Optimal routing in circuit-switched communication networks

We consider the optimal circuit routing problem. The problem consists of accommodating a given circuit demand in an existing circuit-switched network. The objective is to find a circuit accommodation providing the maximum residual capacity over the network under the total circuit cost constraints. Practical considerations require a solution which is robust to the variations in circuit demand and cost. The objective function for the circuit routing problem is not a smooth one. In order to overcome the difficulties of nonsmooth optimization, a sequence of smooth convex optimization problems is considered. The optimal algorithm for the circuit routing problem is obtained as a limiting case of the sequence of the optimal routing strategies for the corresponding smooth optimization problems. The proof of its convergence to the optimal solution is given. This optimization algorithm is capable of efficiently handling networks with a large number of commodities. It also satisfies the above-mentioned robustness requirements. Numerical results are discussed.

[1]  Philip E. Gill,et al.  Numerical methods for constrained optimization , 1974 .

[2]  Dimitri P. Bertsekas,et al.  Data Networks , 1986 .

[3]  E. M. L. Beale,et al.  Nonlinear Programming: A Unified Approach. , 1970 .

[4]  Luigi Fratta,et al.  The flow deviation method: An approach to store-and-forward communication network design , 1973, Networks.

[5]  Bernard Yaged,et al.  Minimum cost routing for static network models , 1971, Networks.

[6]  Anthony V. Fiacco,et al.  Nonlinear programming;: Sequential unconstrained minimization techniques , 1968 .

[7]  D. Bertsekas.  Nondifferentiable optimization via approximation , 1975 .

[8]  Charles J. McCallum.  A generalized upper bounding approach to a communications network planning problem , 1977, Networks.

[9]  Dimitri P. Bertsekas,et al.  Notes on Optimal Routing and Flow Control for Communication Networks. , 1981 .

[10]  F. Clarke.  Optimization And Nonsmooth Analysis , 1983 .

[11]  Eugene Lawler,et al.  Combinatorial optimization , 1976 .

[12]  Michel Minoux,et al.  Graphs and Algorithms , 1984 .

[13]  Leon S. Lasdon,et al.  Optimization Theory of Large Systems , 1970 .

[14]  Elijah Polak,et al.  Computational methods in optimization , 1971 .

[15]  R. F. Rey,et al.  Engineering and Operations in the Bell System , 1983 .

[16]  Naum Zuselevich Shor,et al.  Minimization Methods for Non-Differentiable Functions , 1985, Springer Series in Computational Mathematics.

[17]  A. Gersht,et al.  NOM-a tool for optimal design and performance evaluation of routing strategies and its application to the Telenet network , 1988, IEEE INFOCOM '88,Seventh Annual Joint Conference of the IEEE Computer and Communcations Societies. Networks: Evolution or Revolution?.

[18]  Alexander Gersht,et al.  Optimal routing in circuit-switched communication networks , 1986 .

[19]  Don T. Phillips,et al.  Fundamentals Of Network Analysis , 1981 .