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May 2007 Stationary distributions of multi-type totally asymmetric exclusion processes
Pablo A. Ferrari, James B. Martin
Ann. Probab. 35(3): 807-832 (May 2007). DOI: 10.1214/009117906000000944


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.


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Pablo A. Ferrari. James B. Martin. "Stationary distributions of multi-type totally asymmetric exclusion processes." Ann. Probab. 35 (3) 807 - 832, May 2007.


Published: May 2007
First available in Project Euclid: 10 May 2007

zbMATH: 1117.60089
MathSciNet: MR2319708
Digital Object Identifier: 10.1214/009117906000000944

Primary: 60K35
Secondary: 82C22 , 90B22

Keywords: multiclass queue , multi-type process , Totally asymmetric simple exclusion process

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 3 • May 2007
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