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This paper presents a global optimal solution technique for the joint optimization of link capacity and flow assignment (CFA) in a packet-switched communications network, queueing systems to model existing networks are considered. A continuous lower bound of the average packet delay is used in the formulation of the cost objective function for the capacity and flow assignment. The cost objective function thus formulated is shown to be convex with respect to the network multicommodity flow. This convexity ensures the global optimal solution to the CFA problem via the flow deviation (FD) method. Refinement of the CFA optimization techhique to allow optimal discretization of the continuous solutions to discrete solutions is presented based on dynamic programming and iterations of Flow Optimization and Capacity Optimization. Application examples of these optimization procedures are illustrated.