Thysebaert, B. Volckaert, F. De Turck, B. Dhoedt, P. Demeester, D. Simeonidou, R. Nejabati, G. Zervas, D. Klonidis, M. J. O’Mahony, “A view on enabling consumer-oriented grids through optical burst switching,” IEEE Commun. Mag., vol. 44, no. 3, pp. 124–131, Mar. 2006.
[CrossRef]

D. Simeonidou, R. Nejabati, G. Zervas, D. Klonidis, A. Tzanakaki, M. J. O’Mahony, “Dynamic optical-network architectures and technologies for existing and emerging grid services,” J. Lightwave Technol., vol. 23, no. 10, pp. 3347–3357, Oct. 2005.
[CrossRef]

O’Mahony, M. J.

M. De Leenheer, P. Thysebaert, B. Volckaert, F. De Turck, B. Dhoedt, P. Demeester, D. Simeonidou, R. Nejabati, G. Zervas, D. Klonidis, M. J. O’Mahony, “A view on enabling consumer-oriented grids through optical burst switching,” IEEE Commun. Mag., vol. 44, no. 3, pp. 124–131, Mar. 2006.
[CrossRef]

D. Simeonidou, R. Nejabati, G. Zervas, D. Klonidis, A. Tzanakaki, M. J. O’Mahony, “Dynamic optical-network architectures and technologies for existing and emerging grid services,” J. Lightwave Technol., vol. 23, no. 10, pp. 3347–3357, Oct. 2005.
[CrossRef]

Pickavet, M.

D. Colle, S. De Maesschalck, C. Develder, P. Van Heuven, A. Groebbens, J. Cheyns, I. Lievens, P. Lagasse, M. Pickavet, P. Demeester, “Data-centric optical networks and their survivability,” IEEE J. Sel. Areas Commun., vol. 20, no. 1, pp. 6–20, Jan. 2002.
[CrossRef]

M. Pickavet, P. Demeester, “Long-term planning of WDM networks: a comparison between single-period and multiperiod techniques,” Photonic Network Commun., vol. 1, no. 4, pp. 331–346, Dec. 1999.
[CrossRef]

M. De Leenheer, C. Develder, T. Stevens, B. Dhoedt, M. Pickavet, P. Demeester, “Design and control of optical grid networks (invited),” in Proc. 4th Int. Conf. on Broadband Networks (Broadnets 2007), Raleigh, NC, 2007, pp. 107–115.

Pilz, M.

E. Varvarigos, P. Kokkinos, K. Christodoulopoulos, M. Pilz, C. Barz, T. Stevens, J. Vermeir, C. Develder, M. De Leenheer, B. Dhoedt, “D5.2—QoS-aware resource scheduling,” IST Phosphorus project deliverable, Sept. 2007. Available: http://www.ist-phosphorus.eu/deliverables.php.

C. de Waal, U. Bornhauser, A. Willner, M. Pilz, C. Barz, E. Varvarigos, P. Kokkinos, K. Christodoulopoulos, “D5.4—Support for advance reservations in scheduling and routing,” IST Phosphorus project deliverable, June 2007. Available: http://www.ist-phosphorus.eu/deliverables.php.

Ramamurthy, S.

B. Mukherjee, D. Banerjee, S. Ramamurthy, A. Mukherjee, “Some principles for designing a wide-area WDM optical network,” IEEE/ACM Trans. Netw., vol. 4, no. 5, pp. 684–696, Oct. 1996.
[CrossRef]

Ramaswami, R.

O. Gerstel, R. Ramaswami, G. H. Sasaki, “Cost-effective traffic grooming in WDM rings,” IEEE/ACM Trans. Netw., vol. 8, no. 5, pp. 618–630, Oct. 2000.
[CrossRef]

Rosberg, Z.

Z. Rosberg, H. Vu, M. Zukerman, J. White, “Blocking probabilities of optical burst switching networks based on reduced load fixed point approximations,” in Proc. 22nd Annu. Joint Conf. of the IEEE Computer and Communications Societies (INFOCOM 2003), San Francisco, CA, 2003, pp. 2008–2018.

