The Poisson Cluster Process Runs as a Model for the Internet Traffic
NEW2AN '09 and ruSMART '09 Proceedings of the 9th International Conference on Smart Spaces and Next Generation Wired/Wireless Networking and Second Conference on Smart Spaces
Simulating a Poisson cluster process for Internet traffic packet arrivals
Computer Communications
Modeling network traffic by a cluster Poisson input process with heavy and light-tailed file sizes
Queueing Systems: Theory and Applications
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In this paper we consider a Poisson cluster process N as a generating process for the arrivals of packets to a server. This process generalizes in a more realistic way the infinite source Poisson model which has been used for modeling teletraffic for a long time. At each Poisson point 驴 j , a flow of packets is initiated which is modeled as a partial iid sum process $$\Gamma_j+\sum_i=1^kX_ji, k\le K_j$$ , with a random limit K j which is independent of (X ji ) and the underlying Poisson points (驴 j ). We study the covariance structure of the increment process of N. In particular, the covariance function of the increment process is not summable if the right tail P(K j x) is regularly varying with index 驴驴 (1, 2), the distribution of the X ji 's being irrelevant. This means that the increment process exhibits long-range dependence. If var(K j ) N(t)) t驴 0 and give 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. Using the form of the distribution of the interarrival times of the process N under the Palm distribution, we also conduct an exploratory statistical analysis of simulated data and of Internet packet arrivals to a server. We illustrate how the theoretical results can be used to detect distribution al characteristics of K j , X ji , and of the Poisson process.