We design virtual topologies in wavelength division multiplexing (WDM) networks to minimize the network diameter and average hop count, where network diameter refers to the number of hops of the longest shortest path and average hop count is the average number of hops among the shortest paths of all node pairs. Such objectives are important to WDM networks, especially to those with statistical multiplexing mechanisms such as optical burst switching (OBS) and optical packet switching (OPS). By minimizing the network diameter and average hop count, optical packets or bursts will experience less contention loss and smaller delay due to a reduced number of intermediate nodes en route. In this paper, we first formulate an integer linear program (ILP) for optimal design of virtual topologies with minimized network diameter and average hop count. Then, a novel heuristic least weight minimum diameter (LWMD) is proposed to find good solutions efficiently. Based on the virtual topology obtained, we further design two traffic accommodation schemes to provision wavelengths under a given traffic matrix, with guaranteed network diameter and minimized network resource consumption.
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