Jamming and asymptotic behavior in competitive random parking of bidisperse cars

We propose a generalized car parking problem where either a car of size σ or of size mσ (m>1) is sequentially parked on a line with probability q and (1−q), respectively. The free parameter q interpolates between the classical car parking problem at either extreme (q=0 and 1) and the competitive random sequential adsorption of a binary mixture in between. We find that the coverage in the jamming limit for a mixture always exceeds the value obtained for the uni-sized case. The introduction of a bidisperse mixture results in the slow approach (∼t−1) to the jamming limit by the smaller species while the larger species reach their asymptotic values exponentially fast ∼t−1e−(m−1)qt.