Sasaki, G. H.

O. Gerstel, R. Ramaswami, G. H. Sasaki, “Cost-effective traffic grooming in WDM rings,” IEEE/ACM Trans. Netw., vol. 8, no. 5, pp. 618–630, Oct. 2000.
[CrossRef]

Simeonidou, D.

M. De Leenheer, P. Thysebaert, B. Volckaert, F. De Turck, B. Dhoedt, P. Demeester, D. Simeonidou, R. Nejabati, G. Zervas, D. Klonidis, M. J. O’Mahony, “A view on enabling consumer-oriented grids through optical burst switching,” IEEE Commun. Mag., vol. 44, no. 3, pp. 124–131, Mar. 2006.
[CrossRef]

D. Simeonidou, R. Nejabati, G. Zervas, D. Klonidis, A. Tzanakaki, M. J. O’Mahony, “Dynamic optical-network architectures and technologies for existing and emerging grid services,” J. Lightwave Technol., vol. 23, no. 10, pp. 3347–3357, Oct. 2005.
[CrossRef]

Stevens, T.

E. Varvarigos, P. Kokkinos, K. Christodoulopoulos, M. Pilz, C. Barz, T. Stevens, J. Vermeir, C. Develder, M. De Leenheer, B. Dhoedt, “D5.2—QoS-aware resource scheduling,” IST Phosphorus project deliverable, Sept. 2007. Available: http://www.ist-phosphorus.eu/deliverables.php.

M. De Leenheer, C. Develder, T. Stevens, B. Dhoedt, M. Pickavet, P. Demeester, “Design and control of optical grid networks (invited),” in Proc. 4th Int. Conf. on Broadband Networks (Broadnets 2007), Raleigh, NC, 2007, pp. 107–115.

Telek, M.

M. Telek, A. Heindl, “Matching moments for acyclic discrete and continuous phase-type distributions of second order,” Int. J. Simul. Syst., Sci. Technol., vol. 3, pp. 47–57, 2002.

Thysebaert, P.

M. De Leenheer, P. Thysebaert, B. Volckaert, F. De Turck, B. Dhoedt, P. Demeester, D. Simeonidou, R. Nejabati, G. Zervas, D. Klonidis, M. J. O’Mahony, “A view on enabling consumer-oriented grids through optical burst switching,” IEEE Commun. Mag., vol. 44, no. 3, pp. 124–131, Mar. 2006.
[CrossRef]

F. Farahmand, M. De Leenheer, P. Thysebaert, B. Volckaert, F. De Turck, B. Dhoedt, P. Demeester, J. P. Jue, “A multi-layered approach to optical burst-switched based grids,” in Proc. 2nd Int. Conf. on Broadband Networks (Broadnets 2005), Oct. 2005, pp. 1050–1057.

P. Thysebaert, F. De Turck, B. Dhoedt, P. Demeester, “Using divisible load theory to dimension optical transport networks for grid excess load handling,” in Proc. Int. Conf. on Autonomic and Autonomous Systems & Int. Conf. on Networking and Systems (ICAS/ICNS 2005), Papeete, Tahiti, 2005.

Tzanakaki, A.

Van Heuven, P.

D. Colle, S. De Maesschalck, C. Develder, P. Van Heuven, A. Groebbens, J. Cheyns, I. Lievens, P. Lagasse, M. Pickavet, P. Demeester, “Data-centric optical networks and their survivability,” IEEE J. Sel. Areas Commun., vol. 20, no. 1, pp. 6–20, Jan. 2002.
[CrossRef]

Varvarigos, E.

E. Varvarigos, P. Kokkinos, K. Christodoulopoulos, M. Pilz, C. Barz, T. Stevens, J. Vermeir, C. Develder, M. De Leenheer, B. Dhoedt, “D5.2—QoS-aware resource scheduling,” IST Phosphorus project deliverable, Sept. 2007. Available: http://www.ist-phosphorus.eu/deliverables.php.

