Computing Approximate Blocking Probabilities for Large Loss Networks with State-Dependent Routing

IEEE/ACM Transactions on Networking

Volumn 1, Issue 1, 1993, Pages 105-115

  Chung, Shun Ping ^a   Kashper, Arik ^b   Ross, Keith W ^c  

^a NATIONAL TAIWAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Taiwan)

^b LUCENT TECHNOLOGIES   (United States)

^c UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER NETWORKS; DIGITAL COMMUNICATION SYSTEMS; NONLINEAR EQUATIONS; PROBABILITY; TELECOMMUNICATION LINKS;

BLOCKING PROBABILITIES; CIRCUIT SWITCHED NETWORKS; ERLANG FIXED POINT APPROXIMATION; LOSS NETWORKS; MULTIRATE NETWORKS;

TELECOMMUNICATION TRAFFIC;

EID: 0027542341     PISSN: 10636692     EISSN: 15582566     Source Type: Journal    
DOI: 10.1109/90.222911     Document Type: Article

References (43)

1. J. M. Akinpelu, “The overload performance of engineered networks with nonhierarchical and hierarchical routing,” AT&T Bell Labs Tech. J., vol. 63, pp. 1261–1281, 1984.
2. G. R. Ash, J.-S. Chen, A. E. Frey, and B D. Huang, “Real-time network routing in a dynamic class-of-service network,” in Proc. 13th ITC, Copenhagen, Denmark, 1991.
3. V.P. Chaudhary, K.R. Krishnan, and C.D. Pack, “Implementing dynamic routing in the local telephone companies of the USA,” in Proc. 13th ITC, Copenhagen, Denmark, 1991.
4. S.P. Chung and K.W. Ross, “Reduced load approximations for multirate loss networks,” to appear in IEEE Trans. Commun.
5. R.B. Cooper and S. Katz, “Analysis of alternate routing networks with account taken of nanrandomness of overflow traffic,” Tech. Rep., Bell Telephone Lab. Memo., 1964.
6. E.V. Denardo and H. Park, “Efficient routing of telecommunications traffic,” Yale Univ. Tech. Rep., 1991.
7. Z. Dziong and J. W. Roberts, “Congestion probabilities in a circuit-switched integrated services network,” Perform. Eval., vol. 7, pp. 267–284, 1987.
8. S.G. Eick, A.G. Greenberg, B.D. Lubachevsky, and A. Weiss, “Synchronous relaxation for parallel simulations with applications to circuit-switched networks,” to appear in ACM Trans. Modeling and Simulat.
9. A. Gersht and K.J. Lee, “A bandwidth management strategy in ATM networks,” GTE Lab. Tech. Rep., 1990.
10. R. J. Gibbens, P. J. Hunt, and F. P. Kelly, “Bistability in communication networks,” in Disorder in Physical Systems, G. R. Grimmett and D. J. A, Welsh, Eds. Oxford, England: Oxford Univ. Press, 1990, pp. 113–127.
11. R.J. Gibbens and F.P. Kelly, “Dynamic routing in fully connected networks,” IMA J. Mathematic Contr. and Inform., vol. 7, pp. 77–111, 1990.
12. R.J. Gibbens, F.P. Kelly, and P.B. Key, “Dynamic alternative routing—Modeling and behaviour,” in Proc. 12th ITC, Torino, Italy, 1988.
13. R. J. Gibbens and P. A. Whiting, “An investigation of the accuracy of the implied cost methods of cs network optimization,” in Proc. 5th UK Teletraffic Symp., Ashton Univ., 1989.
14. A. Girard, Routing and Dimensioning in Circuit-Switched Networks. Reading, MA: Addison Wesley, 1990.
15. A. Girard and M.A. Bell, “Blocking evaluation for networks with residual capacity adaptive routing,” IEEE Trans. Commun., vol. 37, pp. 1372–1380, 1990.
16. P. J. Hunt, “Implied costs in loss networks,” Advances in Appl. Prob., vol. 21, pp. 661–680, 1989.
17. P.J. Hunt,, “Limit theorems for stochastic loss networks,” Ph.D. thesis, Univ. Cambridge, 1990.
18. P.J. Hunt and F.P. Kelly, “On critically loaded loss networks,” Advances in Appl. Prob., vol. 21, pp. 661–680, 1989.
19. B.R. Hurley, C.J. Seidl, and W.F. Sewell, “A survey of dynamic routing methods for circuit-switched traffic,” IEEE Commun. Mag., vol. 25, pp. 13–21, 1987.
