Distribution And Modeling Of Communication Services

For the study of human behavior distribution, there have been many conclusions. Opinions about human behaviors have changed from the idea that the human behaviors obey Poisson distribution to a mainstream ideology in recent years that human behavior subject to heavy tailed distribution. The researches of human behaviors are not confined to individual, but also the study in group level. The models which can be used to explain the heavy-tailed characteristics have changed from the initial simple queuing model to complex models considering various factors with the in-depth research. Since BARABASI A L published a paper in Nature named "The origin of bursts mentioned human behavior and heavy tails in human dynamics" which suggest that the human behavior have non Poisson properties in 2005, more and more studies start to show that human behavior distribution follows heavy tailed distribution rather than exponential distribution. For what kind of function can better fit the distribution of human behavior, most scholars believe that the power-law distribution can be suitable for fitting.However, some scholars propose the Lognormal distribution or two segment distribution can better fit it. Researchers have proposed many models to explain how the no Poisson properties of human behavior can be generated. Such as the queue model, the model based on human interest, model based on memory, the return model, the periodic random walk model and some combination models.Study on human behavior distribution is an extremely important role in human society development, urban construction, the development of the market economy, the information dissemination and technology innovation, and so on. For example, through the analysis of inter-event time distribution of users sending email, people can determine the virus propagation mechanism; through the analysis of the distribution of user mobile distance, people can do traffic planning.With the popularity of smart phones and the rapid development of mobile Internet business, more and more people begin to use mobile phones to browse web pages, watch videos, chat, shopping and so on.Therefore, it is very important to analyze the distribution of mobile Internet services for in-depth study of human behavior characteristics.Meanwhile, the number of mobile Internet services have increased rapidly.The emergence of large scale mobile Internet services is likely to bring about some new distribution law. In the paper, we analyze the online records of all users of mobile network services in two cities, and study the law of distribution of different communication services, such as following:Firstly, we study the time characteristics of mobile users accessing the instant messaging (IM) services in two cities. We analyze the distribution of inter-event time which represents the time intervals between two consecutive accessing to IM services and find the inter-event time distributions of IM services follow the mixture distribution of Exponential Power-law distribution. The distribution can be modeled by mixture model of Exponential and interest model.The parameters of distribution of different countries are different,we infer that it's relevant to the popularity of service. Normally, the higher popularity, the larger parameter.Secondly, we study the traffic characteristics of mobile users accessing the communication services in two cities. We analyze the distribution of flow produced by mobile users when they using the streaming media services and IM services, and find that the distributions follow two pieces Power-law distribution, and user's behaviors are periodicity. The periodicity is one of the reason for the heavy-tail characteristics of traffic distribution.Finally, we analyze the proportion distribution of different services,and find that the proportion distribution of services can be divided into three types of distribution including U-Shape distribution, Jump-tail distribution and Long-tail distribution. Then analyzing the relationships between services and distributions.