  We consider the multiparticle asymmetric diffusion model (MADM) introduced by
Sasamoto and Wadati with integrability preserving reservoirs at the boundaries.
In contrast to the open asymmetric simple exclusion process (ASEP) the number
of particles allowed per site is unbounded in the MADM. Taking inspiration from
the stationary measure in the symmetric case, i.e. the rational limit, we first
obtain the length 1 solution and then show that the steady state can be
expressed as an iterated product of Jackson q-integrals. In the proof of the
stationarity condition, we observe a cancellation mechanism that closely
resembles the one of the matrix product ansatz. To our knowledge, the
occupation probabilities in the steady state of the boundary-driven MADM were
not available before.
