Stationary distributions of multi-type totally asymmetric exclusion processes
By Pablo A. Ferrari, James B. Martin. 2005
147 citations recorded by the source corpus.
We consider totally asymmetric simple exclusion processes with n types of particle and holes (n-TASEPs) on Z and on the cycle Z N . 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 Z N , and simple proofs of various independence and regeneration properties for systems on Z.
Subfields: Management Information Systems, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/e436cb90bfedf8208f108a14b13e0b13127d30db
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In Management Information Systems
In Mathematical Physics
In Statistics and Probability
Citations in the corpus
- Nonequilibrium steady states of matrix-product form: a solver's guide (2007, methodology): “eyond simple cases [173] have yet been attempted for the stationary properties of this model. However recently, generalising a construction by Angel [64] for the two-class problem, Ferrari and Martin [174] have shown how to generate the steady state of the multi-class problem. This construction can ”
- Non-equilibrium statistical mechanics: from a paradigmatic model to biological transport (2011, unknown): “Further, the exclusion constraint can be relaxed, 678 so that fast cars are allowed to overtake slower ones, which are known as ‘second class’ 679 or ‘third class’ particles [106, 107, 108, 109, 110, 111, 112].”
- From multiline queues to Macdonald polynomials via the exclusion process (2018, methodology): “particles only hop in one direction), Ferrari and Martin [11] proposed a combinatorial solution for the stationary distribution using multiline queues.”