Stationary distributions of multi-type totally asymmetric exclusion processes
We consider totally asymmetric simple exclusion processes with n types of particle and holes ($n$-TASEPs) on $\mathbb {Z}$ and on the cycle $\mathbb {Z}_N$. Angel recently gave an elegant construction of the stationary measures for the 2-TASEP, based on a pair of independent product measures. We sho...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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2005
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| _version_ | 1797095853624655872 |
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| author | Ferrari, P Martin, J |
| author_facet | Ferrari, P Martin, J |
| author_sort | Ferrari, P |
| collection | OXFORD |
| description | We consider totally asymmetric simple exclusion processes with n types of particle and holes ($n$-TASEPs) on $\mathbb {Z}$ and on the cycle $\mathbb {Z}_N$. 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 $\mathbb {Z}_N$, and simple proofs of various independence and regeneration properties for systems on $\mathbb {Z}$. |
| first_indexed | 2024-03-07T04:33:54Z |
| format | Journal article |
| id | oxford-uuid:cf470b72-1948-4bfb-8b4d-2d35b3cafb08 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T04:33:54Z |
| publishDate | 2005 |
| record_format | dspace |
| spelling | oxford-uuid:cf470b72-1948-4bfb-8b4d-2d35b3cafb082022-03-27T07:41:16ZStationary distributions of multi-type totally asymmetric exclusion processesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:cf470b72-1948-4bfb-8b4d-2d35b3cafb08EnglishSymplectic Elements at Oxford2005Ferrari, PMartin, JWe consider totally asymmetric simple exclusion processes with n types of particle and holes ($n$-TASEPs) on $\mathbb {Z}$ and on the cycle $\mathbb {Z}_N$. 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 $\mathbb {Z}_N$, and simple proofs of various independence and regeneration properties for systems on $\mathbb {Z}$. |
| spellingShingle | Ferrari, P Martin, J Stationary distributions of multi-type totally asymmetric exclusion processes |
| title | Stationary distributions of multi-type totally asymmetric exclusion
processes |
| title_full | Stationary distributions of multi-type totally asymmetric exclusion
processes |
| title_fullStr | Stationary distributions of multi-type totally asymmetric exclusion
processes |
| title_full_unstemmed | Stationary distributions of multi-type totally asymmetric exclusion
processes |
| title_short | Stationary distributions of multi-type totally asymmetric exclusion
processes |
| title_sort | stationary distributions of multi type totally asymmetric exclusion processes |
| work_keys_str_mv | AT ferrarip stationarydistributionsofmultitypetotallyasymmetricexclusionprocesses AT martinj stationarydistributionsofmultitypetotallyasymmetricexclusionprocesses |