Optimization in Telecommunication Networks

Network design and network synthesis have been the classical optimization problems in telecommunication for a long time. In the recent past, there have been many technological developments such as digitization of information, optical networks, internet, and wireless networks. These developments have led to a series of new optimization problems. This manuscript gives an overview of the developments in solving both classical and modern telecom optimization problems. We start with a short historical overview of the technological developments. Then, the classical (still actual) network design and synthesis problems are described with an emphasis on the latest developments on modelling and solving them. Classical results such as Menger’s disjoint paths theorem, and Ford-Fulkerson’s max-flow-min-cut theorem, but also Gomory-Hu trees and the Okamura-Seymour cut-condition, will be related to the models described. Finally, we describe recent optimization problems such as routing and wavelength assignment, and grooming in optical networks. 1 A short history on technological developments This section presents an overview of the technological breakthroughs that resulted in the current level of telecommunication. We start with the fundamental developments that led to the basic usage of telephone (wired and wireless), the classical history. Next, we discuss recent developments such as digitization, optical technology and wireless networks. 1.1 Classical history Fast communication over large distances already appealed the ancient Greeks. Without much technical knowledge of electricity and light they had to resort to human labor. It is not until the end of the 18th century before we see real telecommunication: instant communication over large distances, with little human effort. Claude Chappe (in France, in 1793) and Abraham Edelcrantz (in Sweden, one year later) invented the optical telegraph. This device could send light signals over large distances by use of a series of instruments based on mirrors. Besides the technical details both inventors also developed a protocol for transmitting, which decided when, how and where information was sent. It took only a few years before a nation-wide network of telegraphs was implemented in both countries. This, in spite of strong opposition