Tree network design avoiding congestion

• Published in: Applied mathematical modelling Vol. 35; no. 9; pp. 4175 - 4188
• Main Authors: Miranda, G., Luna, H.P., de Camargo, R.S., Pinto, L.R.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 01.09.2011; Elsevier
• Subjects: Applied sciences; Benders decomposition; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Congestion; Exact sciences and technology; Flows in networks. Combinatorial problems; Generalized Benders decomposition; Ground, air and sea transportation, marine construction; Mathematical models; Mathematical programming; Mixed-integer nonlinear programming; Multi-commodity network design flow problems; Networks; Operational research and scientific management; Operational research. Management science; Optimization; Servers; Software; Steiner tree problems; Switching theory; Transportation planning, management and economics; Trees; Generalized Benders decomposition; Multi-commodity network design flow problems; Mixed-integer nonlinear programming; Steiner tree problems; Tree(graph); Network flow; Partition method; Variable cost; Minimization; Linear programming; Mixed integer programming; Steiner tree problem; Distributed system; Direct problem; Multicommodity flow problem; Computer network; Spanning tree; Non linear model; Transportation network; Telecommunication network
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2011.02.046

We introduce in this paper an optimal method for tree network design avoiding congestion. We see this problem arising in telecommunication and transportation networks as a flow extension of the Steiner problem in directed graphs, thus including as a particular case any alternative approach based on the minimum spanning tree problem. Our multi-commodity formulation is able to cope with the design of centralized computer networks, modern multi-cast multi-party or hub-based transportation trees. The objective in such cases is the minimization of the sum of the fixed (structural) and variable (operational) costs of all the arcs composing an arborescence that links the origin node (switching center, server, station) to every demand node (multi-cast participants, users in general). The non-linear multi-commodity flow model is solved by a generalized Benders decomposition approach.