The ``parking'' problem for segments of different length
\textit{A. Rényi} has considered the parking problem for a segment \([0,x]\) by intervals of length 1 [Publ. Math. Inst. Hung. Acad. Sci. 3, 109-127 (1958; Zbl 0105.11903)]. In the present paper a modified parking problem is considered. Intervals of two different lengths (1 or 2) fill the segment \([0,x]\). Let \(N_x\) be the number of the accommodated intervals on \([0,x]\). The main result is the following theorem: There exists \(\lim_{x\to \infty} EN_x/x=\gamma>0\) (\(E\) stands for expectation). Moreover, \(EN_x = \gamma x + {3 \over 2} \gamma - 1 + O\left(\left(c/x\right)^{x -3/2}\right)\), \(x\to \infty\), where \(c\) is a positive constant. See also \textit{A. Dvoretzky} and \textit{H. Robbins} [ibid., Ser. A 9, 209-225 (1964; Zbl 0251.60023)].
scientific article; zbMATH DE number 1300645
scientific article