## The Annals of Probability

### Stationary distributions of multi-type totally asymmetric exclusion processes

#### Abstract

We consider totally asymmetric simple exclusion processes with n types of particle and holes (n-TASEPs) on ℤ and on the cycle 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 ℤN, and simple proofs of various independence and regeneration properties for systems on ℤ.

#### Article information

Source
Ann. Probab., Volume 35, Number 3 (2007), 807-832.

Dates
First available in Project Euclid: 10 May 2007

https://projecteuclid.org/euclid.aop/1178804315

Digital Object Identifier
doi:10.1214/009117906000000944

Mathematical Reviews number (MathSciNet)
MR2319708

Zentralblatt MATH identifier
1117.60089

#### Citation

Ferrari, Pablo A.; Martin, James B. Stationary distributions of multi-type totally asymmetric exclusion processes. Ann. Probab. 35 (2007), no. 3, 807--832. doi:10.1214/009117906000000944. https://projecteuclid.org/euclid.aop/1178804315

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