2005/01/31 by Pablo A. Ferrari, James B. Martin
Mathematics · Physics and Astronomy · #math.PR #math-ph #math.MP #msc:60K35 #msc:82C22 #msc:90B22
paper · pdf · doi:10.1214/009117906000000944
published as Annals of Probability 2007, Vol. 35, No. 3, 807-832 · Published at http://dx.doi.org/10.1214/009117906000000944 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
arxiv created 2007/07/30 · arxiv updated 2011/11/10
We consider totally asymmetric simple exclusion processes with n types of particle and holes (n-TASEPs) on \mathbb Z and on the cycle \mathbb ZN. Angel recently gave an elegant construction of the stationary measures for the 2-TASEP, based on a pair of independent product measures. We show that Angel's construction can be interpreted in terms of the operation of a discrete-time M/M/1 queueing server; the two product measures correspond to the arrival and service processes of the queue. We extend this construction to represent the stationary measures of an n-TASEP in terms of a system of queues in tandem. The proof of stationarity involves a system of n 1-TASEPs, whose evolutions are coupled but whose distributions at any fixed time are independent. Using the queueing representation, we give quantitative results for stationary probabilities of states of the n-TASEP on \mathbb ZN, and simple proofs of various independence and regeneration properties for systems on \mathbb Z.