In this paper, we address an important telecommunication network design issue through a new approach that incorporates significant uncertainty in the input data. In particular, we focus on locating communication hubs in a star-star network with both demand and cost uncertainties. The research model determines 1) the number of hubs tobe employed, 2) the location of hubs within a given set of pre-determined sites, and 3) the assignment of end-user nodes to these communication hubs without violating their line capacities. The total system cost includes the fixed costs of installing hubs, and the variable costs of connecting end-user nodes to selected hubs. It is assumed that the demand imposed by any end-user node is not known a priori. Furthermore, each end-user node imposes a variable cost that depends on both the processing demand anda time-varying communication charge. The incorporation of uncertainty in end-user demands, and hence the communication costs, adds a new dimension to network management and facility planning