Abstract
We consider here the problem of the optimal network design either for multi‐rate circuit switching or VC switching in an ATM network through the use of effective bandwidth models. We put the emphasis on the development of a fast and stable numerical algorithm for computing solutions of networks of up to 50 nodes. We show that the main difficulty is in the calculation of the gradient of the objective function in the presence of the Erlang fixed point system. We then propose an approximation for this calculation based on the power series of the inverse of a matrix. Next, we review explicit representation techniques for the matrices involved in this calculation and show that reductions in CPU time of factors as large as 20 can be obtained with practically no penalty in terms of memory requirement. We also show that the dimensioning problem is ill‐conditioned and that a simple scaling of the dimensioning variables is sufficient to speed up the convergence. As a final point, we use the algorithm to examine some features of the problem. We show that the objective function has no definite convexity property, that alternate routing is used mostly by wideband calls and that the grade of service constraints are generally binding only for these wideband calls.
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References
F. Kelly, Notes on Effective Bandwidth (Cambridge University, 1995).
A. Girard and N. Lessard, Revenue optimization of virtual circuit ATM networks, in: Proc. Networks '92 (May 1992).
B. Sansó, A. Girard and V.N. Dang, Multi-commodity flow models for robust network design, in: Proc. 4th Network Planning Symposium (September 1994).
G.R. Ash, K.K. Chang and J.-F. Labourdette, Analysis and design of fully shared networks, in: Proc. 14th International Teletraffic Congress, eds. J. Labetoulle and J. Roberts (Elsevier, 1994) pp. 1311-1320.
Y. Watanabe and H. Mori, Dynamic routing schemes for international networks, in: Proc. 5th ITC Seminar (May 1987).
G.R. Ash, B.M. Blake and S.D. Schwartz, Integrated network routing and design, in: Proc. 12th International Teletraffic Congress, ed. M. Bonatti (North-Holland, 1988) pp. 1.4A (3.1–3.8).
D. Medhi and S. Guptan, Network dimensioning and performance of multi-service, multi-rate loss networks with dynamic routing, IEEE/ACM Trans. on Networking 5(6) (December 1997) 944-957.
A. Girard and E.B. Gardouh, Synthesis methods for broadband ISDN networks, in: Proc. 4th International Conference on Advances in Communication and Control (May 1993).
A. Girard and S. St-Georges, Performance evaluation and routing optimization of ISDN networks with nonhierarchical and alternate routing, in: Proc. Telecommunication Systems Modelling and Analysis (March 1993).
J.A. Morrison, D. Mitra and K.G. Ramakrishnan, ATM network design and optimization: a multi-rate loss network framework, IEEE/ACM Trans. on Networking 4(4) (August 1996) 531-543.
Z. Dziong, ATM Network Resource Management (McGraw-Hill, 1997).
A. Girard and H. Bouley, Performance evaluation of B-ISDN networks: Two-moment models and numerical stability, Technical Report 91-37, INRS-Télécommunications, 16 Place du Commerce, Verdun, Québec, H3E 1H6 Canada (1991).
F.P. Kelly, Blocking probabilities in large circuit-switched networks. Adv. in Appl. Probab. 18 (1986) 473-505.
A. Girard, Routing and Dimensioning in Circuit-switched Networks (Addison-Wesley, 1990).
D. G. Luenberger, Linear and Nonlinear Programming (Addison-Wesley, 1984).
J.F.P. Labourdette and G.W. Hart, Link access blocking in very large multi-media networks, Computer Communication Review 20(4) (September 1990) 108-117.
M. Held, P. Wolfe and H.P. Crowder, Validation of subgradient algorithm, Math. Programming 6 (1974) 62-88.
A. Girard and M.T. Ho, Optimization of ISDN networks with partial sharing, in: Proc. 14th International Teletraffic Congress, eds. J. Labetoulle and J. Roberts (Elsevier, 1994) pp. 1251-1260.
A. Girard, P.D. Lansard and B. Liau, A multi-hour ECCS theory and applications, in: Proc. 3rd International Network Planning Symposium, Networks '86 (1986) pp. 78-84.
E. Rosenberg, A nonlinear programming heuristic for computing optimal link capacities in a multi-hour alternate routing communications network, Oper. Res. 35 (1987) 354-364.
D. Medhi, A parallel algorithm for solving a multi-hour network design problem for teletraffic networks, Technical Report, University of Missouri-Kansas City, Computer Science Telecommunications program 5100 Rockhill Road, Kansas City, MO 64110 (October 1991).
A. Girard and F. Paquet, Fast heuristics for modular dimensioning of telecommunication networks, in: Proc. 3rd International Conference on Telecommunication Systems, ed. B. Gavish (March 1995).
J. Labetoulle and J. Roberts, eds., Proc. 14th International Teletraffic Congress (Elsevier, 1994).
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Sun, X., Girard, A. A fast numerical algorithm for multi‐rate network synthesis. Telecommunication Systems 10, 355–388 (1998). https://doi.org/10.1023/A:1019135620931
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DOI: https://doi.org/10.1023/A:1019135620931