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The multispecies asymmetric simple exclusion process (mASEP) is a Markovchain in which particles of different species hop on a one-dimensional lattice.This paper studies the doubly asymmetric simple exclusion process DASEP(n,p,q)in which q particles with species 1 through p hop on a circular lattice with nsites, but also the particles are allowed to spontaneously change theirspecies. In this paper, we introduce two related Markov chains called thecolored Boolean process and the restricted random growth model, and we showthat the DASEP lumps to the colored Boolean process, and the colored Booleanprocess lumps to the restricted random growth model. This allows us togeneralize a theorem of David Ash on the relations between sums of steady stateprobabilities. We also give explicit formulas for the stationary distributionof DASEP(n,2,2).

The doubly asymmetric simple exclusion process, the colored Boolean process, and the restricted random growth model