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By generalizing the algebra of operators of the Asymmetric Simple ExclusionProcess (ASEP), a multi-species ASEP in which particles can overtake eachother,is defined on both open and closed one dimensional chains. On the ringthe steady state and the correlation functions are obtained exactly. Therelation to particle hopping models of traffic and the possibility of shockwaves in open systems is discussed. The effect of the boundary condition on thesteady state properties of the bulk is studied.Comment: References added, typos correcte

A multi-species asymmetric exclusion process, steady state and correlation functions on a periodic lattice