Multiclass Hammersley-Aldous-Diaconis process and multiclass-customer queues
| dc.creator | Ferrari, Pablo A. | |
| dc.creator | Martin, James B. | |
| dc.date | 2007-07-28 | |
| dc.date.accessioned | 2026-07-07T08:20:53Z | |
| dc.date.available | 2026-07-07T08:20:53Z | |
| dc.description | 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 λand the (attempted) services with rate ρ>λ. 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. | |
| dc.description | 21 pages, 6 figures | |
| dc.identifier | https://arxiv.org/abs/0707.4202 | |
| dc.identifier | http://arxiv.org/abs/0707.4202 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135199 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | 60K35, 60K25, 90B22 | |
| dc.title | Multiclass Hammersley-Aldous-Diaconis process and multiclass-customer queues | |
| dc.type | text |