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Using the matrix product formalism we formulate a natural p-species generalization
of the asymmetric simple exclusion process. In this model particles hop with
their own specific rate and fast particles can overtake slow ones with a
rate equal to their relative speed. We obtain the algebraic structure and
study the properties of the representations in detail. The uncorrelated
steady state for the open system is obtained and in the $(p\rightarrow
\infty)$ limit, the dependence of its characteristics on the distribution of
velocities is determined. It is shown that when the total arrival rate
of particles exceeds a certain value, the density of the slowest particles
rises abroptly.
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