Abstract

We consider a circuit-switched network with nonhierarchical alternate routing and trunk reservation involving two types of connections that are modeled as long-lived and short-lived calls. The long-lived calls can be reserved well in advance, and the short-lived calls are provided on demand. Therefore, we assume that the long-lived calls have strict priority over the short-lived ones. We develop approximations for the estimation of the blocking probability based on the quasi-stationary approach in two ways. One uses the Erlang fixed-point approximation (EFPA), and the other uses the overflow priority classification approximation (OPCA). We compare the results of the approximations with simulation results and discuss the accuracy of the approximations under different system parameters, such as ratio of offered load, number of links per trunk, maximum allowable number of deflections, and trunk reservation. We also discuss the robustness of the quasi-stationary approximation to the ratio of the mean holding times of the long-lived and short-lived calls as well as that of EFPA and OPCA to the shape of the holding time distribution. Finally, we demonstrate that OPCA can be applied to a large network such as the Coronet.

© 2013 Optical Society of America

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  13. R. I. Wilkinson, “Theories of toll traffic engineering in the USA,” Bell Syst. Tech. J., vol.  35, pp. 421–514, Mar. 1956.
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  16. K. Jung, Y. Lu, D. Shah, M. Sharma, and M. S. Squillante, “Revisiting stochastic loss networks: structures and algorithms,” ACM SIGMETRICS Perform. Eval. Rev., vol.  36, pp. 407–418, June 2008.
    [CrossRef]
  17. F. P. Kelly, “Loss networks,” Ann. Appl. Probab., vol.  1, pp. 319–378, Aug. 1991.
    [CrossRef]
  18. D. Mitra, “Asymptotic analysis and computational methods for a class of simple circuit-switched networks with blocking,” Adv. Appl. Probab., vol.  19, pp. 219–239, Mar. 1987.
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    [CrossRef]
  25. A. J. Coyle, W. Henderson, and P. G. Taylor, “Reduced load approximations for loss networks,” Telecommun. Syst., vol.  2, pp. 21–50, 1993.
    [CrossRef]
  26. E. W. M. Wong, M. Y. M. Chiu, Z. Rosberg, M. Zukerman, S. Chan, and A. Zalesky, “A novel method for modeling and analysis of distributed video on demand systems,” in Proc. IEEE ICC, Seoul, South Korea, May 2005, vol. 1, pp. 88–92.
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    [CrossRef]
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  29. E. W. M. Wong, B. Moran, A. Zalesky, Z. Rosberg, and M. Zukerman, “On the accuracy of the OPC approximation for a symmetric overflow loss model,” Stoch. Models, vol.  29, no. 2, pp. 149–189, May 2013.
  30. C. Qiao, Y. Mei, M. Yoo, and X. Zhang, “Polymorphic control for cost-effective design of optical networks,” Eur. Trans. Telecommun., vol.  11, pp. 17–26, 2000.
  31. A. Chiu, G. Choudhury, G. Clapp, B. Doverspike, J. Gannett, J. Klincewicz, G. Ligli, R. Skoog, J. Strand, A. Von Lehmen, and D. Xu, “Network design and architectures for highly dynamic next-generation IP-over-optical long distance networks,” J. Lightwave Technol., vol.  27, pp. 1878–1890, 2009.
    [CrossRef]
  32. A. Elwalid, D. Mitra, I. Saniee, and I. Widjaja, “Routing and protection in GMPLS networks: from shortest paths to optimized designs,” J. Lightwave Technol., vol.  21, pp. 2828–2838, 2003.
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  33. M. Youssef, E. Doumith, and M. Gagnaire, “Power-aware multi-rate WDM network design under static/dynamic traffic,” in IEEE Global Telecommunications Conf. (GLOBECOM), Houston, TX, Dec. 2011.
  34. A. Leon-Garcia, R. H. Kwong, and G. F. Williams, “Performance evaluation methods for an integrated voice/data link,” IEEE Trans. Commun., vol.  30, pp. 1848–1858, Aug. 1982.
    [CrossRef]
  35. O. Boxma, A. Gabor, R. Nunez-Queija, and H.-P. Tan, “Performance analysis of admission control for integrated services with minimum rate guarantees,” in Proc. 2nd NGI, Valencia, Spain, Apr. 2006, pp. 41–47.
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    [CrossRef]
  38. I. Katib and D. Medhi, “Adaptive alternate routing in WDM networks and its performance tradeoffs in the presence of wavelength converters,” Opt. Switching Netw., vol.  6, no. 3, pp. 181–193, 2009.
  39. V. B. Iversen, Teletraffic Engineering and Network Planning, 2001 [Online]. Available: FTP: dei.polimi.it. Directory: users/Flaminio.Borgonovo/Teoria. File: teletraffic_Iversen.pdf.
  40. W. Feller, An Introduction to Probability Theory and Its Applications. New York: Wiley, 1968, pp. 460–478.
  41. A. Itai, Y. Perl, and Y. Shiloach, “The complexity of finding maximum disjoint paths with length constraints,” Networks, vol.  12, no. 3, pp. 277–286, 1982.
    [CrossRef]
  42. M. Middendorf and F. Pfeiffer, “On the complexity of the disjoint paths problem,” Combinatorica, vol.  13, pp. 97–107, 1993.
    [CrossRef]
  43. C. Chekuri and S. Khanna, “Edge disjoint paths revisited,” in Proc. SODA, 2003, pp. 628–637.
  44. J. Wolf, A. Viterbi, and G. Dixon, “Finding the best set of k paths through a trellis with application to multitarget tracking,” IEEE Trans. Aerosp. Electron. Syst., vol.  25, pp. 287–296, Mar. 1989.
  45. C. Xin, C. Qiao, and S. Dixit, “Traffic grooming in mesh WDM optical networks—performance analysis,” IEEE J. Sel. Areas Commun., vol.  22, pp. 1658–1669, Nov. 2004.
    [CrossRef]
  46. F. Delcoigne, A. Proutière, and G. Régnie, “Modeling integration of streaming and data traffic,” Perform. Eval., vol.  55, no. 3–4, pp. 185–209, 2004.

2013 (1)

E. W. M. Wong, B. Moran, A. Zalesky, Z. Rosberg, and M. Zukerman, “On the accuracy of the OPC approximation for a symmetric overflow loss model,” Stoch. Models, vol.  29, no. 2, pp. 149–189, May 2013.

2010 (1)

J. F. Pérez and B. V. Houdt, “Markovian approximations for a grid computing network with a ring structure,” Stoch. Models, vol.  26, no. 3, pp. 357–383, 2010.
[CrossRef]

2009 (7)

2008 (1)

K. Jung, Y. Lu, D. Shah, M. Sharma, and M. S. Squillante, “Revisiting stochastic loss networks: structures and algorithms,” ACM SIGMETRICS Perform. Eval. Rev., vol.  36, pp. 407–418, June 2008.
[CrossRef]

2007 (3)

G. Raskutti, A. Zalesky, E. W. M. Wong, and M. Zukerman, “Enhanced blocking probability evaluation method for circuit-switched trunk reservation networks,” IEEE Commun. Lett., vol.  11, pp. 543–545, June 2007.
[CrossRef]

E. W. M. Wong, A. Zalesky, Z. Rosberg, and M. Zukerman, “A new method for approximating blocking probability in overflow loss networks,” Comput. Netw., vol.  51, pp. 2958–2975, Aug. 2007.
[CrossRef]

M. Baldi, G. Marchetto, and Y. Ofek, “A scalable solution for engineering streaming traffic in the future Internet,” Comput. Netw., vol.  51, pp. 4092–4111, Oct. 2007.
[CrossRef]

2004 (2)

C. Xin, C. Qiao, and S. Dixit, “Traffic grooming in mesh WDM optical networks—performance analysis,” IEEE J. Sel. Areas Commun., vol.  22, pp. 1658–1669, Nov. 2004.
[CrossRef]

F. Delcoigne, A. Proutière, and G. Régnie, “Modeling integration of streaming and data traffic,” Perform. Eval., vol.  55, no. 3–4, pp. 185–209, 2004.

