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Biometrika 1976 63(2):361-366; doi:10.1093/biomet/63.2.361
© 1976 by Biometrika Trust
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On random sequential packing in two and three dimensions

YOSHIAKI AKEDA and MOTOO HORI

Department of Applied Physics, Tokyo Institute of Technology

The two- and three-dimensional random packing problems in Palásti's (1960) sense are studied by means of Monte Carlo simulations and extrapolation techniques. In the two-dimensional case, a 95% confidence interval of 0·5629 ± 0·0006 is obtained for the limit of mean random packing density. This estimate is slightly but significantly higher than the value conjectured by Palásti, c20·5589. For the three-dimensional case, we calculate only a lower bound of the limiting density and give a 95% confidence interval of 0·4148 ± 0·0025, which is also fairly near to the conjectured value (c30·4178).

Key Words: Car-parking problem • Monte Carlo simulation • Palásti's conjecture • Random packing density


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