Abstract: The general Multiprotocol Label Switch (MPLS) topology optimisation problem is complex and concerns the optimum selection of links, the assignment of capacities to these links and the routing requirements on these links. Ideally, all these are jointly optimised, leading to a minimum cost network which continually meets given objectives on network delay and throughput. In practice, these problems are often dealt with separately and a solution iterated. In this paper, we propose an algorithm that computes the shortest routes, assigns optimal flows to these routes and simultaneously determines optimal link capacities. We take into account the dynamic adaptation of optimal link capacities by considering the same Quality of Service (QoS) measure used in the flow assignment problem in combination with a blocking model for describing call admission controls (CAC) in multiservice broadband telecommunication networks. The main goal is to achieve statistical multiplexing advantages with multiple traffic and QoS classes of connections that share a common trunk present. We offer a mathematical programming model of the problem and proficient solutions which are founded on a Lagrangean relaxation of the problem. Experimental findings on 2-class and 6-class models are reported.