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By generalizing the algebra of operators of the Asymmetric Simple
Exclusion Process (ASEP), a multi-species ASEP in which particles can
overtake each other, is defined on both open and closed one
dimensional chains. On the ring the steady state and the correlation
functions are obtained exactly. The relation to particle hopping
models of traffic and the possibility of shock waves in open systems is
discussed. The effect of the boundary condition on the steady state
properties of the bulk is studied.
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