幂律指数在1与3之间的一类无标度网络

借助排队系统中顾客批量到达的概念，提出节点批量到达的Poisson网络模型.节点按照到达率为λ的Poisson过程批量到达系统.模型1，批量按照到达批次的幂律非线性增长，其幂律指数为θ(0≤θ<+∞).BA模型是在θ＝0时的特例.利用Poisson过程理论和连续化方法进行分析，发现这个网络稳态平均度分布是幂律分布，而且幂律指数在1和3之间.模型2，批量按照节点到达批次的对数非线性增长，得出当批量增长较缓慢时，稳态度分布幂律指数为3.因此，节点批量到达的Poisson网络模型不仅是BA模型的推广，也为许多幂律指数在1和2之间的现实网络提供了理论依据.

Scale-free networks with the power-law exponent between 1 and 3

Basing on the batch arrival concept in the queue theory, this paper proposes a Poisson network model with node batch arrival. The Nodes arrive the system as a Poisson process with rate λ. In the first model, the batch is a power function of the batch number with exponent θ(0≤θ<+∞). Using Poisson process theory and continuum approach, we found that the stationary mean degree distribution of this model is a power-law distribution, and its power-law exponent is between 1 and 3. In the second model, the batch is a log function of the batch number and we obtained that the power-law exponent of stationary mean degree distribution is 3 when the batch rises more slowly. So our model is not only the extension of the BA model, but also a theoretical foundation of many real networks of which the power-law exponent is between 1 and 2.