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Rényi's Parking Constants comes up when one puts down unit length cars on a interval, such that the probability of covering any two interval is the same.

Are there any published results when the distribution is non-uniform?

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If you don't get any good answers here in the next day or so, you might try this at Math Overflow. – Mike Spivey Jan 2 '11 at 5:44
This was asked recently @ MathOverflow and didn't get much response -… – Dinesh Feb 15 '11 at 17:13
@Dinesh @Mike Spivey: The question was asked on both sites the same day. @Chao Xu: You might care to specify whether the reference provided on the MO page mentioned by @Dinesh satisfied you or not and, if not, why it did not. – Did Feb 15 '11 at 17:25

Here is one: Jean-François Marckert, Parking with density, Random Structures and Algorithms 18 (4), 364-380 (2001). A preprint version is available on this page.

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