2003 (1)

2000 (2)

C. Qiao, Y. Mei, M. Yoo, and X. Zhang, “Polymorphic control for cost-effective design of optical networks,” Eur. Trans. Telecommun., vol.  11, pp. 17–26, 2000.

E. W. M. Wong, A. K. M. Chan, and T. S. Yum, “Analysis of rerouting in circuit-switched networks,” IEEE/ACM Trans. Netw., vol.  8, pp. 419–427, June 2000.

1995 (1)

E. W. M. Wong, T. S. Yum, and K. M. Chan, “Analysis of the m and m2 routings in circuit-switched networks,” Eur. Trans. Telecommun., vol.  6, pp. 613–619, Dec. 1995.

1993 (2)

A. J. Coyle, W. Henderson, and P. G. Taylor, “Reduced load approximations for loss networks,” Telecommun. Syst., vol.  2, pp. 21–50, 1993.
[CrossRef]

M. Middendorf and F. Pfeiffer, “On the complexity of the disjoint paths problem,” Combinatorica, vol.  13, pp. 97–107, 1993.
[CrossRef]

1991 (1)

F. P. Kelly, “Loss networks,” Ann. Appl. Probab., vol.  1, pp. 319–378, Aug. 1991.
[CrossRef]

1989 (1)

J. Wolf, A. Viterbi, and G. Dixon, “Finding the best set of k paths through a trellis with application to multitarget tracking,” IEEE Trans. Aerosp. Electron. Syst., vol.  25, pp. 287–296, Mar. 1989.

1987 (1)

D. Mitra, “Asymptotic analysis and computational methods for a class of simple circuit-switched networks with blocking,” Adv. Appl. Probab., vol.  19, pp. 219–239, Mar. 1987.
[CrossRef]

1986 (1)

F. P. Kelly, “Blocking probabilities in large circuit-switched networks,” Adv. Appl. Probab., vol.  18, pp. 473–505, June 1986.
[CrossRef]

1985 (1)

W. Whitt, “Blocking when service is required from several facilities simultaneously,” AT&T Tech. J., vol.  64, pp. 1807–1856, Oct. 1985.

1983 (1)

L. Delbrouck, “The uses of Kosten’s systems in the provisioning of alternate trunk groups carrying heterogeneous traffic,” IEEE Trans. Commun., vol.  31, pp. 741–749, June 1983.
[CrossRef]

1982 (2)

A. Leon-Garcia, R. H. Kwong, and G. F. Williams, “Performance evaluation methods for an integrated voice/data link,” IEEE Trans. Commun., vol.  30, pp. 1848–1858, Aug. 1982.
[CrossRef]

A. Itai, Y. Perl, and Y. Shiloach, “The complexity of finding maximum disjoint paths with length constraints,” Networks, vol.  12, no. 3, pp. 277–286, 1982.
[CrossRef]

1956 (1)

R. I. Wilkinson, “Theories of toll traffic engineering in the USA,” Bell Syst. Tech. J., vol.  35, pp. 421–514, Mar. 1956.

1937 (1)

L. Kosten, “On the blocking probability of graded multiples,” Nachrichtentech.-Elektron., vol.  14, pp. 5–12, Jan. 1937.

Anselmi, J.

J. Anselmi, Y. Lu, M. Sharma, and M. S. Squillante, “Improved approximations for the Erlang loss model,” Queueing Syst., vol.  63, pp. 217–239, Dec. 2009.
[CrossRef]

Ash, G.

A. Farrel, A. Satyanarayana, A. Iwata, N. Fujita, and G. Ash, “Crankback signaling extensions for MPLS and GMPLS RSVP-TE,” , July 2007 [Online]. Available: http://www.ietf.org/rfc/rfc4920.txt .

Baldi, M.

M. Baldi, G. Marchetto, and Y. Ofek, “A scalable solution for engineering streaming traffic in the future Internet,” Comput. Netw., vol.  51, pp. 4092–4111, Oct. 2007.
[CrossRef]

Baliga, J.

Barczyk, A.

A. Barczyk, “World-wide networking for LHC data processing,” in Nat. Fiber Optic Engineers Conf. (NFOEC), Los Angeles, CA, Mar. 2012, paper NTu1E.1.

Boxma, O.

O. Boxma, A. Gabor, R. Nunez-Queija, and H.-P. Tan, “Performance analysis of admission control for integrated services with minimum rate guarantees,” in Proc. 2nd NGI, Valencia, Spain, Apr. 2006, pp. 41–47.

Chan, A. K. M.

E. W. M. Wong, A. K. M. Chan, and T. S. Yum, “Analysis of rerouting in circuit-switched networks,” IEEE/ACM Trans. Netw., vol.  8, pp. 419–427, June 2000.

Chan, K. M.

E. W. M. Wong, T. S. Yum, and K. M. Chan, “Analysis of the m and m2 routings in circuit-switched networks,” Eur. Trans. Telecommun., vol.  6, pp. 613–619, Dec. 1995.

Chan, S.

E. W. M. Wong, M. Y. M. Chiu, Z. Rosberg, M. Zukerman, S. Chan, and A. Zalesky, “A novel method for modeling and analysis of distributed video on demand systems,” in Proc. IEEE ICC, Seoul, South Korea, May 2005, vol. 1, pp. 88–92.

Chan, V.

Chekuri, C.

C. Chekuri and S. Khanna, “Edge disjoint paths revisited,” in Proc. SODA, 2003, pp. 628–637.

Chiu, A.

A. Chiu, G. Choudhury, G. Clapp, B. Doverspike, J. Gannett, J. Klincewicz, G. Ligli, R. Skoog, J. Strand, A. Von Lehmen, and D. Xu, “Network design and architectures for highly dynamic next-generation IP-over-optical long distance networks,” J. Lightwave Technol., vol.  27, pp. 1878–1890, 2009.
[CrossRef]

A. Mahimkar, A. Chiu, R. Doverspike, M. D. Feuer, P. Magill, E. Mavrogiorgis, J. Pastor, S. L. Woodward, and J. Yates, “Bandwidth on demand for inter-data center communication,” in Proc. 10th ACM Workshop on Hot Topics in Networks (HotNets-X), Cambridge, MA, Nov. 2011.

Chiu, M. Y. M.

E. W. M. Wong, M. Y. M. Chiu, Z. Rosberg, M. Zukerman, S. Chan, and A. Zalesky, “A novel method for modeling and analysis of distributed video on demand systems,” in Proc. IEEE ICC, Seoul, South Korea, May 2005, vol. 1, pp. 88–92.

