Multiclass Hammersley–Aldous–Diaconis process and multiclass-customer queues
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 , whose nearest neighbor to the right is at , jumps at rate − to a position uniformly distributed in the interval (, ). 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...