The Sequential Occupancy Problem through Group Throwing of Indistinguishable Balls

Tamar Gadrich () and Rachel Ravid
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Tamar Gadrich: Ort Braude College
Rachel Ravid: Ort Braude College

Methodology and Computing in Applied Probability, 2011, vol. 13, issue 2, 433-448

Abstract: Abstract The occupancy problem is generalized to the case where instead of throwing one ball at a time, a fixed size group of indistinguishable balls are distributed sequentially into cells. Bose-Einstein statistics is used for analyzing the distribution of the waiting time until each cell is occupied by at least one ball. Each trial is classified according to its jump size, i.e. the number of newly occupied cells. We propose an approach to decompose the occupancy and filling processes in terms of the jumps sizes using a multi-dimensional representation. A set of recursive equations is built in order to obtain the joint generating probability function of a series of random variables, each of which denotes the number of trials for a given jump size that occurred during the filling process. As a special case, the joint probability function of these random variables is obtained.

Keywords: Bose-Einstein statistics; Group throwing; Indistinguishable items; Occupancy problem; Recursive generating functions; Waiting time; Primary 60C05; 62D05; Secondary 05A05; 60J10 (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-009-9161-3

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