Choudhury, G.

Clapp, G.

Cooper, R. B.

R. B. Cooper and S. S. Katz, “Analysis of alternate routing networks with account taken of the nonrandomness of overflow traffic,” Bell Telephone Lab, Tech. Rep., 1964, memo.

Coyle, A. J.

A. J. Coyle, W. Henderson, and P. G. Taylor, “Reduced load approximations for loss networks,” Telecommun. Syst., vol.  2, pp. 21–50, 1993.
[CrossRef]

Delbrouck, L.

L. Delbrouck, “The uses of Kosten’s systems in the provisioning of alternate trunk groups carrying heterogeneous traffic,” IEEE Trans. Commun., vol.  31, pp. 741–749, June 1983.
[CrossRef]

Delcoigne, F.

F. Delcoigne, A. Proutière, and G. Régnie, “Modeling integration of streaming and data traffic,” Perform. Eval., vol.  55, no. 3–4, pp. 185–209, 2004.

Dixit, S.

C. Xin, C. Qiao, and S. Dixit, “Traffic grooming in mesh WDM optical networks—performance analysis,” IEEE J. Sel. Areas Commun., vol.  22, pp. 1658–1669, Nov. 2004.
[CrossRef]

Dixon, G.

J. Wolf, A. Viterbi, and G. Dixon, “Finding the best set of k paths through a trellis with application to multitarget tracking,” IEEE Trans. Aerosp. Electron. Syst., vol.  25, pp. 287–296, Mar. 1989.

Doumith, E.

M. Youssef, E. Doumith, and M. Gagnaire, “Power-aware multi-rate WDM network design under static/dynamic traffic,” in IEEE Global Telecommunications Conf. (GLOBECOM), Houston, TX, Dec. 2011.

Doverspike, B.

Doverspike, R.

A. Mahimkar, A. Chiu, R. Doverspike, M. D. Feuer, P. Magill, E. Mavrogiorgis, J. Pastor, S. L. Woodward, and J. Yates, “Bandwidth on demand for inter-data center communication,” in Proc. 10th ACM Workshop on Hot Topics in Networks (HotNets-X), Cambridge, MA, Nov. 2011.

Elwalid, A.

Farrel, A.

A. Farrel, A. Satyanarayana, A. Iwata, N. Fujita, and G. Ash, “Crankback signaling extensions for MPLS and GMPLS RSVP-TE,” , July 2007 [Online]. Available: http://www.ietf.org/rfc/rfc4920.txt .

Feller, W.

W. Feller, An Introduction to Probability Theory and Its Applications. New York: Wiley, 1968, pp. 460–478.

Feuer, M. D.

A. Mahimkar, A. Chiu, R. Doverspike, M. D. Feuer, P. Magill, E. Mavrogiorgis, J. Pastor, S. L. Woodward, and J. Yates, “Bandwidth on demand for inter-data center communication,” in Proc. 10th ACM Workshop on Hot Topics in Networks (HotNets-X), Cambridge, MA, Nov. 2011.

Fujita, N.

A. Farrel, A. Satyanarayana, A. Iwata, N. Fujita, and G. Ash, “Crankback signaling extensions for MPLS and GMPLS RSVP-TE,” , July 2007 [Online]. Available: http://www.ietf.org/rfc/rfc4920.txt .

Gabor, A.

O. Boxma, A. Gabor, R. Nunez-Queija, and H.-P. Tan, “Performance analysis of admission control for integrated services with minimum rate guarantees,” in Proc. 2nd NGI, Valencia, Spain, Apr. 2006, pp. 41–47.

Gagnaire, M.

M. Youssef, E. Doumith, and M. Gagnaire, “Power-aware multi-rate WDM network design under static/dynamic traffic,” in IEEE Global Telecommunications Conf. (GLOBECOM), Houston, TX, Dec. 2011.

Gannett, J.

Girard, A.

A. Girard, Routing and Dimensioning in Circuit-Switched Networks. Boston, MA: Addison-Wesley Longman, 1990.

Hagesawa, H.

Harada, Y.

A. Inoue, H. Yamamoto, and Y. Harada, “An advanced large scale simulation system for telecommunications networks with dynamic routing,” in Network Planning in the 1990s, D. L. Lada, Ed. New York: Elsevier, 1989, pp. 77–82.

Henderson, W.

A. J. Coyle, W. Henderson, and P. G. Taylor, “Reduced load approximations for loss networks,” Telecommun. Syst., vol.  2, pp. 21–50, 1993.
[CrossRef]

Houdt, B. V.

J. F. Pérez and B. V. Houdt, “Markovian approximations for a grid computing network with a ring structure,” Stoch. Models, vol.  26, no. 3, pp. 357–383, 2010.
[CrossRef]

Inoue, A.

A. Inoue, H. Yamamoto, and Y. Harada, “An advanced large scale simulation system for telecommunications networks with dynamic routing,” in Network Planning in the 1990s, D. L. Lada, Ed. New York: Elsevier, 1989, pp. 77–82.

Itai, A.

A. Itai, Y. Perl, and Y. Shiloach, “The complexity of finding maximum disjoint paths with length constraints,” Networks, vol.  12, no. 3, pp. 277–286, 1982.
[CrossRef]

Iversen, V. B.

V. B. Iversen, Teletraffic Engineering and Network Planning, 2001 [Online]. Available: FTP: dei.polimi.it. Directory: users/Flaminio.Borgonovo/Teoria. File: teletraffic_Iversen.pdf.

Iwata, A.

A. Farrel, A. Satyanarayana, A. Iwata, N. Fujita, and G. Ash, “Crankback signaling extensions for MPLS and GMPLS RSVP-TE,” , July 2007 [Online]. Available: http://www.ietf.org/rfc/rfc4920.txt .

Jung, K.

K. Jung, Y. Lu, D. Shah, M. Sharma, and M. S. Squillante, “Revisiting stochastic loss networks: structures and algorithms,” ACM SIGMETRICS Perform. Eval. Rev., vol.  36, pp. 407–418, June 2008.
[CrossRef]

Katib, I.

I. Katib and D. Medhi, “Adaptive alternate routing in WDM networks and its performance tradeoffs in the presence of wavelength converters,” Opt. Switching Netw., vol.  6, no. 3, pp. 181–193, 2009.

Katz, S. S.

R. B. Cooper and S. S. Katz, “Analysis of alternate routing networks with account taken of the nonrandomness of overflow traffic,” Bell Telephone Lab, Tech. Rep., 1964, memo.

Kelly, F. P.

F. P. Kelly, “Loss networks,” Ann. Appl. Probab., vol.  1, pp. 319–378, Aug. 1991.
[CrossRef]

F. P. Kelly, “Blocking probabilities in large circuit-switched networks,” Adv. Appl. Probab., vol.  18, pp. 473–505, June 1986.
[CrossRef]

F. P. Kelly, Reversibility and Stochastic Networks. Chichester: Wiley, 1979.

Khanna, S.

C. Chekuri and S. Khanna, “Edge disjoint paths revisited,” in Proc. SODA, 2003, pp. 628–637.

Klincewicz, J.

Kosten, L.

