The purpose of this report is to extend Poisson distribution for the study of real Internet traffic by use of a generating function technique.
The well-know Poisson distribution of the traffic model is derived from the three assumptions, (1) "memoryless", (2) "single request" and (3) "stationary" properties of the traffic. I will firstly remove the assumption of single request (separated occurrence) and next remove the stationary assumption in the traffic. Here we will see that the assumption of memoryless and stationary properties for the traffic leads to a special relation that the ratio of the variance to the average of request numbers remains constant with respect to the change of time intervals for counting requests. Then I will analyze the real access log of HTTP server with this extended Poisson distribution. We will see that the ratio of the variances to the averages increases with the increase of the counting time intervals in the real access log of HTTP servers.
This strongly indicates that the memoryless assumption does not hold for real Internet traffic.
By: Akio Koide
Published in: RT0428 in 2002
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