C. de Waal, U. Bornhauser, A. Willner, M. Pilz, C. Barz, E. Varvarigos, P. Kokkinos, K. Christodoulopoulos, “D5.4—Support for advance reservations in scheduling and routing,” IST Phosphorus project deliverable, June 2007. Available: http://www.ist-phosphorus.eu/deliverables.php.

Vermeir, J.

E. Varvarigos, P. Kokkinos, K. Christodoulopoulos, M. Pilz, C. Barz, T. Stevens, J. Vermeir, C. Develder, M. De Leenheer, B. Dhoedt, “D5.2—QoS-aware resource scheduling,” IST Phosphorus project deliverable, Sept. 2007. Available: http://www.ist-phosphorus.eu/deliverables.php.

Volckaert, B.

M. De Leenheer, P. Thysebaert, B. Volckaert, F. De Turck, B. Dhoedt, P. Demeester, D. Simeonidou, R. Nejabati, G. Zervas, D. Klonidis, M. J. O’Mahony, “A view on enabling consumer-oriented grids through optical burst switching,” IEEE Commun. Mag., vol. 44, no. 3, pp. 124–131, Mar. 2006.
[CrossRef]

F. Farahmand, M. De Leenheer, P. Thysebaert, B. Volckaert, F. De Turck, B. Dhoedt, P. Demeester, J. P. Jue, “A multi-layered approach to optical burst-switched based grids,” in Proc. 2nd Int. Conf. on Broadband Networks (Broadnets 2005), Oct. 2005, pp. 1050–1057.

Voß, S.

H. Höller, S. Voß, “A heuristic approach for combined equipment-planning and routing in multi-layer SDH/WDM networks,” Eur. J. Oper. Res., vol. 171, no. 3, pp. 787–796, June 2006.
[CrossRef]

Vu, H.

Z. Rosberg, H. Vu, M. Zukerman, J. White, “Blocking probabilities of optical burst switching networks based on reduced load fixed point approximations,” in Proc. 22nd Annu. Joint Conf. of the IEEE Computer and Communications Societies (INFOCOM 2003), San Francisco, CA, 2003, pp. 2008–2018.

Wessäly, R.

A. Bley, T. Koch, R. Wessäly, “Large-scale hierarchical networks: how to compute an optimal architecture?” in Proc. 11th Int. Telecommunications Network Strategy and Planning Symp. (Networks 2004), Vienna, Austria, 2004, pp. 429–434.

White, J.

Z. Rosberg, H. Vu, M. Zukerman, J. White, “Blocking probabilities of optical burst switching networks based on reduced load fixed point approximations,” in Proc. 22nd Annu. Joint Conf. of the IEEE Computer and Communications Societies (INFOCOM 2003), San Francisco, CA, 2003, pp. 2008–2018.

Wichern, D.

R. Johnson, D. Wichern, Applied Multivariate Statistical Analysis. Prentice-Hall, 1998.

Willner, A.

C. de Waal, U. Bornhauser, A. Willner, M. Pilz, C. Barz, E. Varvarigos, P. Kokkinos, K. Christodoulopoulos, “D5.4—Support for advance reservations in scheduling and routing,” IST Phosphorus project deliverable, June 2007. Available: http://www.ist-phosphorus.eu/deliverables.php.

Zang, H.

K. Zhu, H. Zang, B. Mukherjee, “A comprehensive study on next-generation optical grooming switches,” IEEE J. Sel. Areas Commun., vol. 21, no. 7, pp. 1173–1186, Sept. 2003.
[CrossRef]

Zervas, G.

M. De Leenheer, P. Thysebaert, B. Volckaert, F. De Turck, B. Dhoedt, P. Demeester, D. Simeonidou, R. Nejabati, G. Zervas, D. Klonidis, M. J. O’Mahony, “A view on enabling consumer-oriented grids through optical burst switching,” IEEE Commun. Mag., vol. 44, no. 3, pp. 124–131, Mar. 2006.
[CrossRef]

D. Simeonidou, R. Nejabati, G. Zervas, D. Klonidis, A. Tzanakaki, M. J. O’Mahony, “Dynamic optical-network architectures and technologies for existing and emerging grid services,” J. Lightwave Technol., vol. 23, no. 10, pp. 3347–3357, Oct. 2005.
[CrossRef]

Zhu, K.