L. Kosten, “On the blocking probability of graded multiples,” Nachrichtentech.-Elektron., vol.  14, pp. 5–12, Jan. 1937.

Kwong, R. H.

A. Leon-Garcia, R. H. Kwong, and G. F. Williams, “Performance evaluation methods for an integrated voice/data link,” IEEE Trans. Commun., vol.  30, pp. 1848–1858, Aug. 1982.
[CrossRef]

Leon-Garcia, A.

A. Leon-Garcia, R. H. Kwong, and G. F. Williams, “Performance evaluation methods for an integrated voice/data link,” IEEE Trans. Commun., vol.  30, pp. 1848–1858, Aug. 1982.
[CrossRef]

Ligli, G.

Lu, Y.

J. Anselmi, Y. Lu, M. Sharma, and M. S. Squillante, “Improved approximations for the Erlang loss model,” Queueing Syst., vol.  63, pp. 217–239, Dec. 2009.
[CrossRef]

K. Jung, Y. Lu, D. Shah, M. Sharma, and M. S. Squillante, “Revisiting stochastic loss networks: structures and algorithms,” ACM SIGMETRICS Perform. Eval. Rev., vol.  36, pp. 407–418, June 2008.
[CrossRef]

Magill, P.

A. Mahimkar, A. Chiu, R. Doverspike, M. D. Feuer, P. Magill, E. Mavrogiorgis, J. Pastor, S. L. Woodward, and J. Yates, “Bandwidth on demand for inter-data center communication,” in Proc. 10th ACM Workshop on Hot Topics in Networks (HotNets-X), Cambridge, MA, Nov. 2011.

Mahimkar, A.

A. Mahimkar, A. Chiu, R. Doverspike, M. D. Feuer, P. Magill, E. Mavrogiorgis, J. Pastor, S. L. Woodward, and J. Yates, “Bandwidth on demand for inter-data center communication,” in Proc. 10th ACM Workshop on Hot Topics in Networks (HotNets-X), Cambridge, MA, Nov. 2011.

Marchetto, G.

M. Baldi, G. Marchetto, and Y. Ofek, “A scalable solution for engineering streaming traffic in the future Internet,” Comput. Netw., vol.  51, pp. 4092–4111, Oct. 2007.
[CrossRef]

Mavrogiorgis, E.

A. Mahimkar, A. Chiu, R. Doverspike, M. D. Feuer, P. Magill, E. Mavrogiorgis, J. Pastor, S. L. Woodward, and J. Yates, “Bandwidth on demand for inter-data center communication,” in Proc. 10th ACM Workshop on Hot Topics in Networks (HotNets-X), Cambridge, MA, Nov. 2011.

Medard, M.

Medhi, D.

I. Katib and D. Medhi, “Adaptive alternate routing in WDM networks and its performance tradeoffs in the presence of wavelength converters,” Opt. Switching Netw., vol.  6, no. 3, pp. 181–193, 2009.

Mei, Y.

C. Qiao, Y. Mei, M. Yoo, and X. Zhang, “Polymorphic control for cost-effective design of optical networks,” Eur. Trans. Telecommun., vol.  11, pp. 17–26, 2000.

Middendorf, M.

M. Middendorf and F. Pfeiffer, “On the complexity of the disjoint paths problem,” Combinatorica, vol.  13, pp. 97–107, 1993.
[CrossRef]

Mitra, D.

A. Elwalid, D. Mitra, I. Saniee, and I. Widjaja, “Routing and protection in GMPLS networks: from shortest paths to optimized designs,” J. Lightwave Technol., vol.  21, pp. 2828–2838, 2003.
[CrossRef]

D. Mitra, “Asymptotic analysis and computational methods for a class of simple circuit-switched networks with blocking,” Adv. Appl. Probab., vol.  19, pp. 219–239, Mar. 1987.
[CrossRef]

Moran, B.

E. W. M. Wong, B. Moran, A. Zalesky, Z. Rosberg, and M. Zukerman, “On the accuracy of the OPC approximation for a symmetric overflow loss model,” Stoch. Models, vol.  29, no. 2, pp. 149–189, May 2013.

Nunez-Queija, R.

O. Boxma, A. Gabor, R. Nunez-Queija, and H.-P. Tan, “Performance analysis of admission control for integrated services with minimum rate guarantees,” in Proc. 2nd NGI, Valencia, Spain, Apr. 2006, pp. 41–47.

O’Reilly, P.

P. O’Reilly, “The case for circuit switching in future wide bandwidth networks,” in Proc. IEEE ICC, June 1988, vol. 2, pp. 899–904.

Ofek, Y.

M. Baldi, G. Marchetto, and Y. Ofek, “A scalable solution for engineering streaming traffic in the future Internet,” Comput. Netw., vol.  51, pp. 4092–4111, Oct. 2007.
[CrossRef]

Pastor, J.

A. Mahimkar, A. Chiu, R. Doverspike, M. D. Feuer, P. Magill, E. Mavrogiorgis, J. Pastor, S. L. Woodward, and J. Yates, “Bandwidth on demand for inter-data center communication,” in Proc. 10th ACM Workshop on Hot Topics in Networks (HotNets-X), Cambridge, MA, Nov. 2011.

Pérez, J. F.

J. F. Pérez and B. V. Houdt, “Markovian approximations for a grid computing network with a ring structure,” Stoch. Models, vol.  26, no. 3, pp. 357–383, 2010.
[CrossRef]

Perl, Y.

A. Itai, Y. Perl, and Y. Shiloach, “The complexity of finding maximum disjoint paths with length constraints,” Networks, vol.  12, no. 3, pp. 277–286, 1982.
[CrossRef]

Pfeiffer, F.

M. Middendorf and F. Pfeiffer, “On the complexity of the disjoint paths problem,” Combinatorica, vol.  13, pp. 97–107, 1993.
[CrossRef]

Proutière, A.

F. Delcoigne, A. Proutière, and G. Régnie, “Modeling integration of streaming and data traffic,” Perform. Eval., vol.  55, no. 3–4, pp. 185–209, 2004.

Qiao, C.

C. Xin, C. Qiao, and S. Dixit, “Traffic grooming in mesh WDM optical networks—performance analysis,” IEEE J. Sel. Areas Commun., vol.  22, pp. 1658–1669, Nov. 2004.
[CrossRef]

C. Qiao, Y. Mei, M. Yoo, and X. Zhang, “Polymorphic control for cost-effective design of optical networks,” Eur. Trans. Telecommun., vol.  11, pp. 17–26, 2000.

Raskutti, G.

E. W. M. Wong, J. Baliga, M. Zukerman, A. Zalesky, and G. Raskutti, “A new method for blocking probability evaluation in OBS/OPS networks with deflection routing,” J. Lightwave Technol., vol.  27, pp. 5335–5347, Dec. 2009.
[CrossRef]

G. Raskutti, A. Zalesky, E. W. M. Wong, and M. Zukerman, “Enhanced blocking probability evaluation method for circuit-switched trunk reservation networks,” IEEE Commun. Lett., vol.  11, pp. 543–545, June 2007.
[CrossRef]

Régnie, G.

F. Delcoigne, A. Proutière, and G. Régnie, “Modeling integration of streaming and data traffic,” Perform. Eval., vol.  55, no. 3–4, pp. 185–209, 2004.

Rosberg, Z.

