Abstract
The infinite source Poisson model is a fluid queue approximation of network data transmission that assumes that sources begin constant rate transmissions of data at Poisson time points for random lengths of time. This model has been a popular one as analysts attempt to provide explanations for observed features in telecommunications data such as self-similarity, long range dependence and heavy tails. We survey some features of this model in cases where transmission length distributions have (a) tails so heavy that means are infinite, (b) heavy tails with finite mean and infinite variance and (c) finite variance. We survey the self-similarity properties of various descriptor processes in this model and then present analyses of four data sets which show that certain features of the model are consistent with the data while others are contradicted. The data sets are 1) the Boston University 1995 study of web sessions, 2) the UC Berkeley home IP HTTP data collected in November 1996, 3) traces collected in end of 1997 at a Customer Service Switch in Munich, and 4) detailed data from a corporate Ericsson WWW server from October 1998. #Research supported by the Gothenburg Stochastic Centre, by the EU TMR network ERB-FMRX-CT96-0095 on “Computational and statistical methods for the analysis of spatial data” and by the Knut and Aline Wallenburg Foundation. Sidney Resnick's research was also partially supported by NSF grant DMS-97-04982 and NSA Grant MDA904-98-1-0041 at Cornell University.
Highlights
Statistical simulation is of basic importance for the choice of buffer sizes, protocols, network configurations and other aspects of the design of complex telecommunication systems
A further aim is to survey some statistical methods which we have found helpful, and which may be of use to the engineers and scientists who are coping with these data sets
The left most column contains the shape parameter g (related to the tail index a by a 1⁄4 1=gÞ of the traffic rates estimated by maximum likelihood using a generalized Pareto model (Subsection 3.3)
Summary
Statistical simulation is of basic importance for the choice of buffer sizes, protocols, network configurations and other aspects of the design of complex telecommunication systems. A simple model, here termed “the infinite source Poisson model” and sometimes called the M/G/1 input model, which has the potential to satisfy these requirements for IP; HTTP, FTP, SMTP and other protocols for file transfers is surveyed and tested in this paper. A core issue is the relation between the micro level infinite source Poisson model and limiting aggregated models outlined below. We define the infinite source Poisson model and give basic properties and descriptor quantities, and asymptotic approximations. A further issue is that in the middle case the nature of the approximation depends on the relation between l and T.
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