20. S.S. Katz, “Statistical performance analysis of switched communication networks,” in Proc. 5th ITC, New York, NY, 1967.
21. J.S. Kaufman, “Blocking in a shared resource environment,” IEEE, Trans. Commun., vol. COM-29, no. 10, pp. 1474—1481, 1981.
22. F.P. Kelly, Reversibility and Stochastic Networks. New York: Wiley, 1979.
23. F.P. Kelly, “Blocking probabilities in large circuit-switched networks,” Adv. in Appl. Prob., vol. 18, pp. 473–505, 1986.
24. F.P. Kelly, “Routing and capacity allocation in networks with trunk reservation,” Math, of Operat. Res., vol. 15, pp. 771–792, 1990.
25. F.P. Kelly, “Loss networks,” The Annals of Appl. Prob., vol. 1, pp. 319–378, 1991.
26. P.B. Key, “Optimal control and trunk reservation in loss networks,” Prob. in Eng. and Inform. Sci., vol. 4, pp. 203–242, 1990.
27. K.R. Krishnan, “Performance evaluation of networks under state-dependent routing,” in Proc. Bellcore Symp. Perform. Model, May 1990 and ORSA/TIMS Conf., Philadelphia, PA, Oct. 1990.
28. K.R. Krishnan and T.J. Ott, “State-dependent routing for telephone traffic: Theory and results,” in Proc. 25th IEEE Contr. and Decision Conf., Athens, Greece, 1986, pp. 2124–2128.
29. D. Mitra, “Asymptotic analysis and computational methods for a class of simple, circuit-switched networks with blocking,” Adv. Appl. Prob., vol. 19, pp. 219–239, 1987.
30. D. Mitra and R.J. Gibbens, “State-dependent routing on symmetric loss networks with trunk reservation, Part II: Asymptotics, optimal design,” Annals of Operat. Res., vol. 35, pp. 3–30, 1992.
31. D. Mitra, R.J. Gibbens, and B.D. Huang, “State-dependent routing on symmetric loss networks with trunk reservation, Part I,” to appear in IEEE Trans. Commun.
32. D. Mitra, R. J. Gibbens, and B. D. Huang, “Analysis and optimal design of aggregated-least-busy-alternative routing on symmetric loss networks with trunk reservation,” in Proc. 13th ITC, Copenhagen, Denmark, 1991.
33. D. Mitra and J.B. Seery, “Randomized and deterministic routing strategies for circuit-switched networks: Design and performance,” IEEE Trans. Commun., vol. 39, pp. 102–116, 1991.
34. T.J. Ott and K.R. Krishnan, “Seperable routing: A scheme for state dependent routing of circuit switched traffic,” Annals of Operat. Res., vol. 35, pp 43–68, 1992.
35. M. Prindiville, M. Rajasekaren, and K.W. Ross, “Efficient sequential simulation of large-scale loss networks,” Tech. Rep., Dept. Comput. and Inform. Sci., Univ. Penn., 1991.
36. S. Rajasekaran and K.W. Ross, “Fast algorithms for generating discrete random variates with changing distributions,” Tech. Rep., Dept. Comput. and Inform. Sci., Univ. Penn., 1992.
37. J. Roberts, “Teletraffic models for the Telecom 1 integrated services network,” in Proc. 10th ITC, Montréal, Canada, 1983, 1.1-2.
38. J.W. Roberts, “A service system with heterogeneous user requirements,” Performance of Data Communications Systems and Their Applications, G. Pujolle, Ed. Amsterdam, The Netherlands: North Holland, 1981, pp. 423–431.
39. D. Tsang and K.W. Ross, “Algorithms for determining exact blocking probabilities in tree networks,” IEEE Trans. Cemmun., vol. 38, pp. 1266–1271, 1990.
40. W. Whitt, “Blocking when service is required from several facilities simultaneously,” AT&T Tech. J., vol. 64, pp. 1807–1856, 1985.
41. E. W. M. Wong and T. S. Yum, “Maximum free circuit routing in circuit-switched networks,” in Proc. IEEE INFOCOM, San Francisco, CA, 1990.
42. S. Zachary, “On blocking in loss networks,” Adv. Appl. Prob., vol. 23, pp. 355–372, 1991.
43. I.B. Ziedins and F.P. Kelly, “Limit theorems for loss networks with diverse routing,” Adv. Appl. Prob., vol. 21, pp. 804–830, 1989.