  In the Hammersley-Aldous-Diaconis process infinitely many particles sit in R
and at most one particle is allowed at each position. A particle at x$ whose
nearest neighbor to the right is at y, jumps at rate y-x to a position
uniformly distributed in the interval (x,y). The basic coupling between
trajectories with different initial configuration induces a process with
different classes of particles. We show that the invariant measures for the
two-class process can be obtained as follows. First, a stationary M/M/1 queue
is constructed as a function of two homogeneous Poisson processes, the arrivals
with rate \lambda and the (attempted) services with rate \rho>\lambda. Then put
the first class particles at the instants of departures (effective services)
and second class particles at the instants of unused services. The procedure is
generalized for the n-class case by using n-1 queues in tandem with n-1
priority-types of customers. A multi-line process is introduced; it consists of
a coupling (different from Liggett's basic coupling), having as invariant
measure the product of Poisson processes. The definition of the multi-line
process involves the dual points of the space-time Poisson process used in the
graphical construction of the system. The coupled process is a transformation
of the multi-line process and its invariant measure the transformation
described above of the product measure.