E. W. M. Wong, B. Moran, A. Zalesky, Z. Rosberg, and M. Zukerman, “On the accuracy of the OPC approximation for a symmetric overflow loss model,” Stoch. Models, vol.  29, no. 2, pp. 149–189, May 2013.

E. W. M. Wong, A. Zalesky, Z. Rosberg, and M. Zukerman, “A new method for approximating blocking probability in overflow loss networks,” Comput. Netw., vol.  51, pp. 2958–2975, Aug. 2007.
[CrossRef]

E. W. M. Wong, M. Y. M. Chiu, Z. Rosberg, M. Zukerman, S. Chan, and A. Zalesky, “A novel method for modeling and analysis of distributed video on demand systems,” in Proc. IEEE ICC, Seoul, South Korea, May 2005, vol. 1, pp. 88–92.

Saniee, I.

Sato, K.

Satyanarayana, A.

A. Farrel, A. Satyanarayana, A. Iwata, N. Fujita, and G. Ash, “Crankback signaling extensions for MPLS and GMPLS RSVP-TE,” , July 2007 [Online]. Available: http://www.ietf.org/rfc/rfc4920.txt .

Shah, D.

K. Jung, Y. Lu, D. Shah, M. Sharma, and M. S. Squillante, “Revisiting stochastic loss networks: structures and algorithms,” ACM SIGMETRICS Perform. Eval. Rev., vol.  36, pp. 407–418, June 2008.
[CrossRef]

Sharma, M.

J. Anselmi, Y. Lu, M. Sharma, and M. S. Squillante, “Improved approximations for the Erlang loss model,” Queueing Syst., vol.  63, pp. 217–239, Dec. 2009.
[CrossRef]

K. Jung, Y. Lu, D. Shah, M. Sharma, and M. S. Squillante, “Revisiting stochastic loss networks: structures and algorithms,” ACM SIGMETRICS Perform. Eval. Rev., vol.  36, pp. 407–418, June 2008.
[CrossRef]

Shen, G.

Shiloach, Y.

A. Itai, Y. Perl, and Y. Shiloach, “The complexity of finding maximum disjoint paths with length constraints,” Networks, vol.  12, no. 3, pp. 277–286, 1982.
[CrossRef]

Skoog, R.

Song, W.

W. Song and W. Zhuang, “QoS provisioning via admission control in cellular/wireless LAN interworking,” in Proc. BroadNets, Oct. 2005, vol. 1, pp. 543–550.

Squillante, M. S.

J. Anselmi, Y. Lu, M. Sharma, and M. S. Squillante, “Improved approximations for the Erlang loss model,” Queueing Syst., vol.  63, pp. 217–239, Dec. 2009.
[CrossRef]

K. Jung, Y. Lu, D. Shah, M. Sharma, and M. S. Squillante, “Revisiting stochastic loss networks: structures and algorithms,” ACM SIGMETRICS Perform. Eval. Rev., vol.  36, pp. 407–418, June 2008.
[CrossRef]

Strand, J.

Tan, H.-P.

O. Boxma, A. Gabor, R. Nunez-Queija, and H.-P. Tan, “Performance analysis of admission control for integrated services with minimum rate guarantees,” in Proc. 2nd NGI, Valencia, Spain, Apr. 2006, pp. 41–47.

Taylor, P. G.

A. J. Coyle, W. Henderson, and P. G. Taylor, “Reduced load approximations for loss networks,” Telecommun. Syst., vol.  2, pp. 21–50, 1993.
[CrossRef]

Tucker, R.

Viterbi, A.

J. Wolf, A. Viterbi, and G. Dixon, “Finding the best set of k paths through a trellis with application to multitarget tracking,” IEEE Trans. Aerosp. Electron. Syst., vol.  25, pp. 287–296, Mar. 1989.

Von Lehmen, A.

Weichenberg, G.

Whitt, W.

W. Whitt, “Blocking when service is required from several facilities simultaneously,” AT&T Tech. J., vol.  64, pp. 1807–1856, Oct. 1985.

Widjaja, I.

Wilkinson, R. I.

R. I. Wilkinson, “Theories of toll traffic engineering in the USA,” Bell Syst. Tech. J., vol.  35, pp. 421–514, Mar. 1956.

Williams, G. F.

A. Leon-Garcia, R. H. Kwong, and G. F. Williams, “Performance evaluation methods for an integrated voice/data link,” IEEE Trans. Commun., vol.  30, pp. 1848–1858, Aug. 1982.
[CrossRef]

Wolf, J.

J. Wolf, A. Viterbi, and G. Dixon, “Finding the best set of k paths through a trellis with application to multitarget tracking,” IEEE Trans. Aerosp. Electron. Syst., vol.  25, pp. 287–296, Mar. 1989.

Wong, E. W. M.

E. W. M. Wong, B. Moran, A. Zalesky, Z. Rosberg, and M. Zukerman, “On the accuracy of the OPC approximation for a symmetric overflow loss model,” Stoch. Models, vol.  29, no. 2, pp. 149–189, May 2013.

E. W. M. Wong, J. Baliga, M. Zukerman, A. Zalesky, and G. Raskutti, “A new method for blocking probability evaluation in OBS/OPS networks with deflection routing,” J. Lightwave Technol., vol.  27, pp. 5335–5347, Dec. 2009.
[CrossRef]

G. Raskutti, A. Zalesky, E. W. M. Wong, and M. Zukerman, “Enhanced blocking probability evaluation method for circuit-switched trunk reservation networks,” IEEE Commun. Lett., vol.  11, pp. 543–545, June 2007.
[CrossRef]

E. W. M. Wong, A. Zalesky, Z. Rosberg, and M. Zukerman, “A new method for approximating blocking probability in overflow loss networks,” Comput. Netw., vol.  51, pp. 2958–2975, Aug. 2007.
[CrossRef]

E. W. M. Wong, A. K. M. Chan, and T. S. Yum, “Analysis of rerouting in circuit-switched networks,” IEEE/ACM Trans. Netw., vol.  8, pp. 419–427, June 2000.

E. W. M. Wong, T. S. Yum, and K. M. Chan, “Analysis of the m and m2 routings in circuit-switched networks,” Eur. Trans. Telecommun., vol.  6, pp. 613–619, Dec. 1995.

E. W. M. Wong, M. Y. M. Chiu, Z. Rosberg, M. Zukerman, S. Chan, and A. Zalesky, “A novel method for modeling and analysis of distributed video on demand systems,” in Proc. IEEE ICC, Seoul, South Korea, May 2005, vol. 1, pp. 88–92.

Woodward, S. L.

A. Mahimkar, A. Chiu, R. Doverspike, M. D. Feuer, P. Magill, E. Mavrogiorgis, J. Pastor, S. L. Woodward, and J. Yates, “Bandwidth on demand for inter-data center communication,” in Proc. 10th ACM Workshop on Hot Topics in Networks (HotNets-X), Cambridge, MA, Nov. 2011.

Xin, C.

C. Xin, C. Qiao, and S. Dixit, “Traffic grooming in mesh WDM optical networks—performance analysis,” IEEE J. Sel. Areas Commun., vol.  22, pp. 1658–1669, Nov. 2004.
[CrossRef]

Xu, D.

Yamamoto, H.

