The paper considers 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. It labels the particle initially at 0 as the leading particle. The paper studies the long-term behavior of this process near large sites when the leading particle’s holding time is different from that of the other sites when the leading particle’s holding time is different from that of the other particles. In particular, it assumes that the leading particle moves at a slower rate than the other particles. The paper calls 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.
