### abstract ###
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Traffic forecasting from past observed traffic data with small calculation complexity is one of important problems for planning of servers and networks
Focusing on World Wide Web (WWW) traffic as fundamental investigation, this paper would deal with Bayesian forecasting of network traffic on the time varying Poisson model from a viewpoint from statistical decision theory
Under this model, we would show that the estimated forecasting value is obtained by simple arithmetic calculation and expresses real WWW traffic well from both theoretical and empirical points of view
### introduction ###
Under network environment such as Internet, planning of servers and networks is one of important problems for stable operation
It is often typical situation that administrators analyze logs on their servers and networks
They may frequently look into result of log analysis software where these tools usually have some functions to periodically summarize logs
For example, webalizer  CITATION  and analog  CITATION  etc \, have been widely used among World Wide Web (WWW) server administrators or users for long years
These tools usually summarize the logs by counting hourly, daily, and monthly numbers of hits, files, and pages etc
Administrators would often make their operation plans with combination of their experience and intuition from these logs
In this case, traffic forecasting rule is not clearly formulated and those summarized logs remain in the field of  descriptive statistics  from the statistical point of view
On the other hand, researchers in the field of traffic engineering have been suggesting a lot of analysis models
Probabilistic approach is one of viewpoints in this field
It is wide-spread fact that the stationary Poisson distribution is not always suitable for Internet traffic because of its nature of non-stationality  CITATION   CITATION  and long-range dependence (LRD)  CITATION   CITATION  etc
Therefore desirable conditions of good traffic models are to have structures to express such nature at least
Furthermore, another requirement of models is to have a structure of traffic forecasting
For this point, parameter estimation is often performed at first under assumption of the stationarity  CITATION , then the estimated parameter is substituted for the parameter of model
This approach has been wide-spread in the field of  inferential statistics  from the statistical point of view
However, substituting the estimated parameter as a constant for the model's parameter is not always suitable especially on forecasting problems
This is because there is often no guarantee that the assumptions under the parameter estimation of the model always hold for future unknown data set
Bayesian approach  CITATION  CITATION  is one of alternatives for this point
In Bayesian approach, a probability distribution of parameter is assumed as the prior distribution
If new data is observed, then the Bayes theorem updates the prior distribution of parameter to the posterior distribution and then forecasts the posterior distribution of data
Recently, this approach has been widely applied to many forecasting problems especially in the field of information technologies and bioinformatics etc
In order to take Bayesian approach,  statistical decision theory  is an important theoretical framework from the statistical point of view
Taking the above factors into account, this paper would deal with Bayesian forecasting of WWW traffic on the non-stationary i e time varying Poisson model
Bayesian forecasting on time varying parameter model has been proposed in  CITATION  by defining certain class of parameter transformation function
However, it has not yet been discussed about any predictive estimator nor definite transformation function of parameter  CITATION
This paper would clearly define a random-walking type of transformation function of parameter to obtain the Bayes optimal prediction for WWW traffic
Then its effectiveness would be evaluated with real WWW traffic data
In this model, time varying degree is caught by a real valued constant  SYMBOL  and this constant would play an important role throughout this paper
Another feature is that the traffic forecasting value is obtained by simple arithmetic calculations under known  SYMBOL
In general, the Bayes theorem often results in large calculation costs
However, certain combination of parameter distribution and its transformation function solves this problem
We believe that this point can be helpful not only for theoretical calculation cost but also for real implementation on WWW log analysis tools  CITATION   CITATION
The rest of this paper is organized as the followings
Section  gives some definitions and explanations of the forecasting model with time varying Poisson distribution
Section  shows some analysis examples of real WWW traffic data  to validate this paper's approach and Section  gives{} their discussions
Finally, Section  concludes this paper
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