Shortcut with pool under parallel update rule on one-dimensional lattice totally asymmetric simple exclusion process

This paper studies one-dimensional totally asymmetric simple exclusion process (TASEP) with a pool-shortcut under parallel update rule. Here, the pool is a special area which is introduced into a TASEP on a single lane with shortcut with the probabilities of entering (p) and leaving (q). Different from the existed researches, the parameters of p and q are unequal. To simplify the calculations, the simplest case with parallel update is considered, namely the hopping probability in the bulk equals unity. The theoretical calculation results are compared to the densities acquired by Monte Carlo simulations, and they agree very well. The diagram includes five phases, namely LD/LD/LD, HD/HD/HD, LD/LD/HD, MC/LD/LD and MC/LD/HD phases. It is divided into the LD/LD/LD and HD/HD/HD two regions by the LD/LD/HD phase. Interestingly, the MC/LD/LD and MC/LD/HD phases become a straight line and a point, respectively. The influences of parameters p and q (p>q) on the phases are examined. It is found that the HD/HD/HD phase region shrinks, when the variable q reduces from 0.6 to 0.2 (p is fixed, p=0.8).