Mean First-Passage Time and Robustness of Complex Cellular Mobile Communication Network

With the rapid development of complex network science and the complexity of communication network, it is difficult to research its technical application. In order to solve these problems, we firstly design the cellular mobile communication network as a fractal six-star network <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$G_{t,s}$</tex-math></inline-formula> from the view of complex network science. Secondly, we investigate the analytical expression of the mean first-passage time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M_{G_{t,s}}$</tex-math></inline-formula> of the random walk and the average path length <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\left\langle W \right\rangle$</tex-math></inline-formula> . Both of them are proved to be proportional to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$t$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$s$</tex-math></inline-formula> . Thirdly, taking into account network transmission efficiency and time delay, the recursive expression of diameter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$D_{t}$</tex-math></inline-formula> is derived, which increases exponentially with respect to the size of the network. Fourthly, it is verified that the experimental simulations are in perfect consistent with the theoretical analysis, which shows that the designed network is reasonable. Fifthly, to further proving the stability of the six-star network, the robustness of the network is analyzed, which indicates the robustness and density are positively correlated. Finally, the average value of experiments is used to analyze the decisive effect of the number of nodes removed after network failure on robustness, which is of great significance to the research of communication network in reality.

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