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Random sprouts as internet models, and Pólya processes

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Abstract.

The sprout, a tree growing in real time is introduced. The sprout is a generalization and an embedding in time of the standard recursive tree. The sprout is proposed as a model for the growth of the Internet. The tree size is analyzed via an associated two-color stochastic process (the sprout process), which is a special case of the Pólya process. Owing to its potential as a modeling tool, the more general Pólya process is analyzed on average. In addition to the usage of the Pólya process in evaluating sprouts, we also give a heuristic interpretation of the result for Pólya urns, which might be a first step toward understanding several nonclassic urn models, as those with nonconstant row sum and those with multiple eigenvalues.

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Authors and Affiliations

  1. Department of Statistics, The George Washington University, DC 20052, Washington, USA

    Hosam M. Mahmoud

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  1. Hosam M. Mahmoud
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Correspondence to Hosam M. Mahmoud.

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Received: 23 September 2002, Revised: 6 March 2004, Published online: 14 October 2004

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Mahmoud, H.M. Random sprouts as internet models, and Pólya processes. Acta Informatica 41, 1–18 (2004). https://doi.org/10.1007/s00236-004-0146-y

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  • DOI: https://doi.org/10.1007/s00236-004-0146-y

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