Narrow Results

We propose a symmetrical scheme, by drawing results from group theory, and use it to build a new class of data center network models. The results are superior to current network models with respect to a number of performance criteria. Greater symmetry in networks is important, as it leads to simpler structure and more efficient communication algorithms. It also tends to produce better scalability and greater fault tolerance. Our models are general and are expected to find many applications, but they are particularly suitable for large-scale data-center networks.

As a decisive parameter of network robustness and network economy, the capacity of network edges can directly affect the operation stability and the construction cost of the network. This paper proposes a multilevel load–capacity optimal relationship (MLCOR) model that can substantially improve the network economy on the premise of network safety. The model is verified in artificially created networks including free-scale networks, small-world networks, and in the real network structure of the Shanghai Metro network as well. By numerical simulation, it is revealed that under the premise of ensuring the stability of the network from the destruction caused by initial internal or external damage on edge, the MLCOR model can effectively reduce the cost of the entire network compared to the other two linear load–capacity models regardless of what extent of the destruction that the network edges suffer initially. It is also proved that there exists an optimal tunable parameter and the corresponding optimal network cost for any BA and NW network topology, which can provide the reference for setting reasonable capacities for network edges in a real network at the stage of network planning and construction, promoting security and stability of network operation.

Some of the main known results about efficiency, vulnerability and cost for complex networks are reviewed from a mathematical perspective. Such presentation is then completed by including new results that expand the domain of the theory to the realm of directed networks. This mathematical framework is subsequently used to perform a comparative analysis of those performance measures over a significant sample of subway networks worldwide.