K. Zhu, H. Zang, B. Mukherjee, “A comprehensive study on next-generation optical grooming switches,” IEEE J. Sel. Areas Commun., vol. 21, no. 7, pp. 1173–1186, Sept. 2003.
[CrossRef]

Zukerman, M.

Z. Rosberg, H. Vu, M. Zukerman, J. White, “Blocking probabilities of optical burst switching networks based on reduced load fixed point approximations,” in Proc. 22nd Annu. Joint Conf. of the IEEE Computer and Communications Societies (INFOCOM 2003), San Francisco, CA, 2003, pp. 2008–2018.

Computer (1)

G. Lawton, “Moving the OS to the web,” Computer, vol. 41, no. 3, pp. 16–19, Mar. 2008.
[CrossRef]

Eur. J. Oper. Res. (1)

H. Höller, S. Voß, “A heuristic approach for combined equipment-planning and routing in multi-layer SDH/WDM networks,” Eur. J. Oper. Res., vol. 171, no. 3, pp. 787–796, June 2006.
[CrossRef]

IEEE Commun. Mag. (1)

M. De Leenheer, P. Thysebaert, B. Volckaert, F. De Turck, B. Dhoedt, P. Demeester, D. Simeonidou, R. Nejabati, G. Zervas, D. Klonidis, M. J. O’Mahony, “A view on enabling consumer-oriented grids through optical burst switching,” IEEE Commun. Mag., vol. 44, no. 3, pp. 124–131, Mar. 2006.
[CrossRef]

IEEE J. Sel. Areas Commun. (2)

K. Zhu, H. Zang, B. Mukherjee, “A comprehensive study on next-generation optical grooming switches,” IEEE J. Sel. Areas Commun., vol. 21, no. 7, pp. 1173–1186, Sept. 2003.
[CrossRef]

D. Colle, S. De Maesschalck, C. Develder, P. Van Heuven, A. Groebbens, J. Cheyns, I. Lievens, P. Lagasse, M. Pickavet, P. Demeester, “Data-centric optical networks and their survivability,” IEEE J. Sel. Areas Commun., vol. 20, no. 1, pp. 6–20, Jan. 2002.
[CrossRef]

IEEE/ACM Trans. Netw. (2)

O. Gerstel, R. Ramaswami, G. H. Sasaki, “Cost-effective traffic grooming in WDM rings,” IEEE/ACM Trans. Netw., vol. 8, no. 5, pp. 618–630, Oct. 2000.
[CrossRef]

B. Mukherjee, D. Banerjee, S. Ramamurthy, A. Mukherjee, “Some principles for designing a wide-area WDM optical network,” IEEE/ACM Trans. Netw., vol. 4, no. 5, pp. 684–696, Oct. 1996.
[CrossRef]

Int. J. Simul. Syst., Sci. Technol. (1)

M. Telek, A. Heindl, “Matching moments for acyclic discrete and continuous phase-type distributions of second order,” Int. J. Simul. Syst., Sci. Technol., vol. 3, pp. 47–57, 2002.

J. Lightwave Technol. (1)

Photonic Network Commun. (2)

C. Develder, B. Mukherjee, B. Dhoedt, P. Demeester, “On dimensioning optical grids and the impact of scheduling,” Photonic Network Commun., vol. 17, no. 3, pp. 255–265, June 2009.
[CrossRef]

M. Pickavet, P. Demeester, “Long-term planning of WDM networks: a comparison between single-period and multiperiod techniques,” Photonic Network Commun., vol. 1, no. 4, pp. 331–346, Dec. 1999.
[CrossRef]

Other (11)

A. Bley, T. Koch, R. Wessäly, “Large-scale hierarchical networks: how to compute an optimal architecture?” in Proc. 11th Int. Telecommunications Network Strategy and Planning Symp. (Networks 2004), Vienna, Austria, 2004, pp. 429–434.

