赵 玲，许宏科

(1.西安邮电大学通信与信息工程学院，陕西 西安 710121;2.长安大学电子与控制工程学院，陕西 西安 710064)

Abstract:In order to predict the Internet access population accurately, a forecasting method based on Gray Markov Verhulst model is proposed. The method uses historical data to construct gray Verhulst model, gets the expression of time response series of the Internet access population by determining coefficients, and obtains the development sequences of the Internet access population in the near future. Based on the Markov chain, the sequence states are divided into three parts, the state probability and medium prediction value are obtained by determining the state transition matrix, and further the modification values of each sequence are obtained. Finally, the Internet access population from December 2006 to June 2012 is used as original data to establish the forecasting model so as to predict the number of Internet users from December 2012 to June 2014. The results show that the prediction accuracy of the gray Markov Verhulst forecasting model has fewer errors and better prediction precision, gives the fluctuation range and the probability of the prediction results, and provides the decision-making basis for network construction and management.

Keywords:Internet;population prediction;Gray Markov;Verhulst model;prediction accuracy

1 引言

互联网自1994年进入中国以来，经过20年的快速发展，取得了令人瞩目的成绩。网络规模不断扩大，上网人数跃居世界第二，信息资源开发水平不断提高，互联网已经成为社会重要的信息基础设施。分析、预测我国互联网用户人数的统计信息，可以使国家和企业掌握互联网在我国的动态发展情况，为网络建设及管理提供决策依据。

目前，互联网发展的预测方法很多，如回归分析法、RBF神经网络预测法、Bass模型法和灰色理论预测法等[1～6]。回归分析法需要大量样本数据才能得出相对准确的预测模型，即它依赖于历史数据的完备程度。RBF神经网络法涉及神经网络的建立和训练过程，过程较为复杂，运算量偏大。文献[2]运用Bass模型预测互联网人数，但Bass模型法的缺点是其参数的确定比较麻烦，选用不同的方法确定模型参数对于预测的精度有很大的影响。文献[3]基于灰色灾变原理将GM(1,1)模型和一元线性回归模型结合来解决数据跳变问题，但跳变点的选取凭肉眼观察判断可能会造成误差。文献[4]在GM(1，1)模型基础上建立残差修正GM(1，1)后才取得较好的预测精度，其缺点是运算过程复杂。文献[5,6]均采用灰色Verhulst模型预测因特网访问人数，实例表明其具有理论可靠、方法简单、预测精度高等优点。马尔可夫理论在描述动态系统的状态转移方面独具优势，经常和灰色理论相结合用于预测长期的、波动性大的预测问题，并在诸多领域获得了广泛应用[7，8]。……