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Modeling teletraffic arrivals by a Poisson cluster process. (English) Zbl 1119.60075
The infinite source Poisson model for modeling teletraffic arrivals is considered. This model is also referred to as Poisson cluster process or branching Poisson process. We recall that the Poisson cluster process is obtained by marking the Poisson point \(\Gamma_{j}\) by the pair (\(K_{j}, (X_{ji}, i \geq 1\))). The covariance structure of the increment process of \(N\) is derived. The asymptotic behaviour of the Poisson cluster process is studied. The conditions on the distribution of \(K_{j}\) and \(X_{ji}\) under which the random sums \(\sum_{i=1}^{K_{j}} X_{ji}\) have a regularly varying tail are formulated. Using the form of the distribution of the interarrival times of the process \(N\) under the Palm measure, the authors also conduct an exploratory statistical analysis of internet packet arrivals to a server.
In contrast to other modeling techniques, such as the commonly used ON/OFF or the infinite source Poisson models, the used Poisson cluster process model is more realistic and has significantly higher precision and lower computation overhead.

MSC:
60K25 Queueing theory (aspects of probability theory)
68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
90B20 Traffic problems in operations research
90B15 Stochastic network models in operations research
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