A binomial splitting process in connection with corner parking problems

Michael Fuchs, Hsien Kuei Hwang, Yoshiaki Itoh, Hosam H. Mahmoud

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

This paper studies a special type of binomial splitting process. Such a process can be used to model a high dimensional corner parking problem as well as determining the depth of random PATRICIA (practical algorithm to retrieve information coded in alphanumeric) tries, which are a special class of digital tree data structures. The latter also has natural interpretations in terms of distinct values in independent and identically distributed geometric random variables and the occupancy problem in urn models. The corresponding distribution is marked by a logarithmic mean and a bounded variance, which is oscillating, if the binomial parameter p is not equal to 1/2 , and asymptotic to one in the unbiased case. Also, the limiting distribution does not exist as a result of the periodic fluctuations.

Original languageEnglish
Pages (from-to)971-989
Number of pages19
JournalJournal of Applied Probability
Volume51
Issue number4
DOIs
StatePublished - 1 Dec 2014

Keywords

  • Asymptotic approximation
  • Binomial distribution
  • De-poissonization
  • Digital tree
  • Parking problem
  • Periodic fluctuation

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