A. Inoue, H. Yamamoto, and Y. Harada, “An advanced large scale simulation system for telecommunications networks with dynamic routing,” in Network Planning in the 1990s, D. L. Lada, Ed. New York: Elsevier, 1989, pp. 77–82.

Yates, J.

A. Mahimkar, A. Chiu, R. Doverspike, M. D. Feuer, P. Magill, E. Mavrogiorgis, J. Pastor, S. L. Woodward, and J. Yates, “Bandwidth on demand for inter-data center communication,” in Proc. 10th ACM Workshop on Hot Topics in Networks (HotNets-X), Cambridge, MA, Nov. 2011.

Yoo, M.

C. Qiao, Y. Mei, M. Yoo, and X. Zhang, “Polymorphic control for cost-effective design of optical networks,” Eur. Trans. Telecommun., vol.  11, pp. 17–26, 2000.

Youssef, M.

M. Youssef, E. Doumith, and M. Gagnaire, “Power-aware multi-rate WDM network design under static/dynamic traffic,” in IEEE Global Telecommunications Conf. (GLOBECOM), Houston, TX, Dec. 2011.

Yum, T. S.

E. W. M. Wong, A. K. M. Chan, and T. S. Yum, “Analysis of rerouting in circuit-switched networks,” IEEE/ACM Trans. Netw., vol.  8, pp. 419–427, June 2000.

E. W. M. Wong, T. S. Yum, and K. M. Chan, “Analysis of the m and m2 routings in circuit-switched networks,” Eur. Trans. Telecommun., vol.  6, pp. 613–619, Dec. 1995.

Zalesky, A.

E. W. M. Wong, B. Moran, A. Zalesky, Z. Rosberg, and M. Zukerman, “On the accuracy of the OPC approximation for a symmetric overflow loss model,” Stoch. Models, vol.  29, no. 2, pp. 149–189, May 2013.

E. W. M. Wong, J. Baliga, M. Zukerman, A. Zalesky, and G. Raskutti, “A new method for blocking probability evaluation in OBS/OPS networks with deflection routing,” J. Lightwave Technol., vol.  27, pp. 5335–5347, Dec. 2009.
[CrossRef]

G. Raskutti, A. Zalesky, E. W. M. Wong, and M. Zukerman, “Enhanced blocking probability evaluation method for circuit-switched trunk reservation networks,” IEEE Commun. Lett., vol.  11, pp. 543–545, June 2007.
[CrossRef]

E. W. M. Wong, A. Zalesky, Z. Rosberg, and M. Zukerman, “A new method for approximating blocking probability in overflow loss networks,” Comput. Netw., vol.  51, pp. 2958–2975, Aug. 2007.
[CrossRef]

E. W. M. Wong, M. Y. M. Chiu, Z. Rosberg, M. Zukerman, S. Chan, and A. Zalesky, “A novel method for modeling and analysis of distributed video on demand systems,” in Proc. IEEE ICC, Seoul, South Korea, May 2005, vol. 1, pp. 88–92.

Zhang, X.

C. Qiao, Y. Mei, M. Yoo, and X. Zhang, “Polymorphic control for cost-effective design of optical networks,” Eur. Trans. Telecommun., vol.  11, pp. 17–26, 2000.

Zhuang, W.

W. Song and W. Zhuang, “QoS provisioning via admission control in cellular/wireless LAN interworking,” in Proc. BroadNets, Oct. 2005, vol. 1, pp. 543–550.

Zukerman, M.

E. W. M. Wong, B. Moran, A. Zalesky, Z. Rosberg, and M. Zukerman, “On the accuracy of the OPC approximation for a symmetric overflow loss model,” Stoch. Models, vol.  29, no. 2, pp. 149–189, May 2013.

E. W. M. Wong, J. Baliga, M. Zukerman, A. Zalesky, and G. Raskutti, “A new method for blocking probability evaluation in OBS/OPS networks with deflection routing,” J. Lightwave Technol., vol.  27, pp. 5335–5347, Dec. 2009.
[CrossRef]

E. W. M. Wong, A. Zalesky, Z. Rosberg, and M. Zukerman, “A new method for approximating blocking probability in overflow loss networks,” Comput. Netw., vol.  51, pp. 2958–2975, Aug. 2007.
[CrossRef]

G. Raskutti, A. Zalesky, E. W. M. Wong, and M. Zukerman, “Enhanced blocking probability evaluation method for circuit-switched trunk reservation networks,” IEEE Commun. Lett., vol.  11, pp. 543–545, June 2007.
[CrossRef]

E. W. M. Wong, M. Y. M. Chiu, Z. Rosberg, M. Zukerman, S. Chan, and A. Zalesky, “A novel method for modeling and analysis of distributed video on demand systems,” in Proc. IEEE ICC, Seoul, South Korea, May 2005, vol. 1, pp. 88–92.

ACM SIGMETRICS Perform. Eval. Rev. (1)

K. Jung, Y. Lu, D. Shah, M. Sharma, and M. S. Squillante, “Revisiting stochastic loss networks: structures and algorithms,” ACM SIGMETRICS Perform. Eval. Rev., vol.  36, pp. 407–418, June 2008.
[CrossRef]

Adv. Appl. Probab. (2)

D. Mitra, “Asymptotic analysis and computational methods for a class of simple circuit-switched networks with blocking,” Adv. Appl. Probab., vol.  19, pp. 219–239, Mar. 1987.
[CrossRef]

F. P. Kelly, “Blocking probabilities in large circuit-switched networks,” Adv. Appl. Probab., vol.  18, pp. 473–505, June 1986.
[CrossRef]

Ann. Appl. Probab. (1)

F. P. Kelly, “Loss networks,” Ann. Appl. Probab., vol.  1, pp. 319–378, Aug. 1991.
[CrossRef]

AT&T Tech. J. (1)

W. Whitt, “Blocking when service is required from several facilities simultaneously,” AT&T Tech. J., vol.  64, pp. 1807–1856, Oct. 1985.

Bell Syst. Tech. J. (1)

R. I. Wilkinson, “Theories of toll traffic engineering in the USA,” Bell Syst. Tech. J., vol.  35, pp. 421–514, Mar. 1956.

Combinatorica (1)

M. Middendorf and F. Pfeiffer, “On the complexity of the disjoint paths problem,” Combinatorica, vol.  13, pp. 97–107, 1993.
[CrossRef]

Comput. Netw. (2)

E. W. M. Wong, A. Zalesky, Z. Rosberg, and M. Zukerman, “A new method for approximating blocking probability in overflow loss networks,” Comput. Netw., vol.  51, pp. 2958–2975, Aug. 2007.
[CrossRef]

M. Baldi, G. Marchetto, and Y. Ofek, “A scalable solution for engineering streaming traffic in the future Internet,” Comput. Netw., vol.  51, pp. 4092–4111, Oct. 2007.
[CrossRef]

Eur. Trans. Telecommun. (2)

E. W. M. Wong, T. S. Yum, and K. M. Chan, “Analysis of the m and m2 routings in circuit-switched networks,” Eur. Trans. Telecommun., vol.  6, pp. 613–619, Dec. 1995.

C. Qiao, Y. Mei, M. Yoo, and X. Zhang, “Polymorphic control for cost-effective design of optical networks,” Eur. Trans. Telecommun., vol.  11, pp. 17–26, 2000.