P. Thysebaert, F. De Turck, B. Dhoedt, P. Demeester, “Using divisible load theory to dimension optical transport networks for grid excess load handling,” in Proc. Int. Conf. on Autonomic and Autonomous Systems & Int. Conf. on Networking and Systems (ICAS/ICNS 2005), Papeete, Tahiti, 2005.

M. De Leenheer, C. Develder, F. De Turck, B. Dhoedt, P. Demeester, “Erlang reduced load model for optical burst switched grids,” in Proc. 3rd Int. Conf. on Networking and Services (ICNS 2007), Athens, Greece, 2007.

Z. Rosberg, H. Vu, M. Zukerman, J. White, “Blocking probabilities of optical burst switching networks based on reduced load fixed point approximations,” in Proc. 22nd Annu. Joint Conf. of the IEEE Computer and Communications Societies (INFOCOM 2003), San Francisco, CA, 2003, pp. 2008–2018.

C. de Waal, U. Bornhauser, A. Willner, M. Pilz, C. Barz, E. Varvarigos, P. Kokkinos, K. Christodoulopoulos, “D5.4—Support for advance reservations in scheduling and routing,” IST Phosphorus project deliverable, June 2007. Available: http://www.ist-phosphorus.eu/deliverables.php.

E. Varvarigos, P. Kokkinos, K. Christodoulopoulos, M. Pilz, C. Barz, T. Stevens, J. Vermeir, C. Develder, M. De Leenheer, B. Dhoedt, “D5.2—QoS-aware resource scheduling,” IST Phosphorus project deliverable, Sept. 2007. Available: http://www.ist-phosphorus.eu/deliverables.php.

M. De Leenheer, C. Develder, T. Stevens, B. Dhoedt, M. Pickavet, P. Demeester, “Design and control of optical grid networks (invited),” in Proc. 4th Int. Conf. on Broadband Networks (Broadnets 2007), Raleigh, NC, 2007, pp. 107–115.

F. Farahmand, M. De Leenheer, P. Thysebaert, B. Volckaert, F. De Turck, B. Dhoedt, P. Demeester, J. P. Jue, “A multi-layered approach to optical burst-switched based grids,” in Proc. 2nd Int. Conf. on Broadband Networks (Broadnets 2005), Oct. 2005, pp. 1050–1057.

J. Le Boudec, D. McDonald, J. Mundinger, “A generic mean field convergence result for systems of interacting objects,” in Proc. 4th Int. Conf. on the Quantitative Evaluation of SysTems (QEST 2007), Edinburgh, UK, 2007, pp. 3–15.

R. Johnson, D. Wichern, Applied Multivariate Statistical Analysis. Prentice-Hall, 1998.

Enabling Grids for E-sciencE. Available: http://www.eu-egee.org.

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Figures (5)

Fig. 1
Fig. 1

The Grid dimensioning problem involves both network and Grid resource dimensioning to cater to a given load of jobs submitted by users.

Fig. 2
Fig. 2

Mean field results for a two-class Grid, with variable load for class-1 sites.

Fig. 3
Fig. 3

Mean field results for a single-class Grid, with variable load and number of servers per site.

Fig. 4
Fig. 4

Simulation results match well with the analytical mean field for a variable Grid resource load for (a) mostfree and (b) random scheduling. Note that the curves for classes 3–5 overlap to great extent.

Fig. 5
Fig. 5

Comparison of mostfree and random scheduling for different SCVs of the interarrival distribution. Note that only classes 1–3 are shown since results for classes 4 and 5 overlap with those of class 3.

Tables (1)

Tables Icon

Table 1 Characteristics of the Five Site Clusters

Equations (22)

