Link Capacity Assignment in Packet-Switched Networks: The Case of Piecewise Linear Concave Cost Function


IEICE TRANSACTIONS on Communications   Vol.E82-B   No.10   pp.1566-1576
Publication Date: 1999/10/25
Online ISSN: 
Print ISSN: 0916-8516
Type of Manuscript: PAPER
Category: Communication Networks and Services
communication networks and services,  packet-switched networks,  network design,  link capacity assignment,  non-linear programming,  algorithm,  

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In this paper, we study the link capacity assignment problem in packet-switched networks (CA problem) focusing on the case where link cost function is a piecewise linear concave function. This type of cost function arises in many communication network design problems such as those arising from developments in communication transmission technologies. It is already known that the method of link set assignment is applicable for solving the CA problem with piecewise linear convex cost function. That is, each link in the network is assigned to one of a group of specific sets, and checked for link set contradiction. By extending the method of link set assignment to the case of piecewise linear concave cost function, an important characteristic of the optimal solution of the CA problem is derived. Based on this characteristic, the non-differentiable link cost function can be treated as a differentiable function, and a heuristic algorithm derived from the Lagrange multiplier method is then proposed. Although it is difficult to determine the global optimum of the CA problem due to its non-convexity, it is shown by numerical results that the solution obtained from the proposed algorithm is very close to the global optimum. Moreover, the computation time is linearly dependent on the number of links in the problem. These performances show that the proposed algorithm is very efficient in solving the CA problem, even in the case of large-scale networks.