Topological design of a centralized communication network with unreliable links and node outage costs

In this paper, we present a mathematical formulation of a terminal layout problem in the design of a centralized communication network with unreliable links and node outage costs. The node outage cost associated with a terminal node is a cost incurred by the network user whenever that terminal node is unable to communicate with the central node due to failure of a link. We suggest a two-phase heuristic with a time complexity of O(N³) to solve the problem. We also present a Lagrangean relaxation method to find the lower bound of the objective function value. The lower bound given by the Lagrangean relaxation method is used to estimate the quality of the solution given by the two-phase heuristic. Experimental results over a wide range of problem structures show that the average solution given by the two-phase heuristic is within 10% of the optimal objective function value.