IEEE Commun. Lett. (1)

G. Raskutti, A. Zalesky, E. W. M. Wong, and M. Zukerman, “Enhanced blocking probability evaluation method for circuit-switched trunk reservation networks,” IEEE Commun. Lett., vol.  11, pp. 543–545, June 2007.
[CrossRef]

IEEE J. Sel. Areas Commun. (1)

C. Xin, C. Qiao, and S. Dixit, “Traffic grooming in mesh WDM optical networks—performance analysis,” IEEE J. Sel. Areas Commun., vol.  22, pp. 1658–1669, Nov. 2004.
[CrossRef]

IEEE Trans. Aerosp. Electron. Syst. (1)

J. Wolf, A. Viterbi, and G. Dixon, “Finding the best set of k paths through a trellis with application to multitarget tracking,” IEEE Trans. Aerosp. Electron. Syst., vol.  25, pp. 287–296, Mar. 1989.

IEEE Trans. Commun. (2)

A. Leon-Garcia, R. H. Kwong, and G. F. Williams, “Performance evaluation methods for an integrated voice/data link,” IEEE Trans. Commun., vol.  30, pp. 1848–1858, Aug. 1982.
[CrossRef]

L. Delbrouck, “The uses of Kosten’s systems in the provisioning of alternate trunk groups carrying heterogeneous traffic,” IEEE Trans. Commun., vol.  31, pp. 741–749, June 1983.
[CrossRef]

IEEE/ACM Trans. Netw. (1)

E. W. M. Wong, A. K. M. Chan, and T. S. Yum, “Analysis of rerouting in circuit-switched networks,” IEEE/ACM Trans. Netw., vol.  8, pp. 419–427, June 2000.

J. Lightwave Technol. (3)

J. Opt. Commun. Netw. (3)

Nachrichtentech.-Elektron. (1)

L. Kosten, “On the blocking probability of graded multiples,” Nachrichtentech.-Elektron., vol.  14, pp. 5–12, Jan. 1937.

Networks (1)

A. Itai, Y. Perl, and Y. Shiloach, “The complexity of finding maximum disjoint paths with length constraints,” Networks, vol.  12, no. 3, pp. 277–286, 1982.
[CrossRef]

Opt. Switching Netw. (1)

I. Katib and D. Medhi, “Adaptive alternate routing in WDM networks and its performance tradeoffs in the presence of wavelength converters,” Opt. Switching Netw., vol.  6, no. 3, pp. 181–193, 2009.

Perform. Eval. (1)

F. Delcoigne, A. Proutière, and G. Régnie, “Modeling integration of streaming and data traffic,” Perform. Eval., vol.  55, no. 3–4, pp. 185–209, 2004.

Queueing Syst. (1)

J. Anselmi, Y. Lu, M. Sharma, and M. S. Squillante, “Improved approximations for the Erlang loss model,” Queueing Syst., vol.  63, pp. 217–239, Dec. 2009.
[CrossRef]

Stoch. Models (2)

J. F. Pérez and B. V. Houdt, “Markovian approximations for a grid computing network with a ring structure,” Stoch. Models, vol.  26, no. 3, pp. 357–383, 2010.
[CrossRef]

E. W. M. Wong, B. Moran, A. Zalesky, Z. Rosberg, and M. Zukerman, “On the accuracy of the OPC approximation for a symmetric overflow loss model,” Stoch. Models, vol.  29, no. 2, pp. 149–189, May 2013.

Telecommun. Syst. (1)

A. J. Coyle, W. Henderson, and P. G. Taylor, “Reduced load approximations for loss networks,” Telecommun. Syst., vol.  2, pp. 21–50, 1993.
[CrossRef]

Other (15)

E. W. M. Wong, M. Y. M. Chiu, Z. Rosberg, M. Zukerman, S. Chan, and A. Zalesky, “A novel method for modeling and analysis of distributed video on demand systems,” in Proc. IEEE ICC, Seoul, South Korea, May 2005, vol. 1, pp. 88–92.

A. Farrel, A. Satyanarayana, A. Iwata, N. Fujita, and G. Ash, “Crankback signaling extensions for MPLS and GMPLS RSVP-TE,” , July 2007 [Online]. Available: http://www.ietf.org/rfc/rfc4920.txt .

F. P. Kelly, Reversibility and Stochastic Networks. Chichester: Wiley, 1979.

A. Girard, Routing and Dimensioning in Circuit-Switched Networks. Boston, MA: Addison-Wesley Longman, 1990.

A. Inoue, H. Yamamoto, and Y. Harada, “An advanced large scale simulation system for telecommunications networks with dynamic routing,” in Network Planning in the 1990s, D. L. Lada, Ed. New York: Elsevier, 1989, pp. 77–82.

O. Boxma, A. Gabor, R. Nunez-Queija, and H.-P. Tan, “Performance analysis of admission control for integrated services with minimum rate guarantees,” in Proc. 2nd NGI, Valencia, Spain, Apr. 2006, pp. 41–47.

W. Song and W. Zhuang, “QoS provisioning via admission control in cellular/wireless LAN interworking,” in Proc. BroadNets, Oct. 2005, vol. 1, pp. 543–550.

V. B. Iversen, Teletraffic Engineering and Network Planning, 2001 [Online]. Available: FTP: dei.polimi.it. Directory: users/Flaminio.Borgonovo/Teoria. File: teletraffic_Iversen.pdf.

W. Feller, An Introduction to Probability Theory and Its Applications. New York: Wiley, 1968, pp. 460–478.

A. Mahimkar, A. Chiu, R. Doverspike, M. D. Feuer, P. Magill, E. Mavrogiorgis, J. Pastor, S. L. Woodward, and J. Yates, “Bandwidth on demand for inter-data center communication,” in Proc. 10th ACM Workshop on Hot Topics in Networks (HotNets-X), Cambridge, MA, Nov. 2011.

A. Barczyk, “World-wide networking for LHC data processing,” in Nat. Fiber Optic Engineers Conf. (NFOEC), Los Angeles, CA, Mar. 2012, paper NTu1E.1.

P. O’Reilly, “The case for circuit switching in future wide bandwidth networks,” in Proc. IEEE ICC, June 1988, vol. 2, pp. 899–904.

M. Youssef, E. Doumith, and M. Gagnaire, “Power-aware multi-rate WDM network design under static/dynamic traffic,” in IEEE Global Telecommunications Conf. (GLOBECOM), Houston, TX, Dec. 2011.

R. B. Cooper and S. S. Katz, “Analysis of alternate routing networks with account taken of the nonrandomness of overflow traffic,” Bell Telephone Lab, Tech. Rep., 1964, memo.

C. Chekuri and S. Khanna, “Edge disjoint paths revisited,” in Proc. SODA, 2003, pp. 628–637.

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Figures (16)

Fig. 1.
Fig. 1.

Blocking probabilities for the long-lived traffic (single priority) versus T in (a) a 6-node fully meshed network and (b) an NSF network.

Fig. 2.
Fig. 2.

NSF network topology, where each solid line represents a bidirectional trunk between two nodes.

Fig. 3.
Fig. 3.

Blocking probabilities for the short-lived traffic in (a) a 6-node fully meshed network and (b) an NSF network. The ratio of the offered long-lived traffic to offered short-lived traffic is 1 1 .

