A Central Limit Theorem for the Weakly Asymmetric Simple Exclusion Process

1991 ◽  
Vol 151 (1) ◽  
pp. 75-93 ◽  
Author(s):  
Peter Dittrich ◽  
Jürgen Gärtner
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Exclusion Process ◽  
Asymmetric Simple Exclusion Process ◽  
Simple Exclusion Process ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion

Stochastic comparisons of density profiles for the road-hog process

1991 ◽  
Vol 28 (04) ◽  
pp. 852-863
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.

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