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

S = [ s 0 , 0 0 0 s 1 , 0 s 1 , 1 0 s C , 0 s C , C 1 s C , C ] I h ,
A = [ T θ α 0 0 0 T θ α 0 0 0 T θ α ] .
k = 0 c 1 b k ( t ) < a C + 1 ( t ) k = 0 c b k ( t ) ,
β c [ M N ( t ) ] = k = 0 c [ M N ( t ) ] b k ( t ) a C + 1 ( t ) b c [ M N ( t ) ] ( t ) .
q i , i [ M N ( t ) ] = { 1 β c [ M N ( t ) ] i < i = c [ M N ( t ) ] + 1 C , β c [ M N ( t ) ] i i = c [ M N ( t ) ] < C , 1 i = i > c [ M N ( t ) ] 1 i = C = c [ M N ( t ) ] , }
Q [ M N ( t ) ] = [ q 0 , 0 [ M N ( t ) ] q 0 , 1 [ M N ( t ) ] q 0 , C [ M N ( t ) ] 0 q 1 , 1 [ M N ( t ) ] q 1 , C [ M N ( t ) ] 0 q C , C [ M N ( t ) ] 0 0 1 ] I h ,
q ¯ i , i + i [ M N ( t ) ] = ( C i i ) ( f [ M N ( t ) ] ( C i ) a C + 1 ( t ) i ) ( f [ M N ( t ) ] a C + 1 ( t ) ) ,
K [ M N ( t ) ] = Q [ M N ( t ) ] S A ,
q ¯ i , i + i [ M ( t ) ] = ( C i i ) ( M C + 1 ( t ) f [ M ( t ) ] ) i ( 1 M C + 1 ( t ) f [ M ( t ) ] ) C i i ,
μ ( t + 1 ) = μ ( t ) K [ μ ( t ) ( I C + 2 e h ) ] .
lim N M N ( t ) = μ ( t ) ( I C + 2 e h ) .
λ exc ( k ) = μ ( k ) ( t ) Q ( k ) [ M ( k ) ( t ) ] [ 0 p ( k ) 2 p ( k ) C ( k ) p ( k ) ] e h ( k ) [ λ ( k ) M C ( k ) + 1 ( k ) ( t ) ] ,
r k , j = M C ( k ) + 1 ( k ) ( t ) λ exc ( j ) s = 1 K λ exc ( s ) = λ exc ( j ) M C ( k ) + 1 ( k ) ( t ) s = 1 K M C ( s ) + 1 ( s ) ( t ) ,
P spill , k = ( s class k d s D s , d ) ( s class k d D s , d ) .
K [ M N ( t ) ] = [ K ( 1 ) [ M N ( t ) ] 0 0 0 K ( 2 ) [ M N ( t ) ] 0 0 0 K ( K ) [ M N ( t ) ] ] .
M N ( t ) = [ γ 1 M N , ( 1 ) ( t ) , , γ K M N , ( K ) ( t ) ] .
q ¯ i , i + i ( k ) [ M N ( t ) ] = [ C ( k ) i i ] ( f [ M N ( t ) ] ( C ( k ) i ) k = 1 K a C ( k ) + 1 ( k ) ( t ) i ) ( f [ M N ( t ) ] k = 1 K a C ( k ) + 1 ( k ) ( t ) ) ,
i = d + 1 C ( 1 ) k = 1 K b C ( k ) i ( k ) ( t ) < a T ( t ) i = d C ( 1 ) k = 1 K b C ( k ) i ( k ) ( t ) ,
γ d [ M N ( t ) ] = i = d [ M N ( t ) ] C ( 1 ) k = 1 K b C ( k ) i ( k ) ( t ) a T ( t ) k = 1 K b C ( k ) d [ M N ( t ) ] ( k ) ( t ) .
q i , i ( k ) [ M N ( t ) ] = { 1 γ d [ M N ( t ) ] i < i = C ( k ) d [ M N ( t ) ] + 1 C ( k ) , γ d [ M N ( t ) ] i i = C ( k ) d [ M N ( t ) ] < C ( k ) , 1 i = i > C ( k ) d [ M N ( t ) ] 1 i = C ( k ) = C ( k ) d [ M N ( t ) ] , }
μ ( k ) ( t + 1 ) = μ ( k ) ( t ) K ( k ) [ γ 1 μ ( 1 ) ( t ) ( I C ( 1 ) + 2 e h ( 1 ) ) , , γ K μ ( K ) ( t ) ( I C ( K ) + 2 e h ( K ) ) ] ,
lim N M N , ( k ) ( t ) = μ ( k ) ( t ) ( I C ( k ) + 2 e h ( k ) ) .