Telecommunication Network Design

A telecommunications network contains a management node, a number of satellite nodes and a large number of end user nodes connected to the satellite nodes. The communication may be between any two end users (telephony), between the management node and one end user (Internet download) and a combination of the two (telephony over Internet). In all cases the signalling is between the end user and the management node. Given the geographical distribution of the end users (numbers ranging from six to seven digits), the geographical location of the management node, the cost (one time and monthly) of connecting the end users to satellite nodes and the satellite nodes to each other and to the management node as a function of their location and of the number of end users connected over a particular link, design a network such that: 1. the vulnerability (requires definition) of the network is minimized;