OSA's Digital Library

Journal of Optical Communications and Networking

Journal of Optical Communications and Networking

  • Editors: K. Bergman and O. Gerstel
  • Vol. 5, Iss. 6 — Jun. 1, 2013
  • pp: 621–640

Blocking Probability Analysis of Circuit-Switched Networks With Long-Lived and Short-Lived Connections

Meiqian Wang, Shuo Li, Eric W. M. Wong, and Moshe Zukerman  »View Author Affiliations


Journal of Optical Communications and Networking, Vol. 5, Issue 6, pp. 621-640 (2013)
http://dx.doi.org/10.1364/JOCN.5.000621


View Full Text Article

Enhanced HTML    Acrobat PDF (1862 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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

OCIS Codes
(060.2330) Fiber optics and optical communications : Fiber optics communications
(060.4250) Fiber optics and optical communications : Networks
(060.4510) Fiber optics and optical communications : Optical communications
(060.4253) Fiber optics and optical communications : Networks, circuit-switched
(060.4258) Fiber optics and optical communications : Networks, network topology
(060.6718) Fiber optics and optical communications : Switching, circuit

ToC Category:
Research Papers

History
Original Manuscript: November 8, 2012
Revised Manuscript: April 20, 2013
Manuscript Accepted: April 26, 2013
Published: May 31, 2013

Citation
Meiqian Wang, Shuo Li, Eric W. M. Wong, and Moshe Zukerman, "Blocking Probability Analysis of Circuit-Switched Networks With Long-Lived and Short-Lived Connections," J. Opt. Commun. Netw. 5, 621-640 (2013)
http://www.opticsinfobase.org/jocn/abstract.cfm?URI=jocn-5-6-621


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. 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.
  2. A. Barczyk, “World-wide networking for LHC data processing,” in Nat. Fiber Optic Engineers Conf. (NFOEC), Los Angeles, CA, Mar. 2012, paper NTu1E.1.
  3. K. Sato and H. Hagesawa, “Optical networking technologies that will create future bandwidth-abundant networks,” J. Opt. Commun. Netw., vol.  1, pp. A81–A93, July 2009. [CrossRef]
  4. P. O’Reilly, “The case for circuit switching in future wide bandwidth networks,” in Proc. IEEE ICC, June 1988, vol. 2, pp. 899–904.
  5. G. Weichenberg, V. Chan, and M. Medard, “Design and analysis of optical flow-switched networks,” J. Opt. Commun. Netw., vol.  1, pp. B81–B97, Aug. 2009. [CrossRef]
  6. G. Shen and R. Tucker, “Energy-minimized design for IP over WDM networks,” J. Opt. Commun. Netw., vol.  1, pp. 176–186, June 2009. [CrossRef]
  7. A. Girard, Routing and Dimensioning in Circuit-Switched Networks. Boston, MA: Addison-Wesley Longman, 1990.
  8. 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.
  9. F. P. Kelly, “Blocking probabilities in large circuit-switched networks,” Adv. Appl. Probab., vol.  18, pp. 473–505, June 1986. [CrossRef]
  10. 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 .
  11. F. P. Kelly, Reversibility and Stochastic Networks. Chichester: Wiley, 1979.
  12. L. Kosten, “On the blocking probability of graded multiples,” Nachrichtentech.-Elektron., vol.  14, pp. 5–12, Jan. 1937.
  13. R. I. Wilkinson, “Theories of toll traffic engineering in the USA,” Bell Syst. Tech. J., vol.  35, pp. 421–514, Mar. 1956.
  14. 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]
  15. 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]
  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. [CrossRef]
  19. 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.
  20. 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.
  21. 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.
  22. W. Whitt, “Blocking when service is required from several facilities simultaneously,” AT&T Tech. J., vol.  64, pp. 1807–1856, Oct. 1985.
  23. 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]
  24. 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]
  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.
  27. 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]
  28. 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]
  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. [CrossRef]
  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.
  36. 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.
  37. 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]
  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.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited