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    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 97 (1999), S. 209-231 
    ISSN: 1572-9613
    Keywords: parking ; probability model ; Laplace transform ; vector differential equation ; explicit solution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The car parking problem is a one-dimensional model of random packing. Cars arrive to park on a block of length x, sequentially. Each car has, independently, spin up or spin down, w.p. 0 〈 p ≤ 1, for spin up and q = 1 − p for spin down, respectively. Each car tries to park at a uniformly distributed random point t ∈ [0, x]. If t is within distance 1 of the location of a previously parked car of the same spin, or within distance a of the location of a previously parked car of the opposite spin, then the new car leaves without parking and the next car arrives, until saturation. We study the problem analytically as well as numerically. The expected number of up spins c(p, a) per unit length for sufficiently large x is neither monotonic in p for fixed a, nor is it monotone in a for fixed p, in general. An intuitive explanation is given for this nonmonotonicity.
    Type of Medium: Electronic Resource
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