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Within the Matrix Product Formalism we have already introduced a multi-species exclusion process in which different particles hop with different ratesand fast particles stochastically overtake slow ones. In this letter we showthat on an open chain, the master equation of this process can be exactlysolved via the coordinate Bethe ansatz. It is shown that the N-body S-matrix ofthis process is factorized into a product of two-body S-matrices, which in turnsatisfy the quantum Yang-Baxter equation (QYBE). This solution is to ourknowledge, a new solution of QYBE.Comment: 9 pages, latex, major revisions in the introduction, references adde

A remark on integrability of stochastic systems solvable by matrix product ansatz