Journal of Applied Probability

A binomial splitting process in connection with corner parking problems

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

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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 ½, and asymptotic to one in the unbiased case. Also, the limiting distribution does not exist as a result of the periodic fluctuations.

Article information

J. Appl. Probab., Volume 51, Number 4 (2014), 971-989.

First available in Project Euclid: 20 January 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60C05: Combinatorial probability 68W40: Analysis of algorithms [See also 68Q25]
Secondary: 60F05: Central limit and other weak theorems

Binomial distribution parking problem periodic fluctuation asymptotic approximation digital tree de-Poissonization


Fuchs, Michael; Hwang, Hsien-Kuei; Itoh, Yoshiaki; Mahmoud, Hosam H. A binomial splitting process in connection with corner parking problems. J. Appl. Probab. 51 (2014), no. 4, 971--989.

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