A Binomial Splitting Process in Connection with Corner Parking Problems. (December 2014)

• Record Type: Journal Article
• Authors: Fuchs, Michael; Hwang, Hsien-Kuei; Itoh, Yoshiaki; Mahmoud, Hosam H.
• Is Part Of: Journal of applied probability. Volume 51:Number 4(2014)
• Page Start: 971
• Page End: 989
• Publication Date: 2014-12
• Subjects: Binomial distribution, -- parking problem, -- periodic fluctuation, -- asymptotic approximation, -- digital tree, -- de-Poissonization; 60C05, -- 68W40, -- 60F05; 519.2
• DOI: 10.1017/S002190020001192X
• Languages: English
• ISSNs: 0021-9002

Abstract

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