Phase Diagrams and Current Density Profiles of the Totally Asymmetric Simple Exclusion Process in Two Dimensions, for a Three-Way Junction

We consider the asymmetric simple exclusion process which starts from a product measure such that all the sites to the left of zero (including zero) are occupied and the right of 0 (excluding 0) are empty. We label the particle initially at 0 as the leading particle. We study the long-term behaviour of this process near large sites when the leading particle's holding time is different from that of the other particles. In particular, we assume that the leading particle moves at a slower rate than the other particles. We call this modified asymmetric simple exclusion process the road-hog process. Coupling and stochastic ordering techniques are used to derive the density profile of this process. Road-hog processes are useful in modelling series of exponential queues with Poisson and non-Poisson input process. The density profiles dramatically illustrate the flow of customers through the queues.

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Effect of hopping rates coupled with on-ramp on the phase diagrams of totally asymmetric simple exclusion process

International Journal of Modern Physics B ◽

10.1142/s0217979219501273 ◽

2019 ◽

Vol 33 (13) ◽

pp. 1950127 ◽

Cited By ~ 1

Author(s):

Song Xiao ◽

Xiaoyu Chen ◽

Jianhui Shi ◽

Yanna Liu

Keyword(s):

Field Theory ◽

Phase Diagrams ◽

Mean Field Theory ◽

Mean Field ◽

Exclusion Process ◽

Asymmetric Simple Exclusion Process ◽

Simple Exclusion Process ◽

Asymmetric Simple Exclusion ◽

Simple Exclusion ◽

Theoretical Results

In this paper, the effect of different hopping rates coupled with on-ramp on the phase diagrams has been investigated by totally asymmetric simple exclusion process (TASEP). The topology of phase diagrams on different hopping rates and on-ramp has been obtained. Additionally, the corresponding phase diagrams and the existing condition are given by approximate mean field theory, and the theoretical results agree well with Monte Carlo simulations.

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Stochastic comparisons of density profiles for the road-hog process

Journal of Applied Probability ◽

10.2307/3214688 ◽

1991 ◽

Vol 28 (4) ◽

pp. 852-863 ◽

Cited By ~ 1

Author(s):

Rengarajan Srinivasan

Keyword(s):

Exclusion Process ◽

Stochastic Ordering ◽

Asymmetric Simple Exclusion Process ◽

The Other ◽

Density Profiles ◽

Poisson Input ◽

Simple Exclusion Process ◽

Asymmetric Simple Exclusion ◽

Simple Exclusion ◽

The Right

We consider the asymmetric simple exclusion process which starts from a product measure such that all the sites to the left of zero (including zero) are occupied and the right of 0 (excluding 0) are empty. We label the particle initially at 0 as the leading particle. We study the long-term behaviour of this process near large sites when the leading particle's holding time is different from that of the other particles. In particular, we assume that the leading particle moves at a slower rate than the other particles. We call this modified asymmetric simple exclusion process the road-hog process. Coupling and stochastic ordering techniques are used to derive the density profile of this process. Road-hog processes are useful in modelling series of exponential queues with Poisson and non-Poisson input process. The density profiles dramatically illustrate the flow of customers through the queues.

Download Full-text