Details
| Original language | English |
|---|---|
| Pages (from-to) | 650-656 |
| Number of pages | 7 |
| Journal | Journal of applied probability |
| Volume | 39 |
| Issue number | 3 |
| Publication status | Published - Sept 2002 |
Abstract
We generalize Banach's matchbox problem: demands of random size are made on one of two containers, both initially with content t, where the container is selected at random in the successive steps. Let Zt be the content of the other container at the moment when the selected container is found to be insufficient. We obtain the asymptotic distribution of Zt as t → ∞ under quite general conditions. The case of exponentially distributed demands is considered in more detail.
Keywords
- Asymptotic normality, Bessel functions, Convergence in distribution, Exponential distribution, Knuth's old sum, Renewal theory
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Mathematics(all)
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
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In: Journal of applied probability, Vol. 39, No. 3, 09.2002, p. 650-656.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - From matchbox to bottle
T2 - A storage problem
AU - Baringhaus, Ludwig
AU - Grübel, Rudolf
PY - 2002/9
Y1 - 2002/9
N2 - We generalize Banach's matchbox problem: demands of random size are made on one of two containers, both initially with content t, where the container is selected at random in the successive steps. Let Zt be the content of the other container at the moment when the selected container is found to be insufficient. We obtain the asymptotic distribution of Zt as t → ∞ under quite general conditions. The case of exponentially distributed demands is considered in more detail.
AB - We generalize Banach's matchbox problem: demands of random size are made on one of two containers, both initially with content t, where the container is selected at random in the successive steps. Let Zt be the content of the other container at the moment when the selected container is found to be insufficient. We obtain the asymptotic distribution of Zt as t → ∞ under quite general conditions. The case of exponentially distributed demands is considered in more detail.
KW - Asymptotic normality
KW - Bessel functions
KW - Convergence in distribution
KW - Exponential distribution
KW - Knuth's old sum
KW - Renewal theory
UR - http://www.scopus.com/inward/record.url?scp=0036763559&partnerID=8YFLogxK
U2 - 10.1239/jap/1034082136
DO - 10.1239/jap/1034082136
M3 - Article
AN - SCOPUS:0036763559
VL - 39
SP - 650
EP - 656
JO - Journal of applied probability
JF - Journal of applied probability
SN - 0021-9002
IS - 3
ER -