Fig. 4.
Fig. 4.

Blocking probabilities for the short-lived traffic in a 6-node fully meshed network. The ratio of the offered long-lived traffic to the offered short-lived traffic is (a)  1 2 , (b)  1 5 , (c)  2 1 , and (d)  5 1 .

Fig. 5.
Fig. 5.

Blocking probabilities for the short-lived traffic in an NSF network. The ratio of the offered long-lived traffic to the offered short-lived traffic is (a)  1 2 , (b)  1 5 , (c)  2 1 , and (d)  5 1 .

Fig. 6.
Fig. 6.

Blocking probabilities for (a) long-lived traffic (single priority) and (b) short-lived traffic in a 6-node fully meshed network with 50 links in each trunk.

Fig. 7.
Fig. 7.

Blocking probabilities for (a) long-lived traffic (single priority) and (b) short-lived traffic in a 6-node fully meshed network versus the number of links on each trunk.

Fig. 8.
Fig. 8.

Blocking probabilities for (a) long-lived traffic (single priority) and (b) short-lived traffic in an NSF network with 50 links in each trunk.

Fig. 9.
Fig. 9.

Blocking probabilities for (a) long-lived traffic (single priority) and (b) short-lived traffic in an NSF network versus the number of links per trunk.

Fig. 10.
Fig. 10.

Blocking probability for (a) long-lived traffic (single priority) and (b) short-lived traffic for a 6-node fully meshed network.

Fig. 11.
Fig. 11.

Blocking probability for short-lived traffic in a 6-node fully meshed network with long-lived and short-lived traffic. The ratio of the offered long-lived traffic to the offered short-lived traffic is (a)  1 1 and (b)  5 1 .

Fig. 12.
Fig. 12.

Average blocking probabilities for the short-lived traffic with different values of μ 2 for a 6-node fully meshed network with 20 links in each trunk and μ 1 = 1 .

Fig. 13.
Fig. 13.

Average blocking probabilities for (a) long-lived traffic (single priority) and (b) short-lived traffic, considering different service time distributions for a 6-node fully meshed network with 20 links in each trunk.

Fig. 14.
Fig. 14.

Average blocking probabilities for (a) long-lived traffic (single priority) and (b) short-lived traffic, considering different service time distributions for the NSF network with 20 links in each trunk.

Fig. 15.
Fig. 15.

Coronet topology.

Fig. 16.
Fig. 16.

Blocking probabilities obtained by OPCA for (a) long-lived traffic (single priority), and (b) short-lived traffic for the Coronet with 50 links per trunk.

Tables (7)

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TABLE I Summary of Notation

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Algorithm 1 Compute B ( 1 ) and q ( j , 1 , i ) by EFPA

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Algorithm 2 Compute B ( 2 ) by EFPA

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Algorithm 3 Compute B ( 1 ) and h ( j , i ) by OPCA

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Algorithm 4 Compute B ( 2 ) by OPCA

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TABLE III Computational Complexity of the Algorithms

Equations (25)

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ρ ( m , p ) = λ ( m , p ) μ ( m , p )
ρ ( p ) = m Γ ρ ( m , p ) .
T ( m ) = min { T m , D }
{ U ( m , 0 ) , U ( m , 1 ) , , U ( m , T ( m ) ) }
a ( d , m , p ) = a ( d 1 , m , p ) ( 1 j U ( m , d 1 ) ( 1 b ( d 1 , j , p ) ) )
a ( d , m , p , j ) = a ( d , m , p ) i U ( m , d ) ( 1 b ( d , i , p ) ) 1 b ( d , j , p )
a ( d , j , p ) = m Γ a ( d , m , p , j ) .
a ˜ ( d , j , p ) = i = 0 d a ( i , j , p ) .
q ( j , 1 , i ) = ( a ( 0 , j , 1 ) + 1 { RT ( j , 1 ) > i 1 } n = 1 D a ( n , j , 1 ) ) × q ( j , 1 , i 1 ) / i ,
b ( d , j , 1 ) = { q ( j , 1 , C ( j ) ) d = 0 , i = RT ( j , 1 ) C ( j ) q ( j , 1 , i ) d 1 .
q ( j , k , 2 , i ) = ( a ( 0 , j , 2 ) + 1 { R ( j , k ) > i 1 } n = 1 D a ( n , j , 2 ) ) × q ( j , k , 2 , i 1 ) / i ,
b ( d , j , k , 2 ) = { 1 k = 0 or R ( j , k ) 0 , q ( j , k , 2 , k ) d = 0 and R ( j , k ) > 0 , i = R ( j , k ) k q ( j , k , 2 , i ) d 1 and R ( j , k ) > 0 .
b ( d , j , 2 ) = i = 0 C ( j ) q ( j , 1 , i ) × b ( d , j , C ( j ) i , 2 ) .
B ( m , p ) = 1 d = 0 D a ( d , m , j , p ) ( 1 b ( d , j , p ) ) / ρ ( m , p ) ,
B ( p ) = m Γ B ( m , p ) × ρ ( m , p ) / m Γ ρ ( m , p ) .
j E | b ( d , j , 1 ) b ^ ( d , j , 1 ) | < error .
error = 10 8 .
t ( d , j , 1 , i ) = ( a ( 0 , j , 1 ) + 1 { RT ( j , 1 ) > i 1 } n = 1 d a ( n , j , 1 ) ) × t ( d , j , 1 , i 1 ) / i ,
b ¯ ( d , j , 1 ) = n = 1 d ( a ( n , j , 1 ) i = RT ( j , 1 ) C ( j ) t ( d , j , 1 , i ) ) a ˜ ( d , j , 1 ) + a ( 0 , j , 1 ) t ( d , j , 1 , C ( j ) ) a ˜ ( d , j , 1 )
b ( d , j , 1 ) = { b ¯ ( 0 , j , 1 ) d = 0 , b ¯ ( d , j , 1 ) a ˜ ( d , j , 1 ) b ¯ ( d 1 , j , 1 ) a ˜ ( d 1 , j , 1 ) a ( d , j , 1 ) 1 d D .
h ( j , i ) = ( a ( 0 , j , 1 ) + 1 { RT ( j , 1 ) > i 1 } n = 1 D a ( n , j , 1 ) ) × h ( j , i 1 ) / i ,
t ( d , j , k , 2 , i ) = ( a ( 0 , j , 2 ) + 1 { R ( j , k ) > i 1 } n = 1 d a ( n , j , 2 ) ) × t ( d , j , k , 2 , i 1 ) / i ,
b ¯ ( d , j , k , 2 ) = { t ( 0 , j , k , 2 , k ) d = 0 , i = R ( j , k ) k t ( d , j , i , 2 , i ) d 1 and R ( j , k ) > 0 , 1 otherwise .
b ¯ ( d , j , 2 ) = i = 0 C ( j ) h ( j , i ) × b ¯ ( d , j , C ( j ) i , 2 ) .
b ( d , j , 2 ) = { b ¯ ( 0 , j , 2 ) d = 0 , b ¯ ( d , j , 2 ) a ˜ ( d , j , 2 ) b ¯ ( d 1 , j , 2 ) a ˜ ( d 1 , j , 2 ) a ( d , j , 2 ) 1 d D .